An effective method to study the excited state behaviour and to compute vibrationally resolved optical spectra of large molecules in solution

1 IBB/Consiglio Nazionale Ricerche2 CR-INSTM Village3 IPCF/Consiglio Nazionale Ricerche4 Università Federico II Napoli

Roberto Improta1,2, Fabrizio Santoro3,

Alessandro Lami3, Vincenzo Barone2,4

Excited electronic states are involved in many phenomena/properties of potential technological interest

Non linear opticsElectron transferMolecular electronics/OptoelectronicsConductivityPhotophysics and photochemistry

The study of the processes of charge, energy and excitatation transfer require the detailed knowledge of the static and dynamical behavior of the excited states

The understanding and the tailoring of the properties of a material often

requires

Knowledge of the Excited States of the building blocks

Quantum mecanical calculations have always been very useful but….

A possible(handle with

care) approach:Bottom-up

Definition of suitable subsystems:building blocks

What is the interaction between the excited states of the building blocks?

Materials of technological interest

size

Medium/large size molecule

environmentCondensedphase

Small/medium size molecule

StandardQM calculations

Gas phase

Rigid molecule at 0 K

temperature

vibrations

vibrating molecule at finite temperature

DNA Bases as building blocks for photoactive materials

Base stacking

Base pairing

isolated moleculeIn solution

macromoleculein solution

Final goal describing the static and the dynamical

behavior of the excited states of macromolecular systems

in solution

Where did we arrive, until now?

1)Solvent

2)Vibrations

3)Interactions betweenthe building blocks

Our reference method forelectronic calculations:

Density Functional Theory (DFT)Time Dependent DFT (TD-DFT)

hybrid functionals: PBE0

Best compromise between accuracy and computational cost

Analytic gradients in solution are available: equilibrium geometry of the excited state in solution Properties: dipole, polarizability….

1.The solvent is an infinite, structureless medium

characterised by macroscopic properties (dielectric constants, density,

etc.)

1. Solvent effect

Bulk Solvent effect:PCM model

2.A cavity is defined, such that the solvent distribution function is 0 inside the cavity and 1 outside. 4.The whole reaction field

can be described in terms of an apparent charge density ( ) appearing on the cavity surface

3.The solute with its ownelectron density is inserted within the cavity

Gas Gas Phase+ Gas Phase+ PCM+

Phase 4 H2O PCM 4 H2O

S1 4.77(0.00) 4.98(0.00) 5.14(0.00) 5.23(0.00) S2 5.24(0.14) 5.25(0.14) 5.19(0.19) 5.08(0.20)S3 6.06(0.03) 6.32(0.05) 6.29(0.12) 6.23(0.17) in eV, intensities in parentheses TD-PBE0/PCM calculations

Experimentgas phase water 5.08 4.79 6.05 6.14

The intensity of S2 and S3 increases with the polarity of the solvent

In many cases only the inclusion of both explicit and bulk solvent effects can provide reliable estimates of the solvent shift.

1b. Solvent effect: hydrogen bonding effect

J. Am. Chem. Soc. 2004, 126, 14320 - J. Am. Chem. Soc. 2006, 128, 607 - J. Am. Chem. Soc. 2006, 128, 16312

soluteSolute+1st solvation shell

Solute+1st solvation shel +PCMl

1.c Solvent: Examples

Discrepancy between the computed Vertical Excitation Energies and the

Experimental band maxima in solution ≤ 0.25 eV

TPP4S2-

water

Exp.Band Max.*

Q 1.94(0.25) 1.96(0.1)B 2.95(1) 2.86(1)

TPP4H2+

CH2Cl2

Q 1.94(0.27) 1.91(0.18)B 2.96(1) 2.86(1)

TPP2H benzene

Qx 2.20(0.011) 1.91( 0.005)

Qy 2.35(0.018) 2.25(0.01)

B 2.95(1) 2.96(1)

Computed VEE*transition

*relative intensity in parentheses

Absorption spectra including vibrational effect

Franck-Condon integrals

spectrum

|e

|e′Condon approximation

· · · ·· · · ·

Different methods for computing FC integralsare available….BUT

2. Vibrations

the number of vibrational states (and of the FC integrals to be computed) increases steeply with the dimension of the molecule and with the energy most of them do not contribute to the spectrum

we devised a method to select the relevant contributions, building up a computational tool that is able to automatically compute converged spectra in large molecules without requiring manual and ad hoc choices of the user

typical width of an absorption spectrum

1017 states; computationally unfeasible

0 2000 4000 6000 8000 100000

5

10

15

20

25

Log 1

0 (N

um

ber

of S

tate

s)

frequency (cm-1)

exact count

fit a+bxc

Coumarin C153

vibrational states

the fortran code FCclasses is freely distributed upon request, see also the Village web-site

2. Vibrations

2b. Optical spectra in solution

Coumarin C153

TD-DFT

PCM/PBE0/6-31G(d)

S1S0

20000 22000 24000 26000 28000 30000

Cyclohexane DMSO

frequency (cm-1)

Abs

orpt

ion

(arb

. uni

ts)

ΔE exp.-theor. 400 cm-1

Angew. Chemie (2007) 46, 405

Convolution with a gaussian for

inhomogeneous broadening FWHM larger in the case of polar DMSO

DMSO cyclohexane

J. Chem. Phys. (2007) 126, 84509

Solvent effect on the energy and the shape of absorption spectra is computed with accuracy

Porphyrin (96 normal modes)

12000 11000 10000 9000

frequency (cm-1)

ΔE exp.-theor. 1500 cm-1

cpu time=20 s

Vibrationally Resolved Phophorescence Spectra

2b.Spectra in solution: larger molecules

12000 1100012600exp. frequency (cm-

1)

C60 Phosphorescence Spectrum

174 normal modes

T1(3T2g)S0

Cautions:

•the optical transition is forbidden by symmetry and the spectrum should be computed in the Herzberg-Teller formalism

•Possibility for nonadiabatic couplings (Jahn-Teller distortions)

1200013000

theor. frequency (cm-

1)

ΔE exp.-theor. 400 cm-1

2b.Spectra in solution: larger molecules

PBE0/6-31G(d)

2c. Spectra including the temperature effect

28000 30000 32000 34000 36000 38000

Abso

rptio

n S

pect

rum

(arb

. units

)

frequency (cm-1)

295 K

30000 32000 34000 36000 38000 40000

frequency (cm-1)

Abs

orpt

ion

Spe

ctru

m

(arb

. uni

ts)

77 K

ΔE exp.-theor. 2800 cm-1

Stilbene in cyclohexane PCM/PBE0/6-31+G(d,p)S1S0

28000 30000 32000 34000 36000 38000

Abs

orpt

ion

Spe

ctru

m (

arb.

uni

ts)

frequency (cm-1)

T= 2950 K

T= 770 K

T= 00 K

phenyl torsion9 cm-1 S0 45 cm-1 S1

J. Chem. Phys. (2007) 126, 184102

2d. Spectra including Herzberg-Teller effect

19000 18000 17000 16000 150000.0

0.2

0.4

0.6

0.8

1.0

Em

issi

on S

pect

rum

(ar

b. u

nits

)

frequency (cm-1)

Fluorescence FC Fluorescence HT

shift~1700cm-1

Fluorescence Spectra of porphyrin

Adenine stacked oligomers

3. Interacting excited states

Interaction between UV radiation and nucleic acids

Potential nanotecnologicalinterest

Computed absorption spectra in aqueous solution of different oligomers of 9-methyl-adenine

Computations on systems (with size and in condition) comparable to those studied in the experiments

3. Interacting excited states

Calculations on a stacked dimer of 9-methyladenine

When going from the monomer to the oligomer1)Small blue shift of the band maximum2)Small red shift of the low energy side3)Decrease of the inteensity

Calculations are able to reproduce the effect of stacking on the spectra

Mutual arrangement frozen as in B-DNA

3. Interacting excited states

Proc. Nat. Acad. Sci. U.S.A. (2007) in press

Conclusion

Theor.Chem. Acc. (2007) 117, 1073

Reliable description of the excited state properties

(transition moments, excite state dipole moments)

in the gas phase and in solution

Accurate computation of the energy, the geometry, and the

vibrations of excited states in solution

Computation of optical spectra of moleculesof potential nanotechonological interest in

realistic conditions (environment,temperature)

First encouraging steps towards the study of the excited states of

macromolecular systems

Perspectives

Increasing the complexityof the system under study

Providing the parametersfor excitonic models

Dynamical Simulations on macromolecules

DFT and TD-DFT calculations as basis for Quantum Mechanical dynamical studies

Integration with the results ofother computational methods(CASSCF-CASPT2)

NOW

Perspectives

ottom/ up

technological adva

experim

ents

tion

nce

Acknowledgements

LSDM- Napoli

N. RegaG. MorelliO. CrescenziM. Pavone

Gaussian

M. FrischG. Scalmani

F. SantoroS. Lami

IPCF-CNRPisa

V. BaroneJ. Bloino

Federico IINapoli