Theoretical study of transition metal dimer AuM (M = 3d, 4d, 5d element)

Chemical Physics Letters 406 (2005) 24–28 www.elsevier.com/locate/cplett

Theoretical study of transition metal dimer AuM (M = 3d, 4d, 5d element) Z.J. Wu

*

Key Laboratory of Rare Earth Chemistry and Physics, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Number 5626, Renmin Street, Changchun 130022, PR China Received 27 January 2005; in final form 11 February 2005 Available online 16 March 2005

Abstract Bond distance, vibrational frequency and dissociation energy of AuM (M = 3d, 4d, 5d element) are studied by use of density functional method B3LYP. Possible spin states are considered for each dimer. The calculated results are compared with the available experimental data and theoretical studies. Our calculation shows that except AuLu, B3LYP tends to underestimate the dissociation energy. The vibrational frequency of AuM (M = 3d element) is larger than that of AuM (M = 4d, 5d element) by around 40 cm 1. Ó 2005 Elsevier B.V. All rights reserved.

1. Introduction Transition metal clusters are theoretically one of the most interesting electronic systems because they possess unfilled d orbitals and therefore can form various spin configurations that are composed of the orbitals with different angular momenta in a limited energy region. As the smallest cluster, transition metal dimers have been studied both experimentally and theoretically, and a good summary of these studies can be found in Refs. [1] (for homonuclear and heteronuclear dimers) and [2] (for homonuclear dimers). The force constants of the homonuclear dimers were also predicted empirically by Lombardi and coworkers [3]. For a systematic theoretical study, all homonuclear dimers of the 3d transition metals were conducted independently by Yanasigava et al. [4] and Barden et al. [5]. In both articles [4,5], diverse density functional methods were tested and their performance is compared with the available results. With the same idea, Gutsev and Bauschlicher [6] studied the homonuclear 3d transition metal dimers both at neu*

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0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.02.083

tral and charged species. In addition, systematic theoretical studies on all possible heteronuclear 3d transition metal dimers including neutral and charged species were also conducted [7]. For the 4d transition metal, the homonuclear dimers were examined by present author [8]. However, studies on the 5d transition metal dimers (either homonuclear or heteronuclear) are rare [9]. In recent years, the clusters of containing gold element have been afforded increased importance to both applications and theoretical studies due to their wide use in the catalysis, microelectronics and optical materials. The mechanism of the cluster growth in such systems could not be simply understood as the ionic or covalent type of bonding. This has provided a challenge in experimental science, computational chemistry, and computational physics to reproduce the experimental data and produce accurate predictions of reactivity and properties [10–28]. A thorough and excellent review concerning the theoretical chemistry of gold has been recently given by Pyykko¨ [10]. Stimulated by that work, presented here is a systematic theoretical study of neutral diatomic AuM (M = 3d, 4d, 5d element) based on density function theory (DFT). Among the 30 neutral heteronuclear dimers examined in this study, spectroscopic

Z.J. Wu / Chemical Physics Letters 406 (2005) 24–28

constants (bond distance, vibrational frequency and dissociation energy) were available only for some of them, such as AuCu [11,14–19], AuAg [12–20], AuZn [21], AuLa [22], AuLu [22], AuPd [23–25], AuPt [26] and AuHg [27,28]. Among them, it is seen that the coinage dimers AuAg and AuCu were studied the most. The experimental study by resonant two-photon ionization spectroscopy showed that for the ground state (X1R+), ˚ , vibrational frequency the bond distance is 2.330 A 1 248 cm , dissociation energy 2.34 eV for AuCu [11] and vibrational frequency 196 cm 1, dissociation energy 2.08 eV for AuAg [12]. Theoretical studies include CI (configuration interaction) method on AuAg [13]; quasirelativistic MCPF (modified coupled pair functional) method [14,15], ZORA NLDA (zero-order regular relativistic approximation with non-local density approximation) [16], CCSD(T) (single and double excitation coupled cluster with perturbative triples) method [17], ZORA (MP) (MP stands for model potential) [18], and density functional method [19] on both AuCu and AuAg; and DFT study on AuAg [20]. Other theoretical researches include DFT study on AuNZn (N = 1–6) [21], diverse methods on AuLa and AuLu in which MP4 (M/ ller–Plesset up to fourth-order) gave the best overall performance [22], DFT studies on AuPd [23–25], CASMCSCF (the complete active space multi-configuration self-consistent field) and MRSDCI (multi-reference singles + doubles configuration interaction) studies on AuPt [26], DFT [27] and CCSD(T) [28] studies on AuHg. DFT is now widely used to determine structures for a wide variety of molecules and clusters. Compared to high-level ab initio molecular orbital theories, DFT has the advantage of applicability anywhere in the Periodic table and inherent computational efficiency. This makes it particularly effective for those molecules involving heavy metal elements. In this study, the diatomics of gold with all remaining transition metal element have been studied systematically by density functional method and the results obtained are compared with experiments and previous theoretical studies. We hope this study could serve as a useful guide for future experimental studies, especially for those dimers for which no other data are available.

2. Computational methods All geometry optimizations were performed using the GAUSSIAN 03 suite of programs [29]. Bond distance, vibrational frequency, and dissociation energies were determined by use of density functional method B3LYP [30,31]. The B3LYP functional is a combination of BeckeÕs three-parameter hybrid exchange functional [30], and the Lee–Yang–Parr [31] correlation functional. The basis set used is CEP-121G (relativistic compact

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effective potential) [32] for 4d and 5d elements in which the dependence of spin–orbit effects was averaged out. The CEP-121G basis set was derived from numerical Dirac–Fock atomic wavefunctions using shape-consistent valence pseudo-orbitals and an optimizing procedure based on an energy-overlap functional [32]. Basis set 6-311++G(3df) is used for 3d elements. The valence electrons considered for 4d and 5d elements are or ns2np6ndm(n + 1)s2(n = 4,5) ns2np6ndm(n + 1)s1 depending on the individual element. All-electrons are considered for 3d elements. Possible spin states for each element are considered explicitly. To avoid trapping at local minima of the potential energy surface, different initial geometries (16 bond distances from 0.5 to ˚ ) are used. The calculated dissociation energies 3.6 A were corrected by the zero-point vibrational energies (except AuTc which contains radioactive element Tc, because vibrational frequency is not available by the present method). The calculated results are listed in Table 1. The dissociation energy is only given for the ground state. Electronic states are presented only for some of the dimers, because for many of the dimers, the electronic states cannot be determined.

3. Results and discussion AuSc. It is seen from Table 1 that triplet is the ground ˚ , vibrational frestate with the bond distance 2.576 A quency 223 cm 1 and dissociation energy 2.39 eV. Singlet state is 0.44 eV higher in energy. Compared with experimental dissociation energy 2.86 eV [33], our calculated value is 0.47 eV lower. AuTi and AuV. For these two dimers, studies either experimentally or theoretically are not available. Our calculations show that spin multiplicities at 4 and 5 are the ground state for AuTi and AuV, respectively. For AuTi, the calculated bond distance, vibrational fre˚ , 223 cm 1 quency and dissociation energy are 2.534 A and 2.52 eV. Doublet state gives nearly the same values ˚ , 223 cm 1), but 0.35 eV higher in energy than (2.531 A the ground state. For AuV, the calculated values at ˚ , 217 cm 1 and 2.27 eV. ground state are 2.524 A AuM (M = Cr, Mn, Fe, Co). For these four dimers, the experimental dissociation energies are available [33]. It is seen from Table 1 that our calculations underestimate the experimental value by 0.25 eV for AuCr, 0.27 eV for AuMn, 0.16 eV for AuFe and 0.27 eV for AuCo. The predicted ground state spin multiplicities are 6 for AuCr, 5 for AuMn, 4 for AuFe and 3 for AuCo. AuNi. Doublet state (2R) is the ground state for AuNi. Previous experimental studies suggested a bond ˚ [34], in reasonable agreement distance 2.351 ± 0.001 A ˚ . However, our calculation with our calculation 2.408 A (2.02 eV) underestimates the experimental dissociation energy 2.52 ± 0.17 eV [34] by 0.50 eV.

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Z.J. Wu / Chemical Physics Letters 406 (2005) 24–28

Table 1 ˚ ), vibrational frequency xe (cm 1), relative stability DE (eV) and dissociation energy De (eV) of diatomic AuM at Calculated bond distances d (A various spin multiplicities Sa S

d AuSc 2.525 2.576

1 3 5 7

AuTi 2.531 2.534

2 4 6 8

AuY 2.688 2.731

1 3 5 7

AuZr 2.645 2.660

2 4 6 8

AuLa 2.857 2.886

1 3 5 7

AuHf 2.597 2.633

2 4 6

xe 236 223

223 223

183 168

185 180

149 141

158 147

DE 0.44 0.00

0.35 0.00

0.00 0.30

0.22 0.00

0.13 0.00

0.00 0.51

De

2.39

2.52

2.71

2.57

2.70

2.54

d AuV 2.484 2.511 2.524 AuCr 2.495 2.501 2.523 3.097

xe 226 220 217

DE 2.34 0.65 0.00

218 217 213 60

3.04 1.58 0.00 1.95

AuNb 2.588 111 2.607 186 2.633 182 2.958 81

1.84 0.64 0.00 2.15

AuMo 2.593 184 2.604 183 2.624 177 3.261 44

2.32 1.08 0.00 1.90

AuLu 2.718 2.684

0.00 1.93

AuW 2.577 2.565 2.586

140 134

157 157 159

1.62 0.96 0.00

De

2.27

1.92

2.36

1.95

3.92

2.20

d

xe

DE

AuMn 2.453 2.473 2.488 2.488

225 221 214 218

4.14 2.53 0.35 0.00

AuFe 2.430 2.449 2.434

227 225 227

2.11 0.00 0.10

AuTcb 2.564 2.562 2.597 2.602

na na na na

2.36 1.49 0.04 0.00

AuRu 2.576 182 2.598 175 2.651 113

0.74 0.00 1.64

AuTa 2.568 2.570 2.596

1.33 0.10 0.00

AuOs 2.557 2.561 2.602

165 164 154

171 167 151

0.95 0.00 0.21

De

d

De

d

DE

De

0.00 0.85

2.03

1.98

AuCu 2.396 224 2.696 103

2.02

AuZn 2.475

184

0.00

0.79

1.03 0.00 1.75

0.00 1.78

1.86

2.27

AuAg 2.591 177 3.061 53

175

0.00

1.42

AuCd 2.688 138

0.00

0.75

AuRe 2.525 2.556 2.598 2.630

174 161 148 146

2.81 1.32 0.22 0.00

AuIr 2.557 2.554 2.594

174 169 149

1.42 0.00 0.82

2.18

AuPt 2.543 2.620

170 140

0.00 1.56

AuHg 2.791

93

0.00

0.41

xe

DE

AuCo 2.393 231 2.431 224 2.471 204

2.28 0.00 1.18

AuNi 2.408 2.421

226 212

0.00 1.19

AuRh 2.512 192 2.566 183 2.598 144 AuPd 2.561

xe

1.68

1.79

2.06

2.26

1.93

1.54

1.42 2.02

a

For a good summary of theoretical values of AuCu and AuAg, see Refs. [17,18], only experimental dada are given here for comparison for these two dimers. AuSc: experimental De = 2.86 eV (Ref. [33]). AuCr: experimental De = 2.17 eV (Ref. [33]). AuMn: experimental De = 1.95 eV (Ref. [33]). ˚ (Ref. [34]), AuFe: experimental De = 1.95 eV (Ref. [33]). AuCo: experimental De = 2.25 eV (Ref. [33]). AuNi: experimental d = 2.351 ± 0.001 A ˚ , xe = 248 cm 1, De = 2.34 eV (Ref. [11]). AuZn: De = 2.52 ± 0.17 eV (Ref. 34) or 2.60 eV (Ref. [33]). AuCu: experiment: X1R+, d = 2.330 A ˚ , De = 0.88 eV (Ref. [21]), theoretical study at B3LYP level. For the basis set, LANL2DZ (LANL2DZ is the double-zeta type effective d = 2.475 A core potential developed by Los Alamos National Laboratory) is used for Au, 6-311+G(d) for Zn. AuY: experimental De = 3.03 eV (Ref. [33]). ˚, AuRh: experimental De = 2.38 eV (Ref. [33]). AuPd: experimental De = 1.56 eV (Refs. [33,35]). Theoretical values: (doublet), d = 2.864 A ˚ at B3LYP/LANL2DZ (Ref. [24]); xe = 232 cm 1, De = 1.63 eV by BP functional with relativistic effective core potential (Ref. [23]); d = 2.561 A ˚ , De = 1.84 eV by GGA (generalized gradient approximation) method (Ref. [25]). AuAg: experiment: xe = 196 cm 1, De = 2.08 eV (Ref. d = 2.51 A ˚ , xe = 145 cm 1, De = 2.74 eV by MP4 (M/ller–Plesset up to [12]). AuLa: experimental De = 3.47 eV (Ref. [33]). Theoretical values: d = 2.773 A fourth order). The basis set is (8s6p5d1f)/(7s3p4d1f) for Au, (7s6p5d3f)/(6s4p4d3f) for La (Ref. [22]). AuLu: experimental De = 3.43 eV (Ref. [33]). ˚ , xe = 144 cm 1, De = 3.35 eV by MP4 (M/ller–Plesset up to fourth order). The basis set is (8s6p5d1f)/(7s3p4d1f) for Theoretical values: d = 2.620 A ˚ , xe = 181 cm 1 at MRSDCI level by including spin–orbit Au, (7s6p5d3f)/(6s4p4d3f) for Lu (Ref. [22]). AuPt: theoretical values: 2D, d = 2.574 A ˚ , xe = 99.63 cm 1, ˚ , xe = 103 cm 1, De = 0.40 eV at CCSD(T) level (Ref. [27]); d = 2.67 A effects (Ref. [26]). AuHg: theoretical values: d = 2.711 A De = 0.49 eV at relativistic GGA level (Ref. [28]). b Vibrational frequency cannot be obtained from the present calculation for AuTc.

AuCu. Many studies on this dimer are available both experimentally [11] and theoretically [14–19]. Our calculations show that singlet state (1R) is the ground state, in agreement with experiment (1R+) [11]. The calculated ˚ ), vibrational frequency bond distance (2.396 A (224 cm 1) and dissociation energy (2.03 eV) are compa˚, rable to the corresponding experimental values (2.330 A 248 cm 1 and 2.34 eV) [11]. Our calculated data are also close to previous theoretical study at DPT DFT (firstorder relativistic density functional calculations) level

˚ , 241 cm 1 and 2.17 eV) [18], and at B3LYP level (2.37 A (228 cm 1 and 2.27 eV) [19]. However, from previous ˚ , 247 cm 1, studies, it seems that ZORA (MP) (2.33 A ˚, and 2.49 eV) [18] and ZORA NLDA (2.34 A 245 cm 1 and 2.45 eV) [16] perform better compared with experiment. AuZn. The only spin state for this dimer is doublet state (2R). Since it is known that the dissociation energy represents the difference in energy between the minimum of the potential energy curve and the dissociation limit,

Z.J. Wu / Chemical Physics Letters 406 (2005) 24–28

it is, therefore, a measure of the strength of chemical bonds. For AuZn, due to the closed shell of zinc (3d10s2) and nearly closed shell of gold (5d10s1), the calculated dissociation energy is low (0.79 eV), indicating relatively weak bond for the dimer. Our calculated bond ˚ ) and dissociation energy (0.79 eV) are distance (2.475 A in excellent agreement with previous theoretical study ˚ , 0.88 eV) [21]. The calculated at B3LYP level (2.475 A vibrational frequency (184 cm 1) is about 40 cm 1 smaller than other diatomic AuM (M = 3d element) (Table 1). For 3d transition metals, it is also seen that the bond distance at ground state decreases monotonically from ˚ ) to AuCu (2.396 A ˚ ), then increases at AuSc (2.576 A ˚ AuZn (2.475 A). AuY. Singlet state (1R) is predicted to be the ground state. This is different from its congener AuSc in which triplet state is the ground state. The calculated dissociation energy 2.71 eV is 0.32 eV lower than experimental value 3.03 eV [33]. The triplet state at AuY is 0.30 eV higher in energy than the ground state. AuM (M = Zr, Nb, Mo, Tc, Ru). No data are available for these dimers. Our calculations indicate that the ground state spin multiplicities are 4 for AuZr, 5 for AuNb, 6 for AuMo, 7 for AuTc, and 4 for AuRu. For AuTc, vibrational frequency cannot be obtained by the present method. It is also seen that for AuTc spin multiplicity at 5 are nearly isoenergetic (only 0.04 eV higher in energy) compared with spin multiplicity at 7 (ground state), suggesting that spin multiplicity at 5 is a competitive candidate for the ground state. AuRh. Triplet state is the ground electronic state for this dimer. The calculated dissociation 2.27 eV is slightly lower (by 0.11 eV) than experimental value 2.38 eV [33]. AuPd. Several theoretical studies are available for the dimer. Doublet (2R) is the only spin state for the dimer, in agreement with previous theoretical study [23]. The calculated dissociation energy 1.42 eV is also close to experimental value 1.56 eV [33,35], and previous theoretical study at BP (Becke–Perdew) functional 1.63 eV [23], better than that at GGA calculation of 1.84 eV ˚ is in agree[25]. Our calculated bond distance 2.561 A ment with previous theoretical study at B3LYP ˚ ) [24] and at GGA level (2.51 A ˚ ) [25], shorter (2.561 A ˚ ) [23]. Our calcuthan that by BP functional (2.864 A lated vibrational frequency 175 cm 1 is smaller than that by BP functional (232 cm 1) [23]. AuAg. Like AuCu, there are many studies available both experimentally [12] and theoretically [13–20] for it. Singlet state (1R) is predicted to be the ground state. The calculated vibrational frequency 177 cm 1 and dissociation energy 1.86 eV are close to experimental values 196 cm 1 and 2.08 eV [12]. Our calculated values are also comparable to previous theoretical studies at ˚ , 176 cm 1 and 1.91 eV) [18], DPT DFT level (2.57 A ˚ , 187 cm 1 and 2.15 eV) ZORA (MP) level (2.53 A

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˚ , 185 cm 1 and [18], ZORA NLDA level (2.54 A 2.15 eV) [16], and BPW (Becke–Predew–Wang) level ˚ , 1.98 eV) [20]. (2.57 A AuCd. Like its congener AuZn, the dissociation energy is low (0.75 eV). The calculated bond distance is the longest among all diatomic AuM (M = 4d element). The calculated vibrational frequency (138 cm 1) is about 40 cm 1 smaller than other diatomic AuM (M = 4d element) (see Table 1). It is also interesting to see that for the diatomics of gold with 4d element, the calculated bond distance at ground state decreases from AuY (2.688) to AuPd ˚ ), then increases from AuAg (2.591) to AuCd (2.561 A ˚ ). (2.668 A AuLa. Triplet state is the ground state. The calculated dissociation energy 2.70 eV is 0.77 eV lower than exper˚, imental value 3.47 eV [33]. Our calculated data (2.886 A 1 141 cm , and 2.70 eV) are close to previous theoretical ˚ , 145 cm 1 and 2.74 eV) [22], study at MP4 level (2.773 A in particular for the vibrational frequency and dissociation energy. AuLu. Unlike AuLa, singlet state (1R) is predicted to be the ground state for AuLu. Our calculations on dissociation energy 3.92 eV overestimate the experimental value 3.43 eV [33] by 0.49 eV. Our calculated bond dis˚ and vibrational frequency 140 cm 1 are tance 2.718 A comparable to previous theoretical study at MP4 level ˚ and 144 cm 1) [22], in particular for the vibra(2.620 A tional frequency. While for the dissociation energy, previous study at MP4 level (3.35 eV) [22] gives better agreement with experiment (3.43 eV) [33] than our calculation (3.92 eV). AuM (M = Hf, Ta, W, Re, Os, Ir). No studies are available for these dimers. Ground state spin multiplicities are 2 for AuHf, 3 for AuTa, 6 for AuW, 7(7R) for AuRe, 4 for AuOs and 3(3R) for AuIr. AuPt. Doublet (2R) is the ground state. The electronic state is different from previous study at MRSDCI level, in which 2D is predicted to be the ground state [26]. Our ˚ and vibrational frecalculated bond distance 2.543 A quency 170 cm 1 are in agreement with previous theo˚ and 181 cm 1) retical study at MRSDCI level (2.574 A [26]. AuHg. The calculated dissociation energy 0.41 eV is much lower than its congeners AuZn (0.79 eV) and AuCd (0.75 eV). This suggests much weaker bonding for AuHg compared with AuZn and AuCd. Our calculated dissociation energy is in excellent agreement with previous theoretical studies at CCSD(T) level (0.40) [27], and at relativistic GGA level (0.49 eV) [28]. The calculated vibrational frequency 93 cm 1 is also close to previous study 103 cm 1 [27], and 99.63 cm 1 [28]. For the calculated bond distance, ˚ is slightly shorter than our calculated value 2.791 A ˚ ) [27] and at GGA lethose at CCSD(T) level (2.711 A ˚ vel (2.67 A) [28].

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Z.J. Wu / Chemical Physics Letters 406 (2005) 24–28

4. Conclusions The diatomics of gold with all the other transition metals are studied by use of density functional method B3LYP. The calculated results are compared with experimental data and previous theoretical studies. Our calculation shows that except AuLu, B3LYP tends to underestimate the dissociation energy. The vibrational frequency of AuM (M = 3d element) is larger than that of AuM (M = 4d, 5d element) by around 40 cm 1 or more. For AuM (M = Zn, Cd, Hg), low dissociation energy is found, especially for AuHg. In general, our calculated results are in reasonable agreement with experimental data and could be considered as a helpful guide for future experiments and advanced computations. The further studies may also help to determine the ground state in which electronic states are very close in energy.

Acknowledgement The author is grateful for the financial support from National Natural Science Foundation of China (Grant Nos. 20331030 and 20471059).

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