- Email: [email protected]
Aromaticity of regular heptagonal P73- trianion in the MP72- (M = Li, Na, K, Rb, and Cs) species
Chemical Physics Letters 419 (2006) 439–443 www.elsevier.com/locate/cplett
2 Aromaticity of regular heptagonal P3 7 trianion in the MP7 (M = Li, Na, K, Rb, and Cs) species
Wen Guo Xu *, Biao Jin Institute of Chemical Physics, Beijing Institute of Technology, School of Science, No 5, Zhongguancun Nandajie, Haidian District, Beijing 100081, PR China Received 15 October 2005; in final form 11 November 2005 Available online 27 December 2005
Abstract 2 Geometries, electronic structures and vibrational frequencies of alkali metal–P3 7 compounds MP7 (M = Li, Na, K, Rb, and Cs) were examined using density functional theory (DFT) methods. To our knowledge, these compounds are first reported here. Calculation 2 results show that regular heptagonal P3 7 trianion can coordinate with alkali metal atoms to form the pyramidal structures MP7 species that maintain the planar cyclo-P3 trianion structure. On the basis of the molecular orbital (MO) analysis and nucleus-independent 7 chemical shifts (NICS) analysis, we revealed that regular heptagonal P3 7 trianion exhibits characteristic of p aromaticity with 10 delocalized p electrons and maintains its structural and electronic integrity inside the pyramidal MP2 7 (M = Li, Na, K, Rb, and Cs) clusters. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction ÔAromaticityÕ, one of the most used terms in modern organic chemistry, describes cyclic, planar, and conjugated molecules with 4n + 2p electrons [1]. The concept of aromaticity and anti aromaticity has been successfully extended from traditional organic molecules into pure allmetal [2–8] and inorganic system [9,10]. Li and co-workers [2] presented evidence of aromaticity for MAl 4 (M = Li, Na, and Cu) purely metallic systems. The Al2 4 dianion in a series of bimetallic clusters was found to have two delocalized p electrons conforming to the 4n + 2 electron counting rule for aromaticity. Boldyrev and Wang [8] reported the experimental and theoretical characterization of antiaromaticity in an all-metal system Li3 Al 4 . Molecular orbital analysis revealed that the rectangular Al4 4 tetraanion has four p electrons, consistent with the 4n Hu¨ckel rule for antiaromaticity. In addition, Boldyrev and Wang [10] also investigated theoretical and experimental evidence that the tetrapnictogen dianions in Naþ Pn2 (Pn = P, As, Sb) 4 *
Corresponding author. Fax: +86 10 6891 4780. E-mail addresses: [email protected] (W.G. Xu), [email protected] (B. Jin). 0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.11.119
undergo a transition from being aromatic to antiaromatic upon electron detachment, yielding the first inorganic antiaromatic Naþ Pn 4 molecules. In recent years, theoretical studies of phosphorus clusters are of considerable interest because of a large variety of the form of clusters. Phosphorus clusters included neutral Pn (n = 2–11 [11–13], 18 [14], 20 [15]) clusters, anionic P (n = 2–11) [16] clusters, and cationic Pþ (n = 5, n n 7, 9, 25, 33, 41, 89) [17,18] clusters, as well as multiply charged phosphorus clusters, such as P2 [12,19], P3 4 7 2 2 3 [20], P8 [16], P10 [12], and P11 [12]. A remarkable amount of theoretical studies on phosphorus clusters have been carried out by Jones and co-workers [11–13,16,20]. They investigated some neutral, anionic and cationic clusters up to n = 11 with the density functional method combined with a simulated annealing technique. In addition, Jones et. al. [20] have performed molecular dynamics (MD) simulations to determine the stability of the cage like structure of the P3 and P4S3. However, theoretical investigations on 7 the planar regular heptagonal P3 7 trianion are few. 2 In the present Letter, a series of alkali metal–P3 7 MP7 (M = Li, Na, K, Rb, and Cs) species are theoretically investigated using DFT methods. We explored the aromaticity of regular heptagonal P3 trianion in the MP2 species. 7 7
440
W.G. Xu, B. Jin / Chemical Physics Letters 419 (2006) 439–443
Molecular orbitals (MO) analysis and the nucleus-independent chemical shifts (NICS) analysis are provided insight into the aromaticity of planar P3 trianion. Our results 7 show that inorganic P3 7 trianion exhibits characteristic of aromaticity having 10 delocalized p electrons with structural and magnetic criteria. 2. Computational methods All calculations were performed using the GAUSSIAN 98 program package [21]. Equilibrium geometries and vibrational frequencies of P3 and MP2 (M = Li, Na, K, Rb, 7 7 and Cs) species were fully optimized using the DFT methods. The DFT methods employed in the present work include B3PW91 (BeckeÕs three-parameter hybride functional and Perdew and WangÕs 1991 gradient-corrected correlation functional) and B3LYP (B3 and the non-local correlation of Lee, Yang, and Parr) [22–24]. The 6-311+G* is a split-valence triple-zeta plus polarization basis set augmented with diffuse functions [25]. For the 2 2 2 P3 species, we calculated its 7 , LiP7 , NaP7 , and KP7 vibrational frequencies with the 6-311+G* basis set. The RbP2 and CsP2 model systems were optimized at the 7 7 B3LYP and B3PW91 methods, where the 6-311+G* basis set was used for phosphorus and the SDD basis set was used for the heavier metals Rb and Cs. Stationary points were characterized as minima without any imaginary vibrational frequency and a first-order saddle point with only one imaginary vibrational frequency. 2 2 2 NICSs for P3 7 , LiP7 , NaP7 , and KP7 species were calculated with the GIAO-HF/6-311+G*//B3LYP/6-311+G* method. NICSs for RbP2 and CsP2 7 7 were evaluated by using the GIAO-HF//B3LYP method, where the 6-311+ G* basis set was used for phosphorus and the SDD basis set was used for the heavier metals Rb and Cs. Molecular 2 2 2 orbitals (MOs) of P3 7 , LiP7 , NaP7 , and KP7 were calculated at the RHF/6-311+G* level of theory. MOs of RbP2 7 and CsP2 were calculated at the RHF level of theroy, 7 where the 6-311+G* basis set was used for phosphorus and the SDD basis set was used for the heavier metals Rb and Cs. Since MOs of all similar structural MP2 7 species are almost identical, herein we only display the MOs of LiP2 7 . All MO diagrams were made using the MOLDEN 3.7 program [26]. The natural bond orbital (NBO) [27,28] analysis is also performed to provide insight into the bonding nature and aromaticity of these species. 3. Results and discussion The optimized geometric structures of P3 and MP2 7 7 (M = Li, Na, K, Rb, and Cs) species were illustrated in Fig. 1. Total energies, ZPE, and the number of imaginary frequencies of all species are summarized in Table 1. The ˚ ) and covalent radii calculated average bond lengths (in A ˚ (in A) are listed in Table 2. The calculated NICS values 2 are given in Table 3. MOs pictures for P3 7 and LiP7 are exhibited in Figs. 2 and 3, respectively.
3.1. Geometric structures trianions at the Theoretical studies on various P3 7 B3LYP/6-11+G* and B3PW91/6-311+G* levels of theory showed that the planar regular heptagonal structure with D7h symmetry is the local minimum. We performed DFT methods on a wide variety of metal-polyphosphorus clusters and found that all the ground-state MP2 7 geometries are local minima with all real frequencies at the B3LYP and B3PW91 levels of theory. The planar regular heptagonal P3 7 trianion can coordinate with alkali metal atoms to form the C7v pyramidal structures MP2 7 species that maintain the planar cyclo-P3 7 trianion structure. The P–P bond lengths of regular heptagonal P3 7 trian˚ (B3LYP/6-11+G*) between the double ion are all 2.162 A ˚ ) and the single bond bond length of HP@PH (2.043 A ˚ length of H2PPH2 (2.230 A). The bond lengths in regular heptagonal structure provide the structural criteria of aromaticity. As shown in Fig. 1, the P–P bond lengths (2.162, ˚ ) in the pyramidal (C7v) 2.166, 2.163, 2.168, and 2.166 A 2 2 2 2 LiP7 , NaP7 , KP7 , RbP7 , and CsP2 structures are 7 ˚ ) of covalent radii of much shorter than the sum (2.20 A ˚ ) in reguphosphorus and close to the P–P length (2.162 A 3 lar heptagonal P7 structure. The P–P bond lengths in the pyramidal (C7v) MP2 7 structures indicate the existence of delocalization. The M–P bond lengths in the pyramidal 2 2 2 2 (C7v) LiP2 structures 7 , NaP7 , KP7 , RbP7 , and CsP7 are much longer than the sum of covalent radii of the corresponding metal atoms and phosphorus atom (shown in Table 2), indicating that the portion of covalent bonds is relatively few. The covalent radii for the metal atoms and phosphorus atom were assumed to be 1.22, 1.57, 2.02, ˚ for Li, Na, K, Rb, Cs, and P, respec2.16, 2.35, and 1.10 A tively [29]. Fig. 1 shows that the P3 7 trianion preserves its planar seven-membered ring structural integrity in forming the MP2 7 (M = Li, Na, K, Rb, and Cs) species. The geometric integrity of the P3 7 trianion is easily recognizable. Furthermore, the bond lengths of the seven-membered ring are identical, suggesting the aromaticity of the regular heptagonal P3 7 trianion with structural criteria. 3.2. Natural population analysis In terms of natural population analysis, all positive charge mainly lies on the metal atoms and all negative charge populates on the phosphorus atoms. The MP2 7 clusters can be regarded as complexes of the P3 7 trianion with the metal cations. Bonding is due to electrostatic attraction effect between alkali metals and P3 7 : Q(Li) = 2 +0.82e ðLiP2 Þ, Q(Na) = +0.87e ðNaP Þ, Q(K) = +0.86e 7 7 2 ðKP2 Þ, Q(Rb) = +0.92e ðRbP Þ, and Q(Cs) = +0.92e 7 7 ðCsP2 Þ (all are computed at the B3LYP/6-11+G*). With 7 the increasing of the atom number, the positive charges are mainly located over the alkali metal atoms. In addtion, the Wiberg bond index (WBI) between the metal atom and 2 2 2 phosphorus atom in the LiP2 7 , NaP7 , KP7 , RbP7 , and
W.G. Xu, B. Jin / Chemical Physics Letters 419 (2006) 439–443
441
˚ )) for P3 , LiP2 , NaP2 , KP2 , RbP2 , and CsP2 species at the B3LYP and B3PW91 (bold font) levels Fig. 1. Optimized geometries (bond lengths in (A 7 7 7 7 7 7 of theory.
Table 1 Total energies (E),a zero-point energies (ZPE),b and the number of 2 2 2 2 imaginary frequencies (NImag) for P3 7 , LiP7 , NaP7 , KP7 , RbP7 , and c CsP2 species 7 Species P3 7 , D7h LiP2 7 , C7v NaP2 7 , C7v KP2 7 , C7v RbP2 7 , C7v CsP2 7 , C7v
B3LYP
MP2
Ea
ZPEb
Ea
ZPEb
2389.483369 2397.252687 2552.015211 2989.654663 2413.804467 2409.853857
6.05(0) 7.22(0) 6.88(0) 6.82(0) 6.55(0) 6.52(0)
2389.135516 2396.903020 2551.628231 2989.254745 2413.481605 2409.538334
6.28(0) 7.57(0) 7.17(0) 7.09(0) 6.83(0) 6.80(0)
Table 2 ˚ ) at the B3LYP method and covalent radii Calculated bond lengths (in A ˚ ) for P3 , LiP2 , NaP2 , KP2 , RbP2 , and CsP2 species (in A 7 7 7 7 7 7 Species
P3 7
LiP2 7
NaP2 7
KP2 7
RbP2 7
CsP2 7
P–DP M–DP The sum of covalent radii of metal atom and phosphorus
2.162 – –
2.162 2.602 2.32
2.166 2.912 2.67
2.163 3.238 3.12
2.168 3.520 3.26
2.166 3.696 3.45
a
Total energies in Hartree. Zero-point energies in kcal/mol. c The integers in parentheses are the number of imaginary frequencies (Nimag). b
Table 3 Calculated NICS values (in ppm) at the GIAO-HF//B3LYP method for 2 2 2 2 2 the P3 7 , LiP7 , NaP7 , KP7 , RbP7 , and CsP7 species Species a
CsP2 7 are 0.050, 0.054, 0.040, 0.022, and 0.024, respectively. The very high ionic character in the chemical bonds of these clusters is obvious. The P3 7 trianion might be stabilized as the planar seven-membered ring by the interaction of its p system with the alkali metal atoms. However, the alkali metal cations have strong influences on the electronic structure of the P3 7 trianion for the heavier metal atoms.
NICS (0.0) NICS (0.5)b NICS(1.0) NICS (1.5) NICS(2.0)
P3 7
LiP2 7
NaP2 7
KP2 7
RbP2 7
CsP2 7
12.20 11.66 10.15 8.07 6.00
5.06 6.30 6.72 5.80 4.59
7.19 6.50 6.40 5.91 4.82
8.75 8.49 8.14 6.89 5.12
9.93 9.39 8.56 6.86 4.93
11.51 10.54 9.19 7.21 5.17
a NICS (0.0) Calculated NICS values at the center of the seven-membered ring. b ˚ )) the center of the NICS (0.5) Calculated NICS values above (by 0.5 (A seven-membered ring.
442
W.G. Xu, B. Jin / Chemical Physics Letters 419 (2006) 439–443
Fig. 2. Molecular orbital pictures for P3 7 (D7h) trianion.
Fig. 3. Molecular orbital pictures for LiP2 7 (C7v) species.
3.3. Aromaticity of regular heptagonal P3 7 trianion 3.3.1. Nucleus-independent chemical shifts (NICS) Aromaticity is often discussed in term of various criteria such as energetic, magnetic, and geometric [30–34]. NICS (nucleus-independent chemical shift), proposed by Schleyer and co-workers [32], is based on magnetic shieldings, which have long been calculated by simple methods, and now can be computed with modern ab initio technique. NICS are computed at selected points inside or around molecules, typically at ring centers and above. Aromaticity is characterized by negative NICS values, antiaromaticity by positive NICS, and nonaromatic compounds by values close to zero. In this study we firstly calculated NICS (0.0) at the geometrical centers of the planar seven-membered ring, which provide a direct measure of the ring current effects. The calculated results are listed in Table 3. For the planar sevenmembered ring P3 structure, the NICS value of 12.20 7 ppm computed at the center of the seven-membered ring suggests that this trianionic P3 7 unit is aromatic. NICS values of the other five species are all negative and smaller than that of the P3 7 unit. In order to further analyze the aromaticity, we calculated the NICS (0.5), NICS (1.0), NICS (1.5), and NICS (2.0) values by placing a ghost atom ˚ ) the center of the seven-memabove (by 0.5, 1.0, 1.5, 2.0 A bered ring, respectively. NICS (0.5), NICS (1.0), NICS 2 2 (1.5), and NICS (2.0) for the LiP2 7 , NaP7 , KP7 , 2 2 RbP7 , and CsP7 species are all negative, supporting the existence of delocalization and aromaticity of the P3 7 trianion in these five species. We found that NICS (0.0), NICS
(0.5), NICS (1.0), NICS (1.5), and NICS (2.0) values for the MP2 7 (M = Li, Na, K, Rb, and Cs) species increase with increasing atomic number of the metal, indicating the 2 2 increasing of the aromaticity of LiP2 7 , NaP7 , KP7 , 2 2 RbP7 , and CsP7 species. According to the NBO analysis, the calculated adjacent P–P WBI in the seven-membered 2 ring for P3 species are in the range of 1.1–1.3, 7 , MP7 which are between the standard values of single-bond (1.0) and double-bond (2.0), indicating the existence of delocalization. 3.3.2. Molecular orbital analysis To explore the aromaticity of the planar regular heptagonal P3 trianion, MOs pictures which are relevant 7 HOMOs were exhibited in Figs 2 and 3. As shown in Fig. 2, the highest occupied MO (HOMO) of the planar P3 (D7h) trianion includes two degenerated orbitals, 7 formed from the out-of-plane p orbitals. The two degenerated HOMO orbitals are delocalized p bonding MOs which render p aromaticity. The HOMO-1 including two degenerated orbitals are formed from the in-plane p orbital and they are r-bonding MOs. The HOMO-2 also includes two degenerated orbitals and formes from out-of-plane p orbitals. Clearly the HOMO-4 which is formed from the out-of-plane p orbitals of the seven phosphorus atoms, is delocalized p-bonding MO which renders p-aromaticity. The other MOs are formed primarily from the s and p orbitals. Among these occupied orbitals, the two degenerated HOMO orbitals, the two degenerated HOMO-2 orbitals, and the HOMO-4 are all delocalized p-bonding MO, containing 10 p electrons. The 10 delocalized p electrons give
W.G. Xu, B. Jin / Chemical Physics Letters 419 (2006) 439–443
the agreement with the 4n + 2 p electron counting rule. Molecular orbital analysis for P3 7 trianion revealed interesting and delocalized p MOs. They contribute the property of the p-aromaticity for the P3 7 trianion, due to the presence of 10 p electrons which follow the 4n + 2 electron counting rule. Fig. 3 also shows the 10 valence MOs for the C7v LiP2 7 specie. The canonical MO ordering of LiP2 7 (C7v) is differ2 ent from that of P3 7 trianion. In the C7v LiP7 species, the 3 MOs of the P7 trianion can be easily recognized. They only distort slightly by the presence of the metal cation, exhibiting the electronic integrity of the P3 7 trianion. We found that three similar delocalized p orbitals are also present in the C7v LiP2 7 species, showing the electronic integrity of the P3 anion. Certainly, the presence of three 7 delocalized p orbitals plays an important role in the stabilization of this metal-polyphosphorus species. Furthermore, P3 7 has a perfect planar pentagonal D7h structure, due to the delocalization of p electrons, exactly as expected for an aromatic system. 4. Conclusion In this Letter, the equilibrium geometries, harmonic vibrational frequencies of the low-lying states of alkali 2 metal-P3 (M = Li, Na, K, Rb, and Cs) clusters are 7 MP7 discussed for the first time. Comprehensive calculations show that the planar P3 trianion can coordinate with 7 one metal atom to form the pyramidal MP2 species. 7 Firstly, the presence of 10 delocalized p electrons of P3 7 trianion satisfies the 4n + 2 electron counting rule, exhibiting characteristics of p -aromaticity for the P3 7 trianion. Second, P3 has a planar seven-membered ring structure, 7 due to the delocalized of p electrons. Thirdly, NICSs and WBI suggest the property of aromaticity of the P3 7 anion. Finally, the integrity of structural and electronic of the P3 7 trianion inside of the MP2 species can be presented. 7 Therefore, the planar cyclic P3 7 trianion exhibits characteristic of p aromaticity and maintains its structural and electronic integrity inside of the MP2 7 species. These findings are significant for expanding the aromaticity concept into inorganic P3 7 cluster. References [1] P.J. Garratt, Aromaticity, Wiley, NewYork, 1986. [2] X. Li, A.E. Kuznetsov, H.F. Zhang, A.I. Boldyrev, L.S. Wang, Science 291 (2001) 859. [3] A.E. Kuznetsov, A.I. Boldyrev, X. Li, L.S. Wang, J. Am. Chem. Soc. 123 (2001) 8825.
443
[4] X. Li, H.F. Zhang, L.S. Wang, A.E. Kuznetsov, N.A. Cannon, A.I. Boldyrev, Angew. Chem., Int. Ed. 40 (2001) 1867. [5] A.E. Kuznetsov, L.S. Wang, J.D. Corbett, A.I. Boldyrev, Angew. Chem., Int. Ed. 40 (2001) 3369. [6] A.E. Kuznetsov, A.I. Boldyrev, H.J. Zhai, X. Li, L.S. Wang, J. Am. Chem. Soc. 124 (2002) 11791. [7] X. Li, L.S. Wang, A.I. Boldyrev, J. Simons, J. Am. Chem. Soc. 121 (1999) 6033. [8] A.E. Kuznetsov, K. Alexander Birch, A.I. Boldyrev, X. Li, H.J. Zhai, L.S. Wang, Science 300 (2003) 622. [9] A.N. Alexandrova, A.I. Boldyrev, H.J. Zhai, L.S. Wang, J. Chem. Phys. 122 (2005) 054313. [10] A.E. Kuznetsov, H.J. Zhai, L.S. Wang, A.I. Boldyrev, Inorg. Chem. 41 (2002) 6062. [11] R.O. Jones, D. Hohl, J. Chem. Phys. 92 (1990) 6710. [12] R.O. Jones, G. Seifert, J. Chem. Phys. 96 (1992) 7564. [13] P. Ballone, R.O. Jones, J. Chem. Phys. 100 (1994) 4941. [14] M. Ha¨ser, O. Treutler, J. Chem. Phys. 102 (1995) 3703. [15] B. Song, P.L. Cao, Phys. Lett. A 291 (2001) 343. [16] R.O. Jones, G. Gantefo¨r, S. Hunsicker, P. Pieperhoff, J. Chem. Phys. 103 (1995) 9549. [17] M.D. Chen, J.T. Li, R.B. Huang, L.S. Zheng, C.T. Au, Chem. Phys. Lett. 305 (1999) 439. [18] M.D. Chen, R.B. Huang, L.S. Zheng, Q.E. Zhang, C.T. Au, Chem. Phys. Lett. 325 (2000) 22. [19] Q. Jin, B. Jin, W.G. Xu, Chem. Phys. Lett. 396 (2004) 398. [20] G. Seifert, R.O. Jones, J. Chem. Phys. 96 (1992) 2951. [21] M.J. Frisch et al. GAUSSIAN 98, Revision A.9; Gaussian, Inc., Pittsburgh PA, 1998. [22] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [23] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [24] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [25] W.J. Hehre, L. Radom, P.v.R. Schleyer, J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986. [26] G. Schaftenaar, MOLDEN 3.7, CAOS/CAMM Center: The Netherlands, 1998. [27] J.E. Carpenter, F. Weinhold, J. Mol. Struct. (Theochem) 169 (1988) 41. [28] A.E. Reed, R.B. Weinstock, F. Weinhold, J. Chem. Phys. 83 (1985) 735. [29] Periodic Table of Elements. Wiley-VCH: Weinheim, 1997. [30] P.v.R. Schleyer, G. Subramanian, H. Jiao, K. Najafian, M. Hofmann, in: W. Siebert (Ed.), Advances in Boron Chemistry, Royal Society of Chemistry, Cambridge, 1997, pp. 1–14. [31] (a) P.v.R. Schleyer, K. Najafian, Are polyhedral boranes, carboranes, and carbocations aromatic? in: J. Casanova (Ed.), The Borane, Carborane, Carbocation Continuum, Wiley, New York, 1998, pp. 169–190; (b) P.v.R. Schleyer, K. Najafian, Inorg. Chem. 37 (1998) 3454. [32] (a) M. Hofmann, P.v.R. Schleyer, Inorg. Chem. 38 (1999) 652; (b) M. Unverzagt, H.J. Winkler, M. Brock, M. Hofmann, P.v.R. Schleyer, W. Massa, A. Berndt, Angew. Chem., Int. Ed. Engl. 36 (1997) 853; (c) 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. [33] A. Pasquarello, M. Schlu¨ter, R.C. Haddon, Science 257 (1992) 1660. [34] P.v.R. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N.J.R.v.E. Hommes, J. Am. Chem. Soc. 118 (1996) 6317.
2 Aromaticity of regular heptagonal P3 7 trianion in the MP7 (M = Li, Na, K, Rb, and Cs) species
Wen Guo Xu *, Biao Jin Institute of Chemical Physics, Beijing Institute of Technology, School of Science, No 5, Zhongguancun Nandajie, Haidian District, Beijing 100081, PR China Received 15 October 2005; in final form 11 November 2005 Available online 27 December 2005
Abstract 2 Geometries, electronic structures and vibrational frequencies of alkali metal–P3 7 compounds MP7 (M = Li, Na, K, Rb, and Cs) were examined using density functional theory (DFT) methods. To our knowledge, these compounds are first reported here. Calculation 2 results show that regular heptagonal P3 7 trianion can coordinate with alkali metal atoms to form the pyramidal structures MP7 species that maintain the planar cyclo-P3 trianion structure. On the basis of the molecular orbital (MO) analysis and nucleus-independent 7 chemical shifts (NICS) analysis, we revealed that regular heptagonal P3 7 trianion exhibits characteristic of p aromaticity with 10 delocalized p electrons and maintains its structural and electronic integrity inside the pyramidal MP2 7 (M = Li, Na, K, Rb, and Cs) clusters. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction ÔAromaticityÕ, one of the most used terms in modern organic chemistry, describes cyclic, planar, and conjugated molecules with 4n + 2p electrons [1]. The concept of aromaticity and anti aromaticity has been successfully extended from traditional organic molecules into pure allmetal [2–8] and inorganic system [9,10]. Li and co-workers [2] presented evidence of aromaticity for MAl 4 (M = Li, Na, and Cu) purely metallic systems. The Al2 4 dianion in a series of bimetallic clusters was found to have two delocalized p electrons conforming to the 4n + 2 electron counting rule for aromaticity. Boldyrev and Wang [8] reported the experimental and theoretical characterization of antiaromaticity in an all-metal system Li3 Al 4 . Molecular orbital analysis revealed that the rectangular Al4 4 tetraanion has four p electrons, consistent with the 4n Hu¨ckel rule for antiaromaticity. In addition, Boldyrev and Wang [10] also investigated theoretical and experimental evidence that the tetrapnictogen dianions in Naþ Pn2 (Pn = P, As, Sb) 4 *
Corresponding author. Fax: +86 10 6891 4780. E-mail addresses: [email protected] (W.G. Xu), [email protected] (B. Jin). 0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.11.119
undergo a transition from being aromatic to antiaromatic upon electron detachment, yielding the first inorganic antiaromatic Naþ Pn 4 molecules. In recent years, theoretical studies of phosphorus clusters are of considerable interest because of a large variety of the form of clusters. Phosphorus clusters included neutral Pn (n = 2–11 [11–13], 18 [14], 20 [15]) clusters, anionic P (n = 2–11) [16] clusters, and cationic Pþ (n = 5, n n 7, 9, 25, 33, 41, 89) [17,18] clusters, as well as multiply charged phosphorus clusters, such as P2 [12,19], P3 4 7 2 2 3 [20], P8 [16], P10 [12], and P11 [12]. A remarkable amount of theoretical studies on phosphorus clusters have been carried out by Jones and co-workers [11–13,16,20]. They investigated some neutral, anionic and cationic clusters up to n = 11 with the density functional method combined with a simulated annealing technique. In addition, Jones et. al. [20] have performed molecular dynamics (MD) simulations to determine the stability of the cage like structure of the P3 and P4S3. However, theoretical investigations on 7 the planar regular heptagonal P3 7 trianion are few. 2 In the present Letter, a series of alkali metal–P3 7 MP7 (M = Li, Na, K, Rb, and Cs) species are theoretically investigated using DFT methods. We explored the aromaticity of regular heptagonal P3 trianion in the MP2 species. 7 7
440
W.G. Xu, B. Jin / Chemical Physics Letters 419 (2006) 439–443
Molecular orbitals (MO) analysis and the nucleus-independent chemical shifts (NICS) analysis are provided insight into the aromaticity of planar P3 trianion. Our results 7 show that inorganic P3 7 trianion exhibits characteristic of aromaticity having 10 delocalized p electrons with structural and magnetic criteria. 2. Computational methods All calculations were performed using the GAUSSIAN 98 program package [21]. Equilibrium geometries and vibrational frequencies of P3 and MP2 (M = Li, Na, K, Rb, 7 7 and Cs) species were fully optimized using the DFT methods. The DFT methods employed in the present work include B3PW91 (BeckeÕs three-parameter hybride functional and Perdew and WangÕs 1991 gradient-corrected correlation functional) and B3LYP (B3 and the non-local correlation of Lee, Yang, and Parr) [22–24]. The 6-311+G* is a split-valence triple-zeta plus polarization basis set augmented with diffuse functions [25]. For the 2 2 2 P3 species, we calculated its 7 , LiP7 , NaP7 , and KP7 vibrational frequencies with the 6-311+G* basis set. The RbP2 and CsP2 model systems were optimized at the 7 7 B3LYP and B3PW91 methods, where the 6-311+G* basis set was used for phosphorus and the SDD basis set was used for the heavier metals Rb and Cs. Stationary points were characterized as minima without any imaginary vibrational frequency and a first-order saddle point with only one imaginary vibrational frequency. 2 2 2 NICSs for P3 7 , LiP7 , NaP7 , and KP7 species were calculated with the GIAO-HF/6-311+G*//B3LYP/6-311+G* method. NICSs for RbP2 and CsP2 7 7 were evaluated by using the GIAO-HF//B3LYP method, where the 6-311+ G* basis set was used for phosphorus and the SDD basis set was used for the heavier metals Rb and Cs. Molecular 2 2 2 orbitals (MOs) of P3 7 , LiP7 , NaP7 , and KP7 were calculated at the RHF/6-311+G* level of theory. MOs of RbP2 7 and CsP2 were calculated at the RHF level of theroy, 7 where the 6-311+G* basis set was used for phosphorus and the SDD basis set was used for the heavier metals Rb and Cs. Since MOs of all similar structural MP2 7 species are almost identical, herein we only display the MOs of LiP2 7 . All MO diagrams were made using the MOLDEN 3.7 program [26]. The natural bond orbital (NBO) [27,28] analysis is also performed to provide insight into the bonding nature and aromaticity of these species. 3. Results and discussion The optimized geometric structures of P3 and MP2 7 7 (M = Li, Na, K, Rb, and Cs) species were illustrated in Fig. 1. Total energies, ZPE, and the number of imaginary frequencies of all species are summarized in Table 1. The ˚ ) and covalent radii calculated average bond lengths (in A ˚ (in A) are listed in Table 2. The calculated NICS values 2 are given in Table 3. MOs pictures for P3 7 and LiP7 are exhibited in Figs. 2 and 3, respectively.
3.1. Geometric structures trianions at the Theoretical studies on various P3 7 B3LYP/6-11+G* and B3PW91/6-311+G* levels of theory showed that the planar regular heptagonal structure with D7h symmetry is the local minimum. We performed DFT methods on a wide variety of metal-polyphosphorus clusters and found that all the ground-state MP2 7 geometries are local minima with all real frequencies at the B3LYP and B3PW91 levels of theory. The planar regular heptagonal P3 7 trianion can coordinate with alkali metal atoms to form the C7v pyramidal structures MP2 7 species that maintain the planar cyclo-P3 7 trianion structure. The P–P bond lengths of regular heptagonal P3 7 trian˚ (B3LYP/6-11+G*) between the double ion are all 2.162 A ˚ ) and the single bond bond length of HP@PH (2.043 A ˚ length of H2PPH2 (2.230 A). The bond lengths in regular heptagonal structure provide the structural criteria of aromaticity. As shown in Fig. 1, the P–P bond lengths (2.162, ˚ ) in the pyramidal (C7v) 2.166, 2.163, 2.168, and 2.166 A 2 2 2 2 LiP7 , NaP7 , KP7 , RbP7 , and CsP2 structures are 7 ˚ ) of covalent radii of much shorter than the sum (2.20 A ˚ ) in reguphosphorus and close to the P–P length (2.162 A 3 lar heptagonal P7 structure. The P–P bond lengths in the pyramidal (C7v) MP2 7 structures indicate the existence of delocalization. The M–P bond lengths in the pyramidal 2 2 2 2 (C7v) LiP2 structures 7 , NaP7 , KP7 , RbP7 , and CsP7 are much longer than the sum of covalent radii of the corresponding metal atoms and phosphorus atom (shown in Table 2), indicating that the portion of covalent bonds is relatively few. The covalent radii for the metal atoms and phosphorus atom were assumed to be 1.22, 1.57, 2.02, ˚ for Li, Na, K, Rb, Cs, and P, respec2.16, 2.35, and 1.10 A tively [29]. Fig. 1 shows that the P3 7 trianion preserves its planar seven-membered ring structural integrity in forming the MP2 7 (M = Li, Na, K, Rb, and Cs) species. The geometric integrity of the P3 7 trianion is easily recognizable. Furthermore, the bond lengths of the seven-membered ring are identical, suggesting the aromaticity of the regular heptagonal P3 7 trianion with structural criteria. 3.2. Natural population analysis In terms of natural population analysis, all positive charge mainly lies on the metal atoms and all negative charge populates on the phosphorus atoms. The MP2 7 clusters can be regarded as complexes of the P3 7 trianion with the metal cations. Bonding is due to electrostatic attraction effect between alkali metals and P3 7 : Q(Li) = 2 +0.82e ðLiP2 Þ, Q(Na) = +0.87e ðNaP Þ, Q(K) = +0.86e 7 7 2 ðKP2 Þ, Q(Rb) = +0.92e ðRbP Þ, and Q(Cs) = +0.92e 7 7 ðCsP2 Þ (all are computed at the B3LYP/6-11+G*). With 7 the increasing of the atom number, the positive charges are mainly located over the alkali metal atoms. In addtion, the Wiberg bond index (WBI) between the metal atom and 2 2 2 phosphorus atom in the LiP2 7 , NaP7 , KP7 , RbP7 , and
W.G. Xu, B. Jin / Chemical Physics Letters 419 (2006) 439–443
441
˚ )) for P3 , LiP2 , NaP2 , KP2 , RbP2 , and CsP2 species at the B3LYP and B3PW91 (bold font) levels Fig. 1. Optimized geometries (bond lengths in (A 7 7 7 7 7 7 of theory.
Table 1 Total energies (E),a zero-point energies (ZPE),b and the number of 2 2 2 2 imaginary frequencies (NImag) for P3 7 , LiP7 , NaP7 , KP7 , RbP7 , and c CsP2 species 7 Species P3 7 , D7h LiP2 7 , C7v NaP2 7 , C7v KP2 7 , C7v RbP2 7 , C7v CsP2 7 , C7v
B3LYP
MP2
Ea
ZPEb
Ea
ZPEb
2389.483369 2397.252687 2552.015211 2989.654663 2413.804467 2409.853857
6.05(0) 7.22(0) 6.88(0) 6.82(0) 6.55(0) 6.52(0)
2389.135516 2396.903020 2551.628231 2989.254745 2413.481605 2409.538334
6.28(0) 7.57(0) 7.17(0) 7.09(0) 6.83(0) 6.80(0)
Table 2 ˚ ) at the B3LYP method and covalent radii Calculated bond lengths (in A ˚ ) for P3 , LiP2 , NaP2 , KP2 , RbP2 , and CsP2 species (in A 7 7 7 7 7 7 Species
P3 7
LiP2 7
NaP2 7
KP2 7
RbP2 7
CsP2 7
P–DP M–DP The sum of covalent radii of metal atom and phosphorus
2.162 – –
2.162 2.602 2.32
2.166 2.912 2.67
2.163 3.238 3.12
2.168 3.520 3.26
2.166 3.696 3.45
a
Total energies in Hartree. Zero-point energies in kcal/mol. c The integers in parentheses are the number of imaginary frequencies (Nimag). b
Table 3 Calculated NICS values (in ppm) at the GIAO-HF//B3LYP method for 2 2 2 2 2 the P3 7 , LiP7 , NaP7 , KP7 , RbP7 , and CsP7 species Species a
CsP2 7 are 0.050, 0.054, 0.040, 0.022, and 0.024, respectively. The very high ionic character in the chemical bonds of these clusters is obvious. The P3 7 trianion might be stabilized as the planar seven-membered ring by the interaction of its p system with the alkali metal atoms. However, the alkali metal cations have strong influences on the electronic structure of the P3 7 trianion for the heavier metal atoms.
NICS (0.0) NICS (0.5)b NICS(1.0) NICS (1.5) NICS(2.0)
P3 7
LiP2 7
NaP2 7
KP2 7
RbP2 7
CsP2 7
12.20 11.66 10.15 8.07 6.00
5.06 6.30 6.72 5.80 4.59
7.19 6.50 6.40 5.91 4.82
8.75 8.49 8.14 6.89 5.12
9.93 9.39 8.56 6.86 4.93
11.51 10.54 9.19 7.21 5.17
a NICS (0.0) Calculated NICS values at the center of the seven-membered ring. b ˚ )) the center of the NICS (0.5) Calculated NICS values above (by 0.5 (A seven-membered ring.
442
W.G. Xu, B. Jin / Chemical Physics Letters 419 (2006) 439–443
Fig. 2. Molecular orbital pictures for P3 7 (D7h) trianion.
Fig. 3. Molecular orbital pictures for LiP2 7 (C7v) species.
3.3. Aromaticity of regular heptagonal P3 7 trianion 3.3.1. Nucleus-independent chemical shifts (NICS) Aromaticity is often discussed in term of various criteria such as energetic, magnetic, and geometric [30–34]. NICS (nucleus-independent chemical shift), proposed by Schleyer and co-workers [32], is based on magnetic shieldings, which have long been calculated by simple methods, and now can be computed with modern ab initio technique. NICS are computed at selected points inside or around molecules, typically at ring centers and above. Aromaticity is characterized by negative NICS values, antiaromaticity by positive NICS, and nonaromatic compounds by values close to zero. In this study we firstly calculated NICS (0.0) at the geometrical centers of the planar seven-membered ring, which provide a direct measure of the ring current effects. The calculated results are listed in Table 3. For the planar sevenmembered ring P3 structure, the NICS value of 12.20 7 ppm computed at the center of the seven-membered ring suggests that this trianionic P3 7 unit is aromatic. NICS values of the other five species are all negative and smaller than that of the P3 7 unit. In order to further analyze the aromaticity, we calculated the NICS (0.5), NICS (1.0), NICS (1.5), and NICS (2.0) values by placing a ghost atom ˚ ) the center of the seven-memabove (by 0.5, 1.0, 1.5, 2.0 A bered ring, respectively. NICS (0.5), NICS (1.0), NICS 2 2 (1.5), and NICS (2.0) for the LiP2 7 , NaP7 , KP7 , 2 2 RbP7 , and CsP7 species are all negative, supporting the existence of delocalization and aromaticity of the P3 7 trianion in these five species. We found that NICS (0.0), NICS
(0.5), NICS (1.0), NICS (1.5), and NICS (2.0) values for the MP2 7 (M = Li, Na, K, Rb, and Cs) species increase with increasing atomic number of the metal, indicating the 2 2 increasing of the aromaticity of LiP2 7 , NaP7 , KP7 , 2 2 RbP7 , and CsP7 species. According to the NBO analysis, the calculated adjacent P–P WBI in the seven-membered 2 ring for P3 species are in the range of 1.1–1.3, 7 , MP7 which are between the standard values of single-bond (1.0) and double-bond (2.0), indicating the existence of delocalization. 3.3.2. Molecular orbital analysis To explore the aromaticity of the planar regular heptagonal P3 trianion, MOs pictures which are relevant 7 HOMOs were exhibited in Figs 2 and 3. As shown in Fig. 2, the highest occupied MO (HOMO) of the planar P3 (D7h) trianion includes two degenerated orbitals, 7 formed from the out-of-plane p orbitals. The two degenerated HOMO orbitals are delocalized p bonding MOs which render p aromaticity. The HOMO-1 including two degenerated orbitals are formed from the in-plane p orbital and they are r-bonding MOs. The HOMO-2 also includes two degenerated orbitals and formes from out-of-plane p orbitals. Clearly the HOMO-4 which is formed from the out-of-plane p orbitals of the seven phosphorus atoms, is delocalized p-bonding MO which renders p-aromaticity. The other MOs are formed primarily from the s and p orbitals. Among these occupied orbitals, the two degenerated HOMO orbitals, the two degenerated HOMO-2 orbitals, and the HOMO-4 are all delocalized p-bonding MO, containing 10 p electrons. The 10 delocalized p electrons give
W.G. Xu, B. Jin / Chemical Physics Letters 419 (2006) 439–443
the agreement with the 4n + 2 p electron counting rule. Molecular orbital analysis for P3 7 trianion revealed interesting and delocalized p MOs. They contribute the property of the p-aromaticity for the P3 7 trianion, due to the presence of 10 p electrons which follow the 4n + 2 electron counting rule. Fig. 3 also shows the 10 valence MOs for the C7v LiP2 7 specie. The canonical MO ordering of LiP2 7 (C7v) is differ2 ent from that of P3 7 trianion. In the C7v LiP7 species, the 3 MOs of the P7 trianion can be easily recognized. They only distort slightly by the presence of the metal cation, exhibiting the electronic integrity of the P3 7 trianion. We found that three similar delocalized p orbitals are also present in the C7v LiP2 7 species, showing the electronic integrity of the P3 anion. Certainly, the presence of three 7 delocalized p orbitals plays an important role in the stabilization of this metal-polyphosphorus species. Furthermore, P3 7 has a perfect planar pentagonal D7h structure, due to the delocalization of p electrons, exactly as expected for an aromatic system. 4. Conclusion In this Letter, the equilibrium geometries, harmonic vibrational frequencies of the low-lying states of alkali 2 metal-P3 (M = Li, Na, K, Rb, and Cs) clusters are 7 MP7 discussed for the first time. Comprehensive calculations show that the planar P3 trianion can coordinate with 7 one metal atom to form the pyramidal MP2 species. 7 Firstly, the presence of 10 delocalized p electrons of P3 7 trianion satisfies the 4n + 2 electron counting rule, exhibiting characteristics of p -aromaticity for the P3 7 trianion. Second, P3 has a planar seven-membered ring structure, 7 due to the delocalized of p electrons. Thirdly, NICSs and WBI suggest the property of aromaticity of the P3 7 anion. Finally, the integrity of structural and electronic of the P3 7 trianion inside of the MP2 species can be presented. 7 Therefore, the planar cyclic P3 7 trianion exhibits characteristic of p aromaticity and maintains its structural and electronic integrity inside of the MP2 7 species. These findings are significant for expanding the aromaticity concept into inorganic P3 7 cluster. References [1] P.J. Garratt, Aromaticity, Wiley, NewYork, 1986. [2] X. Li, A.E. Kuznetsov, H.F. Zhang, A.I. Boldyrev, L.S. Wang, Science 291 (2001) 859. [3] A.E. Kuznetsov, A.I. Boldyrev, X. Li, L.S. Wang, J. Am. Chem. Soc. 123 (2001) 8825.
443
[4] X. Li, H.F. Zhang, L.S. Wang, A.E. Kuznetsov, N.A. Cannon, A.I. Boldyrev, Angew. Chem., Int. Ed. 40 (2001) 1867. [5] A.E. Kuznetsov, L.S. Wang, J.D. Corbett, A.I. Boldyrev, Angew. Chem., Int. Ed. 40 (2001) 3369. [6] A.E. Kuznetsov, A.I. Boldyrev, H.J. Zhai, X. Li, L.S. Wang, J. Am. Chem. Soc. 124 (2002) 11791. [7] X. Li, L.S. Wang, A.I. Boldyrev, J. Simons, J. Am. Chem. Soc. 121 (1999) 6033. [8] A.E. Kuznetsov, K. Alexander Birch, A.I. Boldyrev, X. Li, H.J. Zhai, L.S. Wang, Science 300 (2003) 622. [9] A.N. Alexandrova, A.I. Boldyrev, H.J. Zhai, L.S. Wang, J. Chem. Phys. 122 (2005) 054313. [10] A.E. Kuznetsov, H.J. Zhai, L.S. Wang, A.I. Boldyrev, Inorg. Chem. 41 (2002) 6062. [11] R.O. Jones, D. Hohl, J. Chem. Phys. 92 (1990) 6710. [12] R.O. Jones, G. Seifert, J. Chem. Phys. 96 (1992) 7564. [13] P. Ballone, R.O. Jones, J. Chem. Phys. 100 (1994) 4941. [14] M. Ha¨ser, O. Treutler, J. Chem. Phys. 102 (1995) 3703. [15] B. Song, P.L. Cao, Phys. Lett. A 291 (2001) 343. [16] R.O. Jones, G. Gantefo¨r, S. Hunsicker, P. Pieperhoff, J. Chem. Phys. 103 (1995) 9549. [17] M.D. Chen, J.T. Li, R.B. Huang, L.S. Zheng, C.T. Au, Chem. Phys. Lett. 305 (1999) 439. [18] M.D. Chen, R.B. Huang, L.S. Zheng, Q.E. Zhang, C.T. Au, Chem. Phys. Lett. 325 (2000) 22. [19] Q. Jin, B. Jin, W.G. Xu, Chem. Phys. Lett. 396 (2004) 398. [20] G. Seifert, R.O. Jones, J. Chem. Phys. 96 (1992) 2951. [21] M.J. Frisch et al. GAUSSIAN 98, Revision A.9; Gaussian, Inc., Pittsburgh PA, 1998. [22] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [23] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [24] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [25] W.J. Hehre, L. Radom, P.v.R. Schleyer, J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986. [26] G. Schaftenaar, MOLDEN 3.7, CAOS/CAMM Center: The Netherlands, 1998. [27] J.E. Carpenter, F. Weinhold, J. Mol. Struct. (Theochem) 169 (1988) 41. [28] A.E. Reed, R.B. Weinstock, F. Weinhold, J. Chem. Phys. 83 (1985) 735. [29] Periodic Table of Elements. Wiley-VCH: Weinheim, 1997. [30] P.v.R. Schleyer, G. Subramanian, H. Jiao, K. Najafian, M. Hofmann, in: W. Siebert (Ed.), Advances in Boron Chemistry, Royal Society of Chemistry, Cambridge, 1997, pp. 1–14. [31] (a) P.v.R. Schleyer, K. Najafian, Are polyhedral boranes, carboranes, and carbocations aromatic? in: J. Casanova (Ed.), The Borane, Carborane, Carbocation Continuum, Wiley, New York, 1998, pp. 169–190; (b) P.v.R. Schleyer, K. Najafian, Inorg. Chem. 37 (1998) 3454. [32] (a) M. Hofmann, P.v.R. Schleyer, Inorg. Chem. 38 (1999) 652; (b) M. Unverzagt, H.J. Winkler, M. Brock, M. Hofmann, P.v.R. Schleyer, W. Massa, A. Berndt, Angew. Chem., Int. Ed. Engl. 36 (1997) 853; (c) 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. [33] A. Pasquarello, M. Schlu¨ter, R.C. Haddon, Science 257 (1992) 1660. [34] P.v.R. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N.J.R.v.E. Hommes, J. Am. Chem. Soc. 118 (1996) 6317.