doi.org/10.26434/chemrxiv.14494704.v1

A Fragment Diabatization Linear Vibronic Coupling Model for QuantumDynamics of Multichromophoric Systems: Population of the ChargeTransfer State in the Photoexcited Guanine Cytosine PairJames Green, Martha Yaghoubi Jouybari, Haritha Asha, Fabrizio Santoro, Roberto Improta

Submitted date: 27/04/2021 • Posted date: 28/04/2021Licence: CC BY-NC-ND 4.0Citation information: Green, James; Yaghoubi Jouybari, Martha; Asha, Haritha; Santoro, Fabrizio; Improta,Roberto (2021): A Fragment Diabatization Linear Vibronic Coupling Model for Quantum Dynamics ofMultichromophoric Systems: Population of the Charge Transfer State in the Photoexcited Guanine CytosinePair. ChemRxiv. Preprint. https://doi.org/10.26434/chemrxiv.14494704.v1

We introduce a method (FrD-LVC) based on a fragment diabatization (FrD) for the parametrization of a LinearVibronic Coupling (LVC) model suitable for studying the photophysics of multichromophore systems. Incombination with effective quantum dynamics (QD) propagations with multilayer multiconfigurationaltime-dependent Hartree (ML-MCTDH), the FrD-LVC approach gives access to the study of the competitionbetween intra-chromophore decays, like those at conical intersections, and inter-chromophore processes, likeexciton localization/delocalization and the involvement of charge transfer (CT) states. We used FrD-LVCparametrized with TD-DFT calculations, adopting either CAM-B3LYP or ωB97X-D functionals, to study theultrafast photoexcited QD of a Guanine-Cytosine (GC) hydrogen bonded pair, within a Watson-Crickarrangement, considering up to 12 coupled diabatic electronic states and the effect of all the 99 vibrationalcoordinates. The bright excited states localized on C and, especially, on G are predicted to be stronglycoupled to the G->C CT state which is efficiently and quickly populated after an excitation to any of the fourlowest energy bright local excited states. Our QD simulations show that more than 80% of the excitedpopulation on G and ~50% of that on C decays to this CT state in less than 50 fs. We investigate the role ofvibronic effects in the population of the CT state and show it depends mainly on its large reorganization energyso that it can occur even when it is significantly less stable than the bright states in the Franck-Condon region.At the same time, we document that the formation of the GC pair almost suppresses the involvement of darknπ* excited states in the photoactivated dynamics.

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A Fragment Diabatization Linear VibronicCoupling Model for Quantum Dynamics of

Multichromophoric Systems: Population of theCharge Transfer State in the Photoexcited

Guanine Cytosine Pair

James A. Green,† Martha Yaghoubi Jouybari,‡ Haritha Asha,† FabrizioSantoro,∗,‡ and Roberto Improta∗,†

†Consiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR),via Mezzocannone 16, I-80136 Napoli, Italy

‡Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici(ICCOM-CNR), SS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy

E-mail: fabrizio.santoro@pi.iccom.cnr.it; robimp@unina.it

Abstract

We introduce a method (FrD-LVC) based on a fragment diabatization (FrD) for theparametrization of a Linear Vibronic Coupling (LVC) model suitable for studying the photo-physics of multichromophore systems. In combination with effective quantum dynamics (QD)propagations with multilayer multiconfigurational time-dependent Hartree (ML-MCTDH), theFrD-LVC approach gives access to the study of the competition between intra-chromophoredecays, like those at conical intersections, and inter-chromophore processes, like exciton local-ization/delocalization and the involvement of charge transfer (CT) states. We used FrD-LVCparametrized with TD-DFT calculations, adopting either CAM-B3LYP or ωB97X-D func-tionals, to study the ultrafast photoexcited QD of a Guanine-Cytosine (GC) hydrogen bondedpair, within a Watson-Crick arrangement, considering up to 12 coupled diabatic electronicstates and the effect of all the 99 vibrational coordinates. The bright excited states localizedon C and, especially, on G are predicted to be strongly coupled to the G→C CT state whichis efficiently and quickly populated after an excitation to any of the four lowest energy brightlocal excited states. Our QD simulations show that more than 80% of the excited populationon G and ∼50 % of that on C decays to this CT state in less than 50 fs. We investigatethe role of vibronic effects in the population of the CT state and show it depends mainly onits large reorganization energy so that it can occur even when it is significantly less stablethan the bright states in the Franck-Condon region. At the same time, we document that theformation of the GC pair almost suppresses the involvement of dark nπ∗ excited states in thephotoactivated dynamics.

1 Introduction

The excited state dynamics of multichro-mophore systems rules many fundamentalbiochemical and technological phenomena.1–9

These systems are often described within anexcitonic picture, where the focus is usuallyon inter-molecular processes, like the transferof energy or charge from one chromophore toanother, or the delocalization of excited states

1

among many units or “sites”. Model Hamil-tonians have been proposed to describe theseprocesses accounting for electronic couplings(often considered independent of the nuclearcoordinates) and vibrational motions, along“tuning modes” leading toward the energy min-ima of the different states.7,8,10,11 However, inmany cases, each single chromophore is alsocharacterized by a rich intrinsic dynamics, withinternal conversion or inter-system crossing be-tween local excitations (LEs, such as brightππ∗ and dark nπ∗ states). For certain multi-chromophore systems, for example DNA, theseintra-molecular decays of the individual unitsare actually competitive with inter-molecularprocesses.1–4 When such molecular processesare ultrafast, they usually occur at ConicalIntersections (CoIs) of the excited potentialenergy surfaces (PESs). If the chromophoresare rigid enough, the essential features of thedynamics can be captured with simple vibroniccoupling Hamiltonian models,12 like the lin-ear vibronic coupling (LVC) model, where CoIsarise from the combined action of tuning modesand coupling modes.

In this contribution, we introduce an auto-matic parametrization of a generalized LVCmodel of multichromophore systems using afragment based diabatization (FrD-LVC) thatallows the investigation of the competition be-tween intra-molecular and inter-molecular pro-cesses. LVC models have attracted renewedinterest recently, as a cost effective methodto study nonadiabatic spectroscopy and in-tramolecular excited state dynamics.8,9,13–28 Onthe other side, fragment-based models are pop-ular approaches to study the excited state dy-namics of multichromophore systems,8,9,22–31

but in most of their implementations they con-sider each single chromophore (site) as charac-terized by a single relevant excited state, or fewstates but without an internal (nonadiabatic)dynamics.

As a first test application of the FrD-LVCmethod, we choose to study a minimal, yetextremely relevant, system: the dimer formedby Guanine and Cytosine connected by threehydrogen bonds in a Watson and Crick (WC)arrangement, hereafter simply GC (see Fig-

ure 1). GC constitutes ∼40% of the hu-man genome and its photoactivated behav-ior has been thoroughly investigated in thegas phase,32–41 in chloroform solution,42–46 andin DNA duplexes,39,40,47,48 due to its possibleinvolvement in the Proton Coupled ElectronTransfer (PCET) processes in DNA.49–51 Time-resolved (TR) experiments in the gas phaseshow that when GC is in a WC arrangement,after a UV pulse, the absorption of the infraredprobe is broad and featureless, suggesting anultrashort excited state lifetime.52 According tothe seminal contributions by Sobolewski, Dom-cke et al., a very effective PCET process is in-deed operative.32,33 The lowest energy brightexcited states of GC decay to an inter-molecularcharge transfer (CT) quasi-dark excited stateG+C− (G→C), which, in turn, can undergo toa inter-molecular proton transfer (PT). The lat-ter involves the transfer of the H1 atom fromGua-N1 to Cyt-N3 (see Figure 1), and is thedoorway for a sub-ps ground state recovery.32,33

Such combined PCET process should be op-erative also in low-polar solvents,42,43,45 andits involvement in DNA is also matter of de-bate.1,47,48 Many computational dynamics stud-ies have thus been devoted to simulate the pho-toactivated dynamics of GC in different envi-ronments,34–36,39,40,47 but, to the best of ourknowledge, without considering quantum nu-clear effects.

In this study we focus on the first part of thisprocess, i.e. the possible population of the CTstate, using our FrD-LVC Hamiltonian in com-bination with quantum dynamics (QD) simula-tions to explore the excited state dynamics ofGC following the excitation to the four lowestenergy bright excited states. The PCET reac-tion occurs essentially on the PES of the CTstate,32,33 therefore it is fundamental to assesson which timescale it is populated, and whatare the main vibronic effects mediating this pro-cess.

This work gives us the opportunity to tackleanother crucial issue in the field of the photo-physics of nucleic acids, namely the effect thatWC hydrogen bond pairing has on the popu-lation of the dark nπ∗ states localized on indi-vidual nucleobases.1 Actually, there are several

2

computational indications that in the gas phasea significant population transfer to the dark nπ∗

occurs for photoexcited Cytosine.14–17,53 More-over, the spectral signature of a dark state isfound for Cytosine and its derivatives in chlo-roform54 and in water55,56 and it has been pro-posed that this state is populated also withinDNA duplex.57

In this contribution we thus describe ourmethodological approach, focusing on thenew developments, and we use it to studythe photoexcited state dynamics of the WCGC pair formed by 1-methylcytosine and9-methylguanine, i.e. modeling the sugarspresent in the nucleotide by methyl groups.Thanks to the effectiveness of parametriza-tion of the FrD-LVC Hamiltonian from time-dependent density functional theory (TD-DFT), and the potentiality of the multi-layerextension of the multiconfiguration time de-pendent Hartree (ML-MCTDH) method forwavepacket propagation, we included up to12 electronic states and all the 99 vibrationalmodes of the system. However, since our Hamil-tonian is not suited to describe CoIs at verydistorted geometries, our simulations do not in-clude the decays to the ground state, which forboth the bases are known to occur at stronglynon-planar CoIs on the sub-ps timescale ingas-phase.1 Therefore, we will focus on theultrafast timescale (∼ 100 fs) when large out-of-plane deviations of the molecular structureare not expected, and the involvement of tripletexcited states is marginal.58–60

We use TD-DFT as a reference electronicmethod, with two different functionals: CAM-B3LYP61 and ωB97X-D,.62 These two widelyadopted, long range-corrected functionals pro-vide a different estimate of the relative stabil-ity of the lowest energy G→C CT state, thusproviding the opportunity of checking the de-pendence of our predictions on this seeminglycrucial parameter. Quantum dynamical sim-ulations, starting from the four lowest energybright excited states, predict a fast (on the ≤ 50fs time scale) population transfer to the lowestenergy CT state, which is particularly effective(≥80%) when exciting the bright excited statesof G. In contrast to what happens with isolated

cytosine,15–17 no significant population trans-fer to the dark nπ∗ states is predicted. Thisstudy provides, at full QD level, new insights onthe interplay between electronic and vibrationaldegrees of freedom in a process of crucial bio-chemical interest. At the same time, it showsthat FrD-LVC, thanks to its flexibility and rel-atively low computational cost, can be a veryuseful tool for the study of the photoactivateddynamics of multichromophore systems.

2 Methods

The approach taken in the present work isa combination of our fragment diabatizationscheme to parametrize a purely electronic ex-citonic model in Ref. 63, and the diabatiza-tion scheme to parametrize a LVC model inRefs. 14 and 15. The LVC Hamiltonian for acoupled set of diabatic electronic states |d〉 =(|d1〉 , |d2〉 , . . . , |dN〉) may be written as

H =∑i

(K + V dii (q) |di〉 〈di|)+∑

i,j>i

V dij (q)(|di〉 〈dj|+ |dj〉 〈di|),

(1)

where q are the dimensionless normal modecoordinates, defined on the ground electronicstate S0, with conjugate momenta p. The ki-netic K and potential V terms of the Hamilto-nian are defined as

K =1

2pTΩp (2)

V dii (q) = Ed

ii(0) + λTiiq +1

2qTΩq (3)

V dij (q) = Ed

ij(0) + λTijq, (4)

with Ω the diagonal matrix of normal mode fre-quencies ωα, λij the vector of linear couplingconstants, Ed

ii(0) the diabatic energy of statei at the reference geometry (0), and Ed

ij(0) anelectronic coupling constant between diabaticstates i and j at the reference geometry. No-tice that this latter term does not appear inthe standard LVC approach,12 however in theFrD-LVC approach the diabatic states may be

3

Figure 1: Schematic drawing and atom labeling of the computational model of the Guanosine-Cytidine dimer in a Watson-Crick arrangement. Sugar rings are modelled by the methyl groupsbonded at Gua-N9 and Cyt-N1.

coupled electronically even at the reference ge-ometry, as will be revealed below.

Following the procedure established in Ref.63, we define diabatic states of some mul-tichromophoric complex (MC), consisting ofNfrag fragments on the basis of reference states|Rfrags〉 of either the adiabatic states of the frag-ments (for LEs), or orbital transitions betweenthe fragments (for CT states). The diabaticstates are then obtained via a transformationof the adiabatic states of the MC

|d〉 = |aMC〉D= |aMC〉ST (SST )−

12

(5)

where S = 〈Rfrags|aMC〉 is the overlap of thereference states of the fragments with the adia-batic states of the MC. Notice that S is not nec-essarily a square matrix, and in general, in or-der to properly project the selected N diabaticstates one will need to consider M adiabaticstates at the reference geometry with M > N .The derivation of the transformation matrix Din terms of the overlap matrix S uses Lowdinre-orthogonalisation, and has been defined inour previous works.15,63

Performing the transformation at the refer-ence geometry, i.e. S(0) = 〈Rfrags(0)|aMC(0)〉,yields the transformation matrix D(0). Thiscan be applied to the diagonal matrix of adia-

batic energies of the MC computed at the ref-erence geometry

H[aMC(0)] = diag(EMC1 (0), EMC

2 (0),

. . . , EMCM (0)),

(6)

to obtain the diabatic matrix

H[d(0)] = D(0)TH[aMC(0)]D(0), (7)

which contains the diabatic energies Edii(0) on

the diagonal, and electronic couplings Edij(0) on

the off diagonal. In fact, while for a ‘standard’LVC approach it is customary to define the Ndiabatic states to be identical to N adiabaticstates at the reference geometry, in the FrD-LVC approach diabatic states defined on thefragments are in general not eigenstates of theelectronic Hamiltonian of the MC, and there-fore they exhibit non vanishing couplings.

To obtain the linear coupling constants λij,we displace each normal coordinate α by somesmall value ±∆α and perform a numerical dif-ferentiation

λij,α =∂V d

ij (q)

∂qα'Edij(∆α)− Ed

ij(−∆α)

2∆α

. (8)

The diabatic energies and electronic couplingsat displaced geometries Ed

ij(∆α) are obtainedby performing the diabatization based on max-

4

imum overlap of the reference states with thediabatic states at displaced geometry. Thisamounts to computing the overlap of the ref-erence states at equilibrium geometry with theadiabatic states of the MC at displaced geom-etry, i.e. S(∆α) = 〈Rfrags(0)|aMC(∆α)〉, andperforming the transformation in Eq. 5. Thetransformation matrix at displaced geometryD(∆α), can be applied to the diagonal matrixof adiabatic energies of the MC at displaced ge-ometry

H[aMC(∆α)] = diag(EMC1 (∆α), EMC

2 (∆α),

. . . , EMCM (∆α)),

(9)

to obtain the diabatic matrix at displaced ge-ometry

H[d(∆α)] = D(∆α)TH[aMC(∆α)]D(∆α).(10)

This diabatic Hamiltonian matrix containsEdii(∆α) on the diagonal and Ed

ij(∆α) on the offdiagonal, exactly analogous to Eq. 7 at the ref-erence geometry. These values can then be usedin Eq. 8 to obtain the linear coupling constants.

In principle any electronic structure methodcan be used for this diabatization, provid-ing the reference states and overlap ma-trix can be appropriately defined. Re-cently, for instance, some of us adoptedRASPT2/RASSCF to parametrize a LVCmodel to study photoexcited pyrene.18 How-ever, as previously done for DNA nucleobasesand G-quadruplexes,13–15,17,63 we define thesequantities within the framework of TD-DFT.The derivation has been presented in previouspapers,15,63 and we also include it in the Sup-porting Information (SI, Section S1.1), as wehave found a more computationally efficientmethod of calculating the overlap matrix.

For the definition of the reference geometryand normal mode coordinates, in principle twochoices could be made: (i) define the referencegeometry as the ground state equilibrium ge-ometry of the MC, and then the normal coordi-nates as those of the entire MC, or (ii) define thereference geometry as any arrangement of indi-vidual fragments, not necessarily at the equilib-rium geometry of the overall MC, but with the

individual fragments at their own equilibriumgeometry. Then, the normal mode coordinatesare those of the individual fragments. Option(i) is appropriate when vibrational modes arestrongly coupled between fragments, such aswhen strong hydrogen bonds are present. Thedisadvantage would be an expensive optimisa-tion and frequency calculation for a large MC.Option (ii) is appropriate when the converse istrue, and vibrational modes are generally local-ized to individual sites. This therefore neglectslow frequency inter-fragment vibrations, how-ever they could be re-introduced by defining aproper number of degrees of freedom describ-ing such vibrations between rigid monomers.It should be noted that option (ii) would stillcapture the vibronic coupling between excita-tions located on different sites that are due tothe vibrations of a single site. One could alsoimagine a combination of options (i) and (ii),where the entire MC is divided into sub-systemsof multiple fragments, and the sub-system isparametrized according to option (i) and thenthe overall MC according to option (ii). Indeed,the flexibility of the fragment diabatization ap-proach allows one to choose the number of frag-ments (and number of states) to include to bestbalance accuracy and efficiency, as was demon-strated in our excitonic model application.63

In the present application of the GC pair, wechoose option (i) due to the relatively smallsize of the system, and the strong hydrogenbonds between the pair leading to vibrationalmodes that are not localized on either site.64

The reference geometry is therefore the groundstate equilibrium geometry of GC. The FrD-LVC approach is schematically shown in Fig-ure. 2, summarizing the main steps of our pro-cedure, i.e. (1) the choice of reference states,(2) projection of the reference states onto theMC at reference geometry, and (3) projectiononto the MC at displaced geometries.

Our approach bears some similarity to thework of Tamura and Burghardt on conjugatedpolymers and fullerene systems,8,9,22–28 howeverthere are a number of differences in the imple-mentation. Firstly, we calculate the overlap Svia transition densities following Neugebauer,65

rather than Slater determinants. Secondly, we

5

Figure 2: Schematic of the FrD-LVC approach, illustrated with two chromophores (circles) and theMC consisting of these two chromophores (oval). Yellow stars represent reference LEs of individualchromophores, whilst a CT reference state is represented by an arrow from an occupied orbitalof one individual chromophore to a virtual orbital of the other (1). Projections of these referencestates onto the MC are shown by arrows towards the MC at either the reference (2) or displaced(3) geometries. The moiety (i.e single chromophore or MC) involved in a given computational step(excited state calculation, projection, or normal mode displacement) is depicted in black, the onenot involved in gray. Illustration of the diabatic Hamiltonian shown in the centre.

do not use the “electron-hole” formalism to de-scribe local excitations. In this way we accountfor the possible existence of multi-orbital com-ponents in the local excitations a case which,for instance, does occur in DNA nucleobases.Thirdly, we include a vibrational dependenceon the diabatic couplings through the λij pa-rameter, and fourthly, we compute the referencestates based on isolated chromophores, ratherthan well-separated ones.

3 Computational Details

Electronic structure calculations have been per-formed with DFT for the ground state, andTD-DFT for the excited states, using two dif-ferent range-separated functionals that conferdifferent CT state stability, CAM-B3LYP61 andωB97X-D,62 and two basis sets 6-31G(d) and 6-31+G(d,p), using the Gaussian 16 program.66

The 6-31G(d) basis set is used in parametriza-tion of the FrD-LVC models presented in themain text. Single point energy test calcula-

6

tions are performed with the 6-31+G(d,p) basisset for both functionals, which is also used tobuild a test FrD-LVC model with the ωB97X-D functional. These results are shown in theSI, Section S6, to check the solidity of our con-clusion with respect to an increase of the sizeof the basis set. TD-DFT computations wereperformed using tight SCF convergence, with a10−6 a.u. threshold.

As a molecular model, we use 9-methylguanineand 1-methylcytosine to represent GC in Wat-son Crick conformation (see Figure 1), geom-etry optimised with Cs symmetry, which per-mitted electronic decoupling of the A’ (ππ∗

and CT) and A” (nπ∗) states. The vibra-tional frequencies obtained in the S0 state ofGC are utilised for each of the excited statesin the FrD-LVC models. Two different FrD-LVC models are parametrized for each of thefunctionals: (i) a 12 diabatic state model, in-cluding 4 ππ∗, 2 CT and 6 nπ∗ states and bothin-plane (A’) and out of plane (A”) modes fora full-dimensional (99 mode) picture of GC,and (ii) a reduced-dimensionality (65 mode) 5state model, including 4 ππ∗ and 1 CT state,so that out-of-plane A” modes are not activeand have been neglected. These diabatic stateswere defined based on reference states of in-dividual G and C at the same geometry as inthe GC pair, using the procedure described inSection 2, and then projected onto the calcula-tion of 40 adiabatic states of GC by TD-DFT(see Eq. 5). The diabatization was performedwith an in-house code interfaced with Gaussian16 that is freely available upon request. LVCmodels for individual G and C have also beenparametrized at the same level of theory as GC,including 2 ππ∗ and 3 nπ∗ states for each base,following the procedure for individual bases wehave recently used.15–17

Quantum dynamics calculations were per-formed with the ML-MCTDH method,67–69

adopting the implementation within the Quan-tics package.70 We used a variable mean field(VMF) with a Runge–Kutta integrator of or-der 5 and accuracy 10−7, as in the providedexamples for S2/S1 dynamics of pyrazine with24 normal modes.68,71 For the primitive basisset we adopted Hermite DVR functions, as ap-

propriate for harmonic potentials. We checkedconvergence by monitoring the populations atthe beginning and end of the grid using therdgpop tool provided in Quantics, and ensur-ing that they did not exceed 10−9. For the ML“tree” expansion, we chose the number of singleparticle functions (SPFs) for each node basedon the magnitude of the linear coupling con-stants λii,α, with modes with larger couplingsassigned larger numbers of SPFs, as we havedone in recent studies of single nucleobases.13–17

Mode combination was also utilised for modeswith similar character. The eigenvalues of thedensity matrices of each node in the ML tree,also known as the natural weights, were moni-tored, ensuring that the smallest natural weightwas always less than 1% to obtain a reasonablequality calculation, as indicated in the Quanticsmanual.

Absorption spectra of GC, G, and C werecalculated following the procedure we have re-cently utilised, via the Fourier transform ofthe auto-correlation function produced by thequantum dynamics calculations, weighted bythe transition dipoles.17,19 For GC, the tran-sition dipoles of the diabatic states were ob-tained by application of the transformation ma-trix D(0) to the adiabatic transition dipolemoments obtained by TD-DFT at the Franck-Condon (FC) point, in the same manner asEq. 7 and as previously described in Ref. 63.For monomeric G and C, the diabatic transitiondipoles are equivalent to the adiabatic TD-DFTones. The absorption spectra include contribu-tions from initial excitation to each of the ππ∗

states, and are phenomenologically broadenedwith a Gaussian of half-width half-maximumHWHM=0.04 eV. Further details may be foundin the SI, Section S1.2.

Expectation values of the FrD-LVC diabaticpotential diagonal (V d

ii ) and off diagonal (V dij )

terms are also calculated by integrating thewavepacket over all normal modes. Sinceeach diabatic potential is the sum of indepen-dent terms on the different modes V d

ij (q) =∑α V

dij (qα), it is straightforward to define

the expectation value of such potential terms〈Ψ|V d

ij (qα)|Ψ〉 on each mode.

7

4 Results

4.1 Adiabatic and diabatic states:FC point and minima

The 12 lowest singlet state energies of GC,calculated by the CAM-B3LYP and ωB97X-Dfunctionals and 6-31G(d) basis set are shownin Table 1 (TD-DFT column). WC pairingleads to a non-negligible mixing between theππ∗ states on G and C (especially accordingto ωB97X-D), and the CT state, as shownwith the natural transition orbitals (NTOs)in the SI, Figures S1 and S2. Nonethe-less, we can identify 2 ππ∗ states on C, 2ππ∗ states on G (commonly referred to as La

and Lb following Platt’s nomenclature), 3 nπ∗

states of C, 3 nπ∗ states of G, and 2 G→CCT states. The G→C(CT)1 state involves aHOMO(G)→LUMO(C) transition, whilst theG→C(CT)2 state a HOMO(G)→LUMO+1(C)transition. Considering the differences in thebasis set, CAM-B3LYP and, especially, ωB97X-D provide a description of the FC region in good

agreement with the EOM-CCSD(T) results ofRef. 72 that are also shown in the Table.

The ordering and relative energy gaps be-tween the states is quite similar for ωB97X-D and EOM-CCSD(T), with the main differ-ence being that the stability of the C(ππ∗2) andG(Lb) states is switched. For CAM-B3LYP,as well as the C(ππ∗2) and G(Lb) switch, theG→C(CT)1 state is predicted to be the low-est energy excited state, and its relative sta-bility to the other bright states is overesti-mated by ∼0.45 eV and ∼0.65 eV comparedto ωB97X-D and EOM-CCSD(T), respectively.The comparison with the results obtained forthe isolated bases (see Ref. 17 and SI Table S1)shows that WC pairing strongly destabilizes thenπ∗ states, and, in particular the G(nOπ

∗) andC(nOπ

∗) states. Confirming a trend already dis-cussed in the literature,1,73 the transfer of anelectron from the lone pair involved in a hydro-gen bond towards a π∗ delocalized on the ringweakens the hydrogen bonds and destabilizesthe associated excited states. The strong hy-drogen bonding is also responsible for the mix-

Table 1: Energies (eV) of the diabatic states from the FrD-LVC 12 state models Edii(0), compared

with adiabatic energies with same predominant character from TD-DFT and via diagonalizationof the FrD-LVC Hamiltonian (see text for details). State ordering in parentheses. Calculated onGC in Cs symmetry at equilibrium geometry by CAM-B3LYP/6-31G(d) and ωB97X-D/6-31G(d).Also shown are EOM-CCSD(T)/TZVP results from Ref. 72.

CAM-B3LYP ωB97X-D

Diab. State Edii(0) Ad. LVC TD-DFT Ed

ii(0) Ad. LVC TD-DFT EOM-CCSD(T)

G→C(CT)1 5.17 5.12 (S1) 5.07 (S1) 5.54 5.56 (S3) 5.50 (S3) 5.36

C(ππ∗1) 5.33 5.29 (S2) 5.27 (S2) 5.31 5.25 (S1) 5.28 (S2) 4.92

G(La) 5.42 5.36 (S3) 5.31 (S3) 5.42 5.31 (S2) 5.21 (S1) 4.85

G(Lb) 5.66 5.75 (S4) 5.69 (S4) 5.65 5.74 (S4) 5.69 (S4) 5.48

C(ππ∗2) 5.92 5.96 (S7) 5.93 (S7) 5.89 5.93 (S6) 5.90 (S6) 5.37

G→C(CT)2 6.39 6.40 (S8) 6.33 (S8) 6.67 6.68 (S11) 6.60 (S11)

C(nNπ∗) 5.92 5.92 (S5) 5.79 (S5) 5.88 5.88 (S5) 5.77 (S5) 5.65

G(nOπ∗) 5.94 5.93 (S6) 5.93 (S6) 5.95 5.94 (S7) 5.93 (S7) 5.76

G(nNπ∗1) 6.50 6.46 (S10) 6.44 (S9) 6.47 6.43 (S8) 6.43 (S8)

C(nOπ∗1) 6.54 6.46 (S9) 6.45 (S10) 6.53 6.47 (S9) 6.46 (S9) 6.27

C(nOπ∗2) 6.55 6.64 (S11) 6.60 (S11) 6.53 6.59 (S10) 6.56 (S10) 6.42

G(nNπ∗2) 6.73 6.78 (S12) 6.71 (S12) 6.73 6.77 (S12) 6.70 (S12)

8

ing between the different excited states, as wellas the close proximity of the bases.

Single point energy calculations with thelarger 6-31+G(d,p) basis set are shown in theSI, Table S14. They reveal a very similar en-ergy ordering, and the changes in the relativestability of the different states are small. SeeSection S6 of the SI for further details on the6-31+G(d,p) basis set test.

Also shown in Table 1 are the energies of thediabatic states at the FC point, Ed

ii(0), calcu-lated by the FrD procedure and used in the LVCmodel. In contrast to the TD-DFT states, byconstruction our LEs are fully localized eitheron G or on C. The mixing of LE and CT statesat the FC point is accounted for through theconstant coupling parameter Ed

ij(0), see Table 2for a selected few, and Tables S2 and S3 in theSI for all. The energies of the adiabatic statesof the FrD-LVC model at the FC point, i.e. theeigenvalues of the FrD-LVC Hamiltonian, arereported in the ‘Ad. LVC’ column of Table 1(the corresponding eigenvectors are shown inthe SI, Tables S8 and S9). These energies arewithin ∼0.05-0.1 eV of the TD-DFT energies,and in predominantly the same order, indicat-

ing that our model appropriately reproducesthe low-energy adiabatic states of the dimer atthe FC point. The only exceptions are the or-dering of the G(nNπ

∗1) and C(nOπ∗1) states in

the CAM-B3LYP model, and the C(ππ∗1) andG(La) states in the ωB97X-D model. The en-ergies, however, are not greatly different, and itshould be reminded that the TD-DFT C(ππ∗1)and G(La) ωB97X-D states are significantlymixed.

Inspection of Table 2 and S2 in the SI showsthat diabatic states localized on G are moresignificantly coupled with G→C CT states. Inparticular, G(La) is the excited state with thelargest coupling with G→C(CT)1, almost twiceas large as those involving the other brightexcited states. A similar trend is found forG→C(CT)2, though in this case, the most cou-pled state is G(Lb). Interestingly, ωB97X-D and CAM-B3LYP provides a similar pic-ture, i.e. G(La) has the largest coupling withG→C(CT)1, notwithstanding that according toωB97X-D the G→C(CT)1 state is energeticallycloser to other bright excited states. Our analy-sis thus suggests that ‘hole’ coupling is most im-portant than the ‘electron’ one. In other words,

Table 2: ππ∗-CT, excitonic, and intra-monomer ππ∗ mixing couplings between diabatic states at theFC point (Ed

ij(0), eV) as predicted by the 12 state FrD-LVC models parametrized by CAM-B3LYPand ωB97X-D.

Coupling CAM-B3LYP ωB97X-D

ππ∗-CT

G(La) : G→C(CT)1 0.065 0.067

G(Lb) : G→C(CT)1 0.038 0.037

C(ππ∗1) : G→C(CT)1 0.022 0.023

C(ππ∗2) : G→C(CT)1 −0.039 −0.036

Excitonic

G(La) : C(ππ∗1) 0.002 0.002

G(La) : C(ππ∗2) 0.053 0.052

G(Lb) : C(ππ∗1) −0.020 −0.018

G(Lb) : C(ππ∗2) 0.041 0.037

ππ∗ Mixing

G(La) : G(Lb) −0.171 −0.176

C(ππ∗1) : C(ππ∗2) 0.160 0.155

9

Table 3: Energies (eV, relative to S0 minimum) of adiabatic (coordinates qad,mmin ) and diabatic(coordinates qd,imin) excited state planar minima. In each minima, the diabatic energies from theFrD-LVC model are shown (V d

ii (q) column) as well as the adiabatic energies predicted by TD-DFT,and the adiabatic energies from the FrD-LVC model (Ad. LVC column). Also shown is the RMSDbetween the Cartesian coordinates of the qad,mmin and qd,imin geometries in A. Further details in text.

qad,mmin qd,imin

State V dii (q) Ad. LVC TD-DFT V d

ii (q) Ad. LVC TD-DFT RMSD

CAM-B3LYP

G→C(CT)1 4.04 4.03 4.00 3.94 3.93 4.00 0.060

C(ππ∗1) 4.95 4.95 4.94 4.94 4.95 4.95 0.007

G(La) 5.18 5.11 5.07 5.09 5.03 5.01 0.052

G(nOπ∗) 5.57 5.56 5.42 5.50 5.50 5.45 0.054

G(nNπ∗1) 6.02 5.79 5.68 5.93 5.81 5.74 0.030

C(nOπ∗1) 5.91 5.56 5.40 5.66 5.57 5.54 0.052

ωB97X-D

G→C(CT)1 4.48 4.47 4.40 4.39 4.39 4.36 0.045

C(ππ∗1) 4.94 4.94 4.91 4.93 4.92 4.92 0.006

G(La) 5.21 5.06 5.02 5.10 5.07 5.05 0.039

G(nOπ∗) 5.59 5.59 5.44 5.53 5.52 5.47 0.059

G(nNπ∗1) 5.94 5.73 5.65 5.87 5.75 5.69 0.025

C(nOπ∗1) 5.70 5.48 5.36 5.56 5.48 5.45 0.044

that the LUMO’s of G and C are more coupledthan the HOMO’s.

Table 2 also shows that hydrogen bondingleads to a significant intra-monomer couplingbetween the bright excited states localized on Gand C, i.e. G(La)-G(Lb) and C(ππ∗1)-C(ππ∗2),which we refer to as ππ∗ mixing couplings. Thiseffect, which we have discussed in detail in Ref.63, mirrors the changes in the shape of the ex-cited states of the isolated chromophore due tosurrounding molecules and is crucial for the ap-plication of excitonic Hamiltonians to closelyspaced MC assemblies. In contrast, the inter-monomer excitonic couplings, i.e. those possi-bly promoting energy transfer between the ππ∗

states are much smaller, in particular for G(La)-C(ππ∗1).

For the nπ∗ states, as shown in Table S3 in theSI, hydrogen bonding affects the intra-monomermixing couplings in a similar manner to the ππ∗

states, in particular for G(nNπ∗1)-G(nNπ

∗2)and C(nOπ

∗1)-C(nOπ∗2) mixing. Whilst the

inter-monomer couplings of the nπ∗ states arerelatively small, consulting the eigenvectors ofthe nπ∗ FrD-LVC adiabatic states in Table S9shows some mixing of the states localized onG and C at the FC point, in particular for theCAM-B3LYP model, due to the closeness in en-ergy of the nπ∗ diabatic states. This indicatesthat the hydrogen bonding could induce a smallamount of delocalization of the dark states.

The general trends in terms of the strengthof coupling are confirmed when considering theeffect of vibrations, which allows the couplingbetween ππ∗ and nπ∗ states. Interestingly, asshown in Tables S12 and S13 in the SI, nπ∗

states localized on C are significantly vibroni-cally coupled with G→C(CT)1.

As an additional characterisation and test ofthe robustness of our approach, we have com-pared the energies and geometries of planar adi-abatic excited state minima from TD-DFT ge-ometry optimisations (qad,mmin for adiabatic statem, see also Section S2.2 and S3.2.2 in the SI)

10

with the diabatic minima predicted by the FrD-LVC models (qd,imin for diabatic state i). Asshown in Table 3, the geometries (see the lowroot-mean-square-deviation, RMSD) and rela-tive energy of the two different sets of minimaare quite similar.

Moreover, in general, in its minimum eachadiabatic state has a more predominant con-tribution from a single diabatic state than inthe FC region, as shown by the comparison ofthe eigenvectors of the diabatization procedurein the different structures (see Tables S8-S11in the SI). For example, at the FC point theS1 and S2 states of ωB97X-D have significantmixing of the ππ∗ states localized on G withthose localized on C (Table S8). However, atboth qad,mmin and qd,imin geometries of the G(La) andC(ππ∗1) states, the FrD-LVC adiabatic statesare instead predominantly composed of eitherG(La) or C(ππ∗1) diabatic states (Tables S10and S11, respectively). These results supportthe physical significance of the ‘monomer-like’diabatic states, as well as benefitting the inter-pretation of the dynamics results in the follow-ing section.

4.2 Excited state dynamics ofGC

In Figure 3 we report the excited state dy-namics computed by using a FrD-LVC Hamil-tonian including 12 states (solid lines) andparametrized with CAM-B3LYP or ωB97X-Dfor initial excitations to each of the four low-est bright excited states. When exciting G(La),CAM-B3LYP predicts that, after an ultrashort‘spike’ due to the coupling with G(Lb) at theFC point, an effective population transfer toG→C(CT)1 occurs. After ∼25 fs, the popu-lation of G→C(CT)1 is 0.5, and after 60 fs itis 0.9, and the transfer is virtually complete.No significant changes are then predicted until250 fs, when the population of the other ex-cited states is close to zero, the most populatedone being C(ππ∗1). When exciting to G(Lb),an ultrafast decay to G(La) is predicted, inline with the results obtained on G monomer.17

However, then G(La) acts as ‘doorway’ state toG→C(CT)1, whose population after ∼60 fs is

0.8. Interestingly, a small fraction of the pop-ulation is ‘trapped’ on G(La) and then trans-ferred to C(ππ∗1), whose population after 250fs is non-negligible (∼0.05).

When exciting to C(ππ∗1), the populationis also effectively transferred to G→C(CT)1,though the transfer is slower and less completethan when exciting the G La/Lb states. Af-ter 60 fs, the population of C(ππ∗1) is still 0.5,and after 250 fs 0.15. Finally, excitation ofC(ππ∗2) triggers an ultrafast decay to C(ππ∗1)and, then, to G→C(CT)1. In this case how-ever, a plateau is reached after ∼ 100 fs, withC(ππ∗1) and G→C(CT)1 exhibiting a similarpopulation (∼0.3 and ∼0.5, respectively).

The picture provided by ωB97X-D is basi-cally consistent with that of CAM-B3LYP. The∼0.4 eV larger energy of the G→C(CT)1 statein the ωB97X-D model confers only a minorslow down of the population transfer, and after100 fs the population of G→C(CT)1 is ≥ 0.8when exciting G(La) or G(Lb), and ≥ 0.4 whenexciting C(ππ∗1) or C(ππ∗2). In this lattercase the transfer to G→C(CT)1 is actually evenlarger than according to CAM-B3LYP, and aplateau in the populations of G→C(CT)1 andC(ππ∗1) is reached at a later stage, after ∼150fs.

Figure 3 also highlights that the populationof the dark nπ∗ excited states is extremelysmall, their sum being ≤ 0.02 for all calcula-tions except for an initial excitation to C(ππ∗2)where it is marginally larger (∼0.06 for theCAM-B3LYP and∼0.04 for the ωB97X-D mod-els). WC pairing thus suppresses these deac-tivation channels, which are active in the cy-tosine monomer.15,17 Indeed, our recent QDstudies on cytosine and 1-methylcytosine witha LVC Hamiltonian parametrized with CAM-B3LYP predict that after initial photoexcita-tion of ππ∗1 ∼20-25% of the population istransferred to the nπ∗ states for cytosine and∼10% for 1-methylcytosine, while exciting ππ∗2the population transfer increases up to ∼50%for cytosine and ∼30% for 1-methylcytosine.

Given the small participation of the nπ∗ statesand the G→C(CT)2 state, it is unsurprisingthat the population dynamics predicted by thereduced-dimensionality 5-state model, includ-

11

0

0.2

0.4

0.6

0.8

1a)

CAM-B3LYP

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1G->C(CT)2

G(nOπ*)G(nNπ*1)G(nNπ*2)

C(nNπ*)C(nOπ*1)C(nOπ*2)

ωB97X-D

0

0.2

0.4

0.6

0.8b)

12 State

5 State

5 State, λi,CT=0

Popula

tion

0

0.2

0.4

0.6

0.8c)

0

0.2

0.4

0.6

0.8

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure 3: Diabatic state populations for FrD-LVC models with 12 states (solid line), 5 states(dotted line), and 5 states with λij = 0 for all the ππ∗ states coupled to G→C(CT)1 (dashed line).Dynamics initiated on a) G(La), b) G(Lb), c) C(ππ∗1) and d) C(ππ∗2) states. Parametrized byCAM-B3LYP (left) and ωB97X-D (right).

ing only the ππ∗ and G→C(CT)1 states, andthe 65 A’ vibrational modes, are similar to thatdescribed above (dotted lines in Figure 3). Themain difference is the 5 state model predicts agreater population transfer to the G→C(CT)1state and reduced ‘trapping’ in the C(ππ∗1)state after excitation to C(ππ∗2) in the CAM-B3LYP model. Similar effects are seen, al-though to a lesser extent, in the ωB97X-Dmodel, and also in the CAM-B3LYP model af-

ter excitation to the G(Lb) state (where in thiscase there is less trapping in the G(La) state).Whilst part of the less effective population ofthe G→C(CT)1 state in the 12 state model canbe attributed to the small population of the nπ∗

states, the remainder may be attributed to thistrapping on the ππ∗ states.

12

4.2.1 Vibrational effects

In order to investigate the cause of the ‘trap-ping’ in the 12 state model, we have analysedthe expectation values of the diabatic potentialsof the different states, integrating over all nor-mal modes of the wavepacket as a function oftime in Figure. 4. For clarity, this figure onlyshows the potentials of the ππ∗ and nπ∗ states

on the base that is initially excited, as well asthe G→C(CT)1 state. The full figure may befound in the SI, Figure S9.

For initial excitation to C(ππ∗2) in the CAM-B3LYP model, where the trapping effect is mostclearly observed, the left panel of Figure 4dshows that the potential of C(ππ∗1) in the12 state model almost plateaus after ∼50 fs,

-1

0

1

2

3 a)

12 State5 State

CAM-B3LYP

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1G(nOπ*)

G(nNπ*1)G(nNπ*2)

C(nNπ*)C(nOπ*1)C(nOπ*2)

ωB97X-D

-1

0

1

2

3 b)

<Ψ

|Vd ii(

q)|

Ψ>

(eV

)

0

1

2c)

0

1

2

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure 4: Expectation of diabatic state potential energies, (〈Ψ|V dii (q)|Ψ〉) shifted by −Ed

CT1(0) −1/4

∑α ωα so that the G→C(CT)1 energy is 0 initially. For the 12 state (solid lines) and 5 state

(dotted lines) FrD-LVC models for GC, parametrized by left: CAM-B3LYP and right: ωB97X-Dfor dynamics initiated on a) G(La), b) G(Lb), c) C(ππ∗1) and d) C(ππ∗2) states. For clarity, onlythe potentials of the G→C(CT)1 state, and the ππ∗ and nπ∗ states localized on the base that isinitially excited are shown.

13

whereas in the 5 state model it is destabilised.Many vibrations are slightly more active in the5 state than the 12 state model, resulting inthis destabilisation of C(ππ∗1) and, therefore,to a larger transfer to the G→C(CT)1 statefor the 5 state model. The expectation ofthe C(ππ∗1) diabatic potential along a repre-sentative few normal modes is shown in Fig-ure 5, with the displacement vectors of the vi-brations illustrated in the SI Figure S6. In the12 state model there is a larger bath of vibra-tional modes where the excess energy depositedwhen exciting C(ππ∗2) can be dissipated (as the12 state model includes all 99 A’ and A” modes,whereas the 5 state model includes only the 65A’ modes), cooling down the vibrations thatdestabilize the C(ππ∗1) state. In contrast, cool-ing down these vibrations does not affect theG→C(CT)1 state as significantly. This expla-nation correlates with the fact that the energygap between initial excitation and G→C(CT)1state is largest for initial excitation to C(ππ∗2)in the CAM-B3LYP model, hence this is thecase where the largest amount of energy hasto be dissipated in the vibrational modes inthe subsequent reorganisation, and where the

largest trapping is observed.Figure. 4 also reveals that the nπ∗ states

are immediately destabilised upon excitation,within ∼10 fs the diabatic potential of thelowest nπ∗ state on each base reaches a value> 0.5 eV larger than at the FC point. In par-ticular, when the initial excitation is close inenergy to the nπ∗ state, so to either G(Lb) orC(ππ∗2), the ππ∗ state of initial excitation isimmediately stabilised and the closest nπ∗ statedestabilised. This helps to explain why there isonly small population transfer to the nπ∗ states,as by the time the vibrational motions bringthe G(Lb)/G(nOπ

∗) or C(ππ∗2)/C(nNπ∗) states

close in energy once more, after∼20 fs, the pop-ulation has already been deposited to the lowerG(La) or C(ππ∗1) states and subsequently tothe G→C(CT)1.

Whilst this is very much a multi-vibrationalmode effect, we have identified two normalmodes that provide a large contribution to thisprocess, q76 for the G(Lb)-G(nOπ

∗) gap, and q77for the C(ππ∗2)-C(nNπ

∗) gap. The q76 mode ispredominantly localized on G, and consists ofan N1-H1 and C8-H8 bending motion, whilstq77 is predominantly localized on C, and consti-

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200 250

<Ψ

|Vd C

(ππ*1

)(q

α)|

Ψ>

(eV

)

Time (fs)

q07 q14

q76 q77

q80 q92

q95 q97

Figure 5: Expectation of diabatic state potential energy along various normal modes for the C(ππ∗1)state (〈Ψ|V d

C(ππ∗1)(qα)|Ψ〉), after initial excitation to the C(ππ∗2) state for the 12 state (solid lines)

and 5 state (dotted lines) CAM-B3LYP parametrized FrD-LVC models. Each mode offset bydifferent values so that they do not overlap.

14

tutes a combined NH2 bend, C4-C5 ring stretchand C5-H5 and C6-H6 bend. The expectationof the diabatic potentials along the q76 modeafter initial excitation to G(Lb), and along theq77 mode after initial excitation to C(ππ∗2) areshown in Figure 6, panels a) and b) respec-tively, for the first 25 fs of the calculation withthe ωB97X-D FrD-LVC model. In this Fig-ure we observe, indeed, that after initial ex-citation, the G(Lb)/C(ππ∗2) states are imme-diately stabilised, whilst the G(nOπ

∗)/C(nNπ∗)

states are destabilised within half a vibrationalperiod (∼10 fs). After the vibrational period iscomplete (∼20 fs) and the ππ∗ and nπ∗ statesare close in energy once more, the populationfrom the G(Lb)/C(ππ∗2) states is already close

to zero (dotted lines in Figure 6).In the SI we show that the results for the

CAM-B3LYP model are the same, the effect ofthese modes after initial excitation to the otherstates, and their value for the full 250 fs of thepropagation (Figures S10 and S11). Interest-ingly the mode q77, despite being localized onC, significantly affects the states localized on G.

Another interesting vibrational effect is thelarge reorganisation energy of the G→C(CT)1state after it is populated, leaving it ∼0.5 eVmore stable after 250 fs than at the FC point,whilst the ππ∗ states are > 0.5 eV destabilised,leaving the gap between the G→C(CT)1 andlowest ππ∗ state > 1 eV (Figure 4). The q76and q77 modes previously mentioned contribute

-0.2

0

0.2

0.4

0.6

0

0.2

0.4

0.6

0.8

1

a)

Potential

Population

<Ψ

|Vd ii(

q7

6)|

Ψ>

(eV

)

G(L

b)

Popula

tion

G(La)

G(Lb)

G(nOπ*)

G->C(CT)1

C(ππ*1)

C(ππ*2)C(nNπ*)

-0.4

-0.2

0

0.2

0.4

0.6

0 5 10 15 20 25 0

0.2

0.4

0.6

0.8

b)

<Ψ

|Vd ii(

q7

7)|

Ψ>

(eV

)

C(π

π*2

) P

opula

tion

Time (fs)

ω76 = 1586 cm−1

ω77 = 1607 cm−1

Figure 6: Left: Expectation of diabatic state potential energies (solid lines) along the a) q76 normalmode after initial excitation to G(Lb) and b) q77 normal mode after initial excitation to C(ππ∗2).Calculated with the 12 state FrD-LVC model for GC parametrized by ωB97X-D. For clarity thepotentials are shifted so that the G→C(CT)1 energy is 0 initially, i.e. by −Ed

CT1(0) − 1/4ω76/77,and only the potentials of the G→C(CT)1 state, and the ππ∗ and lowest nπ∗ states localized on thebase that is initially excited are shown. The dotted lines show the population of the G(Lb) statein a) and the C(ππ∗2) state in b). On the right hand side are the displacement vectors of the q76and q77 normal modes and their frequencies.

15

somewhat to this effect (see SI, Figures S10 andS11), however a much larger contribution arisesfrom a low frequency mode q07, that involvesa shearing motion between the bases. An ex-ample of its affect on the expectation of thediabatic potential energies following initial ex-citation to a) G(La) and b) C(ππ∗1) is shownin Figure 7 for the ωB97X-D model. It is notactive for the first 50 fs of the calculation, how-ever when the G→C(CT)1 state is significantlypopulated it becomes active and stabilises theG→C(CT)1 state, whilst destabilising the oth-ers. The effect of this mode on the diabatic po-tentials following excitations to the other ππ∗

states is shown in the SI, Figure S12 along withthe CAM-B3LYP results, and the effect is muchthe same.

The impact of the vibrational motion on

the diabatic coupling terms (i.e. V dij (q)) be-

tween the ππ∗ and G→C(CT)1 states is in-stead more limited. In particular, Figure S13in the SI shows after an excitation to G(La)or G(Lb) the coupling between the doorwaystate G(La) and the G→C(CT)1 does not sig-nificantly deviate from its initial value at theFC point (Table 2). An analogously weaktime-dependence is observed for the coupling ofC(ππ∗1) with G→C(CT)1 after an initial ex-citation to C(ππ∗1) and C(ππ∗2). As a conse-quence, the dashed lines Figure. 3 show that ne-glecting the dependence of V d

ij (q) on coordinatefor the ππ∗-G→C(CT)1 couplings (i.e. settingthe linear terms λij = 0 for i, j=G→C(CT)1)produces no discernible difference to the dy-namics of the 5 state FrD-LVC models.

The excitonic couplings, i.e. those between

-0.5

0

0.5

1

1.5

2

a)

<Ψ

|Vd ii(

q0

7)|

Ψ>

(eV

)

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1G(nOπ*)

G(nNπ*1)G(nNπ*2)

C(nNπ*)C(nOπ*1)C(nOπ*2)

-0.5

0

0.5

1

0 50 100 150 200 250

b)

Time (fs)

ω07 = 115 cm−1

Figure 7: Left: Expectation of diabatic state potential energies along the q07 normal mode (i.e.〈Ψ|V d

ii (q07)|Ψ〉) from the 12 state FrD-LVC model for GC parametrized by ωB97X-D after initialexcitation to a) G(La) and b) C(ππ∗1). For clarity the potentials are shifted so that the G→C(CT)1energy is 0 initially, i.e. by −Ed

CT1(0) − 1/4ω07, and only the potentials of the G→C(CT)1 state,and the ππ∗ and nπ∗ states localized on the base that is initially excited are shown. On the righthand side are the displacement vectors of the q07 normal mode and its vibrational frequency.

16

ππ∗ states localized on each base, are similarlyunaffected by the vibrations, see Figure S14 inthe SI. In particular, the excitonic coupling be-tween the doorway states, G(La)-C(ππ∗1), re-mains very small during the propagation, ex-plaining the limited population transfer fromstates localized on one base to ones localizedon the other.

On the contrary, the couplings between thebright states localized on the same base arestrongly affected by vibrational motions, seeFigure S15 in the SI. A tangible consequence,for example, is that the strong mixing of G(La)-G(Lb) and C(ππ∗1)-C(ππ∗2) states observed inthe adiabatic states at the FC point decreasesduring the propagation, such that the adiabaticstates end up resembling much more the refer-ence states on isolated monomers.

Finally, we have analysed how the excitedstate dynamics is affected by deuteration, i.e.

the substitution of the five ’exchangeable’ pro-tons (the amino and imino ones) by deuterium.Many TR studies on DNA are performed indeuterated solvents,50 and isotope substitutionhas been suggested to affect the PCET pro-cesses.74 As shown in Figure S7 of the SI thepopulation dynamics is very little affected bydeuteration, which decreases the transfer toG→C(CT)1 by ≤5%. As a consequence thefirst step of the PCET reaction is not expectedto be very sensitive to isotope effect, at least inthe gas phase.

4.2.2 GC absorption spectrum

We have also computed the absorption spec-trum of the GC pair, based on our 12 stateFrD-LVC model calculations, using the proce-dure described in the Computational Details,and SI, Section S1.2. These are shown in Fig-ure 8, with panel a) illustrating the individ-

0

0.5

1

1.5

2

2.5

a)

ε/1

04 (

M-1

cm

-1)

GC: TotalGC: G(La)

GC: G(Lb)

GC: C(ππ*1)

GC: C(ππ*2)

CAM-B3LYP ωB97XD

0

0.5

1

1.5

2

200 220 240 260 280 300 320

b)

Wavelength (nm)

G: G(La)

G: G(Lb)

C: C(ππ*1)

C: C(ππ*2)

200 220 240 260 280 300 320

G+C

G

C

Figure 8: Absorption spectra of GC calculated from the 12 state FrD-LVC models (solid blackline) with a) individual diabatic state components (solid blue, red, light and dark green lines)and b) compared to monomeric spectra of G (purple) and C (turquoise) with individual statecomponents (dashed red, blue, light and dark green lines) and the sum of G and C (grey). LVCmodels parametrized by CAM-B3LYP (left) and ωB97X-D (right). All spectra shifted by -0.75 eVand broadened with Gaussian HWHM=0.04 eV.

17

ual state components of the GC spectrum, andpanel b) comparing it to absorption spectra ofisolated G and C and their sum. The absorp-tion spectra of isolated G and C are calculatedusing 5 state LVC models, including 2 ππ∗ and3 nπ∗ states for each base, in the same man-ner as our recent work on single nucleobases.17

All spectra are shifted by -0.75 eV to matchthe onset of the GC spectrum in chloroform,42

(see Figure S18 in SI) and plotted on the wave-length scale. The parametrizations with CAM-B3LYP and ωB97X-D predicted quite similarspectra, therefore our analysis below applies toboth models.

Figure 8a shows that the region of themaximum absorption at ∼ 250-260 nm isdominated by the contribution of the G(Lb).At shorter wavelengths it is reinforced andthen slightly overcome by the contribution ofC(ππ∗2). Whilst on the red-wing, at longerwavelengths, most of the signal arises fromG(La) and C(ππ∗1). In this red wing, accord-ing to our computations most of the wavepacketshould be located on G in the ∼280-295 nmwindow, whilst the contribution from C(ππ∗1)is only predominant at ≥ 295 nm.

Comparison with the results in Figure 8b in-dicate that the contribution of each individ-ual state is broader in GC than the individualmonomers, due to the large ππ∗ mixing cou-plings and coupling to the G→C(CT)1 statein GC. Furthermore, the GC spectrum exhibitsinteresting differences with respect to the sumof monomer spectrum (G+C). First, the G+Cspectrum exhibits a longer red wing tail, com-ing from the C contribution, which disappearsin GC. This outcome is due to blue shifting ofC(ππ∗1) due to hydrogen bonding.75 Second,the maximum of the absorption band of GCis weakly red-shifted with respect to G+C oneand it is more intense in the region 260-290 nm.A similar effect is observed, although to a lesserextent, in experiment.42 Here we assign it par-tially to the blue shifting of C(ππ∗1), and par-tially due to weak red-shifting of the G(Lb) con-tribution.

5 Concluding remarks

In this contribution we have introduced amethod for an automatic parametrizationof a generalised LVC Hamiltonian suitablefor studying the photophysics of multichro-mophoric assemblies, exploiting TD-DFT. Itsmain methodological novelty concerns the pos-sibility of defining the reference diabatic stateson the basis of isolated fragments. In combi-nation with effective wavepacket propagations,for instance with the ML-MCTDH method, ourapproach makes it rather straightforward to de-scribe the competition between inter- and intra-chromophore photophysical pathways withina fully quantum dynamical approach. Thismethod is thus an attractive option to studyphenomena where the timescale of internal con-version processes on individual chromophoresis expected to be similar to that of energy andcharge transfer between multiple chromophores.Furthermore, it can also account for the possi-ble coupling between these processes.

Due to the efficiency of the parametriza-tion of the LVC Hamiltonian and capabilityof ML-MCTDH propagations, it is possibleto include many electronic states (> 10) anddozen/hundreds of normal coordinates in themodel. This permits the investigation of the ul-trafast vibronic dynamics following a photoex-citation in significantly broad energy ranges.For example, in the present study we focused onthe region above ∼220 nm, i.e. that ‘covered’by the four lowest energy bright states of a GCpair. However, we have simulated the dynamicsconsidering up to 12 excited states (i.e. includ-ing also the lowest energy dark states). Thisis typically more than can be considered with‘on-the-fly’ dynamics calculations, such as sur-face hopping (although, one should rememberthat the number of adiabatic states to describethe same dynamics could be smaller).76 There-fore, even in cases where an LVC Hamiltoniancannot capture all the details of the adiabaticPES explored with surface hopping methods,this approach could complement these calcula-tions by providing a relatively quick assessmentof the role of higher excited states and/or therole quantum dynamics effects. Indeed, the pro-

18

posed parametrization is quite effective: TD-DFT calculations for the diabatization with 6-31G(d) basis set in the present work took only∼24 hours using 28 cores, whilst the diaba-tization took ∼30 minutes on 12 cores. Forthe quantum dynamics calculations themselvesthe computation times ranged between 100-300hours on a single core for the 12 state calcu-lations, and 20-100 hours for the 5 state cal-culations. These values could be feasibly re-duced through appropriate tuning of param-eters in the ML-MCTDH computations, suchas choice of integrator, mode combination, andmultilayer ‘tree’, or by discarding smaller termsin the FrD-LVC Hamiltonian.

The application of FrD-LVC is most suitedwhen couplings between the different monomersare not excessively strong, and more in generalwhen it is conceivable or interesting to hypoth-esize to have prepared an initial state localizedon one single monomer. In those cases, theproposed approach also has the advantage tobe naturally allied with the chemical point ofview that breaks the investigated photophysi-cal event into elementary processes on the in-dividual molecular components and their possi-ble interactions. For example, this is typicallydone, more or less implicitly, for charge sep-aration/migration/recombination in multichro-mophore assemblies.

The application of FrD-LVC should be han-dled with more care when the coupling be-tween the different units is so strong to makeany connection with the behavior of the sepa-rated unit too weak. The analysis of the resultsof the fragment diabatization procedure, suchas calculated couplings and predicted minima,and/or of the subsequent dynamics can provideuseful diagnostics to identify these ’problem-atic’ cases. However, it is important to stressthat FrD-LVC could still be used even in thesecases by considering initial states coherently ex-cited on more than one diabatic state or, alter-natively, performing propagations by explicitlyincluding the interaction with the pump laserpulse in the dynamics.

Our approach also obviously suffers from allthe limitations of LVC models, such as lackof large amplitude motions, Duschinsky mix-

ings and anharmonicity. Several strategies maybe employed to ameliorate these deficiencies,such as moving to a quadratic vibronic cou-pling model (or at least some quadratic correc-tions like done in Refs. 16,71,77), fitting withnon-harmonic functions when anharmonicity isconfined to a few degrees of freedom, and mixedquantum classical approaches to deal with largeamplitude motions.78 Such developments fall,however, outside the aim of the present contri-bution and will be tackled in future studies.

In the present, first, application of FrD-LVCwe have studied the excited state dynamics ofGC adopting a WC hydrogen bond arrange-ment, after exciting each of the four lowestenergy bright states. We predict a substan-tial and fast population transfer from the ini-tially excited bright state towards the low-est energy G→C CT state. This transfer ismore effective for initial excitations on G brightstates, with ∼80% of the population trans-ferred in ∼50 fs. However, also when excit-ing C(ππ∗1) and C(ππ∗2), in less than 100 fs∼50% of the population is transferred to theG→C(CT)1 state. Therefore, the fact thatour Hamiltonian does not include the monomerG(La) and C(ππ∗1) decay channels to S0, in-volving large out-of-plane distortions,1 does notbias the qualitative reliability of our conclusion,given that the transfer to the CT states occurson a time-scale (<100 fs) for which the decayto S0 of the bright states should play a minorrole.

Our dynamical calculations are thus consis-tent with the experimental picture in the gasphase,52 with the population of the bright ex-cited states disappearing on a <100 fs timescale. Considering that on the CT PES the pro-ton transfer is barrierless, our study also seemsto support the reliability of the mechanism pro-posed by Sobolweski and Domcke .32,33 A forth-coming work will be devoted to study in depththe quantum dynamics of the coupling betweenthe CT formation and the PT process.

FrD-LVC provides interesting insights on theeffects ruling the yield of the CT population.For example, G(La) appears to be the excitedstate most strongly coupled to G→C(CT)1, andpermits the fastest and most effective popula-

19

tion of G→C(CT)1. This is true even when theG→C(CT)1 state is closer in energy to otherππ∗ states, such as predicted with the ωB97X-D functional. Moreover, the extremely fastG(Lb)→G(La) decay suggests that G(La) is the‘main’ doorway state to G→C(CT)1.

Despite the smaller coupling of the C ππ∗

states to the G→C(CT)1 state, we still observeeffective (albeit slightly slower) populationtransfer when the initial excitation is localizedon C. The extremely fast C(ππ∗2)→C(ππ∗1)decay, combined with the small C(ππ∗1)-G(La)excitonic coupling indicates that C(ππ∗1) actsas a secondary doorway state to G→C(CT)1.These evidences lead us to conclude that a dra-matic dependence of the CT process on theexcitation wavelength should not be expected.

Interestingly, vibrational motions play onlyminor role in modulating the coupling betweenlocal excitations on different chromophores andwith CT states. This does not mean, how-ever, that vibrations do not drastically affectthe yield of the population transfer, since theydetermine the reorganization energy of any ex-cited state and, therefore, the relative stabil-ity of their minima. In Section S4.4 in theSI, we show that a trivial purely electronic dy-namics with nuclei frozen at the FC positionwould provide a much smaller average popula-tion of G→C(CT)1, even when it is the lowestenergy excited state in the FC region. Further-more, the purely electronic dynamics with theωB97X-D model also predicts a significant exci-tonic transfer between the doorway G(La) andC(ππ∗1) states, in contrast with the vibronicdynamics in Figure 3.

Our calculations indicate that the large re-organisation energy of the G→C(CT)1 is thekey to explain its population. As shown inTable 3, the predicted planar adiabatic anddiabatic minima of the G→C(CT)1 state are∼1 eV more stable than those of the ππ∗ statesaccording to CAM-B3LYP, and ∼0.6 eV morestable according to ωB97X-D. This stabilityresults in similar population transfer to theG→C(CT)1 state by both CAM-B3LYP andωB97X-D models, despite the G→C(CT)1 statenot being the lowest lying state at the FC pointwith ωB97X-D, and it lying 0.4 eV higher in en-

ergy than with CAM-B3LYP. Numerical experi-ments in the SI Section S4.5 indicate that, in or-der to overcome this effect and make populationtransfer to G→C(CT)1 significantly smaller,the diabatic energy gap between the CT stateand doorway state should be ≥ 0.6 eV.

WC pairing, besides allowing the formationof the CT states, has another important effecton the photoactivated dynamics of G and C,almost suppressing any population transfer tothe dark nπ∗ states. This internal conversionroute is significant for isolated bases in the gasphase, in particular for C in the context of thepresent work.14–17,53 As well as the significantdestabilization of nπ∗ transitions by hydrogenbond formation, we have identified N-H bend-ing vibrations that further destabilise the nπ∗

states upon initial excitation, whilst converselystabilising the ππ∗ states.

The results of our dynamical simulations arestrictly valid only in the gas phase, nonethe-less some of the effects we have discussed arelikely operative also for a GC pair in solutionand within DNA. For example, we can expectthat the nπ∗ states should also not be signifi-cantly populated within a duplex, since there isno reason to believe that a polar environmentwould increase their stability. Analogously,G→C(CT)1 should also be significantly popu-lated in solution. On the other hand, within aduplex, the population of additional CT statesinvolving the adjacent, stacked, bases to G, canbecome competitive46,50,79 and we will investi-gate the interplay of intra- and inter-strand CTstates in future work.

As shown in the present contribution, theFrD-LVC approach can thus provide many in-teresting insights into complex phenomena in-volving both intra- and inter-chromophoric ex-cited states, in a fully quantum dynamical pic-ture. Furthermore, in cases when an LVC PESdoes not suffice to completely describe the dy-namics, it can give useful indications on the rel-ative importance of the different excited statesand be used as a ‘first’ check before apply-ing more computationally expensive dynamicalcalculations, such as the ‘on-the fly’ methods,on reduced dimensionality systems. Alterna-tively, the FrD-LVC approach can be used as a

20

building block onto which a more sophisticatedmodel may be constructed, such as by consider-ing anharmonic or dissociative coordinates likethe proton transfer process in GC, or inclusionof solvent effects,80,81 and we intend to exploreboth of these avenues in future work.

Acknowledgement This project has re-ceived funding from the European Union’sHorizon 2020 Research and Innovation Pro-gramme under the Marie Sklodowska-Curiegrant agreement No 765266 (LightDyNAmics).

Supporting Information Avail-

able

Numerical details of the diabatization scheme inTD-DFT and calculation of absorption spectra.Electronic structure data including NTOs, nor-mal mode displacement vectors and monomervs dimer energies. Characterisation of the FrD-LVC models including energies, couplings, andeigenvectors of adiabatic FrD-LVC states atthe FC point and various excited state min-ima. Additional dynamics results including ef-fect of deuteration, electronic only dynamics,dependence on CT-ππ∗ diabatic energy gap,and time-dependence of energies and couplings.Comparison of absorption spectra to experi-ment. Test calculation with larger basis set.

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26

download fileview on ChemRxivmain_FrD-LVC.pdf (2.14 MiB)

Supporting Information: A FragmentDiabatization Linear Vibronic Coupling

Model For Quantum Dynamics OfMultichromophoric Systems: Population Of

The Charge Transfer State In ThePhotoexcited Guanine Cytosine Pair

S-1

Contents

S1 Additional Numerical Details S-3

S1.1 Diabatization Scheme in TD-DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-3

S1.2 Absorption Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-6

S2 Electronic Structure Details and Data S-7

S2.1 Natural Transition Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-7

S2.2 Adiabatic TD-DFT Minima Calculation Details . . . . . . . . . . . . . . . . . . . . . . . . . S-10

S2.3 Normal Modes CAM-B3LYP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-11

S2.4 Monomer vs WC Dimer Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-12

S3 FrD-LVC Models Data S-13

S3.1 Diabatic Energies and Couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-13

S3.1.1 FC Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-13

S3.1.2 Excited State Minima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-15

S3.2 Eigenvalues and Eigenvectors of Adiabatic FrD-LVC States . . . . . . . . . . . . . . . . . . . S-19

S3.2.1 FC Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-19

S3.2.2 Excited State Minima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-21

S3.3 Norm of Coupling Vector: FC Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-23

S4 Additional Dynamics Results S-25

S4.1 Deuterated Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-25

S4.2 Diabatic Potential Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-26

S4.3 Diabatic Potential Couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-30

S4.4 Electronic Only Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-33

S4.5 G→C(CT)1 Diabatic Energy Gap Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . S-34

S5 Additional Absorption Spectra S-35

S5.1 Comparison To Experimental Absorption Spectrum in Chloroform . . . . . . . . . . . . . . . S-35

S6 6-31+G(d,p) Basis Set Test S-36

S6.1 Single Point Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-36

S6.2 ωB97X-D 6-31+G(d,p) FrD-LVC Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-37

S-2

S1 Additional Numerical Details

S1.1 Diabatization Scheme in TD-DFT

As discussed in the Methods section in the main text, we define the reference states of the fragments |Rfrags(0)〉and overlap matrix between these reference states and the adiabatic states of the multichromophore (MC) at

reference geometry S(0) = 〈Rfrags(0)|aMC(0)〉 and displaced geometry S(∆α) = 〈Rfrags(0)|aMC(∆α)〉 within

the framework of TD-DFT. For this, we use transition densities, which in super-operator notation may be

written as:

|ρ〉〉 =∑ir

Xir |Φr〉 〈Φi|+∑ir

Yir |Φi〉 〈Φr| (S1)

where Xir and Yir are the response vectors, Φ the molecular orbitals (MOs), and i and j will be used to signify

occupied MOs, and r and s virtual MOs. The response vectors are output by standard electronic structure

packages, typically written on the basis of molecular orbitals, and allow the local excitation reference states

to be defined as equivalent to local excitations of individual fragments. Charge transfer reference states may

be defined as single orbital transitions between an occupied orbital on one fragment, and a virtual orbital on

another. Of course, a user-defined local excitation (such as HOMO-LUMO transition) is also possible.

Proceeding with the derivation of the overlap matrix, the inner product between two transition densities

for states A and B may be written as a trace operation over the MOs

〈〈ρA|ρB〉〉 = TrΦ[

(∑ir

XAir |Φi〉 〈Φr| −

∑ir

Y Air |Φr〉 〈Φi|

)∑

js

XBjs |Φs〉 〈Φj |+

∑js

Y Bjs |Φj〉 〈Φs|

].

(S2)

If the above was computed for two states of the same system with the same MOs, it would be equal to the

Kronecker delta δAB. However, if state A is a reference state of the fragments, and state B is an adiabatic

state of the MC, then in general MOs of the fragments will not be orthogonal to the MOs of the MC either at

the reference or displaced geometry. For the remainder of the derivation we illustrate how S(∆α) is calculated,

and then state how S(0) is obtained at the end. Eq. S2 can be expanded as

〈〈ρA(0)|ρB(∆α)〉〉 =TrΦ(0)[∑ir,js

XA,0ir XB,∆α

js |Φfragsi (0)〉 〈Φfrags

r (0)|ΦMCs (∆α)〉 〈ΦMC

j (∆α)|]

− TrΦ(0)[∑ir,js

Y A,0ir Y B,∆α

js |Φfragsr (0)〉 〈Φfrags

i (0)|ΦMCj (∆α)〉 〈ΦMC

s (∆α)|]

+ TrΦ(0)[∑ir,js

XA,0ir Y B,∆α

js |Φfragsi (0)〉 〈Φfrags

r (0)|ΦMCj (∆α)〉 〈ΦMC

s (∆α)|]

− TrΦ(0)[∑ir,js

Y A,0ir XB,∆α

js |Φfragsr (0)〉 〈Φfrags

i (0)|ΦMCs (∆α)〉 〈ΦMC

j (∆α)|].

(S3)

where the MOs have been explicitly labelled as to whether they are those of the fragments or the MC, and

labels have been added for the reference (0) and displaced (∆α) geometries. Performing the trace operations

S-3

yields:

〈〈ρA(0)|ρB(∆α)〉〉 =∑ir,js

XA,0ir XB,∆α

js 〈Φfragsr (0)|ΦMC

s (∆α)〉 〈ΦMCj (∆α)|Φfrags

i (0)〉

−∑ir,js

Y A,0ir Y B,∆α

js 〈Φfragsi (0)|ΦMC

j (∆α)〉 〈ΦMCs (∆α)|Φfrags

r (0)〉

+∑ir,js

XA,0ir Y B,∆α

js 〈Φfragsr (0)|ΦMC

j (∆α)〉 〈ΦMCs (∆α)|Φfrags

i (0)〉

−∑ir,js

Y A,0ir XB,∆α

js 〈Φfragsi (0)|ΦMC

s (∆α)〉 〈ΦMCj (∆α)|Φfrags

r (0)〉

(S4)

As the MOs are calculated at different geometries, we will now move in a basis of atomic orbitals (AOs) by intro-

ducing two resolutions of identity for the AOs of the MC at the reference geometry∑

λ |φMCλ (0)〉 〈φMC

λ (0)| and∑µ |φMC

µ (0)〉 〈φMCµ (0)| and two at displaced geometry

∑ν |φMC

ν (∆α)〉 〈φMCν (∆α)| and

∑σ |φMC

σ (∆α)〉 〈φMCσ (∆α)|.

The response vectors in the AO basis are then

XAO,A,0µλ =

∑ir

XA,0ir 〈φ

MCλ (0)|Φfrags

r (0)〉 〈Φfragsi (0)|φMC

µ (0)〉 (S5)

Y AO,A,0µλ =

∑ir

Y A,0ir 〈φ

MCµ (0)|Φfrags

i (0)〉 〈Φfragsr (0)|φMC

λ (0)〉 (S6)

XAO,B,∆ασν =

∑js

XB,∆α

js 〈φMCν (∆α)|ΦMC

s (∆α)〉 〈ΦMCj (∆α)|φMC

σ (∆α)〉 (S7)

Y AO,B,∆ασν =

∑js

Y B,∆α

js 〈φMCσ (∆α)|ΦMC

j (∆α)〉 〈ΦMCs (∆α)|φMC

ν (∆α)〉 (S8)

For the calculation of overlaps in Eq. S5 and S6 between the AOs of the MC and MOs of the fragments at

reference geometry, given that the AOs of the fragments will be the same as the AOs for the MC at the same

geometry, and that the linear combination of atomic orbitals is written as

|Φfragsr (0)〉 =

∑η

cfragsrη |φfragsη (0)〉 (S9)

where crη are the MO coefficients, then the overlap is

〈φMCλ (0)|Φfrags

r (0)〉 =∑η

cfragsrη 〈φMCλ (0)|φfragsη (0)〉

=∑η

cfragsrη 〈φMCλ (0)|φMC

η (0)〉 .(S10)

S-4

Then, in the AO basis the trace over the transition density scalar product is:

〈〈ρA(0)|ρB(∆α)〉〉 =∑µλ,σν

XAO,A,0µλ XAO,B,∆α

σν 〈φMCλ (0)|φMC

ν (∆α)〉 〈φMCσ (∆α)|φMC

µ (0)〉

−∑µλ,σν

Y AO,A,0µλ Y AO,B,∆α

σν 〈φMCµ (0)|φMC

σ (∆α)〉 〈φMCν (∆α)|φMC

λ (0)〉

+∑µλ,σν

XAO,A,0µλ Y AO,B,∆α

σν 〈φMCλ (0)|φMC

σ (∆α)〉 〈φMCν (∆α)|φMC

µ (0)〉

−∑µλ,σν

Y AO,A,0µλ XAO,B,∆α

σν 〈φMCµ (0)|φMC

ν (∆α)〉 〈φMCσ (∆α)|φMC

λ (0)〉

(S11)

Finally, following Ref. 1 and our previous works,2–6 we make the approximation that the AO overlap at two

different but similar geometries of the MC can be approximated by one at the reference geometry to get

〈〈ρA(0)|ρB(∆α)〉〉 '∑µλ,σν

XAO,A,0µλ XAO,B,∆α

σν 〈φMCλ (0)|φMC

ν (0)〉 〈φMCσ (0)|φMC

µ (0)〉

−∑µλ,σν

Y AO,A,0µλ Y AO,B,∆α

σν 〈φMCµ (0)|φMC

σ (0)〉 〈φMCν (0)|φMC

λ (0)〉

+∑µλ,σν

XAO,A,0µλ Y AO,B,∆α

σν 〈φMCλ (0)|φMC

σ (0)〉 〈φMCν (0)|φMC

µ (0)〉

−∑µλ,σν

Y AO,A,0µλ XAO,B,∆α

σν 〈φMCµ (0)|φMC

ν (0)〉 〈φMCσ (0)|φMC

λ (0)〉

= ρABXX(∆α)− ρABY Y (∆α) + ρABXY (∆α)− ρABYX(∆α).

(S12)

So the elements of the overlap matrix S(∆α) are

SAB(∆α) = ρABXX(∆α)− ρABY Y (∆α) + ρABXY (∆α)− ρABYX(∆α). (S13)

Note that we can take advantage of the symmetry of the AO overlap matrix in Eq. S12 to efficiently calculate

the overlap in terms of matrix multiplications and a final sum over two indeces, reducing the problem from

a O(N4) cost to O(N3). This immediately becomes apparent by re-arranging the order of multiplication in

Eq. S12 in the following manner, using the shorthand notation SAO,MC,0λ,ν to represent 〈φMC

λ (0)|φMCν (0)〉, and

noting that SAO,MC,0λ,ν = SAO,MC,0

ν,λ

ρABXX(∆α) =∑µλ,σν

XAO,A,0µλ SAO,MC,0

µ,σ XAO,B,∆ασν SAO,MC,0

ν,λ (S14)

ρABY Y (∆α) =∑µλ,σν

Y AO,A,0µλ SAO,MC,0

µ,σ Y AO,B,∆ασν SAO,MC,0

ν,λ (S15)

ρABXY (∆α) =∑µλ,σν

XAO,A,0µλ SAO,MC,0

λ,σ XAO,B,∆ασν SAO,MC,0

ν,µ (S16)

ρABYX(∆α) =∑µλ,σν

Y AO,A,0µλ SAO,MC,0

λ,σ XAO,B,∆ασν SAO,MC,0

ν,µ (S17)

S-5

The final three terms in each of the above equations are evaluated by matrix multiplication, removing the σ

and ν indeces, and leaving a final sum over the µ and λ indeces. This is the more computationally efficient

method of calculating the overlap matrix compared to our previous applications mentioned in the main text.

The calculation of S(0) can also utilise Eqs. S13 - S17, simply by replacing the response vectors at displaced

geometries XAO,B,∆ασν and Y AO,B,∆α

σν by those at the reference geometry XAO,B,0σν and Y AO,B,0

σν .

Since we define CT states including only the excitation response vector, for a balanced treatment of LE

and CT states we use the Tamm-Dancoff approximation so that we take only the ρABXX element of the inner

product, and the elements of the overlap matrix are

SAB = ρABXX . (S18)

S1.2 Absorption Spectra

The transition dipole moments of the diabatic states at the reference geometry µ[d(0)] may be obtained by

applying the transformation matrix D(0) to the diagonal matrix of adiabatic transition dipole moments of the

MC at reference geometry µ[aMC(0)]

µ[d(0)] = D(0)Tµ[aMC(0)]D(0). (S19)

This is the same procedure as the calculation of the diabatic Hamiltonian matrix in Eq. 7 in the main text,

and we also adopted this in Ref. 7 to calculate diabatic transition dipole moments.

Then, the absorption spectra ε(ω) at zero Kelvin, can be expressed in a TD framework as:

ε(ω) =2πωNA

3000× ln 10× ~c0(4πε0)

∑ji

∫ ∞−∞

dteiωt−Γt2〈0; dj |µdgje−iHt/~µd

ig|di;0〉

=∑i

εii(ω) +∑i,j 6=i

εij(ω) = εauto(ω) + εcross(ω) (S20)

where NA is Avogadro’s number, c0 is the speed of light in vacuo, ε0 is the vacuum permittivity and we

introduced a quadratic damping ruled by a parameter Γ, corresponding to a Gaussian broadening in the

frequency domain. We represent the diabatic transition dipole moments obtained by the transformation in

Eq. S19 with the shorthand µdgj for the transition from ground state g to diabatic state dj . The diabatic

transition dipole moment is considered independent of the nuclear coordinates (Condon approximation), and

the ground-vibrational state of the ground electronic state is represented by 0 and its energy is set to zero.

The auto (εauto) and cross (εcross) correlation functions are obtained by numerical propagation in time

under the effect of the FrD-LVC Hamiltonian of the doorway states |dj ;0〉 obtained by a vertical excitation of

the vibrational state 0 to the bright diabatic states (i.e. for which µig is non vanishing). Then, the vibronic

absorption spectrum is obtained by Fourier transform of the sum of the correlations functions weighted by the

scalar products of the diabatic transition dipoles (as reported in Equation S20). Cross-correlations functions

usually have a very small effect and have been neglected.2,6

S-6

S2 Electronic Structure Details and Data

S2.1 Natural Transition Orbitals

Figure S1: Frontier NTOs (occupied on the left and virtual on the right) and their eigenvalues for the first 12singlet states of GC in the gas phase at ground state geometry Cs symmetry using the CAM-B3LYP functionaland 6-31G(d) basis set with an isovalue 0.02 for all orbitals.

S-7

Figure S2: Frontier NTOs (occupied on the left and virtual on the right) and their eigenvalues for the first 12singlet states of GC in the gas phase at ground state geometry Cs symmetry using the ωB97X-D functionaland 6-31G(d) basis set with an isovalue 0.02 for all orbitals.

Figure S3: Frontier NTOs (occupied on the left and virtual on the right) and their eigenvalues for the adiabaticplanar excited state minima of GC in the gas phase using the CAM-B3LYP functional and 6-31G(d) basis setwith an isovalue 0.02 for all orbitals.

S-8

Figure S4: Frontier NTOs (occupied on the left and virtual on the right) and their eigenvalues for the adiabaticplanar excited state minima of GC in the gas phase using the ωB97X-D functional and 6-31G(d) basis set withan isovalue 0.02 for all orbitals.

Figure S5: Frontier NTOs (occupied on the left and virtual on the right) for the S5 adiabatic planar excitedstate minimum of GC in the gas phase using the CAM-B3LYP functional and 6-31G(d) basis set with anisovalue 0.02 for the orbitals.

S-9

S2.2 Adiabatic TD-DFT Minima Calculation Details

We succeeded in optimizing the minima of G→C(CT)1, C(ππ∗1), G(La), G(nOπ∗), G(nNπ

∗1) and C(nOπ∗1)

states (see NTOs in Figures S3 and S4). For the G→C(CT)1 optimisation, the N-H bond lengths on G had to

be frozen at the same distance as in the S0 minimum, to prevent the H atom being transferred to C. Geometry

optimizations of the adiabatic states corresponding to C(ππ∗2), G(Lb), G(nNπ∗2), C(nOπ

∗2) and G→C(CT)2

states lead to the minima of the corresponding lower lying excited state (C(ππ∗1), G(La), G(nNπ∗1), C(nOπ

∗1),

and G→C(CT)1). Finally, attempted geometry optimization of the adiabatic state corresponding to C(nNπ∗)

(S5 at the FC position) with CAM-B3LYP instead leads to a state which appears to resemble the nπ∗-CT state

with ‘wobble GC’ configuration recently put forward in Ref.8 (see Figure S5). Given this different hydrogen

bonding arrangement, we do not consider this state in the present work. Attempted geometry optimisation of

the C(nNπ∗) (S5) state with ωB97X-D lead to a similar structure, but then was unable to be converged.

S-10

S2.3 Normal Modes CAM-B3LYP

07 = 112.32 cm1

14 = 238.56 cm1

76 = 1584.09 cm1

77 = 1607.06 cm1

80 = 1693.61 cm1

92 = 3209.84 cm1

95 = 3275.04 cm1

97 = 3429.32 cm1

Figure S6: Normal modes shown in Figure 5 in the main text, at the CAM-B3LYP/6-31G(d) level of theory.

S-11

S2.4 Monomer vs WC Dimer Energies

Table S1: TD-DFT excitation energies (eV) and oscillator strengths (in parentheses) of the 9-methylguanine1-methylcytosine WC pair and individual monomers in Cs symmetry at their respective equilibrium geometries,obtained with the CAM-B3LYP and ωB97X-D functionals and 6-31G(d) basis set.

CAM-B3LYP ωB97X-D

Char. G/C Mon. GC Dimer G/C Mon. GC Dimer

C(ππ∗) 5.09 (0.090) 5.27 (0.114) 5.07 (0.090) 5.28 (0.140)

G(La) 5.33 (0.154) 5.31 (0.087) 5.32 (0.151) 5.21 (0.071)

G(Lb) 5.80 (0.271) 5.69 (0.403) 5.78 (0.273) 5.69 (0.402)

C(nNπ∗) 5.40 (0.001) 5.79 (0.001) 5.36 (0.001) 5.77 (0.001)

G(nOπ∗) 5.63 (0.000) 5.93 (0.000) 5.64 (0.000) 5.93 (0.000)

C(ππ∗2) 6.07 (0.153) 5.93 (0.126) 6.03 (0.148) 5.90 (0.112)

G(nNπ∗1) 6.51 (0.005) 6.44 (0.004) 6.50 (0.004) 6.43 (0.003)

C(nOπ∗1) 5.95 (0.001) 6.45 (0.000) 5.93 (0.001) 6.46 (0.000)

C(nOπ∗2) 6.18 (0.000) 6.60 (0.000) 6.14 (0.000) 6.56 (0.000)

G(nNπ∗2) 6.63 (0.001) 6.71 (0.000) 6.60 (0.000) 6.70 (0.000)

S-12

S3 FrD-LVC Models Data

S3.1 Diabatic Energies and Couplings

S3.1.1 FC Point

Table S2: Diabatic energies (Edii(0)) and electronic couplings (Ed

ij(0)) of bright ππ∗ and CT states of GC in Cs

symmetry at equilibrium geometry from the FrD-LVC CAM-B3LYP and ωB97X-D 6-31G(d) 12 state models(eV)

G→C(CT)1 C(ππ∗1) G(La) G(Lb) C(ππ∗2) G→C(CT)2

CAM-B3LYP

G→C(CT)1 5.169

C(ππ∗1) 0.022 5.325

G(La) 0.065 0.002 5.425

G(Lb) 0.038 -0.020 -0.171 5.658

C(ππ∗2) -0.039 0.160 0.053 0.041 5.915

G→C(CT)2 -0.061 -0.004 -0.027 0.035 0.003 6.393

ωB97X-D

G→C(CT)1 5.540

C(ππ∗1) 0.023 5.311

G(La) 0.067 0.002 5.418

G(Lb) 0.037 -0.018 -0.176 5.650

C(ππ∗2) -0.036 0.155 0.052 0.037 5.886

G→C(CT)2 -0.097 -0.004 -0.027 0.033 0.005 6.673

S-13

Table S3: Diabatic energies (Edii(0)) and electronic couplings (Ed

ij(0)) of nπ∗ states of GC in Cs symmetry atequilibrium geometry from the FrD-LVC CAM-B3LYP and ωB97X-D 6-31G(d) 12 state models (eV)

C(nNπ∗) G(nOπ

∗) G(nNπ∗1) C(nOπ

∗1) C(nOπ∗2) G(nNπ

∗2)

CAM-B3LYP

C(nNπ∗) 5.921

G(nOπ∗) 0.005 5.935

G(nNπ∗1) -0.002 -0.048 6.496

C(nOπ∗1) 0.013 -0.002 0.001 6.543

C(nOπ∗2) 0.004 0.001 -0.001 -0.093 6.554

G(nNπ∗2) -0.001 -0.019 -0.112 0.001 0.001 6.731

ωB97X-D

C(nNπ∗) 5.884

G(nOπ∗) 0.005 5.948

G(nNπ∗1) -0.003 -0.053 6.470

C(nOπ∗1) 0.019 -0.002 0.001 6.526

C(nOπ∗2) 0.005 0.000 -0.001 -0.059 6.530

G(nNπ∗2) 0.001 -0.022 -0.114 0.000 0.001 6.728

S-14

S3.1.2 Excited State Minima

Table S4: Diabatic energies (V dii (q)) for each of the states in the 12 state FrD-LVC models at the minima of

every A’ (i.e. ππ∗ and CT) diabatic state (qd,imin). Parametrized by CAM-B3LYP and ωB97X-D with 6-31G(d)basis set.

In Min Diab. State → G→C(CT)1 C(ππ∗1) G(La) G(Lb) C(ππ∗2) G→C(CT)2

CAM-B3LYP

G→C(CT)1 3.938 4.923 5.130 5.023 4.970 4.695

C(ππ∗1) 5.920 4.935 5.661 5.667 5.196 6.628

G(La) 6.287 5.821 5.094 5.379 5.858 6.272

G(Lb) 6.409 6.057 5.610 5.325 6.081 6.417

C(ππ∗2) 6.516 5.746 6.248 6.241 5.485 7.255

G→C(CT)2 5.960 6.897 6.381 6.295 6.973 5.203

C(nNπ∗) 6.732 5.986 6.258 6.289 5.999 7.174

G(nOπ∗) 7.280 6.335 6.156 6.147 6.384 7.187

G(nNπ∗1) 7.546 6.896 6.601 6.384 6.921 7.532

C(nOπ∗1) 7.114 6.142 6.888 6.895 6.551 7.837

C(nOπ∗2) 7.412 6.522 6.895 6.889 6.651 7.455

G(nNπ∗2) 7.875 7.134 6.541 6.880 7.155 7.839

ωB97X-D

G→C(CT)1 4.394 5.321 5.504 5.392 5.354 5.128

C(ππ∗1) 5.852 4.925 5.636 5.650 5.188 6.573

G(La) 6.209 5.810 5.100 5.381 5.851 6.259

G(Lb) 6.319 6.046 5.602 5.321 6.078 6.378

C(ππ∗2) 6.416 5.719 6.208 6.213 5.456 7.158

G→C(CT)2 6.270 7.184 6.695 6.593 7.238 5.536

C(nNπ∗) 6.656 5.951 6.211 6.254 5.947 7.119

G(nOπ∗) 7.207 6.347 6.154 6.161 6.393 7.152

G(nNπ∗1) 7.450 6.863 6.571 6.355 6.897 7.471

C(nOπ∗1) 6.964 6.013 6.855 6.872 6.431 7.877

C(nOπ∗2) 7.418 6.591 6.857 6.861 6.737 7.307

G(nNπ∗2) 7.758 7.127 6.511 6.873 7.158 7.772

S-15

Table S5: Diabatic energies (V dii (q)) for each of the states in the 12 state FrD-LVC models at the minima of

every A” (i.e. nπ∗) diabatic state (qd,imin). Parametrized by CAM-B3LYP and ωB97X-D with 6-31G(d) basisset.

In Min Diab. State → C(nNπ∗) G(nOπ

∗) G(nNπ∗1) C(nOπ

∗1) C(nOπ∗2) G(nNπ

∗2)

CAM-B3LYP

G→C(CT)1 5.329 5.716 5.554 5.397 5.414 5.599

C(ππ∗1) 5.580 5.767 5.901 5.421 5.520 5.856

G(La) 6.011 5.748 5.765 6.327 6.053 5.422

G(Lb) 6.274 5.969 5.778 6.564 6.278 5.992

C(ππ∗2) 6.143 6.366 6.475 6.380 6.199 6.427

G→C(CT)2 7.036 6.887 6.805 7.385 6.721 6.828

C(nNπ∗) 5.341 6.345 6.501 6.459 6.785 6.430

G(nOπ∗) 6.507 5.503 6.349 6.857 6.570 6.311

G(nNπ∗1) 7.090 6.776 5.930 7.399 7.119 6.320

C(nOπ∗1) 6.773 7.010 7.124 5.655 6.258 7.077

C(nOπ∗2) 7.380 7.003 7.125 6.539 5.936 7.090

G(nNπ∗2) 7.303 7.022 6.603 7.636 7.367 6.214

ωB97X-D

G→C(CT)1 5.739 6.076 5.971 5.808 5.869 5.965

C(ππ∗1) 5.566 5.748 5.916 5.388 5.574 5.866

G(La) 6.000 5.729 5.798 6.405 6.014 5.424

G(Lb) 6.265 5.957 5.803 6.643 6.239 6.008

C(ππ∗2) 6.093 6.325 6.480 6.337 6.250 6.427

G→C(CT)2 7.345 7.163 7.134 7.863 6.900 7.121

C(nNπ∗) 5.311 6.303 6.500 6.462 6.761 6.422

G(nOπ∗) 6.517 5.525 6.366 6.961 6.546 6.354

G(nNπ∗1) 7.062 6.714 5.873 7.458 7.060 6.304

C(nOπ∗1) 6.702 6.986 7.135 5.550 6.289 7.085

C(nOπ∗2) 7.394 6.963 7.130 6.682 5.943 7.087

G(nNπ∗2) 7.298 7.016 6.618 7.721 7.330 6.187

S-16

Table S6: Diabatic energies (V dii (q)) for each of the states in the 12 state FrD-LVC models at the TD-DFT

adiabatic planar minima (qad,mmin ) discussed in the main text. Parametrized by CAM-B3LYP and ωB97X-D with6-31G(d) basis set.

In Min Ad. State → G→C(CT)1 C(ππ∗1) G(La) G(nOπ∗) G(nNπ

∗1) C(nOπ∗1)

CAM-B3LYP

G→C(CT)1 4.038 4.844 4.898 6.087 5.821 5.591

C(ππ∗1) 5.716 4.951 5.504 6.084 6.103 5.548

G(La) 6.109 5.826 5.180 6.007 5.983 6.668

G(Lb) 6.252 6.057 5.559 6.245 5.989 6.903

C(ππ∗2) 6.334 5.743 6.101 6.668 6.671 6.351

G→C(CT)2 6.064 6.838 6.239 7.236 7.079 8.017

C(nNπ∗) 6.582 6.014 6.112 6.622 6.700 6.504

G(nOπ∗) 7.162 6.367 6.029 5.565 6.428 7.189

G(nNπ∗1) 7.388 6.908 6.526 7.035 6.020 7.740

C(nOπ∗1) 6.858 6.063 6.697 7.323 7.313 5.914

C(nOπ∗2) 7.133 6.424 6.769 7.321 7.320 6.802

G(nNπ∗2) 7.705 7.151 6.581 7.267 6.712 7.976

ωB97X-D

G→C(CT)1 4.477 5.289 5.430 6.461 6.203 5.999

C(ππ∗1) 5.675 4.939 5.536 6.078 6.102 5.511

G(La) 6.081 5.823 5.206 5.999 5.992 6.676

G(Lb) 6.211 6.056 5.562 6.253 6.007 6.915

C(ππ∗2) 6.272 5.718 6.095 6.639 6.661 6.316

G→C(CT)2 6.360 7.145 6.640 7.523 7.359 8.323

C(nNπ∗) 6.514 5.980 6.127 6.594 6.680 6.579

G(nOπ∗) 7.121 6.368 6.028 5.592 6.449 7.225

G(nNπ∗1) 7.339 6.879 6.481 6.988 5.943 7.730

C(nOπ∗1) 6.723 5.954 6.735 7.314 7.311 5.701

C(nOπ∗2) 7.183 6.500 6.766 7.293 7.313 6.865

G(nNπ∗2) 7.627 7.143 6.581 7.281 6.722 7.990

S-17

Table S7: ππ∗-CT, excitonic, and ππ∗ mixing couplings between diabatic states (V dij(q), eV) at the FC point

(S0 minimum column), and the G→C(CT)1, C(ππ∗1) and La adiabatic (qad,mmin ) and diabatic (qd,imin) minima aspredicted by the 12 state FrD-LVC models parametrized by CAM-B3LYP and ωB97X-D with 6-31G(d) basisset.

qad,mmin qd,imin

In Min. State → S0 G→C(CT)1 C(ππ∗1) G(La) G→C(CT)1 C(ππ∗1) G(La)

Coupling ↓ CAM-B3LYP

G(La) : G→C(CT)1 0.065 0.066 0.057 0.065 0.069 0.057 0.065

G(Lb) : G→C(CT)1 0.038 0.014 0.031 0.033 0.014 0.032 0.034

C(ππ∗1) : G→C(CT)1 0.022 0.038 0.022 0.025 0.045 0.021 0.020

C(ππ∗2) : G→C(CT)1 −0.039 −0.005 −0.032 −0.035 −0.001 −0.033 −0.038

G(La) : C(ππ∗1) 0.002 0.002 0.000 0.003 0.002 −0.001 0.002

G(La) : C(ππ∗2) 0.053 0.049 0.049 0.053 0.048 0.049 0.054

G(Lb) : C(ππ∗1) −0.020 −0.026 −0.024 −0.021 −0.027 −0.025 −0.021

G(Lb) : C(ππ∗2) 0.041 0.034 0.040 0.042 0.034 0.040 0.042

G(La) : G(Lb) −0.171 −0.018 −0.167 −0.201 −0.038 −0.169 −0.068

C(ππ∗1) : C(ππ∗2) 0.160 0.031 0.025 0.148 0.045 0.063 0.164

Coupling ↓ ωB97X-D

G(La) : G→C(CT)1 0.067 0.083 0.065 0.076 0.087 0.065 0.067

G(Lb) : G→C(CT)1 0.037 0.013 0.030 0.037 0.014 0.030 0.034

C(ππ∗1) : G→C(CT)1 0.023 0.040 0.023 0.025 0.046 0.022 0.022

C(ππ∗2) : G→C(CT)1 −0.036 −0.009 −0.030 −0.040 −0.007 −0.030 −0.036

G(La) : C(ππ∗1) 0.002 0.002 0.000 0.001 0.001 −0.001 0.000

G(La) : C(ππ∗2) 0.052 0.049 0.049 0.054 0.049 0.048 0.052

G(Lb) : C(ππ∗1) −0.018 −0.022 −0.020 −0.020 −0.022 −0.021 −0.020

G(Lb) : C(ππ∗2) 0.037 0.029 0.035 0.041 0.029 0.035 0.038

G(La) : G(Lb) −0.176 −0.032 −0.181 −0.232 −0.044 −0.179 −0.072

C(ππ∗1) : C(ππ∗2) 0.155 0.034 0.025 0.149 0.044 0.054 0.160

S-18

S3.2 Eigenvalues and Eigenvectors of Adiabatic FrD-LVC States

S3.2.1 FC Point

Table S8: Eigenvalues (eV) of A’ adiabatic FrD-LVC states and corresponding normalised eigenvectors showingthe contribution of the ππ∗ and CT diabatic states from the 12 state FrD-LVC models of GC in Cs symmetryat the FC point. Parametrized by CAM-B3LYP and ωB97X-D with 6-31G(d) basis set.

CAM-B3LYP

Adiabatic states → S1 S2 S3 S4 S7 S8

Eigenval. (eV) → 5.125 5.291 5.360 5.746 5.963 6.399

Eigenvec. ↓

G→C(CT)1 0.898 0.266 0.346 0.012 -0.031 -0.050

C(ππ∗1) -0.208 0.934 -0.157 -0.050 0.239 -0.004

G(La) -0.318 0.025 0.822 -0.464 0.071 -0.040

G(Lb) -0.185 0.059 0.421 0.882 0.071 0.054

C(ππ∗2) 0.117 -0.229 -0.041 -0.018 0.965 0.010

G→C(CT)2 0.041 0.017 0.028 -0.066 -0.011 0.996

ωB97X-D

Adiabatic states → S1 S2 S3 S4 S6 S11

Eigenval. (eV) → 5.248 5.313 5.557 5.744 5.932 6.683

Eigenvec. ↓

G→C(CT)1 -0.234 -0.203 0.945 0.023 -0.054 -0.085

C(ππ∗1) 0.778 -0.574 0.083 -0.040 0.237 -0.004

G(La) 0.445 0.707 0.275 -0.470 0.071 -0.031

G(Lb) 0.276 0.356 0.130 0.880 0.059 0.035

C(ππ∗2) -0.254 0.055 0.005 -0.009 0.965 0.009

G→C(CT)2 -0.010 -0.011 0.085 -0.043 -0.012 0.995

S-19

Table S9: Eigenvalues (eV) of A” adiabatic FrD-LVC states and corresponding normalised eigenvectors showingthe contribution of the nπ∗ diabatic states from the 12 state FrD-LVC models of GC in Cs symmetry at theFC point. Parametrized by CAM-B3LYP and ωB97X-D with 6-31G(d) basis set.

CAM-B3LYP

Adiabatic states → S5 S6 S9 S10 S11 S12

Eigenval. (eV) → 5.918 5.932 6.455 6.457 6.642 6.776

Eigenvec. ↓

C(nNπ∗) 0.920 0.392 0.023 0.003 -0.008 0.000

G(nOπ∗) -0.391 0.915 0.033 -0.094 0.002 0.000

G(nNπ∗1) -0.032 0.087 -0.312 0.870 -0.003 -0.371

C(nOπ∗1) -0.021 -0.007 0.685 0.244 -0.686 0.001

C(nOπ∗2) -0.009 -0.004 0.645 0.236 0.727 0.005

G(nNπ∗2) -0.013 0.035 -0.128 0.346 -0.005 0.929

ωB97X-D

Adiabatic states → S5 S7 S8 S9 S10 S12

Eigenval. (eV) → 5.883 5.941 6.433 6.470 6.587 6.771

Eigenvec. ↓

C(nNπ∗) 0.996 0.083 -0.005 0.029 -0.013 0.002

G(nOπ∗) -0.083 0.990 -0.118 -0.003 0.003 -0.002

G(nNπ∗1) -0.004 0.109 0.929 0.012 -0.002 -0.354

C(nOπ∗1) -0.030 0.000 -0.013 0.718 -0.695 -0.004

C(nOπ∗2) -0.011 -0.001 -0.004 0.695 0.719 0.007

G(nNπ∗2) -0.004 0.044 0.351 0.002 -0.009 0.935

S-20

S3.2.2 Excited State Minima

Table S10: Eigenvalues (eV) of adiabatic FrD-LVC states in diabatic minima geometries (qd,imin) shown in Table 3in the main text, and the corresponding normalised eigenvectors. From 12 state FrD-LVC models parametrizedby CAM-B3LYP and ωB97X-D functionals and 6-31G(d) basis set.

In Min Diab. State → G→C(CT)1 C(ππ∗1) G(La) G(nOπ∗) G(nNπ

∗1) C(nOπ∗1)

Eigenvec. ↓ CAM-B3LYP

Eigenval. (eV) → 3.934 4.948 5.030 5.501 5.811 5.572

G→C(CT)1 -0.999 0.607 -0.596 0.000 0.000 0.000

C(ππ∗1) 0.023 0.793 0.038 0.000 0.000 0.000

G(La) 0.030 -0.037 0.788 0.000 0.000 0.000

G(Lb) 0.006 -0.004 0.134 0.000 0.000 0.000

C(ππ∗2) -0.002 -0.036 -0.063 0.000 0.000 0.000

G→C(CT)2 0.016 0.011 -0.016 0.000 0.000 0.000

C(nNπ∗) 0.000 0.000 0.000 0.005 -0.002 0.095

G(nOπ∗) 0.000 0.000 0.000 -0.999 0.351 0.000

G(nNπ∗1) 0.000 0.000 0.000 0.021 0.905 0.000

C(nOπ∗1) 0.000 0.000 0.000 -0.001 0.000 -0.959

C(nOπ∗2) 0.000 0.000 0.000 0.000 0.000 0.269

G(nNπ∗2) 0.000 0.000 0.000 0.033 0.239 0.001

Eigenvec. ↓ ωB97X-D

Eigenval. (eV) → 4.388 4.920 5.074 5.523 5.746 5.475

G→C(CT)1 -0.998 -0.063 -0.170 0.000 0.000 0.000

C(ππ∗1) 0.032 0.995 0.029 0.000 0.000 0.000

G(La) 0.048 0.014 0.972 0.000 0.000 0.000

G(Lb) 0.009 0.025 0.149 0.000 0.000 0.000

C(ππ∗2) -0.006 -0.071 -0.059 0.000 0.000 0.000

G→C(CT)2 -0.007 -0.001 0.003 0.000 0.000 0.000

C(nNπ∗) 0.000 0.000 0.000 0.006 -0.001 0.063

G(nOπ∗) 0.000 0.000 0.000 -0.999 0.342 0.000

G(nNπ∗1) 0.000 0.000 0.000 0.021 0.912 0.000

C(nOπ∗1) 0.000 0.000 0.000 -0.001 0.000 -0.970

C(nOπ∗2) 0.000 0.000 0.000 0.000 0.000 0.235

G(nNπ∗2) 0.000 0.000 0.000 0.030 0.228 0.000

S-21

Table S11: Eigenvalues (eV) of adiabatic FrD-LVC states in TD-DFT adiabatic minima geometries (qad,mmin )shown in Table 3 in the main text, and the corresponding normalised eigenvectors. From 12 state FrD-LVCmodels parametrized by CAM-B3LYP and ωB97X-D functionals and 6-31G(d) basis set.

In Min Ad. State → G→C(CT)1 C(ππ∗1) G(La) G(nOπ∗) G(nNπ

∗1) C(nOπ∗1)

Eigenvec. ↓ CAM-B3LYP

Eigenval. (eV) → 4.033 4.955 5.114 5.559 5.790 5.556

G→C(CT)1 0.999 0.197 0.320 0.000 0.000 0.000

C(ππ∗1) -0.022 0.980 0.015 0.000 0.000 0.000

G(La) -0.033 -0.009 0.869 0.000 0.000 0.000

G(Lb) -0.007 0.015 0.372 0.000 0.000 0.000

C(ππ∗2) 0.003 -0.023 -0.053 0.000 0.000 0.000

G→C(CT)2 -0.026 0.000 0.033 0.000 0.000 0.000

C(nNπ∗) 0.000 0.000 0.000 0.004 0.004 0.232

G(nOπ∗) 0.000 0.000 0.000 -0.998 -0.328 0.000

G(nNπ∗1) 0.000 0.000 0.000 0.043 -0.867 0.000

C(nOπ∗1) 0.000 0.000 0.000 -0.001 -0.001 -0.875

C(nOπ∗2) 0.000 0.000 0.000 0.000 0.000 0.424

G(nNπ∗2) 0.000 0.000 0.000 0.052 -0.374 0.002

Eigenvec. ↓ ωB97X-D

Eigenval. (eV) → 4.471 4.936 5.065 5.586 5.730 5.481

G→C(CT)1 -0.998 0.071 -0.237 0.000 0.000 0.000

C(ππ∗1) 0.034 -0.996 0.055 0.000 0.000 0.000

G(La) 0.052 -0.012 0.865 0.000 0.000 0.000

G(Lb) 0.009 -0.023 0.431 0.000 0.000 0.000

C(ππ∗2) -0.007 0.036 -0.079 0.000 0.000 0.000

G→C(CT)2 -0.004 0.000 -0.008 0.000 0.000 0.000

C(nNπ∗) 0.000 0.000 0.000 -0.005 0.002 0.129

G(nOπ∗) 0.000 0.000 0.000 0.998 -0.324 0.000

G(nNπ∗1) 0.000 0.000 0.000 -0.049 -0.883 0.000

C(nOπ∗1) 0.000 0.000 0.000 0.001 -0.001 -0.929

C(nOπ∗2) 0.000 0.000 0.000 0.000 0.000 0.346

G(nNπ∗2) 0.000 0.000 0.000 -0.049 -0.339 0.000

S-22

S3.3 Norm of Coupling Vector: FC Point

Table S12: Norm of coupling vector√λij · λij of GC in Cs symmetry at equilibrium geometry from the

FrD-LVC CAM-B3LYP/6-31G(d) 12 state model

G→C(CT)1 C(ππ∗1) G(La) G(Lb) C(ππ∗2) G→C(CT)2

G→C(CT)1 0.608

C(ππ∗1) 0.008 0.364

G(La) 0.012 0.005 0.327

G(Lb) 0.010 0.005 0.183 0.342

C(ππ∗2) 0.012 0.171 0.006 0.008 0.383

G→C(CT)2 0.239 0.001 0.012 0.007 0.003 0.560

C(nNπ∗) 0.030 0.116 0.005 0.005 0.100 0.005

G(nOπ∗) 0.003 0.002 0.032 0.042 0.012 0.002

G(nNπ∗1) 0.006 0.001 0.040 0.131 0.002 0.007

C(nOπ∗1) 0.037 0.102 0.007 0.003 0.084 0.025

C(nOπ∗2) 0.022 0.051 0.007 0.002 0.054 0.046

G(nNπ∗2) 0.002 0.002 0.141 0.039 0.003 0.003

C(nNπ∗) G(nOπ

∗) G(nNπ∗1) C(nOπ

∗1) C(nOπ∗2) G(nNπ

∗2)

C(nNπ∗) 0.369

G(nOπ∗) 0.003 0.412

G(nNπ∗1) 0.002 0.093 0.406

C(nOπ∗1) 0.136 0.001 0.001 0.586

C(nOπ∗2) 0.090 0.001 0.001 0.285 0.496

G(nNπ∗2) 0.005 0.078 0.209 0.003 0.002 0.373

S-23

Table S13: Norm of coupling vector√λij · λij of GC in Cs symmetry at equilibrium geometry from the

FrD-LVC ωB97X-D 12 state model

G→C(CT)1 C(ππ∗1) G(La) G(Lb) C(ππ∗2) G→C(CT)2

G→C(CT)1 0.591

C(ππ∗1) 0.008 0.363

G(La) 0.013 0.005 0.321

G(Lb) 0.010 0.004 0.182 0.340

C(ππ∗2) 0.010 0.165 0.005 0.007 0.382

G→C(CT)2 0.227 0.002 0.011 0.007 0.004 0.546

C(nNπ∗) 0.034 0.113 0.005 0.003 0.100 0.005

G(nOπ∗) 0.003 0.002 0.033 0.044 0.011 0.001

G(nNπ∗1) 0.002 0.001 0.029 0.131 0.002 0.003

C(nOπ∗1) 0.047 0.106 0.007 0.001 0.092 0.024

C(nOπ∗2) 0.022 0.039 0.007 0.002 0.047 0.062

G(nNπ∗2) 0.004 0.002 0.142 0.035 0.004 0.003

C(nNπ∗) G(nOπ

∗) G(nNπ∗1) C(nOπ

∗1) C(nOπ∗2) G(nNπ

∗2)

C(nNπ∗) 0.368

G(nOπ∗) 0.003 0.411

G(nNπ∗1) 0.002 0.103 0.415

C(nOπ∗1) 0.146 0.001 0.001 0.611

C(nOπ∗2) 0.090 0.000 0.001 0.261 0.485

G(nNπ∗2) 0.003 0.080 0.211 0.001 0.001 0.382

S-24

S4 Additional Dynamics Results

S4.1 Deuterated Calculations

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200

a)

Deut. FrD-LVC

Undeut. FrD-LVC N-D Freq.

Undeut. FrD-LVC

Po

pu

latio

n

Time (fs)

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1

0 50 100 150 200 250

b)

Figure S7: Populations for 5-state, A’ vibrational mode GC FrD-LVC model built with the five central hydrogensdeuterated (solid line), the FrD-LVC model from undeuterated GC in which the five N-H stretch frequenciesare replaced with their deuterated value (dashed line), and the FrD-LVC model from undeuterated GC as inthe main text Figure 3 (dotted line). Dynamics initated on a) G(La) state and b) C(ππ∗1) state. Parametrizedby CAM-B3LYP/6-31G(d)

-1

-0.5

0

0.5

1

1.5

2

2.5

0 50 100 150 200

a)

Deut.

Undeut.

<Ψ

|Vd ii(

q)|

Ψ>

(e

V)

Time (fs)

G(La)G(Lb)

G->C(CT)1

0 50 100 150 200 250

b)

C(ππ*1)C(ππ*2)

Figure S8: Expectation of diabatic state potential energies, (〈Ψ|V dii (q)|Ψ〉) for the 5 state deuterated (solid

line) and undeuterated (dashed line) FrD-LVC models. Dynamics initated on a) G(La) state and b) C(ππ∗1)state. Parametrized by CAM-B3LYP/6-31G(d). Shifted by −Ed

CT1(0) − 1/4∑

α ωα so that the G→C(CT)1energy is 0 initially. Only the ππ∗ states on the base of initial photoexcitation are shown for simplicity.

S-25

S4.2 Diabatic Potential Energies

-1

0

1

2

3 a)

12 State5 State

CAM-B3LYP

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1G->C(CT)2

G(nOπ*)G(nNπ*1)

G(nNπ*2)C(nNπ*)

C(nOπ*1)C(nOπ*2)

ωB97X-D

-1

0

1

2

3 b)

<Ψ

|Vd ii(

q)|

Ψ>

(e

V)

-1

0

1

2

3 c)

-1

0

1

2

3

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure S9: Expectation of diabatic state potential energies, (〈Ψ|V dii (q)|Ψ〉) shifted by −Ed

CT1(0)− 1/4∑

α ωαso that the G→C(CT)1 energy is 0 initially. For the 12 state (solid lines) and 5 state (dotted lines) FrD-LVCmodels for GC, parametrized by left: CAM-B3LYP and right: ωB97X-D with 6-31G(d) basis set, for dynamicsinitiated on a) G(La), b) G(Lb), c) C(ππ∗1) and d) C(ππ∗2) states.

S-26

0

1

2a)

CAM-B3LYP

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1G(nOπ*)

G(nNπ*1)G(nNπ*2)

C(nNπ*)C(nOπ*1)C(nOπ*2)

ωB97X-D

0

1

2b)

<Ψ

|Vd ii(

q76)|

Ψ>

(e

V)

0

0.5

1

1.5

2c)

-0.5

0

0.5

1

1.5

2

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure S10: Expectation of diabatic state potential energies along mode q76 (〈Ψ|V dii (q76)|Ψ〉), shifted by

−EdCT1(0) − 1/4ω76 that the G→C(CT)1 energy is 0 initially. For the 12 state FrD-LVC models for GC,

parametrized by left: CAM-B3LYP and right: ωB97X-D with 6-31G(d) basis set for dynamics initiated on a)G(La), b) G(Lb), c) C(ππ∗1) and d) C(ππ∗2) states. For clarity, only the potentials of the G→C(CT)1 andthe ππ∗ and nπ∗ states localised on the base that is initially excited are shown.

S-27

0

1

2a)

CAM-B3LYP

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1G(nOπ*)

G(nNπ*1)G(nNπ*2)

C(nNπ*)C(nOπ*1)C(nOπ*2)

ωB97X-D

0

1

2b)

<Ψ

|Vd ii(

q77)|

Ψ>

(e

V)

0

0.5

1

1.5

2c)

-0.5

0

0.5

1

1.5

2

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure S11: Expectation of diabatic state potential energies along mode q77 (〈Ψ|V dii (q77)|Ψ〉), shifted by

−EdCT1(0) − 1/4ω77 so that the G→C(CT)1 energy is 0 initially. For the 12 state FrD-LVC models for GC,

parametrized by left: CAM-B3LYP and right: ωB97X-D with 6-31G(d) basis set for dynamics initiated on a)G(La), b) G(Lb), c) C(ππ∗1) and d) C(ππ∗2) states. For clarity, only the potentials of the G→C(CT)1 andthe ππ∗ and nπ∗ states localised on the base that is initially excited are shown.

S-28

0

1

2a)

CAM-B3LYP

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1G(nOπ*)

G(nNπ*1)G(nNπ*2)

C(nNπ*)C(nOπ*1)C(nOπ*2)

ωB97X-D

0

1

2b)

<Ψ

|Vd ii(

q07)|

Ψ>

(e

V)

0

0.5

1

1.5

2c)

-0.5

0

0.5

1

1.5

2

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure S12: Expectation of diabatic state potential energies along mode q07, (〈Ψ|V dii (q07)|Ψ〉) shifted by

−EdCT1(0) − 1/4ω07 so that the G→C(CT)1 energy is 0 initially. For the 12 state FrD-LVC models for GC,

parametrized by left: CAM-B3LYP and right: ωB97X-D with 6-31G(d) basis set for dynamics initiated on a)G(La), b) G(Lb), c) C(ππ∗1) and d) C(ππ∗2) states. For clarity, only the potentials of the G→C(CT)1 andthe ππ∗ and nπ∗ states localised on the base that is initially excited are shown.

S-29

S4.3 Diabatic Potential Couplings

-0.04

0

0.04

0.08 a)

CAM-B3LYP

G(La)-CT1

G(Lb)-CT1C(ππ*1)-CT1

C(ππ*2)-CT1

ωB97X-D

-0.04

0

0.04

0.08 b)

12 State

5 State

<Ψ

|Vd ij(

q)|

Ψ>

(e

V)

-0.04

0

0.04

0.08 c)

-0.04

0

0.04

0.08

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure S13: Expectation of ππ∗-G→C(CT)1 diabatic state coupling potential energy, (〈Ψ|V dij(q)|Ψ〉) for the

12 state (solid lines) and 5 state (dotted lines) FrD-LVC models for GC. Parametrized by left: CAM-B3LYPand right: ωB97X-D with 6-31G(d) basis set for dynamics initiated on a) G(La), b) G(Lb), c) C(ππ∗1) and d)C(ππ∗2) states.

S-30

-0.04

0

0.04

0.08 a)

CAM-B3LYP

G(La)-C(ππ*1)

G(La)-C(ππ*2)

G(Lb)-C(ππ*1)

G(Lb)-C(ππ*2)

ωB97X-D

-0.04

0

0.04

0.08 b) 12 State5 State

<Ψ

|Vd ij(

q)|

Ψ>

(e

V)

-0.04

0

0.04

0.08 c)

-0.04

0

0.04

0.08

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure S14: Expectation of excitonic diabatic state coupling potential energy (〈Ψ|V dij(q)|Ψ〉) for the 12 state

(solid lines) and 5 state (dotted lines) FrD-LVC models for GC. Parametrized by left: CAM-B3LYP and right:ωB97X-D with 6-31G(d) basis set for dynamics initiated on a) G(La), b) G(Lb), c) C(ππ∗1) and d) C(ππ∗2)states.

S-31

-0.2

-0.1

0

0.1

0.2a)

CAM-B3LYP

G(La)-G(Lb) C(ππ*1)-C(ππ*2)

ωB97X-D

-0.2

-0.1

0

0.1

0.2b)

12 State

<Ψ

|Vd ij(

q)|

Ψ>

(e

V)

5 State

-0.2

-0.1

0

0.1

0.2c)

-0.2

-0.1

0

0.1

0.2

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure S15: Expectation of the ππ∗ mixing diabatic state coupling potential energy (〈Ψ|V dij(q)|Ψ〉) for the

12 state (solid lines) and 5 state (dotted lines) FrD-LVC models for GC. Parametrized by left: CAM-B3LYPand right: ωB97X-D with 6-31G(d) basis set for dynamics initiated on a) G(La), b) G(Lb), c) C(ππ∗1) and d)C(ππ∗2) states.

S-32

S4.4 Electronic Only Dynamics

0

0.2

0.4

0.6

0.8

1a)

CAM-B3LYP

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1G->C(CT)2

G(nOπ*)G(nNπ*1)

G(nNπ*2)C(nNπ*)

C(nOπ*1)C(nOπ*2)

ωB97X-D

0

0.2

0.4

0.6

0.8

b)

Po

pu

latio

n

0

0.2

0.4

0.6

0.8

c)

0

0.2

0.4

0.6

0.8

0 50 100 150 200

d)

Time (fs)

0 50 100 150 200 250

Figure S16: Diabatic state populations for 12 state electronic only dynamics at the FC point. Initiated ona) G(La), b) G(Lb), c) C(ππ∗1) and d) C(ππ∗2) states. Parametrized by CAM-B3LYP (left) and ωB97X-D(right) with 6-31G(d) basis set.

S-33

S4.5 G→C(CT)1 Diabatic Energy Gap Dependence

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200

a)

CAM-B3LYP FrD-LVC

ωB97X-D FrD-LVC

G->

C(C

T)1

Popula

tion

Time (fs)

CAM-B3LYP gap at FC point

ωB97X-D gap at FC point

0 eV

0.2 eV

0.4 eV

0.6 eV

0 50 100 150 200 250

b)

Figure S17: G→C(CT)1 populations for 5 state FrD-LVC models parametrized by CAM-B3LYP (solid lines)and ωB97X-D (dashed lines) with 6-31G(d) basis set, with different diabatic energy gaps between the ππ∗

state of initial excitation and G→C(CT)1 state (i.e. EdCT1(0) − Ed

ππ∗(0)) for dynamics initiated on a) G(La)and b) C(ππ∗1). The purple line is the CAM-B3LYP gap obtained by FrD at the FC point (-0.26 eV forG→C(CT)1-G(La) and -0.16 eV for G→C(CT)1-C(ππ∗1)), the red line is the ωB97X-D gap obtained by FrDat the FC point (0.12 eV for G→C(CT)1-G(La) and 0.23 eV for G→C(CT)1-C(ππ∗1)).

S-34

S5 Additional Absorption Spectra

S5.1 Comparison To Experimental Absorption Spectrum in Chloroform

0

0.2

0.4

0.6

0.8

1

1.2

4 4.5 5 5.5 6

a) CAM-B3LYP

Norm

alis

ed A

bso

rban

ce

Energy (eV)

FrD-LVC

Exp

4 4.5 5 5.5 6

b) ωB97X-D

Energy (eV)

Figure S18: Absorption spectra of GC calculated from the 12 state FrD-LVC models (solid black lines)parametrized by a) CAM-B3LYP and b) ωB97X-D with 6-31G(d) basis set, compared to experimental re-sults in chloroform.9 Intensity of most intense peaks normalised to 1, plotted on the energy scale, withFrD-LVC spectra shifted by -0.75 eV.

S-35

S6 6-31+G(d,p) Basis Set Test

S6.1 Single Point Energies

Table S14: TD-DFT excitation energies (eV) of GC in Cs symmetry at equilibrium geometry obtained withthe CAM-B3LYP and ωB97X-D functionals and 6-31G(d) and 6-31+G(d,p) basis sets. Also shown are EOM-CCSD(T)/TZVP results from Ref. 10.

CAM-B3LYP ωB97X-D

Char. 6-31+G(d,p) 6-31G(d) 6-31+G(d,p) 6-31G(d) EOM-CCSD(T)

G→C(CT)1 4.89 (S1) 5.07 (S1) 5.46 (S4) 5.50 (S3) 5.36

C(ππ∗) 5.15 (S2) 5.27 (S2) 5.15 (S2) 5.28 (S2) 4.92

G(La) 5.21 (S3) 5.31 (S3) 5.01 (S1) 5.21 (S1) 4.85

G(Lb) 5.39 (S5) 5.69 (S4) 5.44 (S3) 5.69 (S4) 5.48

C(nNπ∗) 5.71 (S6) 5.79 (S5) 5.71 (S6) 5.77 (S5) 5.65

G(nOπ∗) 5.86 (S9) 5.93 (S6) 5.86 (S8) 5.93 (S7) 5.76

C(ππ∗2) 5.73 (S7) 5.93 (S7) 5.73 (S7) 5.90 (S6) 5.37

G→C(CT)2 6.14 (S13) 6.33 (S8) 6.54 (S17) 6.60 (S11)

G(nNπ∗1) 6.30 (S14) 6.44 (S9) 6.30 (S10) 6.43 (S8)

C(nOπ∗1) 6.40 (S17) 6.45 (S10) 6.42 (S14) 6.46 (S9) 6.27

C(nOπ∗2) 6.51 (S20) 6.60 (S11) 6.48 S(16) 6.56 (S10) 6.42

G(nNπ∗2) 6.56 (S21) 6.71 (S12) 6.56 (S18) 6.70 (S12)

Table S14 shows the vertical excitation energies calculated by the CAM-B3LYP and ωB97X-D functionals

with the 6-31+G(d,p) basis set, compared to the results of the 6-31G(d) basis set shown in the main text, and

the EOM-CCSD(T)/TZVP results from Ref. 10. TD-DFT excitation energies calculated following geometry

optimisation of GC with the same functional and basis set. The calculations with 6-31+G(d,p) yielded a large

number of Rydberg states, not shown in the Table, and a slight red-shifting of the ππ∗, nπ∗ and CT energies.

For both functionals, there is a ∼0.1 eV red-shift of the nπ∗ states, and a ∼0.1-0.3 red-shift of the ππ∗ states,

whilst the CT states are predicted to be ∼0.2 eV red-shifted by CAM-B3LYP and ∼0.05 eV red-shifted by

ωB97X-D. The relative ordering of the states, however, is quite similar between the basis sets.

S-36

S6.2 ωB97X-D 6-31+G(d,p) FrD-LVC Model

Table S15: Diabatic energies (Edii(0)) and electronic couplings (Ed

ij(0)) of nπ∗ states of GC in Cs symmetryat equilibrium geometry from a 12 state FrD-LVC model parametrized by ωB97X-D/6-31+G(d,p) (eV).

G→C(CT)1 C(ππ∗1) G(La) G(Lb) C(ππ∗2) G→C(CT)2

G→C(CT)1 5.417

C(ππ∗1) 0.037 5.198

G(La) 0.133 -0.003 5.227

G(Lb) 0.058 -0.020 -0.156 5.409

C(ππ∗2) -0.048 0.161 0.062 0.041 5.709

G→C(CT)2 -0.097 -0.002 -0.036 0.052 -0.008 6.487

Table S16: Diabatic energies (Edii(0)) and electronic couplings (Ed

ij(0)) of nπ∗ states of GC in Cs symmetryat equilibrium geometry from a 12 state FrD-LVC model parametrized by ωB97X-D/6-31+G(d,p) (eV).

C(nNπ∗) G(nOπ

∗) G(nNπ∗1) C(nOπ

∗1) C(nOπ∗2) G(nNπ

∗2)

C(nNπ∗) 5.829

G(nOπ∗) -0.012 5.869

G(nNπ∗1) -0.003 -0.058 6.318

C(nOπ∗1) -0.007 -0.004 -0.003 6.484

C(nOπ∗2) -0.010 0.000 0.001 -0.034 6.449

G(nNπ∗2) -0.014 -0.016 -0.067 -0.006 0.004 6.573

We performed a test on the effect of basis set on the dynamics, by parametrizing 12 state and 5 state

FrD-LVC models with the 6-31+G(d,p) basis set and ωB97X-D functional. The population dynamics after

propagation by ML-MCTDH with these models is shown in Figure S19. Similar conclusions to the main

text are found, namely: fast and efficient transfer from initially excited ππ∗ state to the G→C(CT)1 state

that is quicker for an initial excitation on G than C; the G(La) and C(ππ∗1) states act as doorway states

to G→C(CT)1; there is limited involvement of the nπ∗ states; a reduced dimensionality (5 state) model can

reproduce the population dynamics of the full dimensional (12 state) model; and there is limited dependence

of the ππ∗-G→C(CT)1 coupling on coordinate. The main difference to the models presented in the main text

concerns the rate at which the G→C(CT)1 state is populated, with it being faster for this 6-31+G(d,p) basis

set parametrized model. The reason for this is due to larger constant coupling terms (Edij(0)) between the

ππ∗ and G→C(CT)1 state, as shown in Table S15. This is despite a slightly larger energy gap between the

G→C(CT)1 and ππ∗ doorway states, as shown in Tables S14 and S15.

S-37

0

0.2

0.4

0.6

0.8

1

a)

12 State

5 State

5 State, λi,CT=0

Popula

tion

G(La)G(Lb)

C(ππ*1)C(ππ*2)

G->C(CT)1G->C(CT)2

G(nOπ*)G(nNπ*1)

G(nNπ*2)C(nNπ*)

C(nOπ*1)C(nOπ*2)

b)

0

0.2

0.4

0.6

0.8

0 50 100 150 200

c)

Time (fs)

0 50 100 150 200

d)

Figure S19: Diabatic state populations for FrD-LVC models with 12 states (solid line), 5 states (dotted line),and 5 states with λij = 0 for all the ππ∗ states coupled to CT (dashed line). Dynamics initiated on a) G(La),b) G(Lb), c) C(ππ∗1) and d) C(ππ∗2) states. Parametrized by ωB97X-D/6-31+G(d,p).

S-38

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S-39

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