Chemical Physics Letters 476 (2009) 236–239

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Chemical Physics Letters

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Electronic structure of the mixed aluminum and sodium cluster Al2Na

Ling Lin a, Yuki Kita b, Taro Udagawa b, Shogo Sakai b,*, Minh Tho Nguyen a,c,*

a Department of Chemistry, and Institute for Nanoscale Physics and Chemistry (INPAC), Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgiumb Department of Chemistry, Faculty of Engineering, Gifu University, Yanagido, Gifu 501-1193, Japanc Saigon Institute of Computational Science and Technology, Thu Duc, Ho Chi Minh City, Viet Nam

a r t i c l e i n f o

Article history:Received 3 May 2009In final form 5 June 2009Available online 9 June 2009

0009-2614/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cplett.2009.06.008

* Corresponding authors. Address: Department ofNanoscale Physics and Chemistry (INPAC), Katholiektijnenlaan 200F, B-3001 Leuven, Belgium.

E-mail addresses: sakai@apchem.gifu-u.ac.jp (S.kuleuven.be (M.T. Nguyen).

a b s t r a c t

Electronic structure of Al2Na was reinvestigated using MP2, CCSD(T) and MRMP2/CASSCF(7,7) calcula-tions with aug-cc-pVnZ (n = D, T and Q) basis sets. In contrast to a recent report, the triangular Al2Nahas a 2B1 ground state with a 4B1–2B1 gap of 2.5 kcal/mol, rather than a 2A1 state (13.7 kcal/mol higher).In addition, Al2Na+ exhibits a linear 1R+ ground state with a singlet–triplet gap of �5.2 kcal/mol ratherthan a cyclic 1A1 state (6.0 kcal/mol above the linear). Al2Na� has a triangular 3B1 ground state and a sin-glet–triplet gap of 6.9 kcal/mol. We obtained IEa(Al2Na) = 5.3 ± 0.2 eV and EAa(Al2Na) = 1.3 ± 0.2 eV.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

There has been considerable interest in doped metal clusterswith alkali metals as dopants [1–4]. An inherent property of theseelements is that they often have a mono-valence, and the valenceelectron is rather weakly bound. When interacting with othermetallic elements, alkali metals tend to easily eject that electrongiving rise to interesting electron transfer phenomena. For exam-ple, when adsorbed on a metal surface, alkali metals could act,by electron transfer, as promoter of a catalytic effect [5,6]. There-fore the small mixed clusters are often used as simple theoreticalmodels for systems featuring catalytic activities. A variety of mixedclusters including alkali metals have thus been investigated. Re-cent studies on the effects of lithium atoms on the simplest germa-nium clusters GenLim clearly demonstrated that the presence of Libasically modifies the properties of Gen clusters [7,8]. While thelithium-doped aluminum clusters (AlnLim) have been well studied[9–11], a few experimental and theoretical studies have also beendevoted to the sodium-doped aluminum clusters [12–19].

Using a combined ultraviolet laser vaporization technique withtime-of-flight mass spectrometry, Nakajima and coworkers [12]were able to generate the AlnNam bimetallic clusters (n = 2–26,m = 0–3) and determine their ionization energies. Ishikawa [13]subsequently studied the simplest cluster Al2Na using quantumchemical calculations with the quadratic configuration interactionmethod (QCISD(T)/6-31G(d)) and found that the minimum energystructure of Al2Na is an isosceles triangle (C2v) having a low spin2B1 ground electronic state. While the high spin 4B1 state wasfound to lie almost degenerate with the ground 2B1 state, the 2A1

ll rights reserved.

Chemistry, and Institute fore Universiteit Leuven, Celes-

Sakai), minh.nguyen@chem.

state was located at �15 kcal/mol (0.65 eV) higher in energy thanthe 2B1 state. More recently, Matsuzawa and coworkers [18] inves-tigated theoretically the equilibrium geometries and structural sta-bilities of the neutral AlnNam clusters, with n = 2–4 and m = 1–8,using density functional theory with the popular hybrid B3LYPfunctional and the 6-311G(d) basis set. These authors reported,among other findings, that the neutral Al2Na cluster exhibits in-stead a 2A1 ground state, in conflict with the previous MO resultsmentioned above [13]. However, the discrepancy was not dis-cussed. The most striking result concerns the vertical ionizationenergy (IEv) of Al2Na whose experimental value is IEv = 5.7 ± 0.1 eV[12]. While the MO 2B1-based calculations provided a vertical IEv of6.2 eV [13], the DFT 2A1-based calculations resulted in a vertical IEv

of �5.7 eV [18] even though there was a difference in the neutralground state. In view of such a discrepancy on a simple but basicmolecular system for the understanding of cluster growth, we setout to reinvestigate the electronic states of Al2Na using reliablequantum chemical methods. To determine its adiabatic ionizationenergy and electron affinity, we also considered the charged sys-tems including the anion Al2Na– and cation Al2Na+. In addition,we have examined the topology of electron densities to probe fur-ther the bonding phenomenon in the cyclic systems.

2. Computational methods

Quantum chemical calculations were carried out making use ofthe conventional methods of molecular orbital theory. In the firstseries of calculations, second-order perturbation MP2 and cou-pled-cluster CCSD(T) [20] theories in conjunction with the all elec-tron correlation consistent basis sets aug-cc-pVnZ with n = D, T andQ [21] were employed to optimize the structures, harmonic vibra-tional frequencies were subsequently calculated at the same levelto characterize the located stationary points as equilibriumstructures having all real vibrational frequencies. We used the

Table 2Calculated relative energies (DE, kcal/mol), adiabatic ionization energy (IEa, eV) andelectron affinity (EAa, eV) of Al2Na considered at different levels.a

Property Species State CCSD(T) CAS(7,9) MRMP2

aVDZb aVTZb aVQZb aVDZ aVDZ

DE (kcal/mol) Al2Na 2B1 0.0 0.0 0.0 0.0 0.02A1 14.1 13.7 13.6 2.2 4.64B1 1.6 2.5 2.9 3.9 0.64B2 39.1 41.7 42.9 – –

Al2Na+ 1A1 0.0 0.0 0.03B1 1.1 1.3 1.31R+ �5.7 �6.0 �6.13G �0.5 �0.8 �0.9

Al2Na– 1A1 7.5 6.9 6.33B1 0.0 00 0.0

IEa (eV)c Al2Na 5.14 5.26 5.30EAa (eV) Al2Na 1.24 1.26 1.25

a All values are corrected for zero-point energies.b aVnZ stands for aug-cc-pVnZ basis sets, with n = D, T and Q.c Calculated as the difference between total energies of the 1R+ and 2B1 states,

with ZPE corrections.

L. Lin et al. / Chemical Physics Letters 476 (2009) 236–239 237

R/UCCSD(T) method in which the restricted open-shell Hartree–Fock determinants were used as references for unrestricted cou-pled-cluster calculations. In such a way, the spin-contaminationin UHF wavefunctions can be avoided. In the second series of com-putations, for the neutral species, complete active space CASSCFwavefunctions have been constructed and the dynamic correlationwere subsequently evaluated by second-order perturbation ex-panded on the basis of multi-reference MRMP2 wavefunctions.Calculations were performed using the GAUSSIAN 03 [22] programfor geometry optimizations, MOLPRO 2006 [23] for R/UCCSD(T) cal-culations, and GAMESS [24] for MRMP2 calculations. To analyze theelectronic distribution, we considered electron localization func-tion (ELF) [25–28], and the isosurfaces were plotted with thegraphical program gOpenMol [29]. As an additional attempt toinvestigate the electronic structure of the clusters, the total andthe partial density of states (DOS) computed with PYMOLYZE program[30] were also plotted.

3. Results and discussion

3.1. Energetics

Combination of the sodium atom with the aluminum dimer inits 3R�g ground state invariably leads to a symmetric triangular cy-cle as the most stable form, irrespective of the spin state. The linearform lies higher in energy, and a similar situation is found for theanionic state. On the contrary, in the cationic state, the linear formturns out to be more stable than the cyclic counterpart.

The main orbital configurations of the lower-lying electronicstates of the cyclic neutral Al2Na are depicted as follows: 2B1:. . .(8a1)2(9a1)2(6b2)2(3b1)1, 2A1: . . .(8a1)2(6b2)2(9a1)2(10a1)1, and4B1: . . .(8a1)2(6b2)2(9a1)1(10a1)1(3b1)1. Accordingly, the activespace used in CASSCF computations should include electrons dis-tributed in the highest-lying a1 and b1 orbitals. In the present work,we chose an active space of seven electron in nine orbitals includ-ing also one a1, two b2 and one a2 orbital (denoted as CASSCF(7,9)),which appears sufficient to cover the electronic configurations ofthe neutral states considered. As mentioned above, in coupled-cluster calculations, we employed the unrestricted formalismwhich is based on a spin restricted reference R/UCCSD [20]. To sim-plify the presentation of data, only optimized geometrical parame-ters optimized at the CCSD(T)/aug-cc-pVTZ level are recorded inTable 1. Calculated relative energies with different methods aresummarized in Table 2.

In all states of the cyclic form, the Al�Na distance is rather long,ranging from �3.10 Å in the neutral (Table 1), stretched to �3.45 Åin the cation and slightly shortened to �3.10 Å in the anion. TheAl�Al distance varies from 2.47 to 2.62 Å, and these are slightlyshorter than that of the experimental result (2.70 Å) in Al2 [31].So due to the adsorption of the alkali metal, the Al�Al distanceof Al2 molecule becomes shorter, similar change has also beenfound in the case of Al2Li [11]. In the linear form, the Al–Na dis-

Table 1Optimized geometrical parameters of the cyclic Al2Na system on the level of CCSD(T)/aug-cc-pVTZ.

Species Electronic state r(Al�Al)(Å)

r(Al�Na)(Å)

\AlNaAl(�)

Al2Na 2B1 2.470 3.146 46.22A1 2.480 3.072 47.64B1 2.613 3.095 49.9

Al2Na+ 1A1 2.617 3.431 44.83B1 2.538 3.454 43.1

Al2Na– 1A1 2.463 3.073 47.23B1 2.572 3.141 48.3

tance is getting compressed to �2.90 Å in the neutral, �3.14 Å inthe cation and �3.05 Å in the anion.

The harmonic vibrational frequencies of the neutral (2B1) arequite low, situated in the far IR domain from 70 to 360 cm�1 (Ta-ble S1 in ESI). The asymmetric bending mode b2 corresponds tothe lowest one (�70–150 cm�1), followed by the symmetricAl�Na stretching a1 (�120–190 cm�1) and the Al�Al stretchingmode a1 (�280–360 cm-1). The low vibrational frequency ofAl�Na stretching suggests that the interaction between Al andNa is very weak.

We note a difference between CCSD(T) and MRMP2 values forrelative energies, which can in part be accounted for by the useof the aug-cc-pVDZ basis set in the later set of calculations (Table2). In the neutral Al2Na, the wavefunction of each of the states con-sidered is dominated by the main determinant given above, withcoefficient C0 > 0.90. In the following discussion, we use the cou-pled-cluster results with the largest basis set. Results shown in Ta-ble 2 are internally consistent and clearly establish that the lowspin 2B1 state represents the ground electronic state of the neutralAl2Na. The high spin 4B1 state is located at �3.0 kcal/mol above it.Within the expected error bar of calculations, both states could beregarded to be nearly degenerate but with a preference for the lowspin state. The 2A1 state is calculated to be �13 kcal/mol higher inenergy. We found another high spin state having the orbital config-uration 4B2: . . .(6b2)2(9a1)2(1a2)1(10a1)1(3b1)1 which is located at�42 kcal/mol above the ground state 2B1.

These results are consistent with the earlier findings of Ishika-wa [13], but at variance with the more recent B3LYP results ofMatsuzawa and coworkers [18]. As for a further check, we carriedout B3LYP calculations and found that depending on the startinggeometry and the MO guess, the SCF process could converge eitherto a 2A1 or a 2B1 state. With the B3LYP functional and the 6-311G(d)basis set, the 2A1 state is lower by 0.11 kcal/mol than the 2B1 state.However, using the same functional but with a larger basis set suchas the aug-cc-pVTZ, the 2B1 turns out to be 0.10 kcal/mol lower inenergy than the 2A1. When using other available functionalsincluding the BLYP, BP86, B3PW91, PW91PW91 or PBEPBE, evenwith the 6-311G(d) basis set, the 2B1 state is correctly found asthe ground state, even though the 2A1–2B1 separation gap variesfrom 1.1 to 3.5 kcal/mol. It is thus likely that Matsuzawa andcoworkers [18] first obtained a 2A1 state from B3LYP/6-311G(d)calculations, and then did not consider the other states and theirdependence on the methods employed.

The triatomic neutral Al2Na is not particularly stable with re-spect to the simple bond cleavage. In fact, the binding energy with

Symmetry Isosurfaces Cutplane

Al2Na 2B1

Al2Na+ 1A1

Al2Na– 3B1

Fig. 1. ELF isosurfaces and cutplanes for Al2Na, Al2Na+ and Al2Na– (N = 0.80–0.86).The calculations were carried out with B3LYP/aug-cc-pVTZ.

Table 4Calculated Wiberg indices (Wi) and NBO charges of the cyclic neutral, anionic andcationic Al2Na on different electronic states at MP2/aug-cc-pVTZ level.

Species State Wiberg indices (Wi) NBO charges (au.)

Al�Al Al�Na Na Al

Al2Na 2B1 1.71 0.34 0.56 �0.284B1 0.99 0.12 0.74 �0.37

Al2Na+ 1A1 1.33 0.22 0.75 0.123B1 1.01 0.05 0.92 0.04

Al2Na– 1A1 2.50 0.45 0.37 �0.683B1 1.38 0.49 0.13 �0.56

Table 3Mean electronic populations computed for basins localized in the cyclic neutral,anionic and cationic Al2Na with B3LYP/aug-cc-pVTZ method.

Species State Basins

C(Al) C(Na) V(Al, Na) V(Al) V(Na)

Al2Na 2B1 10.04 10.02 1.50 1.92Al2Na+ 1A1 10.04 10.03 1.40 1.53Al2Na– 3B1 10.04 10.02 2.82 1.61 0.45

238 L. Lin et al. / Chemical Physics Letters 476 (2009) 236–239

respect to the separated fragments Al2(3R�g ) + Na amounts to only1.32 eV.

The linear AlAlNa form is calculated to be energy minimum inboth quartet and doublet states, being 7.7 (4R+) and 11.7(2G) kcal/mol above the 2B1 state, respectively. The symmetricalisomer AlNaAl (2Rþu ) is 37.8 kcal/mol higher in energy than the tri-angular 2B1 structure.

Our calculations reveal that removal of an electron from theneutral Al2Na in keeping the triangular form leads to either a sin-glet state 1A1: . . .(6b2)2(1a2)2(9a1)2 or a triplet state 3B1:. . .(6b2)2(1a2)2(9a1)1(3b1)1. The calculated values show that bothstates are again close in energy. The 3B1–1A1 energy separationamounts to about 1.0 kcal/mol. In any case, the absolute value ofthe calculated gap lies well within the error bar of the methodsemployed, and both states can thus be considered as quasidegenerate.

Removal of an electron from the linear AlAlNa also leads to the1R+ and 3G states of the cation AlAlNa+ that are also close in energy.CCSD(T) calculations point out that the linear 1R+ state turns out tohave the lowest energy, which lies 6.0 and 5.2 kcal/mol below thecyclic 1A1 and linear 3G forms, respectively. It can thus be con-cluded that the cation Al2Na+ exhibits a linear singlet ground state(1R+).

The adiabatic ionization energy of Al2Na, which is calculated asthe energy difference between both 1R+ and 2B1 states, amounts toIEa(Al2Na) = 5.3 eV, with an expected error bar of ± 0.2 eV. We alsocalculated the corresponding vertical ionization energy from theAl2Na(2B1) and obtained IEv = 5.7 eV giving a vertical 1A1 state. Thislarger value is due to a significant geometry relaxation followingionization (from cyclic to linear), and it compares well with theexperimental estimate of 5.7 ± 0.1 eV [12]. This agreement lendsan additional support for the identity of these ground states foundhere, and contributes to clarify a certain confusion mentionedabove. The calculated IEa value of 5.3 eV, which is slightly largerthan the IE(Na) = 5.1 eV, indicates that the removed electron ofAl2Na arises from Na, and condensation of Na onto the Al2 appearsto slightly decrease its capacity for electron detachment. RegardingNa as a dopant, it induces an increase of the ability of Al2 to loseelectron, since the adiabatic ionization energy of Al2Na is smallerthan that of 6.3 eV for Al2. The sodium cation affinity (SCA) ofAl2, calculated as the energy difference between the singlet linearAlAlNa+ and the separated Al2 + Na+ fragments, amounts toSCA(Al2) = 23.1 kcal/mol (1.0 eV). This value is smaller than theNa atom affinity of 1.32 eV given above.

Addition of an excess electron to the triatomic neutral Al2Naholds the cyclic form and gives rise to two separate states ofthe anion, namely 1A1: . . .(6b2)2(1a2)2(9a1)2(3b1)2 and 3B1:. . .(6b2)2(1a2)2(9a1)1(3b1)1(10a1)1. In this case, CCSD(T) calcula-tions clearly demonstrate a preference for the high spin groundstate, with a singlet–triplet energy separation of 6.9 kcal/mol.The adiabatic electron affinity, which is evaluated as the 2B1–3B1

energy difference, is calculated to be EAa(Al2Na) = 1.3 ± 0.2 eV.The corresponding vertical electron affinity amounts to 1.0 eV.Compared with EA(Al2) = 1.51 eV [32], the Na dopant thus tendsto marginally reduce the ability of diatomic aluminum to receiveelectron. The linear AlAlNa� anion is found to be higher in energythan the cyclic counterpart (�10 kcal/mol).

3.2. Electron distribution

Since Al2Na+ contains 6 valence electrons, which satisfies theHückel rule, a cyclic form is usually expected to be stabilized byaromaticity. As shown above, it turns out that the linear interactionbetween the Na+ cation with an Al end is more favored. This resultwas not reported in previous studies. To probe further this finding,we performed ELF and NBO analyses to investigate the electronic

properties of the neutral, cationic and anionic Al2Na cycles. TheELF is a simple measure of the electron localization in atomicand molecular systems [25–28]. The ELF values are always in arange of [0;1] and relatively large where the electrons are unpairedor formed into pairs with antiparallel spins [25–28]. The ELF iso-surfaces and their cut planes of the cyclic cation, neutral and anio-nic form of Al2Na are shown in Fig. 1. The mean electronicpopulations computed for the basins localized for each moleculeare summarized in Table 3. The results of NBO analysis are listedin Table 4.

For Al2Na+, calculations suggest the presence of two V(Al) ba-sins, which could be regarded as the lone pair basins of Al atoms,each having an electronic population of 1.5 electrons. For the coreC(Al) basins the electronic population is computed to be 10.0 elec-trons for each. We also locate two disynaptic basin V(Na, Al) withan electronic population of 1.4 electrons for each, which is smallerthan the corresponding value computed for Al2Na (1.5) and Al2Na–

(2.8), implying that the interaction between Na and Al is weaker inAl2Na+.

Fig. 2. The total and partial density of states of cyclic Al2Na+ calculated with B3LYP/aug-cc-pVTZ.

L. Lin et al. / Chemical Physics Letters 476 (2009) 236–239 239

For the singlet Al2Na+ (1A1), Wiberg indices indicate a bond or-der of 0.22 for Al�Na bond, while the corresponding value of theneutral counterpart (2B1) is larger (0.34), implying that the Al�Nabond is weakened upon the electron detachment, which is similarwith Al�Al bond. While for the electron attachment, the Al�Albond index decreases but that of the Al�Na increases. As for thestructural changes, both the Al�Al and Al�Na bonds are elongatedfrom Al2Na (2B1) to Al2Na+ (1A1), while the structure does notchange much upon receiving one extra electron. According to theNBO charges, q(Na) of 2B1 and 4B1 of the neutral Al2Na are 0.56and 0.74e, suggesting that the Al�Na bonds are ionic.

The DOS plot of cyclic Al2Na+ is shown in Fig. 2, and it revealstwo narrow bands at �14.6 and �11.5 eV, respectively, which aremainly composed of s(Al) electrons. The band at �8.6 eV corre-sponds to the HOMO (18th MO), and the p(Al) electrons has thelargest contribution (�62%), and followed by the s(Na) electrons(�28%). Compared with the DOS of the neutral, the s(Na) contribu-tions decreases considerably in the cyclic cation. Overall, it isapparent that following electron removal from the cyclic neutral,the Na–Al interaction becomes much weaker. As a consequence,the linear form becomes slightly more favored. This is consistentwith the small sodium cation affinity given above.

4. Concluding remarks

In the present study, we employ quantum chemical calculationsto probe the electronic structure of the simple triatomic Al2Na sys-tem. In contrast to a recent report, Al2Na is found to have a 2B1

ground state even though the 4B1–2B1 energy gap is very small.The cation Al2Na+ is found to prefer a linear structure whose 1R+

state is the ground state. Addition of an electron produces the an-ion Al2Na– for which the 3B1 state is established as the groundstate, but with a small singlet–triplet gap. Regarding Na as a dop-

ant, it induces a decrease of the ability of aluminum dimer to at-tach electron, but increases its capacity to eject electron.

Acknowledgements

MTN is indebted to the Japan Society for the Promotion of Sci-ence (JSPS) for supporting his short and enjoyable stay in Gifu.L.L. thanks the INPAC-K. U. Leuven for a postdoctoral fellowship.S.S. thanks the Ministry of Education, Science and Culture of Japanfor financial support by a Grant-in-Aid for Scientific Research (C,No.18550015) and a Grant-in-Aid for Scientific Research on Prior-ity Areas (No. 20038020).

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.cplett.2009.06.008.

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