fournal of Molecular Structure (Theochem), 280 (1993) 223-231 Elsevier Science Publishers B.V., Amsterdam

223

Ab initio studies on the electronic structures of certain 1 On-electron six-membered ring compounds

Jun Li, Chun-Wan Liu* and Jia-Xi Lu

Fujkm Institute of Research on the Structure of Matter, Chinese Academy of Sciences, State Key Laboratory of Structural Chemistry, Fuzhou, Fujian 350002 (People’s Republic of China)

(Received 6 July 1992)

Abstract

By using ab initio methods of all-electron or effective core potential calculations, the electronic structures and the possible aromaticity of some lOn-electron systems, C,H:- (l), Ni- (2), e- (3), $+ (4), Te:+ (5) and S,N; (6), have been studied at the SCF levels using 4-31G//431G and 6-31G*//6-31G* basis sets. The bonding characteristics of these systems are analysed in terms of the canonical molecular orbital and the Foster-Boys localized molecular orbital results. The apportion of the second-order Jahn-Teller theorem to the stability of these ~arna~eti~ planar species is presented.

Introduction

The famous “4n + 2 rule” [1] has become an effective criterion for the aromaticity of various

compounds. There are, however, some fundamen- tal questions about the aromaticity of six- membered ring compounds still to be resolved, namely, are the 10x-electron molecules with six- membered rings, which superficially obey the 4n + 2 rule where n = 2, of aromatic character, and what is the fundamental bonding model for these electron-rich systems? The importance of these questions was increased with the successful synthe- sis, in the last two decades, of compounds contain- ing anions and cations such as the P;t- [2], Teg+ [3] and &N; [4], and with the demand for elucidating the bonding patterns of the superconducting elec- tron-rich polys~phur nitrides (SN)x [S]. In this paper, we attempt to answer these questions by

* Co~~~n~ng author.

investigating the electronic structures of several iso-n-electronic homocyclic and heterocyclic species possessing six-membered ring skeletons:

C,Hi- (l), Nz- (2), e- (3), Sz’ (4), Tei+ (5) and S,N; (6). The related 6n-electron systems C,H, (7), N, (8) and P6 (9) are also included for the sake of comparison.

Of the systems studied, the electronic structure of the S3N; anion has continually engaged the interest of theoretical chemists since it was first synthesized in 1977 [4]. It has been extensively investigated by the use of various theoretical ap proaches and the major conclusions relating to this work are briefly summarized here. Gimarc and Trinajstic [6] discussed the lOa-electronic structure in terms of a simple Hiickel method. Turner and co-workers [7J carried out a CND0/2-LMO cal- culation within the Edmiston-Ru~en~rg scheme and concluded that the S3N; anion is a 4rr-electron system with non-equivalent nitrogen atoms as well as non-equivalent sulphur atoms. This strange conclusion about the breaking-symmetry and the localized molecular orbital (LMO) model has been

0166-1280/93/$06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.

224 J. Li et al./J. Mol. Struct. (Theochem) 280 (1993) 223-231

argued by many authors. Using the DV-Xa method, Chivers et al. [8] considered this species to

be entirely a 10x-electron system with all the sulphur and nitrogen atoms equivalent. However, they assumed this 4x-electron pattern to the non- uniqueness of the Edmiston-Ruedenberg localiza- tion results. Employing the HFS-Xa-SW method, Laidlaw and Trsic [9] systematically studied a series of polysulphur nitrides including the &N; species. Smith et al. [lo] re-examined this species by using both SW-Xa and CNDO/ZLMO (Edmiston- Ruedenberg) methods and obtained equivalent populations and charges. It was pointed out that the breaking-symmetry consequences and hence the non-equivalent LMO pattern resulted from an artefact of the previous CND0/2 scheme which was not rotationally invariant. Nguyen and Ha [l l] confirmed this species to be a IOn-electron system by making use of an ab initio calculation at the SCF/6-21 G* level and a double-zeta basis. However, they concluded that both the Edmiston- Ruedenberg and the Foster-Boys schemes are not applicable to electron-rich systems. The localized

pictures for these systems were assumed to be an artefact of the localization scheme. From our point of view, however, it is necessary to investigate further the n-electron bonding picture and the applicability of the prevalent localization schemes of Edmiston-Ruedenberg or Foster-Boys to these electron-rich systems.

Contrary to the state of the studies on S,N;, relatively less attention has been paid to the other systems considered here. The electronic structures of the p;l- and Tez+ systems have been studied at the level of the EHMO method by Burns et al. [12], and that of C,Hi- and non-planar Si+ have been explored recently [ 131. Nevertheless, there seems, to our knowledge, to have been no ab initio theoreti- cal work published about the 10x-electron systems of the planar CgHz- and Nz- anions and the planar Si+ and Tei+ cations. In order to supply reliable electronic structures and a localized bonding picture of these kinds of electron-rich systems, we present here an ab initio study with the localization MO results.

Calculations

Ab initio calculations within a spin-restricted Hartree-Fock framework were carried out on species l-9. For Tei+ (6), the effective core poten- tial (ECP) and the pseudopotential basis of Hay and Wadt [14] were used and the geometrical optimizations were carried out within the &, symmetry on the pseudopotential basis of minimum basis, (3s3p)/[lslp], and a double-zeta basis, (3s3p)/[2s2p]. The geometries of the other systems were optimized within the D6,, or D3,,

symmetry by using a gradient optimization tech- nique at the level of all-electron ab initio SCF/C 31G [15], as well as SCF/6-31G* [16], in order to determine the importance of the d orbitals in these sorts of electron-rich systems.

The canonical molecular orbitals (CMOS) were obtained using 4-31G and 6-31G* basis sets at the SCF level and the LMOs were produced by a unitary transformation on the CMOS according to the Foster-Boys localization scheme [ 171, where the procedure of separately transforming the 0 and 7c subsets of the CMOS was adopted. All the calcula- tions were accomplished on a DEC VAX-l l/785 computer using a revised GAUSSIAN 82 system of programs [ 181 modified by the authors, wherein we incorporated the subroutines for ECP and LMO calculations [19]. The population analysis and the LMO percentage compositions were derived from the Mulliken scheme [20].

Results and discussion

In Table 1, we list the optimized bond lengths and bond angles of the 10x-electron systems l-6 and the optimized values of their 6x-electron neutral counterparts (where they exist). The opti- mized bond lengths for C,Hi- (l), Nz- (2) and Si+ (4) are slightly shorter than those of their covalent single bonds. The bond lengths of Pi- (3) optimized using the 4-31G basis set are larger than the exper- imental values, whereas those optimized using the 6-31G* basis set roughly approach the experimen- tal values, 2.15-2.20& in the M,P6 (M = K, Rb)

J. Li et al.{J. Mol. Struct. (Theochem) 280 (1993) 223-231 225

TABLE 1

Bond lengths and bond angles for A,X, within species l-9 optimized with 4-31G and 6-31G* basis sets’

A-X (A) LAXA (de& L XAX (deg)

Charged species W-K- (1) 1.5088 120.0 120.0

1.5069 120.0 120.0 N:- (2) 1.4463 120.0 120.0

1.4116 120.0 120.0 p;l- (3) 2.3227 120.0 120.0

2.1931 120.0 120.0 S;+ (4) 2.2116 120.0 120.0

2.0097 120.0 120.0 Tei+ (5) 2.9705 120.0 120.0

2.7884 120.0 120.0 S, W (6) 1.7128 124.2 115.8

1.6060 125.4 114.6

Neutral species W-b (7) 1.3840 120.0 120.0

1.3861 120.0 120.0 I’& (8) 1.3097 120.0 120.0

1.2854 120.0 120.0 F6 (9) 2.2114 120.0 120.0

2.0945 120.0 120.0

“The optimizations were carried out at the SCF level under D, or D, symmetries. bSZ and DZ denote the (3s3s)/[lslp] and (3s3p)/[2s2p] pseudopotential basis sets respectively.

Basis set

4-31G 6-31G* 4-31G 6-31G* 4-31G 6-31G* 4-31G 6-31G* SZb DZb 4-31G 6-31G*

4-31G 6-31G* 4-31G 6-31G* 4-31G 6-31G*

compounds [2]. Similarly, the bond length of Tez+ (5), 2.9705& obtained with the minimum ECP basis, is longer than the experimental one, whereas the value optimized with the double-zeta basis is comparable to the experimental value for the element tellurium (2.864 A) [21].

Nevertheless, for the heterocyclic system S,N; (6) the optimized bond length (1.7128& using the 4-31G basis set is unduly large, although the bond angles are close to the actual values. Moreover, this geometry would give rise to a rather small overlap population (0.167) between the sulphur and nitrogen atoms, which is not consistent with the stability of the system. This indicated that a somewhat larger basis containing d-type polar functions on the sulphur centre might be important in order to acquire a satisfactory optimum geometry. Therefore the 6-31G* basis set was used for the geometrical optimization, resulting in a geometry consistent with experiments. For

example, the optimized bond length of S-N is 1.606 8, whereas the X-ray crystallographic S-N values lie in the region 1.58-1.63 A, averaging 1.6OA [4].

Table 1 demonstrates that the bond lengths of the charged species l-6 and the neutral ones 7-9 decrease when the basis sets are improved from 4-31G to 6-31G*. However, the reductions are somewhat larger in the systems containing second- or third-row elements than in those of the first-row elements. These facts imply that d orbitals are important in characterizing the electronic proper- ties of the compounds relative to the second- and thirdArow elements, such as the (SN), compounds, as was observed in the ab initio calculation of the S,N, molecule [22]. It is interesting to note that the skeletal bond lengths of 7-9 lie between the lengths of the single and double bonds but approach closer to that of the double bonds, while those of l-6 lie between the lengths of the single and double bonds

226 J. Li et al./J. Mol. Struct. (Theochem) 280 (1993) 223-231

TABLE 2

The eigenvalues (au.) of the valence CMOS for the charged species l-6 calculated using the 6-31G* basis set

b 2s alg e:, elg a2” e28 b ZU e,, al, b 1” e2, elU al,

C,H4,-

1.045 0.944 0.710 0.472 0.362 0.359 0.307 0.275 0.178 0.163 0.044

-0.111 - 0.208

b,, eZ e2, e,, eu

au a2U b,, b,, e2,

e,, a&

Ni-

1.083 0.717 0.556 0.461 0.452 0.344 0.333 0.324 0.266 0.003

- 0.253 - 0.388

b,, e& e2g elU eu

a,, alg b,, b,, eg elU ak

p;t-

0.644 0.422 0.306 0.282 0.281 0.223 0.210 0.156 0.113

- 0.054 -0.198 - 0.260

b, e% e,, e2g eu

a,, au b2” b,, e2s elU alg

S:+

-0.467 - 0.721 -0.876 -0.881 -0.890 -0.957 - 0.967 - 1.091 - 1.120 - 1.340 - 1.517 - 1.591

a; e”* e’ e” e’ a; a; a; a; e’ e’ a;

S,N;

0.243 - 0.083 -0.231 -0.315 -0.316 - 0.411 -0.417 -0.455 -0.523 - 0.756 - 1.009 - 1.119

b2, e& elU eu ezs

azU au b, b,, e2g elU alg

Te:+

- 0.435 - 0.592 - 0.678 - 0.689 - 0.699 - 0.727 - 0.727 - 0.809 - 0.989 - 1.085 - 1.192 - 1.234

but are closer to the length of the single bonds, thus supporting the assumption of aromatic character, although very weak, within these systems. However, the bond lengths of the systems studied increase regularly on going from the 6x-electron systems to the lOA-electron counterparts. This means that the bond strengths are reduced accor- dingly, which may be expected when we take account of the occupation of the MOs with anti- bonding nature in the Ion-electron systems.

The CM0 eigenvalues of the occupied MOs, the LUMO and the unoccupied K-MO, obtained using the 6-31G*//6-31G* basis sets, are listed in Table 2 and the diagrams of the k-type MOs are qualita- tively illustrated in Fig. 1. The HOMOs (marked with asterisks) are all the e” or ezu orbitals, while the LUMOs are the a” or big antibonding orbitals except for 1 where the b, orbital is higher than the LUMO (a,,). Consequently, the identical n-elec- tronic bonding configuration is formed: (a*“)* (eJ4(e,J4 (in molecules of & symmetry) or (a”)2(e”)4(e”)4 (in the molecule of D,, symmetry). These closed-shell electronic states and the compar- able low energy levels of the HOMOs suggest the diamagnetism and stability of these systems. From the nodal properties of these n-type MOs (Fig. l), one can clarify the effects of the occupation of these MOs on the chemical binding and the stability of

one molecule. The SCF calculation of the CMOS

indicated that the antibonding e,, MOs for 1-5 as well as the antibonding 2e” MO for 6, the lowest unoccupied n-MOs in the 6x-electron systems, are populated entirely. This feature concurs with the tendency of the bond lengths, to change, i.e. the bond strengths in the lOn-electron sysems are not as large as those in the 6x-electron systems. The data in Table 2 may be used to gain a full correla- tion of these iso-symmetrical (except for 6) and

t’

Fig. 1. The Z-CMOS for the species 1-9.

J. Li et al./J. Mol. Strut. (Theochem) 280 (1993) 223-231 227

TABLE 3

Molecular total energy (E,), nuclear repulsion energy (I$) and the HOMO-LUMO energy gaps (A&) in l-6 calculated using the 4-31G and 6-31G* basis sets (SZ and DZ for Tez+ )

CBH:- NZ- p;t-

El - 228.5865 - 324.4664 -2040.9712 - 228.9378 - 324.9664 - 2043.5244

E, 188.9606 196.5666 562.0436 189.2889 201.3891 595.2485

AEm 0.2267 0.3468 0.1991 0.2345 0.3667 0.2220

S:+

- 238 1.3865 - 2384.1587

671.5968 739.0736

0.2008 0.2536

S,N;

- 1353.9782 - 1355.7109

420.6055 448.0194

0.2861 0.3260

Te:+

- 46.2766 - 46.3677

74.0544 74.9077

0.1390 0.1564

Basis set

4-31G 6-31G*

4-31G 6-31G*

4-31G 6-31G*

iso-x-electronic systems, by taking advantage of the group correlations of the MO irreducible repre- sentations, such as azu and big 3 a”, erg and e,, --) e”, etc., if the skeletal group alters from Dsh to &,.

The molecular total energies, the nuclear repul- sion energies and the HOMO-LUMO energy gaps calculated at the SCF level using 4-3 1G and 6-3 1 G* basis sets are listed in Table 3. Just as indicated by the tendency of the bond lengths to change, the large alteration of the calculated results of these quantities with the improvement of the bases has intimated further the significance of including the d orbitals in calculations of the compounds of second-row elements. It is worth noting that, with the increase in accuracy of the basis sets from 4- 3 1G to 6-3 lG*, the nuclear repulsion energies increase and the molecular total energies decrease on account of the reduction in the bond lengths, while the HOMO-LUMO energy gaps expand accordingly. These facts show that the electronic energy, i.e. the amount of kinetic and potential energies, is altered owing to the improvement in the basis set.

The HOMO-LUMO energy gaps in Table 3 may be used to investigate the possibility of the systems undergoing second-order Jahn-Teller (SOJT) dis- tortion, i.e. the SOJT instability. No first-order Jahn-Teller (FOJT) effect will emerge owing to the closed-shell configurations. From the SOJT theory [23], the symmetries of the ground state and the first excited state (or the next one or two neighbouring excited states), typically the HOMO and the LUMO, dictate the type of nuclear displacement

that will occur most easily if two (or more) alterna- tive geometries have very similar total energies. Thus, a molecule with a small energy gap between the occupied and unoccupied MOs may result in a new geometry owing to the interaction between the HOMO and the LUMO when it undergoes some geometrical perturbation, e.g. a thermal vibration. Therefore if the HOMO-LUMO energy gap is small and the direct product of the irreducible representations of the HOMO and LUMO, when resolved into the sum of the irreducibles, contains one of the normal vibrational modes which trans- forms the molecule into a new geometry, then the molecule will rearrange to the new geometry via this normal mode.

The SOJT instability is usually considered to be possible for a HOMO-LUMO energy gap (A&) of approximately 4 eV (about 0.147 a.u.) [24]. From Table 3, the HOMO-LUMO energy gaps are all larger than this threshold value, hence indicating that the distortion of the SOJT instability in these species is not facile from the standpoint of energy. With regard to symmetry, the direct products of the HOMOs and the LUMOs in 1, 2-5 and 6 are expressed respectively as eqns. (l), (2) and (3):

& x A,, = Ku (1)

Ku x Kg = El, (2)

E” x A” = E’ (3)

Inasmuch as the derived vibrational modes, E,, in De,, symmetry and E’ in Djh symmetry, are all in-plane distortions, therefore, in conjunction with

228

TABLE 4

J. Li et al./J. Mol. Struct. (Theochem) 280 (1993) 223-231

Percentage composition of the occupied LMOs of l-6 calculated using the 4-31G basis set

No. of LMO &.)

Main composition of LMO

(“/)

Assignment of LMO”

C,H:- 19 0.5487 20 0.5487 21 0.5487 22 0.5487 23 0.5487

N;-

e-

S:+

Te:+

19 0.5264 20 0.5264 21 0.5264 22 0.5264 23 0.5264

43 0.3924 44 0.3924 45 0.3924 46 0.3924 47 0.3924

43 0.8166 44 0.8166 45 0.8166 46 0.8166 47 0.8166

13 0.4934 14 0.4934 15 0.4934 16 0.4934 17 0.4934

S,N; 31 - 0.2427 32 - 0.2333 33 - 0.2474 34 - 0.2296 35 - 0.2516

“1, II denote the lone pair and z-type LMOs respectively.

the results of the energy criterion described above, the systems studied seem stable in keeping the planar six-membered ring skeletons (although Ezu

in D,, symmetry is an out-of-plane distortion, the large HOMO-LUMO energy gap is unfavourable for other conformations). The large AEHL values of 2 and 6 suggest that synthesizing compounds of Nz- or the sandwich compounds is feasible.

The percentage compositions of the a-LMOs calculated using the 4-31G basis set in l-6 are presented in Table 4, while those for the other

C(59.2) + C(38.5) n (C...C) C(63.1) + C(34.4) x (C . ’ . C) C(79.6) + C(16.4) 7c (C . * . C) C(82.0) + C( 13.4) R (C...(z) C(88.3) 1 (G,)

N(52.0) + N(43.8) N(67.1) + N(28.3) N(73.7) + N(21.1) N(83.0) + N(9.7) N(85.6)

R (N . . N) x (N...N) IL (N...N) II (N . . . N) 1 (N2pz)

P(49.2) + P(44.4) P(66.8) + P(26.4) P(70.6) + P(22.3) P(81.5) + P(9.2) P(83.0)

n (P . . . P) Ic (P...P) x (P . . . P) R (P...P)

A (P3pr)

S(55.9) + S(37.4) S(60.5) + S(32.8) S(75.3) + S(16.8) S(78.1) + S(13.4) S(83.8)

A (S . . . S) 7c (S . . . S) n (S . . S) 77. (S . . . S) 1 (S,,)

Te(55.9) + Te(37.4) Te(60.7) + Te(32.5) Te(75.3) + Te(16.9) Te(78.0) + Te(13.5) Te(83.9)

x (Te..,Te) x (Te...Te) n (Te . . . Te) K (Te . . . Te)

1 (Te,,,)

S(54.0) + N(41 .O) N(69.6) + S(22.8) S(70.2) + N(25.1) N(80.2) + S(9.7) S(86.3)

K (S . . N) IL (S . . . N) 7[ (S . . . N) II (S*..N)

1 (S,,)

LMOs are omitted for brevity. The localized MO results give a bonding picture that is fully consistent with the expectations of classical valence bond theory. Apart from the inner orbitals that are all localized into lone pair LMOs with low localized orbital energy, the valence orbitals are divided into two subsets, u and n. There are six C-C d bonds and six C-H r~ bonds in 1, six lone pairs and six A-A (A = N, P, S, Te) g bonds in 2-5 respectively. In 6 there are six S-N r~ bonds and three lone pairs on S and three lone pairs on N. These CJ LMOs,

J. Li et al./J. Mol. Struct. (Theo&em) 280 (1993) 223-231

(cl Cd)

Fig. 2. Total localized pictures and n-LMOs for the 10x- electron systems ((a) and (b)) and 6x-electron systems ((c) and (d)).

one-centred lone pairs and two-centred e bonds, are highly localized. The total amount of the per- centage compositions of any one of these LMOs is almost 100%. However, the x-type LMOs are highly delocalized. The n-LMOs of l-6 are very similar to each other. They possess four multicen- tred (mainly two-centred) bonds distributed con- tinuously in the five interadjacent atoms, and one somewhat delocalized n-type lone pair in the left atom. Each rc-LMO is localized partially over two neighbouring centres with a small amount of electron density delocalized over the entire planar skeleton. The n-LMOs and their multi-centred bonds of 1-6, in contrast to the rr-LMOs and the three-centred bonds of the 6x-electron systems, are depicted in Fig. 2.

This unique localized picture of the lOa-electron six-membered ring systems seems reasonable and in accordance with the resonance canonical structures (Fig. 3). The LMO investigation provides us with a logical and intuitive A-bonding model, thus con- firming the applicability of the LMO method in studying electron-rich systems. Nguyen and Ha [ 1 l] calculated the LMOs of &N; (6) and found the

LMO results to be unreasonable. This is because their LMO result was obtained by using the Foster-Boys localization scheme with a complete localization procedure with 6-a mixing, which would destroy the CV-‘II symmetry in the planar systems and sometimes result in certain absurdities, especially in the electron-rich systems where full localization is a problem. However, as we have noticed, the LMO results obtained by transforming e and n subsets separately are still well behaved. Therefore the LMO methods are, in our opinion, also available for the electron-rich systems.

The LMO interaction energy (&,), i.e. the off- diagonal element of the Fock matrix on the LMOs, as well as the populations, is listed in Table 5. Comparing the cY values for l-6 and 7-9, we can conclude that the physical quantity, Fij, is not merely decided by the bond type but is dependent upon the degree of bond accumulation and the related bond length. On going from a 6rt-electron system to the corresponding lOlc-electron system, the I$ value will increase. However, the $$ values are not only affected by the n-bonding strength, but vary according to whether the molecules are related to the first-row elements or to the second- or third- row elements. It follows that a comparison of the aromaticity, based on Q values, should be made for molecules having similar bond types and the periodic factors should be considered.

The Mulliken overlap populations between the skeletal atoms indicate that the bond strengths of the lOlr-electron systems are less than the 67t- electron systems, which is in line with the occupa- tion of the antibonding MOs in the former. In addition, the following sequence of bond strengths in IOn-electron systems l-6 should exist: C-C > S-N > N-N > P-P > S-S > Te-Te. From this result and the LMO interaction energies, it

Fig. 3. The resonance canonical structures for 1-6.

230 J. Li et al.lJ. Mol. Struct. (Theochem) 280 (1993) 223-231

TABLE S

The atomic populations (A, X), overlap populations (A-X) and LMO interactions energies (4j) for A,X, within l-9”

A X A-X Q

Charged species C,H:- (1) -0.33

N:- (2) - 0.67

E- (3) - 0.67

s:+ (4) 0.33 Tez+ (5) 0.33

S,N- (6) 0.53

Neutral species

GH, (7) -0.19

N (8) 0.0

P6 (9) 0.0

-0.33 0.7830 - 0.67 0.3410 - 0.67 0.3373

0.33 0.2883 0.33 0.2624

- 0.86 0.3538

0.19 1.0414 - 0.0562 0.0 0.3689 - 0.0622 0.0 0.4421 - 0.0266

-0.1000 -0.1043 - 0.0525 - 0.0523 - 0.0476 - 0.083-- 0.085

“The populations are derived using the 6-31G* basis set and the interaction energies using the 4-31G basis set.

seems possible, by taking into account the realiz- ation of the synthesis of the compounds con- taining E&N;, e- and Tei+, to attempt the syn- thesis of the sandwich or ionic compounds of the other species.

The aromaticity of these IOn-electron systems may be deduced from the following facts.

(1) As confirmed by the simple Hiickel calcula- tions, the delocalized energies are positive in these systems, thus verifying the relative stability of the cyclic compounds with respect to their chain compounds.

(2) The large HOMO-LUMO energy gaps and the forbidden symmetry maintain the planar con- formations of these species at a certain stability and prevent them from undergoing SOJT distortion.

(3) The large Mulliken bond orders obtained in this work imply some stability in these species.

(4) From the electronic configurations of the CMOS, it is clear that a net bonding effect remains, even though the stabilization energy of the e,, or e” bonding MOs is completely cancelled out by the destabilization energy of the e2,, or e” antibonding MOs.

(5) The LMO interaction energies suggest a rela- tively large conjugation stability of the localized n bonds.

(6) The localized MO pictures of these electron- rich systems, i.e. the multicentred bonds, exhibit extensive delocalization of the K electrons over the entire ring, which lays the foundation for the sta- bility of the aromaticity and conjugated effect in the systems. These results indicate that the lOlr- electron systems do indeed exhibit aromaticity, although it is much weaker than in their 6n-electron counterparts.

Conclusions

The electron-rich systems under consideration follow the 4n + 2 rule and are therefore of weak aromaticity, which is evident from either the delo- calized or the localized molecular orbital approach. As a result of the occupation of the weak antibond- ing MOs, the bonding strengths of the 10~electron systems decrease with respect to their 6n-electron counterparts. They possess similar n-bonding spectra and unique n-type localized bonding pictures, i.e. extensively delocalized four multicen- tred (mainly two-centred) two-electron bonds and one lone pair. Use of Foster-Boys localization scheme with separately transforming 0 and A orbitals to the lOa-electron six-membered ring systems demonstrated its effectiveness in rationaliz- ing the bonding nature of electron-rich systems. The lOn-electron systems are deduced to have dia- grammatic and planar conformations possessing certain stability from the viewpoint of the SOJT theorem.

Acknowledgements

We are grateful to the National Natural Science Foundation of China and the Foundation of Chinese Academy of Sciences for grants in support of this work.

References

1 E. Hiickel, Z. Phys., 70 (1931) 204; 72 (1931) 310; 76 (1932) 628.

2 W. Schmettow, A. Lipka and H.G. von Schnering, Angew. Chem., Int. Ed. Engl., 13 (1974) 345.

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13

14

D.J. Prince, J.D. Corbett and B. Garbisch, Inorg. Chem., 9 (1970) 2731. C.H.W. Jones. Can. J. Chem., 55 (1977) 3076. J. Bojes and T. Chivers, J. Chem. Sot., Chem. Commun., (1977) 453. R.L. Greene, G.B. Street and L.J. Suter, Phys. Rev. Lett., 34 (1975) 577. B.N. Gimarc and N. Trinajstic, Pure Appl. Chem., 52 (1980) 1443. A.A. Bhattacharyya, A. Bhattacharyya and A.G. Turner, Inorg. Chim. Acta, 45 (1980) L13; 64 (1982) L33. J. Bojes, T. Chivers, W.G. Laidlaw and M. Trsic, J. Am. Chem. Sot., 101 (1979) 4517. T. Chivers, W.G. Laidlaw, R.T. Oakley and M. Trsic, Inorg. Chim. Acta, 53 (1981) L189. W.G. Laidlaw and M. Trsic, in D.H. Smith, Jr., H.F. Schaefer III and K. Morokuma (Eds.), Applied Quantum Chemistry, Reidel, Dordrecht, 1987, p. 269. V.H. Smith, Jr., J.R. Sabin, E. Broclawik and J. Mrozek, Inorg. Chim. Acta, 77 (1983) LlOl. N.T. Nguyen and T.-K. Ha, J. Mol. Struct. (Theochem), 105 (1983) 129. R.C. Bums, R.J. Gillespie, J.A. Barnes and M.J. McGlinchey, Inorg. Chem., 21 (1982) 799. D.S. Salahub, A.E. Foti and V.H. Smith, Jr., J. Am. Chem. Sot., 100 (1978) 7847. M. Nakayama, H. Ishikana, T. Nakano and 0. Kikuchi, J. Mol. Struct. (Theochem), 184 (1989) 369. P.J. Hay and W.R. Wadt, J. Chem. Phys., 82 (1985) 270; 82 (1985) 299. W.R. Wadt and P.J. Hay. J. Chem. Phys., 82 (1985) 284.

15

16

17

18

19

20 21

22

23

24

R. Ditchheld, W.J. Hehre and J.A. Pople, J. Chem. Phys., 54 (1971) 724. W.J. Hehre and J.A. Pople, J. Chem. Phys., 56 (1972) 4233. J.D. Dill and J.A. Pople, J. Chem. Phys., 62 (1975) 2921. W.J. Hehre and W.A. Lathan, J. Chem. Phys., 56 (1972) 5255. P.C. Hariharan and J.A. Pople, Chem. Phys. Lett., 66 (1972) 217. M.M. Fran&, W.J. Pietro, W.J. Hehre, J.S. Binkley, M.S. Gordon, D.J. DeFrees and J.A. Pople, J. Chem. Phys., 77 (1982) 3654. SF. Boys, Rev. Mod. Phys., 32 (1960) 296. J.M. Foster and SF. Boys, Rev. Mod. Phys., 32 (1960) 300. J.S. Binkley, M.J. Frisch, D.J. DeFrees, K. Raghava- chari, R.A. Whiteside, H.B. Schlegel, E.M. Fluder and J.A. Pople, GAUSSIAN 82, Department of Chemistry, Carnegie-Mellon University, Pittsburgh, PA, 1983. R.C. Haddon and R.J. Williams, Chem. Phys. L&t., 42 (1976) 453. L.R. Kahn, P. Baybutt and D.G. Truhlar, J. Chem. Phys., 65 (1976) 3826. R.S. Mulliken, J. Chem. Phys., 23 (1955) 1833. L.E. Sutton, Tables of Interatomic Distances and Con- figurations in Molecules and Ions, No. 18, Burlington House, London, 1965. R.H. Findlay, M.H. Palmer, A.J. Downs, R.G. Egdell and R. Evans, Inorg. Chem., 19 (1980) 1307. L.S. Bar-tell, J. Chem. Educ., 45 (1969) 754. R.F.W. Bader, Can. J. Chem., 40 (1962) 1164. R.G. Pearson, J. Am. Chem. Sot., 91(1969) 1252,4947.