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Aromaticity of the Square As42− Dianion in the MAs4− (M=Li, Na, K, Rb, and Cs) and MAs4 (M=Be, Mg, Ca, Sr, and Ba) Clusters
Journal of Molecular Structure: THEOCHEM 731 (2005) 61–66 www.elsevier.com/locate/theochem
K Aromaticity of the Square As2K 4 Dianion in the MAs4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) Clusters
Wen Guo Xu*, Biao Jin School of Science, Beijing Institute of Technology, Beijing 100081, P. R. China Received 26 February 2005; revised 10 June 2005; accepted 27 June 2005 Available online 24 August 2005
Abstract Geometrical structures, electronic structures, and vibrational frequencies of alkali metal MAsK 4 (MZLi, Na, K, Rb, and Cs) clusters and alkali earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters were investigated with density functional theory (DFT) methods. Calculation K results show that the square As2K 4 dianion can coordinate with metal atoms to form the pyramidal MAs4 and MAs4 complexes maintaining the dianion structure. Structural and electronic criteria, the presence of six delocalized p electrons (satisfying the 4nC2 electron square As2K 4 and MAs clusters confirmed that the square planar counting rule), and maintaining its structural and electronic integrity inside the MAsK 4 4 As2K 4 dianion exhibits characteristics of p-aromaticity. q 2005 Elsevier B.V. All rights reserved. Keywords: As2K 4 dianion; Aromaticity; DFT calculation dianionAromaticityDFT calculation
1. Introduction The concept of aromaticity is one of the most significant concepts in modern chemistry. It is generally used to describe cyclic, planar, and conjugated molecules with 4nC 2p electrons. Despite the undeniable usefulness of the aromaticity concept, its physical origin is still being controversially debated [1,2]. The development of various criteria of aromaticity and theoretical investigations aimed at gaining a deeper insight into the origin of this phenomenon [3–5]. Today, this concept has been successfully extended from traditional organic molecules into pure all-metal clusters [6–9]. Arsenic is a group V elements, which is more likely to form homonuclear clusters than nitrogen. Elemental arsenic has been shown to have important effects on the molecular beam epitaxy (MBE) growth of GaAs and related films because of its convenient and easy use [10–14]. The tetrahedral As4 structure is the dominant form of elemental arsenic in the vapor phase, where each arsenic atom has three nearest neighbors with angle As–As–As 96.78. * Corresponding author. Fax: C86 10 6891 4780. E-mail address: [email protected] (W.G. Xu).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.06.043
Consequently, there have been a considerable number of experimental and theoretical studies on As4 [15–20]. In the last few years, the molecular structures, electron affinities, and dissociation energies of the Asn =AsK n (n%20) have been investigated in detail [21–22]. Up to now, little is known about the dianionic As2K clusters. The As2K 4 4 dianion is valent isoelectronic with C4 H2K 4 and presents an excellent opportunity to examine aromaticity in the inorganic species [23]. In the present article, a series of alkali metal MAsK 4 (MZ Li, Na, K, Rb, and Cs) and alkali earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters are theoretically investigated using DFT methods. We explored the aromaticity of square K As2K 4 dianion in the two kinds of MAs4 and MAs4 species. Molecular orbitals (MO) analysis, the natural bond orbital (NBO) analysis, and the nucleus-independent chemical shifts (NICS) are explored into the aromaticity of square 2K As2K 4 dianion. Our results show that inorganic As4 dianion exhibits characteristics of aromaticity having six delocalized p electrons with structural and magnetic criteria.
2. Computational methods All calculations were performed using the Gaussian 98 program package [24]. Equilibrium geometries and
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W.G. Xu, B. Jin / Journal of Molecular Structure: THEOCHEM 731 (2005) 61–66
˚ , bond angles in degrees) of As2K Fig. 1. Optimized geometries (bond lengths in A 4 dianion at the B3LYP/6-311CG* and B3PW91/6-311CG* (bold font) levels of theory. K vibrational frequencies of As2K 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZBe, Mg, Ca, Sr, and Ba) were fully optimized using the DFT methods. The DFT methods employed in the present work include B3PW91 (Becke’s three-parameter hybride functional and Perdew and Wang’s 1991 gradient-corrected correlation functional) and B3LYP (B3 and the non-local correlation of Lee, Yang, and Parr) [25–27]. The 6-311CG* basis set is a split-valence triplezeta plus polarization basis set augmented with diffuse K functions. For the RbAsK 4 , CsAs4 , SrAs4, and BaAs4 species, we optimized at the B3LYP and B3PW91 levels of theory, where the 6-311CG* basis set was used for arsenic and the LANL2DZ basis set was used for the heavier metals Rb (ZZ37), Cs (ZZ55), Sr (ZZ38), and Ba (ZZ56). Vibrational frequencies at the B3LYP and B3PW91 methods were calculated to characterize stationary points as minima (number of imaginary frequencies (NIMAGZ0)) or transition states (NIMAGZ1). Molecular orbitals (MO) for the most stable As2K 4 , the K pyramidal LiAsK 4 , CsAs4 , BeAs4, and BaAs4 species were calculated by the HF method with the corresponding basis set. All MO pictures were made using the MOLDEN 3.4 K program [28]. NICS values for the most stable As2K 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZBe, Mg, Ca, Sr, and Ba) species were calculated with the GIAO-HF// B3LYP method, where the 6-311CG* basis set was used
for As, Li, Na, K, Be, Mg, and Ca and the LANL2DZ basis set was used for Rb, Cs, Sr, and Ba. In addition to the structural and energetic investigations, natural population analysis was also presented using the natural bond orbital (NBO) [29–30].
3. Results and discussion The optimized geometric structures for As2K 4 dianion, alkali metal MAsK 4 (MZLi, Na, K, Rb, and Cs), and alkali earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters are illustrated in Figs. 1 and 2. Their total energies, zero-point energies (ZPE), relative energies (with ZPE corrections), and the number of imaginary frequencies of all species are summarized in Table 1. The calculated average bond ˚ ) and covalent radii (in A ˚ ) are listed in lengths (in A Table 2. The calculated NICS values are given in Table 3. K MOs pictures for the square As2K 4 , the pyramidal LiAs4 , K CsAs4 , BeAs4, and BaAs4 species are exhibited in Fig. 3. 3.1. Geometric structures We firstly performed DFT calculations on a wider of singlet structures of As2K 4 at the B3LYP/6-311CG* and B3PW91/6-311CG* levels of theory. Theoretical studies
˚ , bond angles in degrees) of MAsK Fig. 2. Optimized geometries (bond lengths in A 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters at the B3LYPand B3PW91 (bold font) methods.
W.G. Xu, B. Jin / Journal of Molecular Structure: THEOCHEM 731 (2005) 61–66
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Table 1 K Total energies (E),a Zero-Point energies (ZPE),b relative energies (RE),c and the number of imaginary frequencies (NImag)d for As2K 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZBe, Mg, Ca, Sr, and Ba) species Species
As2K 4
MAsK 4
MAs4
a b c d
B3LYP
1a, D4h 1b, C2v 1c, C2h 1d, C2v LiAsK 4 NaAsK 4 KAsK 4 K RbAs4 , CsAsK 4 BeAs4 MgAs4 CaAs4 SrAs4 BaAs4
2a,C4v 2b,C4v 2c,C4v 2d,C4v 2e,C4v 2f,C4v 2g,C4v 2h,C4v 2i,C4v 2j,C4v
B3PW91
Ea
ZPEb
REc
Ea
ZPEb
REc
K8943.566548 K8943.541075 K8943.53698 K8943.509737 K8951.235207 K9105.992077 K9543.628784 K8967.546885 K8963.557676 K8958.348539 K9143.700986 K9621.237167 K8951.235207 K9105.992077
1.82(0) 1.68(0) 1.41(0) 1.62(0) 3.37(0) 2.56(0) 2.38(0) 2.19(0) 2.13(0) 4.03(0) 2.89(0) 2.64(0) 3.37(0) 2.56(0)
0.0 16.0 18.6 35.7
K8943.472134 K8943.448258 K8943.434069 K8943.412957 K8951.13673 K9105.856812 K9543.481547 K8967.478883 K8963.493646 K8958.252574 K9143.566524 K9621.093255 K8951.13673 K9105.856812
1.90(0) 1.77(0) 1.46(0) 1.70(0) 3.49(0) 2.66(0) 2.49(0) 2.31(0) 2.26(0) 4.18(0) 3.02(0) 2.76(0) 3.49(0) 2.66(0)
0.0 15.0 23.9 37.1
Total energies in Hartree. Zero-point energies in kcal/mol. Relative energies with ZPE corrections in kcal/mol. The integers in parentheses are the number of imaginary frequencies (NImag).
Table 2 K ˚ ) (at the B3LYP method) and covalent radii (in A ˚ ) for the most stable As2K Calculated bond lengths (in A 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZ Be, Mg, Ca, Sr, and Ba) species Species
As2K 4
LiAsK 4
NaAsK 4
KAsK 4
RbAsK 4
CsAsK 4
BeAs4
MgAs4
CaAs4
SrAs4
BaAs4
As–As M–As The sum of covalent radii of metal and arsenic
2.419 – 2.40
2.429 2.543 2.42
2.433 2.911 2.77
2.426 3.279 3.22
2.428 3.551 3.36
2.427 3.772 3.55
2.463 2.464 2.09
2.469 2.619 2.57
2.434 2.919 2.94
2.450 3.207 3.11
2.441 3.382 3.08
on various As2K 4 dianions showed that the planar square structure, with D4h symmetry at the 1 A state, is the global minimum. For doubly charged As2K 4 species, we obtain four isomers, i.e. the square planar structure 1a, the roof structure 1b, the chain structure 1c, and the capped triangle structure 1d. All the four isomers of As2K 4 clusters with low spin are minima on the B3LYP/6-311CG* and B3PW91/6-311C G* potential energy surfaces with all real vibrational frequencies. As seen from Table 1, the energetic stability ordering of the four isomers is 1aO1bO1cO1d at the B3LYP/6-311CG* and B3PW91/6-311CG* levels of theory. Isomer 1a is energetically lower than 1b by 16.0 and 15.0 kcal/mol at the B3LYP/6-311CG* and B3PW91/ 6-311CG* levels of theory, respectively. The As–As bond ˚ length of the square planar As2K dianion is 2.419 A 4 ˚ (B3LYP/6-311CG*) and 2.396 A (B3PW91/6-311CG*), which conforms rather closely to the sum of covalent radii ˚ ). In 1966, Morino and co-workers of arsenic atom (2.40 A [15] reported a high-temperature gas phase electron diffraction (GED) study of arsenic vapor, and confirmed that gas-phase arsenic is tetrahedral As4 with an As–As ˚ . The equal bond lengths in bond distance of 2.435G0.004 A the square planar structure provide the structural criteria of
aromaticity. For structure 1a, all the Wiberg bond index (WBI) of bonds between adjacent As atoms is 1.245, which is between the standard values of single-bond (1.0) and double-bond (2.0). It indicates that the p electrons are delocalized in the square planar structure. As shown in Fig. 1, isomer 1b is the ‘roof’ structure with C2v symmetry, which is energetically lower than 1c by 2.6 Table 3 Calculated NICS Values (in ppm) with GIAO-HF//B3LYP Method for the K most stable As2K 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters Species
NICS(0.0)
NICS(0.5)
NICS(1.0)
As2K 4 , D4h LiAsK 4 , C4v NaAsK 4 , C4v KAsK 4 , C4v RbAsK 4 , C4v CsAsK 4 , C4v
K0.38 K3.59 1.95 2.18 2.83 1.45 K4.30 4.64 5.22 11.12 1.29
K0.05 K5.85 K0.64 K0.89 K0.83 K2.51 K0.67 K1.61 K6.43 K6.38 K17.71
K0.12 K10.42 K10.99 K3.38 K11.39 K12.11 K35.12 K36.63 K4.75 K13.09 K48.15
BeAs4, C4v MgAs4, C4v CaAs4, C4v SrAs4,C4v BaAs4, C4v
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K K Fig. 3. Molecular orbital pictures for the square As2K 4 (D4h) dianion, the pyramidal LiAs4 (C4v), BeAs4 (C4v), As4Cs (C4v), and As4Ba (C4v) clusters.
and 8.9 kcal/mol at the B3LYP/6-311CG* and B3PW91/ 6-311CG* levels of theory, respectively. The bond lengths ˚ at the of As1–As2 and As2–As3 are 2.516 and 2.403 A B3LYP/6-311CG* level of theory, respectively. The other structural parameters are a132Z61.58 and a134Z91.58 (B3LYP/6-311CG*). In terms of NBO analysis, all the WBI for the bonds between adjacent phosphorous atoms in structure 1b are close to 1.0, supporting the existence of the As-As s single bonds. The chain structure 1c with C2h symmetry is another genuine minimum, which is energetically lower than 1d by 17.1 and 13.3 kcal/mol at the B3LYP/6-311CG* and B3PW91/6-311CG* levels of theory, respectively. Due to its high energy, there will be no further discussion for isomer 1d.
Extensive searches were carried out for the metalpolyarsenic MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters at the B3LYP and B3PW91 methods. The square planar As2K 4 dianion can coordinate with alkali metal atoms and alkali earth metal atoms to form metal-polyarsenic MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) complexes that maintain the square planar As2K 4 dianion structure. The and MAs complexes possess the C4v square-pyramid MAsK 4 4 structure containing the metal cation interacting with a K square As2K 4 unit. We found that the pyramidal MAs4 and MAs4 complexes are local minima with all real frequencies at the B3LYP and B3PW91 methods. Fig. 2 show that the dianion preserves its square planar most stable As2K 4
W.G. Xu, B. Jin / Journal of Molecular Structure: THEOCHEM 731 (2005) 61–66
structural integrity in forming the square-pyramidal MAsK 4 and MAs4 complexes, suggesting the aromaticity of the square planar As2K 4 dianion with structural integrity criteria. ˚ [31]. As The covalent radius for arsenic atom is 1.20 A shown in Table 2, the As As bond lengths in the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) complexes are close to the sum of covalent ˚ ). The covalent radii for Li, Na, K, radii of arsenic (2.40 A Rb, Cs, Be, Mg, Ca, Sr, and Ba is 1.22, 1.57, 2.02, 2.16, ˚ , respectively [31]. 2.35, 0.89, 1.37, 1.74, 1.91, and 1.98 A The M-As bond lengths in the pyramidal MAsK 4 and MAs4 complexes are longer than the sum of covalent radii of the corresponding metal atoms and arsenic atom (shown in Table 2). 3.2. Natural population analysis Natural population analysis show that all positive charge mainly lies on the metal atoms and all negative charge populates on the arsenic atoms. The pyramidal MAsK 4 and MAs4 species can be regarded as complexes of the As2K 4 dianion with the metal cations. Bonding is due to electrostatic attraction effect between metal cations and As2K 4 dianion for the pyramidal MAs4 (MZBe, Mg, Ca, Sr, and Ba) structures: Q(Be)ZC1.20 e, Q(Mg)ZC1.39 e, Q(Ca)ZC1.49 e, Q(Sr)ZC1.62 e, and Q(Ba)ZC1.70 e (all are computed at the B3LYP method). Natural population analysis show that Q(Li)ZC0.77 e, Q(Na)ZC0.78 e, Q(K)ZC0.83 e, Q(Rb)ZC0.84 e, Q(Cs)ZC0.87 e for the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) complexes (all are computed at the B3LYP method). With the increasing of the atom number, the positive charges are mainly located over the metal atoms. In other hand, the WBI between the metal atom and arsenic atom in the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) complexes are 0.139, 0.105, 0.084, 0.077, and 0.064, respectively. The WBI between the metal atom and arsenic atom in the pyramidal MAs4 (MZBe, Mg, Ca, Sr, and Ba) are 0.336, 0.251, 0.236, 0.171, and 0.138, respectively. According to the NBO analysis, the calculated adjacent As-As WBI in the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) complexes are in the range of 1.14w1.22, which are between the standard values of single-bond (1.0) and double-bond (2.0), indicating the existence of delocalization. It might be stabilized as the square structure by the interaction of its p system with the metal cations. The metal cations will stabilize the square As2K dianion without changing its 4 geometrical structure. 3.3. Aromaticity of Square As2K 4 Dianion 3.3.1. Nucleus-independent chemical shifts (NICS) Aromaticity is often definable via magnetic criteria, such as NICS, which is based on the negative value of the magnetic shielding computed at or above the geometrical
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centers of rings or clusters. NICS is a simple and efficient aromaticity criterion in a wide range of molecules. Aromaticity is characterized by the negative NICS values (given in ppm), antiaromaticity by positive NICS values, and non-aromatic compound by NICS values close to zero [4,5]. In this study we first calculated NICS (0.0) at the GIAOHF//B3LYP method by placing a ghost atom at the geometric center of the arsenic four-membered ring. NICS (0.0) values for the square As2K 4 dianion is K0.38 ppm, suggesting the nonaromatic or weakly aromatic according to the yardstick of ˚ ). To further a 50% value of benzene (K7.8 at zZ0.0 A analyze the aromaticity, we also calculated NICS (0.5) and ˚ ) the geometric NICS (1.0) values above (by 0.5 and 1.0 A centers of the arsenic four-membered ring. The calculated results are also listed in Table 3. We found that the NICS (0.5) and NICS (1.0) values for the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) species are all negative, exhibiting aromatic character. As tabulated in Table 3, the NICS(0.5) value is intermediate between that of NICS (0.0) and NICS (1.0) for all species. In addition, NICS (0.0) values in the ring plane are influenced by the local contributions of the As–As s bonds and lone pairs. Therefore, as Schleyer et al. [5] reported, NICS (1.0) values are better suited for the interpretation of e-contributions and to answer the question whether the pyramidal MAsK 4 and MAs4 species are really aromatic. As shown in Table 3, the absolute NICS(1.0) values for all the pyramidal MAsK 4 and MAs4 species are larger than that of the isolated As2K 4 dianion. The introduction of counterions seems to result in an increase in aromaticity to some extent. It should be mentioned that the GIAO NICS seems to show that the As2K 4 dianion is not so aromatic. But considering it is a small-ring molecule, the NICS values based on the GIAO method may be greatly influenced by As–As s-bonds and lone pairs. Although we cannot say As2K 4 is more aromatic than benzene, it is surely aromatic. We believe that a similar situation K would happen for the As2K 4 rings in the MAs4 and MAs4 species; that is, they are aromatic. 3.3.2. Molecular orbital analysis In this section, we will explore the aromaticty of the K square planar As2K 4 dianion in the MAs4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters by MO analysis. Fig. 3 exhibits some the highest occupied K K MOs of the square As2K 4 , the pyramidal LiAs4 , CsAs4 , BeAs4, and BaAs4 species. As seen from the first line of Fig. 3, the highest occupied MO (HOMO, 1eg) of the most 1 stable As2K 4 (D4h, A) dianion includes two degenerated orbitals, formed from the out-of-plane p orbitals. The two degenerated HOMO (1eg) orbitals are delocalized p bonding MOs which render p aromaticity. The HOMO-1 (1eu) including two degenerated orbitals are formed from the in-plane p orbital and they are s-bonding MOs. Clearly the HOMO-2 (1a1g), which is formed from the outof-plane P orbitals of the four arsenic atoms, is delocalized p-bonding MO which renders p-aromaticity. The HOMO-3
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W.G. Xu, B. Jin / Journal of Molecular Structure: THEOCHEM 731 (2005) 61–66
(1a2u) forms from the s and in-plane p orbitals. The other MOs are formed primarily from the s and p orbitals. Among these occupied orbitals, the two degenerated HOMO (1eg) orbitals and the HOMO-2 (1a1g) are all delocalized p-bonding MOs, containing six p electrons. The six delocalized p electrons give the agreement with the 4nC2 electron counting rule. Molecular orbital analysis for the square As2K 4 dianion revealed interesting and delocalized p MOs. They contribute the property of the p-aromaticity for the As2K 4 dianion, due to the presence of six p electrons which follow the 4nC2 electron counting rule. Fig. 3 also shows the eight valence MOs for the C4v K LiAsK 4 , CsAs4 , BeAs4, and BaAs4 species (seen in the Fig. 3). The canonical MO ordering of the C4v LiAsK 4, CsAsK 4 , BeAs4, and BaAs4 species is different from that of K K the square As2K 4 dianion. In the C4v LiAs4 , CsAs4 , BeAs4, 2K and BaAs4 species, the MOs of the As4 dianion can be easily recognized. They only distort slightly by the presence of the metal cations, exhibiting the electronic integrity of the As2K 4 anion. We found that three similar delocalized p K orbitals are also present in the C4v LiAsK 4 , CsAs4 , BeAs4, and BaAs4 species, showing the electronic integrity of the As2K 4 dianion. Certainly, the presence of three delocalized p orbitals plays an important role in the stabilization of this metal-polyarsenic species. Furthermore, As2K 4 has a perfect planar square D4h structure, due to the delocalization of p electrons, exactly as expected for an aromatic system.
4. Conclusion In this paper, the equilibrium geometries, harmonic vibrational frequencies and electronic structure of the lowlying states of alkali metal MAsK 4 (MZLi, Na, K, Rb, and Cs) clusters and alkali earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters are discussed. Comprehensive calculations show that the planar square As2K 4 dianion can coordinate with metal atom to form the pyramidal MAsK 4 and MAs4 complexes maintaining the square As2K 4 dianion structure. Firstly, As2K 4 has a square planar structure, due to the delocalized of six p electrons. Second, the presence of six delocalized p electrons of the square As2K 4 dianion satisfies the 4nC2 electron counting rule, exhibiting characteristics of p-aromaticity for the As2K dianion. 4 Thirdly, NICS and WBI values suggest the property of aromaticity of the As2K 4 dianion. Finally, the integrity of structural and electronic of the As2K 4 dianion inside of alkali metal MAsK (MZLi, Na, K, Rb, and Cs) clusters and alkali 4 earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) species can be presented. Therefore, the square planar As2K 4 dianion exhibits characteristics of p-aromaticity and maintains its structural and electronic integrity inside of the pyramidal MAsK 4 and MAs4 complexes. These findings are significant for expanding the aromaticity concept into inorganic As2K 4 cluster.
References [1] P. Garratt, J. Aromaticity, Wiley: NewYork, 1986. [2] V. I. Minkin, M.N. Glukhovtsev, B.Y. Simkin, Aromaticity and antiaromaticity, Wiliey: New York, 1994. [3] S. Shaik, A. Shurki, D. Danovich, P.C. Hiberty, J. Mol. Struct. (Theochem.) 155 (1997) 398. [4] a)P. v.R. Schleyer, H. Jiao, Pure Appl. Chem. 68 (1996) 209; (b) P.v.R. Schleyer, C.Maerker, A.Dransfekd, H.Jiao, N.J.v. E.Hommes, J. Am. Chem. Soc. 118 (1996) 6317. [5] P. v.R. Schleyer, H. Jiao, N.J.R.v.E. Hommes, V.G. Malkin, O.L. Malkina, J. Am. Chem. Soc. 119 (1997) 12669. [6] X. Li, A.E. Kuznetsov, H.F. Zhang, A.I. Boldyrev, L.S. Wang, Science 291 (2001) 859. [7] A. E. Kuznetsov, L.S. Wang, J.D. Corbett, A.I. Boldyrev, Angew. Chem., Int. Ed. 40 (2001) 3369. [8] A.E. Kuznetsov, A.I. Boldyrev, X. Li, L.S. Wang, J. Am. Chem. Soc. 123 (2001) 8825. [9] A.E. Kuznetsov, K. Alexander, Birch, A.I. Boldyrev, X. Li, H.J. Zhai, L.S. Wang, Science 300 (2003) 622. [10] B.J. Wu, Y.J. Mii, M. Chen, K.L. Wang, J.J. Murray, J. Cryst. Growth 111 (1991) 252. [11] Y. Fukunishi, H. Nakatsuji, Surf. Sci. 316 (1994) 168. [12] K. Shiraishi, T. Ito, J. Cryst. Growth 150 (1995) 159. [13] R.W. Bernstein, A. Borg, H. Husby, B.-O. Fimland, J.K. Grepstad, Appl. Surf. Sci. 56 (1992) 74. [14] Y. Fukunishi, H. Nakatsuji, Surf. Sci. 291 (1993) 281. [15] Y. Morino, T. Ukaji, T. Ito, Bull. Chem. Soc. Jpn. 39 (1966) 64. [16] Y.M. Bosworth, R.J.H. Clark, D.M. Rippon, J. Mol. Spectrosc. 46 (1973) 240. [17] U. Meier, S.D. Peyerimhoff, F. Grein, Chem. Phys. 150 (1991) 331. [18] H. Zhang, K. Balasubramanian, J. Chem. Phys. 97 (1992) 3437. [19] G. Trinquier, J.P. Malrieu, J.P. Daudey, Chem. Phys. Lett. 80 (1981) 52. [20] A.A. Bonapasta, M.R. Bruni, A. Lapiccirella, P. Nota, G. Scavia, N. Tomassini, Surf. Sci. 204 (1988) 273. [21] M. Shen, H.F. Schaefer, J. Chem. Phys. 101 (1994) 2261. [22] Y. Zhao, W.G. Xu, Q.S. Li, Y.M. Xie, H.F. Schaefer, J. Comput. Chem. In Press. [23] A.E. Kuznetsov, H.J. Zhai, L.S. Wang, A.I. Boldyrev, Inorg. Chem. 41 (2002) 6062. [24] Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, Jr., J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.;Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P.M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J.A. Gaussian 98, Revision A.9; Gaussian, Inc., Pittsburgh PA, 1998. [25] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [26] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [27] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [28] G. Schaftenaar, MOLDEN 3.4, CAOS/CAMM Center, The Netherlands. 1998. [29] A.E. Reed, L.A. Curtiss, Weinhold, F. Chem. Rev. 88 (1988) 899. [30] A.E. Reed, R.B. Weinstock, F. Weinhold, J. Chem. Phys. 83 (1985) 735. [31] Periodic Table of Elements. Wiley-VCH: Weinheim, 1997.
K Aromaticity of the Square As2K 4 Dianion in the MAs4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) Clusters
Wen Guo Xu*, Biao Jin School of Science, Beijing Institute of Technology, Beijing 100081, P. R. China Received 26 February 2005; revised 10 June 2005; accepted 27 June 2005 Available online 24 August 2005
Abstract Geometrical structures, electronic structures, and vibrational frequencies of alkali metal MAsK 4 (MZLi, Na, K, Rb, and Cs) clusters and alkali earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters were investigated with density functional theory (DFT) methods. Calculation K results show that the square As2K 4 dianion can coordinate with metal atoms to form the pyramidal MAs4 and MAs4 complexes maintaining the dianion structure. Structural and electronic criteria, the presence of six delocalized p electrons (satisfying the 4nC2 electron square As2K 4 and MAs clusters confirmed that the square planar counting rule), and maintaining its structural and electronic integrity inside the MAsK 4 4 As2K 4 dianion exhibits characteristics of p-aromaticity. q 2005 Elsevier B.V. All rights reserved. Keywords: As2K 4 dianion; Aromaticity; DFT calculation dianionAromaticityDFT calculation
1. Introduction The concept of aromaticity is one of the most significant concepts in modern chemistry. It is generally used to describe cyclic, planar, and conjugated molecules with 4nC 2p electrons. Despite the undeniable usefulness of the aromaticity concept, its physical origin is still being controversially debated [1,2]. The development of various criteria of aromaticity and theoretical investigations aimed at gaining a deeper insight into the origin of this phenomenon [3–5]. Today, this concept has been successfully extended from traditional organic molecules into pure all-metal clusters [6–9]. Arsenic is a group V elements, which is more likely to form homonuclear clusters than nitrogen. Elemental arsenic has been shown to have important effects on the molecular beam epitaxy (MBE) growth of GaAs and related films because of its convenient and easy use [10–14]. The tetrahedral As4 structure is the dominant form of elemental arsenic in the vapor phase, where each arsenic atom has three nearest neighbors with angle As–As–As 96.78. * Corresponding author. Fax: C86 10 6891 4780. E-mail address: [email protected] (W.G. Xu).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.06.043
Consequently, there have been a considerable number of experimental and theoretical studies on As4 [15–20]. In the last few years, the molecular structures, electron affinities, and dissociation energies of the Asn =AsK n (n%20) have been investigated in detail [21–22]. Up to now, little is known about the dianionic As2K clusters. The As2K 4 4 dianion is valent isoelectronic with C4 H2K 4 and presents an excellent opportunity to examine aromaticity in the inorganic species [23]. In the present article, a series of alkali metal MAsK 4 (MZ Li, Na, K, Rb, and Cs) and alkali earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters are theoretically investigated using DFT methods. We explored the aromaticity of square K As2K 4 dianion in the two kinds of MAs4 and MAs4 species. Molecular orbitals (MO) analysis, the natural bond orbital (NBO) analysis, and the nucleus-independent chemical shifts (NICS) are explored into the aromaticity of square 2K As2K 4 dianion. Our results show that inorganic As4 dianion exhibits characteristics of aromaticity having six delocalized p electrons with structural and magnetic criteria.
2. Computational methods All calculations were performed using the Gaussian 98 program package [24]. Equilibrium geometries and
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W.G. Xu, B. Jin / Journal of Molecular Structure: THEOCHEM 731 (2005) 61–66
˚ , bond angles in degrees) of As2K Fig. 1. Optimized geometries (bond lengths in A 4 dianion at the B3LYP/6-311CG* and B3PW91/6-311CG* (bold font) levels of theory. K vibrational frequencies of As2K 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZBe, Mg, Ca, Sr, and Ba) were fully optimized using the DFT methods. The DFT methods employed in the present work include B3PW91 (Becke’s three-parameter hybride functional and Perdew and Wang’s 1991 gradient-corrected correlation functional) and B3LYP (B3 and the non-local correlation of Lee, Yang, and Parr) [25–27]. The 6-311CG* basis set is a split-valence triplezeta plus polarization basis set augmented with diffuse K functions. For the RbAsK 4 , CsAs4 , SrAs4, and BaAs4 species, we optimized at the B3LYP and B3PW91 levels of theory, where the 6-311CG* basis set was used for arsenic and the LANL2DZ basis set was used for the heavier metals Rb (ZZ37), Cs (ZZ55), Sr (ZZ38), and Ba (ZZ56). Vibrational frequencies at the B3LYP and B3PW91 methods were calculated to characterize stationary points as minima (number of imaginary frequencies (NIMAGZ0)) or transition states (NIMAGZ1). Molecular orbitals (MO) for the most stable As2K 4 , the K pyramidal LiAsK 4 , CsAs4 , BeAs4, and BaAs4 species were calculated by the HF method with the corresponding basis set. All MO pictures were made using the MOLDEN 3.4 K program [28]. NICS values for the most stable As2K 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZBe, Mg, Ca, Sr, and Ba) species were calculated with the GIAO-HF// B3LYP method, where the 6-311CG* basis set was used
for As, Li, Na, K, Be, Mg, and Ca and the LANL2DZ basis set was used for Rb, Cs, Sr, and Ba. In addition to the structural and energetic investigations, natural population analysis was also presented using the natural bond orbital (NBO) [29–30].
3. Results and discussion The optimized geometric structures for As2K 4 dianion, alkali metal MAsK 4 (MZLi, Na, K, Rb, and Cs), and alkali earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters are illustrated in Figs. 1 and 2. Their total energies, zero-point energies (ZPE), relative energies (with ZPE corrections), and the number of imaginary frequencies of all species are summarized in Table 1. The calculated average bond ˚ ) and covalent radii (in A ˚ ) are listed in lengths (in A Table 2. The calculated NICS values are given in Table 3. K MOs pictures for the square As2K 4 , the pyramidal LiAs4 , K CsAs4 , BeAs4, and BaAs4 species are exhibited in Fig. 3. 3.1. Geometric structures We firstly performed DFT calculations on a wider of singlet structures of As2K 4 at the B3LYP/6-311CG* and B3PW91/6-311CG* levels of theory. Theoretical studies
˚ , bond angles in degrees) of MAsK Fig. 2. Optimized geometries (bond lengths in A 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters at the B3LYPand B3PW91 (bold font) methods.
W.G. Xu, B. Jin / Journal of Molecular Structure: THEOCHEM 731 (2005) 61–66
63
Table 1 K Total energies (E),a Zero-Point energies (ZPE),b relative energies (RE),c and the number of imaginary frequencies (NImag)d for As2K 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZBe, Mg, Ca, Sr, and Ba) species Species
As2K 4
MAsK 4
MAs4
a b c d
B3LYP
1a, D4h 1b, C2v 1c, C2h 1d, C2v LiAsK 4 NaAsK 4 KAsK 4 K RbAs4 , CsAsK 4 BeAs4 MgAs4 CaAs4 SrAs4 BaAs4
2a,C4v 2b,C4v 2c,C4v 2d,C4v 2e,C4v 2f,C4v 2g,C4v 2h,C4v 2i,C4v 2j,C4v
B3PW91
Ea
ZPEb
REc
Ea
ZPEb
REc
K8943.566548 K8943.541075 K8943.53698 K8943.509737 K8951.235207 K9105.992077 K9543.628784 K8967.546885 K8963.557676 K8958.348539 K9143.700986 K9621.237167 K8951.235207 K9105.992077
1.82(0) 1.68(0) 1.41(0) 1.62(0) 3.37(0) 2.56(0) 2.38(0) 2.19(0) 2.13(0) 4.03(0) 2.89(0) 2.64(0) 3.37(0) 2.56(0)
0.0 16.0 18.6 35.7
K8943.472134 K8943.448258 K8943.434069 K8943.412957 K8951.13673 K9105.856812 K9543.481547 K8967.478883 K8963.493646 K8958.252574 K9143.566524 K9621.093255 K8951.13673 K9105.856812
1.90(0) 1.77(0) 1.46(0) 1.70(0) 3.49(0) 2.66(0) 2.49(0) 2.31(0) 2.26(0) 4.18(0) 3.02(0) 2.76(0) 3.49(0) 2.66(0)
0.0 15.0 23.9 37.1
Total energies in Hartree. Zero-point energies in kcal/mol. Relative energies with ZPE corrections in kcal/mol. The integers in parentheses are the number of imaginary frequencies (NImag).
Table 2 K ˚ ) (at the B3LYP method) and covalent radii (in A ˚ ) for the most stable As2K Calculated bond lengths (in A 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZ Be, Mg, Ca, Sr, and Ba) species Species
As2K 4
LiAsK 4
NaAsK 4
KAsK 4
RbAsK 4
CsAsK 4
BeAs4
MgAs4
CaAs4
SrAs4
BaAs4
As–As M–As The sum of covalent radii of metal and arsenic
2.419 – 2.40
2.429 2.543 2.42
2.433 2.911 2.77
2.426 3.279 3.22
2.428 3.551 3.36
2.427 3.772 3.55
2.463 2.464 2.09
2.469 2.619 2.57
2.434 2.919 2.94
2.450 3.207 3.11
2.441 3.382 3.08
on various As2K 4 dianions showed that the planar square structure, with D4h symmetry at the 1 A state, is the global minimum. For doubly charged As2K 4 species, we obtain four isomers, i.e. the square planar structure 1a, the roof structure 1b, the chain structure 1c, and the capped triangle structure 1d. All the four isomers of As2K 4 clusters with low spin are minima on the B3LYP/6-311CG* and B3PW91/6-311C G* potential energy surfaces with all real vibrational frequencies. As seen from Table 1, the energetic stability ordering of the four isomers is 1aO1bO1cO1d at the B3LYP/6-311CG* and B3PW91/6-311CG* levels of theory. Isomer 1a is energetically lower than 1b by 16.0 and 15.0 kcal/mol at the B3LYP/6-311CG* and B3PW91/ 6-311CG* levels of theory, respectively. The As–As bond ˚ length of the square planar As2K dianion is 2.419 A 4 ˚ (B3LYP/6-311CG*) and 2.396 A (B3PW91/6-311CG*), which conforms rather closely to the sum of covalent radii ˚ ). In 1966, Morino and co-workers of arsenic atom (2.40 A [15] reported a high-temperature gas phase electron diffraction (GED) study of arsenic vapor, and confirmed that gas-phase arsenic is tetrahedral As4 with an As–As ˚ . The equal bond lengths in bond distance of 2.435G0.004 A the square planar structure provide the structural criteria of
aromaticity. For structure 1a, all the Wiberg bond index (WBI) of bonds between adjacent As atoms is 1.245, which is between the standard values of single-bond (1.0) and double-bond (2.0). It indicates that the p electrons are delocalized in the square planar structure. As shown in Fig. 1, isomer 1b is the ‘roof’ structure with C2v symmetry, which is energetically lower than 1c by 2.6 Table 3 Calculated NICS Values (in ppm) with GIAO-HF//B3LYP Method for the K most stable As2K 4 , MAs4 (MZLi, Na, K, Rb, and Cs), and MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters Species
NICS(0.0)
NICS(0.5)
NICS(1.0)
As2K 4 , D4h LiAsK 4 , C4v NaAsK 4 , C4v KAsK 4 , C4v RbAsK 4 , C4v CsAsK 4 , C4v
K0.38 K3.59 1.95 2.18 2.83 1.45 K4.30 4.64 5.22 11.12 1.29
K0.05 K5.85 K0.64 K0.89 K0.83 K2.51 K0.67 K1.61 K6.43 K6.38 K17.71
K0.12 K10.42 K10.99 K3.38 K11.39 K12.11 K35.12 K36.63 K4.75 K13.09 K48.15
BeAs4, C4v MgAs4, C4v CaAs4, C4v SrAs4,C4v BaAs4, C4v
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K K Fig. 3. Molecular orbital pictures for the square As2K 4 (D4h) dianion, the pyramidal LiAs4 (C4v), BeAs4 (C4v), As4Cs (C4v), and As4Ba (C4v) clusters.
and 8.9 kcal/mol at the B3LYP/6-311CG* and B3PW91/ 6-311CG* levels of theory, respectively. The bond lengths ˚ at the of As1–As2 and As2–As3 are 2.516 and 2.403 A B3LYP/6-311CG* level of theory, respectively. The other structural parameters are a132Z61.58 and a134Z91.58 (B3LYP/6-311CG*). In terms of NBO analysis, all the WBI for the bonds between adjacent phosphorous atoms in structure 1b are close to 1.0, supporting the existence of the As-As s single bonds. The chain structure 1c with C2h symmetry is another genuine minimum, which is energetically lower than 1d by 17.1 and 13.3 kcal/mol at the B3LYP/6-311CG* and B3PW91/6-311CG* levels of theory, respectively. Due to its high energy, there will be no further discussion for isomer 1d.
Extensive searches were carried out for the metalpolyarsenic MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters at the B3LYP and B3PW91 methods. The square planar As2K 4 dianion can coordinate with alkali metal atoms and alkali earth metal atoms to form metal-polyarsenic MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) complexes that maintain the square planar As2K 4 dianion structure. The and MAs complexes possess the C4v square-pyramid MAsK 4 4 structure containing the metal cation interacting with a K square As2K 4 unit. We found that the pyramidal MAs4 and MAs4 complexes are local minima with all real frequencies at the B3LYP and B3PW91 methods. Fig. 2 show that the dianion preserves its square planar most stable As2K 4
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structural integrity in forming the square-pyramidal MAsK 4 and MAs4 complexes, suggesting the aromaticity of the square planar As2K 4 dianion with structural integrity criteria. ˚ [31]. As The covalent radius for arsenic atom is 1.20 A shown in Table 2, the As As bond lengths in the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) complexes are close to the sum of covalent ˚ ). The covalent radii for Li, Na, K, radii of arsenic (2.40 A Rb, Cs, Be, Mg, Ca, Sr, and Ba is 1.22, 1.57, 2.02, 2.16, ˚ , respectively [31]. 2.35, 0.89, 1.37, 1.74, 1.91, and 1.98 A The M-As bond lengths in the pyramidal MAsK 4 and MAs4 complexes are longer than the sum of covalent radii of the corresponding metal atoms and arsenic atom (shown in Table 2). 3.2. Natural population analysis Natural population analysis show that all positive charge mainly lies on the metal atoms and all negative charge populates on the arsenic atoms. The pyramidal MAsK 4 and MAs4 species can be regarded as complexes of the As2K 4 dianion with the metal cations. Bonding is due to electrostatic attraction effect between metal cations and As2K 4 dianion for the pyramidal MAs4 (MZBe, Mg, Ca, Sr, and Ba) structures: Q(Be)ZC1.20 e, Q(Mg)ZC1.39 e, Q(Ca)ZC1.49 e, Q(Sr)ZC1.62 e, and Q(Ba)ZC1.70 e (all are computed at the B3LYP method). Natural population analysis show that Q(Li)ZC0.77 e, Q(Na)ZC0.78 e, Q(K)ZC0.83 e, Q(Rb)ZC0.84 e, Q(Cs)ZC0.87 e for the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) complexes (all are computed at the B3LYP method). With the increasing of the atom number, the positive charges are mainly located over the metal atoms. In other hand, the WBI between the metal atom and arsenic atom in the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) complexes are 0.139, 0.105, 0.084, 0.077, and 0.064, respectively. The WBI between the metal atom and arsenic atom in the pyramidal MAs4 (MZBe, Mg, Ca, Sr, and Ba) are 0.336, 0.251, 0.236, 0.171, and 0.138, respectively. According to the NBO analysis, the calculated adjacent As-As WBI in the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) complexes are in the range of 1.14w1.22, which are between the standard values of single-bond (1.0) and double-bond (2.0), indicating the existence of delocalization. It might be stabilized as the square structure by the interaction of its p system with the metal cations. The metal cations will stabilize the square As2K dianion without changing its 4 geometrical structure. 3.3. Aromaticity of Square As2K 4 Dianion 3.3.1. Nucleus-independent chemical shifts (NICS) Aromaticity is often definable via magnetic criteria, such as NICS, which is based on the negative value of the magnetic shielding computed at or above the geometrical
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centers of rings or clusters. NICS is a simple and efficient aromaticity criterion in a wide range of molecules. Aromaticity is characterized by the negative NICS values (given in ppm), antiaromaticity by positive NICS values, and non-aromatic compound by NICS values close to zero [4,5]. In this study we first calculated NICS (0.0) at the GIAOHF//B3LYP method by placing a ghost atom at the geometric center of the arsenic four-membered ring. NICS (0.0) values for the square As2K 4 dianion is K0.38 ppm, suggesting the nonaromatic or weakly aromatic according to the yardstick of ˚ ). To further a 50% value of benzene (K7.8 at zZ0.0 A analyze the aromaticity, we also calculated NICS (0.5) and ˚ ) the geometric NICS (1.0) values above (by 0.5 and 1.0 A centers of the arsenic four-membered ring. The calculated results are also listed in Table 3. We found that the NICS (0.5) and NICS (1.0) values for the pyramidal MAsK 4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) species are all negative, exhibiting aromatic character. As tabulated in Table 3, the NICS(0.5) value is intermediate between that of NICS (0.0) and NICS (1.0) for all species. In addition, NICS (0.0) values in the ring plane are influenced by the local contributions of the As–As s bonds and lone pairs. Therefore, as Schleyer et al. [5] reported, NICS (1.0) values are better suited for the interpretation of e-contributions and to answer the question whether the pyramidal MAsK 4 and MAs4 species are really aromatic. As shown in Table 3, the absolute NICS(1.0) values for all the pyramidal MAsK 4 and MAs4 species are larger than that of the isolated As2K 4 dianion. The introduction of counterions seems to result in an increase in aromaticity to some extent. It should be mentioned that the GIAO NICS seems to show that the As2K 4 dianion is not so aromatic. But considering it is a small-ring molecule, the NICS values based on the GIAO method may be greatly influenced by As–As s-bonds and lone pairs. Although we cannot say As2K 4 is more aromatic than benzene, it is surely aromatic. We believe that a similar situation K would happen for the As2K 4 rings in the MAs4 and MAs4 species; that is, they are aromatic. 3.3.2. Molecular orbital analysis In this section, we will explore the aromaticty of the K square planar As2K 4 dianion in the MAs4 (MZLi, Na, K, Rb, and Cs) and MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters by MO analysis. Fig. 3 exhibits some the highest occupied K K MOs of the square As2K 4 , the pyramidal LiAs4 , CsAs4 , BeAs4, and BaAs4 species. As seen from the first line of Fig. 3, the highest occupied MO (HOMO, 1eg) of the most 1 stable As2K 4 (D4h, A) dianion includes two degenerated orbitals, formed from the out-of-plane p orbitals. The two degenerated HOMO (1eg) orbitals are delocalized p bonding MOs which render p aromaticity. The HOMO-1 (1eu) including two degenerated orbitals are formed from the in-plane p orbital and they are s-bonding MOs. Clearly the HOMO-2 (1a1g), which is formed from the outof-plane P orbitals of the four arsenic atoms, is delocalized p-bonding MO which renders p-aromaticity. The HOMO-3
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W.G. Xu, B. Jin / Journal of Molecular Structure: THEOCHEM 731 (2005) 61–66
(1a2u) forms from the s and in-plane p orbitals. The other MOs are formed primarily from the s and p orbitals. Among these occupied orbitals, the two degenerated HOMO (1eg) orbitals and the HOMO-2 (1a1g) are all delocalized p-bonding MOs, containing six p electrons. The six delocalized p electrons give the agreement with the 4nC2 electron counting rule. Molecular orbital analysis for the square As2K 4 dianion revealed interesting and delocalized p MOs. They contribute the property of the p-aromaticity for the As2K 4 dianion, due to the presence of six p electrons which follow the 4nC2 electron counting rule. Fig. 3 also shows the eight valence MOs for the C4v K LiAsK 4 , CsAs4 , BeAs4, and BaAs4 species (seen in the Fig. 3). The canonical MO ordering of the C4v LiAsK 4, CsAsK 4 , BeAs4, and BaAs4 species is different from that of K K the square As2K 4 dianion. In the C4v LiAs4 , CsAs4 , BeAs4, 2K and BaAs4 species, the MOs of the As4 dianion can be easily recognized. They only distort slightly by the presence of the metal cations, exhibiting the electronic integrity of the As2K 4 anion. We found that three similar delocalized p K orbitals are also present in the C4v LiAsK 4 , CsAs4 , BeAs4, and BaAs4 species, showing the electronic integrity of the As2K 4 dianion. Certainly, the presence of three delocalized p orbitals plays an important role in the stabilization of this metal-polyarsenic species. Furthermore, As2K 4 has a perfect planar square D4h structure, due to the delocalization of p electrons, exactly as expected for an aromatic system.
4. Conclusion In this paper, the equilibrium geometries, harmonic vibrational frequencies and electronic structure of the lowlying states of alkali metal MAsK 4 (MZLi, Na, K, Rb, and Cs) clusters and alkali earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) clusters are discussed. Comprehensive calculations show that the planar square As2K 4 dianion can coordinate with metal atom to form the pyramidal MAsK 4 and MAs4 complexes maintaining the square As2K 4 dianion structure. Firstly, As2K 4 has a square planar structure, due to the delocalized of six p electrons. Second, the presence of six delocalized p electrons of the square As2K 4 dianion satisfies the 4nC2 electron counting rule, exhibiting characteristics of p-aromaticity for the As2K dianion. 4 Thirdly, NICS and WBI values suggest the property of aromaticity of the As2K 4 dianion. Finally, the integrity of structural and electronic of the As2K 4 dianion inside of alkali metal MAsK (MZLi, Na, K, Rb, and Cs) clusters and alkali 4 earth metal MAs4 (MZBe, Mg, Ca, Sr, and Ba) species can be presented. Therefore, the square planar As2K 4 dianion exhibits characteristics of p-aromaticity and maintains its structural and electronic integrity inside of the pyramidal MAsK 4 and MAs4 complexes. These findings are significant for expanding the aromaticity concept into inorganic As2K 4 cluster.
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