This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 18393–18397 18393

Cite this: Phys. Chem. Chem. Phys., 2011, 13, 18393–18397

Al(CN)3�6 and Al(NC)3�6 trianions

Thomas Sommerfeld* and Bijay Bhattarai

Received 15th May 2011, Accepted 1st August 2011

DOI: 10.1039/c1cp21570a

At this time the smallest trianions observed in the gas phase are fluorinated fullerenes and large

organic ring systems with attached sulfonic acid groups. Considerably smaller trianions have been

predicted to be sufficiently stable for observation in mass spectrometers, but have not yet been

detected. Here two isomers of the aluminium cyanide trianion, Al(CN)3�6 and Al(NC)3�6 , are

studied using ab initio methods. These two isomers are predicted to be electronically stable and to

show substantial barriers with respect to dissociation of CN� units. Thus, the investigated

trianions hit a sweat-spot regarding the possibility of detection, as they are by far more robust

with respect to dissociation than alkali halide trianions, while at the same time materials from

which these trianions can at least in principle be formed are much more readily available than

those needed for producing small covalently bound trianions.

1. Introduction

What was true for doubly-charged anions two decades ago is

currently true for triply-charged anions. The only trianions

that have been observed in the gas phase are large,1 while

several small species that have been predicted to show a sufficient

lifetime for experimental detection still await observation. Gas

phase trianions that have been observed include fluorinated

fullerenes,2 C60F3�47 , large organic ring systems with attached

sulfonic acid groups,3,4 and biological polymers (cf. ref. 1).

Much smaller species that have been predicted to be long-lived

on a mass spectrometric time scale include Li2F3�5 and related

systems,5 N(BF3)3�4 ,6 and B(C3O2)

3�3 ,7 and for a discussion of

systems where a sufficient lifetime is rather questionable see ref. 1.

For doubly-charged anions experimental observation has

now caught up with theoretical predictions, and even the

tetratomic LiF2�3 has been detected;8 for trianions this is not

yet the case. The main challenge of observing the predicted,

small trianions is most probably not their inherent stability,

but rather the lack of an efficient ion source. Sizable quantities

of, say, B(C3O2H)3 are not easy to come by, and regarding

multiply-charged anions that could at least in principle be

formed from more readily available materials, such as

LiF2�3 from LiF, this well studied system8–10 reveals a telling

story. The LiF2�3 dianion had been predicted to be very long-

lived at 0 K in 1992,9 and predissociation lifetimes at finite

temperatures were found to be still more than sufficient for

survival in a mass spectrometer in 1999.10 Yet, electro-spray

sources did not simply produce any small dianions whatso-

ever, with Cs5Br2�7 being the smallest alkali dianion that could

be detected, and Li15F2�17 being the smallest dianion observable

from spraying LiF solutions.11 Only in 2005 the LiF2�3 dianion

was finally identified using a sputter source8 demonstrating

that this gas phase dianion does indeed exist, but is hard

to make.

Here a theoretical investigation of the Al(CN)3�6 trianion and

its Al(NC)3�6 isomer is presented. These trianions represent a

tradeoff in the sense that they are not quite as small as Li2F3�5 ,

but while the materials from which these trianions could be

formed are still readily available, they are by many orders of

magnitude less fragile than alkali-halide trianions of comparable

size. Computational methods employed in this study are briefly

described in the next section, Section 3 presents ab initio results

regarding the stability of Al(CN)3�6 and Al(NC)3�6 with respect

to electron detachment and with respect to loss of a

CN� ligand, and Section 4 concludes.

2. Computational methods

Three basis sets were used in this study, Dunning’s correlation

consistent double-z (aug-cc-pVDZ) and triple-z (aug-cc-pVTZ)sets, as well as the aug-cc-pVDZ set augmented with

core-polarization functions (aug-cc-pCVDZ).12–15 All species

investigated have closed-shell electronic states, and this is not

only true for the equilibrium geometries, but also for the

studied dissociation processes into aluminium cyanide

dianions and cyanide ions. Thus, similar to the related alkali

and alkaline earth halide ions,16–18 self-consistent-field (SCF)

calculations are able to describe equilibrium geometries as well

as the relevant low-energy fragmentation pathways associated

with loss of cyanide ions. Here, second-order Møller–Plesset

perturbation theory (MP2) was used for geometry optimization,

computing vibrational frequencies, and computing dissociation

pathways. In contrast, it is imperative to treat electron

Department of Chemistry and Physics, Southeastern LouisianaUniversity, SLU 10878, Hammond, LA 70402, USA.E-mail: Thomas.Sommerfeld@selu.edu

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18394 Phys. Chem. Chem. Phys., 2011, 13, 18393–18397 This journal is c the Owner Societies 2011

correlation beyond second-order perturbation theory when

computing electron detachment energies of anions in general,19

and in particular for multi-charged systems (see e.g. ref. 20 and 21).

Consequently, uncorrelated electron detachment energies

obtained through Koopmans’s Theorem (KT) are compared

with results of the equation-of-motion coupled-cluster with

single and double substitution methods for ionized states

(EOM-IP-CCSD).22,23 We note that EOM-IP-CCSD is

comparable in quality to the third-order Green’s function methods

used for studying multiply-charged metal halide systems.16,18,20

Core electrons were not correlated in calculations with the

aug-cc-pVDZ and aug-cc-pVTZ sets, but were included in

calculations with the aug-cc-pCVDZ set. The CFOUR

package was used for all calculations.24

3. Ab initio results

In contrast to neutral and singly-charged systems, low-energy

fragments of multiply-charged anions repel each other, and

therefore the question of the ‘‘stability’’ of a multiply-charged

anion is more involved than that for a singly-charged or uncharged

system. To be considered ‘‘stable’’, multiply-charged anions need to

be stable with respect to both electron autodetachment and

dissociation of the nuclear framework.20 However, many small

dianions are only metastable with respect to at least one of

these decay processes, but show nevertheless long lifetimes

owing to a combination of broad Coulomb barriers in the

decay channels and markedly different geometries of their

decay products.6,20,25,26 Thus, in order to make predictions

about whether Al(CN)3�6 and Al(NC)3�6 are stable or at

least metastable, first, minimal energy structures must be

established, and then these need to be examined with regard

to electron autodetachment and dissociation into CN� and

Al(CN)2�5 or Al(NC)2�5 dianions.

As a first step structures of all three isomer pairs, Al(CN)3�6 and

Al(NC)3�6 , Al(CN)2�5 and Al(NC)2�5 , and Al(CN)�4 and Al(NC)�4have been optimized, and found to represent minimal energy

structures on their respective potential energy surfaces with the

lowest vibrational frequencies being in all cases in the 70 to

80 cm�1 range. All structures are highly symmetric, with Oh

symmetry for the trianions, D3h symmetry for the dianions, and

Td symmetry for the monoanions. The computed bond lengths

are listed in Table 1. Aluminium–carbon bonds have lengths in

the 1.99 to 2.16 A range with somewhat longer bonds for the

trianion and for the axial ligands of the dianion, while

aluminium–nitrogen bonds tend to be somewhat shorter

(1.87 to 2.03 A), but show the same trends as the Al–C bonds.

In contrast, the CN bond length of the ligands is practically

independent of the charge or orientation, and is very close to

1.2 A. Core-polarization effects on the bond lengths were

investigated using the aug-cc-pCVDZ set, and slightly shorter

bonds were found, but the effects are small, 0.6% for the Al–C

distances, and 0.2% for the C–N distances. Comparing the

different CN-orientations, the Al–CN isomers are predicted to

be more stable regardless of the number of ligands, yet, the

differences are not large, and starting at an energy difference of

about 50 kJ mol�1 for the monoanions, the difference de-

creases with increasing charge, and for the trianions it is only

17 kJ mol�1.

For both trianions all occupied orbitals have negative

energies at the respective equilibrium structures, with the

energies of the t1g symmetrical highest occupied molecular

orbitals (HOMO) being �1.51 eV for Al(CN)3�6 and �1.14 eV

for Al(NC)3�6 , and thus both are predicted to be stable with

respect to electron autodetachment at the level of Koopmans’s

theorem. Koopmans’s theorem however is well known to

overestimate the electronic stability of dianions, and since a

similar trend can be expected for trianions, a method including

electron correlation effects, preferably well beyond second-order,

is needed to predict detachment energies reliably. Here the

third-order EOM-IP-CCSD method is used for this purpose,

and the detachment energies obtained from EOM-IP-CCSD

calculations are compared with the Koopmans values in

Tables 2 and 3. All detachment energies are indeed predicted

to be smaller at the EOM-IP-CCSD level, yet, the electron

correlation effects on the detachment energies are remarkably

non-uniform. For orbitals that are combinations of CN-porbitals, including the HOMO, the differences are only a few

Table 1 Bond lengths of Al(CN)3�6 , Al(NC)3�6 , Al(CN)2�5 , Al(NC)2�5 ,Al(CN)�4 , and Al(NC)�4 . The two trianions have Oh symmetry, the twodianions have D3h symmetry, and the two monoanions have Td

symmetry. The geometries have been optimized using the MP2 methodand the aug-cc-pVDZ basis set, and the bond lengths are given in A

R(Al–C) R(C–N) R(Al–N) R(N–C)

Al(CN)3�6 2.158 1.201 Al(NC)3�6 2.025 1.200

Al(CN)2�5 2.138a 1.196a Al(NC)2�5 1.993a 1.199a

2.052b 1.199b 1.936b 1.198b

Al(CN)�4 1.989 1.193 Al(NC)�4 1.871 1.199

a Axial CN groups. b Equatorial CN groups.

Table 2 Electron detachment energies of Al(CN)3�6 . The detachmentenergies have been computed at the equilibrium geometry predictedwith the MP2/aug-cc-pVDZ method, and the values are given in eV

Koopmans’s theorem EOM-IP-CCSD

aug-cc-pVDZ

aug-cc-pCVDZ

aug-cc-pVTZ

aug-cc-pVDZ

aug-cc-pCVDZ

aug-cc-pVTZ

t1g 1.51 1.50 1.52 1.13 1.12 1.29t1u 1.65 1.64 1.66 0.87 0.86 1.05t2u 1.78 1.77 1.79 1.39 1.38 1.54eg 2.21 2.19 2.26 0.11 0.10 0.36t2g 2.30 2.31 2.30 1.90 1.91 2.04t1u 3.92 3.93 3.92 2.12 2.12 2.28a1g 4.82 4.81 4.80 2.56 2.56 2.73

Table 3 Electron detachment energies of Al(NC)3�6 . The detachmentenergies have been computed at the equilibrium geometry predictedwith the MP2/aug-cc-pVDZ method, and the values are given in eV

Koopmans’s theorem EOM-IP-CCSD

aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVDZ aug-cc-pVTZ

t1g 1.14 1.12 0.89 1.02t1u 1.54 1.54 0.48 0.64t2u 1.64 1.63 1.33 1.45eg 1.91 1.92 0.33 0.50t1u 2.49 2.48 1.60 1.73a1g 2.52 2.52 1.01 1.17t2g 2.59 2.57 2.15 2.27

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tenth of an eV, while for orbitals that have at least some

s character the differences are as large as 2 eV. Consequently,

electron correlation dramatically changes the ordering of the

detachment states, and for both isomers the smallest detachment

energy predicted at the EOM-IP-CCSD level is associated with

a s-eg orbital (Tables 2 and 3) showing values of 0.11 eV

for Al(CN)3�6 and 0.33 eV for Al(NC)3�6 with the aug-

cc-pVDZ basis set.

The influence of the basis set on the computed detachment

energy is much smaller than the electron correlation effects.

Core-polarization effects are tiny and reduce the predicted

detachment energies by about 20 meV, while going to a triple-zvalence set increases the computed values by about 0.2 eV. The

latter trend is typical for negatively charged systems in general,

there is more correlation in the trianion than in its

doubly-charged decay product, and thus using a more flexible

basis set that is able to recover a larger percentage of the

correlation energy tends to stabilize the trianion in the sense of

predicting higher detachment energies. The most reliable values

are those obtained using the EOM-IP-CCSD method and the

aug-cc-pVTZ set, 0.36 eV for Al(CN)3�6 and 0.50 eV for

Al(NC)3�6 , andwe are confident to predict the two trianion isomers

to be stable with respect to vertical electron autodetachment.

The question of adiabatic electron autodetachement is more

challenging as we were unable to find minima corresponding

to Al(CN)2�6 or Al(NC)2�6 . Similar to the metal halide systems16

the (N � 1) electron systems are predicted to be unstable to

fragmentation, and thus the variation of the detachment energy

in the Franck–Condon region of the trianions was investigated. As

one would expect for a multiply-charged anion, the electron

detachment energy of the aluminium hexacyanide trianions

decreases when the bond lengths are reduced, and for

Al(NC)3�6 the electron detachment energy approaches zero at the

inner turning point of the symmetric stretch vibration, whereas

Al(CN)3�6 is predicted to be slightly unstable (�0.1 eV) at this

geometry. Since adiabatic electron detachment is therefore

possibly close to the Franck–Condon region, the Coulomb

barrier to autodetachment must be considered (cf. ref. 6 and 27).

A local approximation of the repulsive Coulomb barrier was

computed by using the frozen orbitals of the Al(CN)3�6 trianion

to represent the charge distribution of the Al(CN)2�6 dianion.6

The barrier height varies between 5.5 and more than 9 eV, and a

cut through the barrier in one of the main symmetry planes is

shown in Fig. 1. A very conservative estimate for the tunneling

rate through the three-dimensional barrier can be obtained by

considering only a single tunneling path along the minimal

energy pathway. For this one-dimensional path the tunneling

time can be computed using the well-known semiclassical

approximation

t ¼ 1

PT � nð1Þ

where PT is the tunneling probability for a one-dimensional

barrier, and n is the frequency with which the electron impinges

on the barrier. The tunneling probability was computed by

integrating the computed barrier along the tunneling path

described above. In this way the average height of the three-

dimensional barrier is strongly underestimated, and the

tunneling probability will be far overestimated. Assuming an

impinging frequency n of 1 fs�1 the autodetachment lifetime for

an electron unstable by 0.1 eV is 1013 years. For electrons with

energies of up to 0.4 eV it is still longer than one year, and only at

energies of more than 0.8 eV does the lifetime become too short

for mass spectrometric detection (10�5 s). Thus, even though

autodetachment is in principle possibly close to the inner turning

points of the Franck–Condon zone, the associated lifetimes are

long, and both trianions, Al(CN)3�6 and Al(NC)3�6 , are predicted

to be electronically stable for all practical purposes.

Having established very long lifetimes with respect to

electron loss, the second decay process to be considered is

dissociation into two or more anions. In view of the large

Coulomb repulsion between the negatively charged CN� units

it is hardly surprising to see that both trianions are unstable

with respect to loss of a CN� ligand, and the same is in turn

true for the resulting Al(CN)2�5 and Al(NC)2�5 dianions.

Similar to alkali-halide systems the key question is not whether

the aluminium cyanide trianions are stable to dissociation,

they are clearly not, but rather whether the Coulomb barrier

to dissociation is sufficiently high to support a large number of

long-lived vibrational states at finite temperatures.5,9,10

For both trianions the adiabatic dissociation pathway of a

CN� ligand was computed by fixing one Al–C or Al–N bond

length and optimizing all other geometrical parameters using

the MP2 method and the aug-cc-pVDZ basis set. The two

curves are displayed in Fig. 2, and the transition state structures

representing the tops of the barriers are displayed in Fig. 3. The

nature of these structures as first-order transition states was

confirmed by computing vibrational frequencies and finding a

single mode with an imaginary frequency. The transition states

occur when the Al–C and Al–N bonds are stretched to 3.46

and 3.34 A, respectively, and the heights of the barriers as

measured from the bottom of the respective minima are 52.8

and 70.5 kJ mol�1. Zero-point corrections to the barrier heights

are small and positive, and the zero-point corrected values

are 57.0 and 74.7 kJ mol�1. As the relevant stretching

mode associated with the dissociative motion is predicted to

have a vibrational frequency of 120 cm�1 corresponding to

1.4 kJ mol�1, there is no doubt that both trianions will have a

large number of vibrational states that are long-lived on the

time scale of any conceivable experiment.

A rough estimate for the number of long-lived vibrational

states can be obtained using the approximations established

Fig. 1 Coulomb barrier for detachment of an electron from

Al(CN)3�6 . The length units on the x and y-axes are A, the energy

unit on the z-axis and color-coded is eV.

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in ref. 10. The lifetime of a vibrational state is estimated as the

semiclassical tunneling time through the one dimensional

barrier shown in Fig. 2 at the energy of the state, and then

the number of all vibrational states up to a certain lifetime

threshold is counted using the harmonic approximation for

the number of states with a certain energy. This yields an

underestimate of the true number of states, as the semiclassical

tunneling time is in this case a conservative lower bound for

the true lifetime, and the same is true for the harmonic

approximation for the number of states up to a specific energy

(cf. ref. 10). For Al(CN)3�6 this scheme yields 3 � 1012

vibrational states with a lifetime in excess of one second, a

very large number, in particular in comparison with the

estimate of less than 100 long-lived vibrational states for the

LiF2�3 dianion,10 which has nevertheless been observed.8

Last, a few comments on some related systems. Since the

Al(CN)3�6 and Al(NC)3�6 trianions are already predicted to be

stable for all practical purposes, it is not surprising that the

same holds for the Al(CN)2�5 and Al(NC)2�5 dianions, and that

these dianions are in fact surprisingly stable for their size.

Using the EOM-IP-CCSD method and the aug-cc-pVTZ basis

set the smallest electron detachment energies of Al(CN)2�5 and

Al(NC)2�5 are predicted to be 3.78 and 5.01 eV, and the barrier

for dissociation of a CN� unit from Al(CN)3�6 is predicted to

be 90 kJ mol�1. On the other hand, one can consider related

trianions such as Mg(CN)3�5 and Na(CN)3�4 . The latter is

predicted to be stable with respect to vertical electron loss,

but its barrier to dissociation is practically negligible. It may

thus be of interest as a threshold case, but it is not a system

that can be detected in a mass spectrometer. Mg(CN)3�5 , on the

other hand, shows a dissociation barrier of 12 kJ mol�1 similar

to alkali halide dianions, but it is predicted to be electronically

unstable (vertical detachment energy = �0.2 eV). Nevertheless,

owing to the Coulomb barrier any autodetaching electron needs

to tunnel through, it may still have a sufficient lifetime for mass

spectrometric observation, but its stability is clearly less

convincing than that of the aluminium cyanide trianions, and

in view of the challenges of observing trianions in the first place

it represents a much weaker candidate.

4. Summary and conclusions

Two isomers of the aluminium cyanide trianion, Al(CN)3�6 and

Al(NC)3�6 , have been studied using MP2 and EOM-IP-CCSD

ab initio methods. As for any small multiply-charged anion, the

question of ‘‘stability’’ involves not so much the comparison of

different structures as it would for a neutral system, but rather

the investigation of the two possible decay channels, electron

autodetachment and dissociation into two or several anions.

Both isomers considered are predicted to be stable with respect

to vertical electron autodetachment, and our best calculations

using the EOM-IP-CCSD method and the aug-cc-pVTZ

basis set yield electron detachment energies of 0.36 eV for

Al(CN)3�6 and 0.50 eV for Al(NC)3�6 . As typical for multiply-

charged anions, using Koopmans’s theorem to predict electron

detachment energies overestimates the results found at correlated

levels. Moreover, in this case electron correlation causes a

substantial reordering of the uncorrelated detachment states, and

focusing alone on the HOMO from self-consistent-field

Fig. 2 Dissociation barriers for Al(CN)3�6 (blue) and Al(NC)3�6 (red).

The energy profiles have been computed by fixing the Al/C or Al/N

distance corresponding to the breaking bond, and optimizing all other

degrees of freedom with the MP2/aug-cc-pVDZ method. The

associated transition state structures are displayed in Fig. 3, and the

inset shows the Coulomb repulsion of the dissociation products.

Fig. 3 Geometrical structures of the transition states for dissociation

of Al(CN)3�6 and Al(NC)3�6 . At the transition state the systems are still

very close to C4v symmetry, and the breaking Al–C and Al–N

bonds have been stretched to 3.46 and 3.34 A, respectively. The

MP2/aug-cc-pVDZ method has been used to compute the transition

state structures, and the adiabatic energy profiles for the dissociations

are displayed in Fig. 2. The color coding is Al, brown; C, turquoise; N,

blue.

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calculations would lead to the severely misleading conclusion of a

detachment energy in excess of one eV. For any multiply-charged

system the detachment energy decreases when the inner turning

points of stretching vibrations are approached, and with the basis

sets used Al(CN)3�6 is slightly unstable (0.1 eV) at the inner turning

point, while Al(NC)3�6 is still stable. Investigation of the Coulomb

barrier associated with electron detachment reveals however that

the lifetimes of the two trianions are still long (billions of years),

and that both can be considered to be electronically stable for all

practical purposes.

Regarding dissociation, both, Al(CN)3�6 and Al(NC)3�6 , are

predicted to be metastable with respect to the loss of one or two

CN� anions, as expected for multiply-charged anions with

essentially ionic bonding. The barriers for the dissociation pro-

cesses have been found to have heights of, 57 and 75 kJ mol�1,

respectively, a substantial barrier height, even at elevated

temperatures, and estimates for the number of long-lived

(41 s) vibrational states yield a staggering 300 billion. These

numbers are in particular impressive in comparison with the

typical dissociation barriers of alkali halide trianions in the order

of 10 kJ mol�15 as well as with the LiF2�3 dianion, which has a

dissociation barrier with a height of 20 kJ mol�19 and an

estimated number of less than 100 long-lived states, but has

nevertheless been observed.8 Thus, both aluminium cyanide

trianions are predicted to possess a large number of vibrational

states with lifetimes well beyond any human timescale, and one

may indeed consider Al(CN)3�6 and Al(NC)3�6 as ‘‘stable for all

practical purposes’’. Owing to its substantial barriers and the

associated large number of long-lived vibrational states, we

conclude that this trianion has a very good chance to be

observable, either from sputtering aluminium cyanide or from

electro-spraying an aluminium cyanide solution possibly mixed

with excess cyanide either from a salt with a very large cation or

from potassium cyanide in combination with a potassium ion

selective crown ether.

Acknowledgements

The authors are grateful for financial support through a

Research Competitiveness Grant from the Louisiana Board

of Regents.

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