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Ab initio study of the outer valence ionization potentials and electron affinities of nonconjugated π-electron cyclic systems
Chemical Physics 138 (1989) 231-235 North-Holland, Amsterdam
AB INITIO STUDY OF THE OUTER VALENCE IONIZATION F’OTENTIALS AND ELECTRON AFFINITIES OF NONCONJUGATED n-ELECTRON CYCLIC SYSTEMS
V. GALASSO Dipartimento di Scienze Chimiche, Universitd di Trieste, 34127 Trieste, Italy Received 5 June 1989
Nonempirical calculations using the OVGF approach, which incorporates the main portion of the electron correlation and reorganization effects, are reported for the vertical ionization potentials of 1,4cyclohexadiene, norbomadiene, 7-silanorbomadiene, kxanorbomadiene, bicycle [ 2.2.2]octadiene, and bicyclo[ 3.2.2lnonadiene. The results provide an overall, consistent reproduction of the main features in the photoelectron spectra, in particular of the x bands which are efficient monitors of the competitive through-space and through-bond stereoelectronic effects operating in these molecules. The sequence of the first two negative electron affinities is analysed by using Koopmans’ theorem estimates.
1. Introduction
In recent years the structural parameters and spectroscopic properties, governed by a subtle interplay of stereoelectronic factors, of the nonconjugated IEelectron systems, 1,Ccyclohexadiene ( CH ) , bicyclo [ 2.2.11 hepta-2,5-diene or norbomadiene (NO), bicycle [ 2.2.21 -octa-2,5diene (BO), and bicyclo [ 3.2.2]nona-6,8-diene (BN), have been a topic of continuous experimental and theoretical work.
CH
NO
BO
EN
In particular, the UV photoelectron (PE ) spectra of these compounds have been extensively investigated by Heilbronner and co-workers [ l-4 ] and the corresponding orbital descriptions have been advanced for all molecules [ l-91 but NO [ 1O-12 ] by assuming the validity of Koopmans’ theorem (KT) mainly at the semiempirical level. The major focus of this effort has been devoted to rationalize the ordering and splitting of the uppermost two rt bands. These aspects have also been discussed in great detail by many authors [ l-9,1 3- 16 ] in terms of the classic dissection of in-
tramolecular orbital interactions into throughspace (TS) and through-bond (TB ) components. Nevertheless, only a systematic ab initio analysis, to an accuracy surpassing that afforded by KT, can provide general, quantitative information which reliably complements the available experimental data and further helps in the detailed interpretation of the PE spectra of the bicycle [ n.2.21 alkadiene series. In the present study, we report on ab initio many-body results for the ionization potentials (IPs) according to Cederbaum’s outer-valence Green-function (OVGF) method [ 171, which uses Green functions and includes the effects of electron correlation and reorganization beyond the Hartree-Fock approximation. Furthermore, the consequences of the progressive lengthening of the aliphatic bridge on the first two negative electron affinities (EAs), associated with the IC*MOs, are also examined by appealing to the KT theoretical estimates.
2. Computational details The vertical IPs were calculated at ab initio level according to Cederbaum’s OVGF method [ 17 1, by expanding the self-energy part up to third order and estimating the contributions of higher orders by a renormalization procedure. In order to calculate the
0301-0104/89/$03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
232
V. Galasso / Nonconjugated n-electron cyclic systems
self-energy part, all occupied valence MOs and the 24, 20, 18, and 15 lowest virtual MOs for CH, NO, BO, and BN, respectively, were considered. A similar OVGF calculation has already been reported by von Niessen and Diercksen [ lo] for NO; nevertheless, the calculation was repeated here in order to have, for the entire class of molecules, consistent results achieved with the same computational details. The [ 3s2p ] basis set was used for carbon and a single 1s4G function for hydrogen [ 181. Experimental geometries were used for CH, NO, and BO [ 191. For BN, a geometrical model was built on the basis of that of BO by assuming a CZv symmetry on account of the high conformational mobility in this system [ 201 and by optimizing the flap angle between the rings ( 130” ) with a STO-3G calculation.
3. Results and discussion Before starting the discussion, two preliminar comments are in order. Firstly, the use of the OVGF method relies on the assumption that the one-particle picture of the ionization process holds, i.e. that the Green function is diagonal and the satellite structure of the bands is negligible [ 171. Secondly, as shown by von Niessen et al. [ 2 1 ] highly accurate predictions of the IPs require both very large basis sets and full exhaustion of the particle space, but to meet these requirements is too expensive for such large molecules as the present ones. Therefore, because of the implications of these two factors, the theoretical relevance of the present OVGF results is restricted to an analysis of the main features in the PE spectra. The ab initio OVGF IPs, pole strengths (P) and assignments are shown in table 1 together with the experimental values. The overall agreement with experiment is satisfactory and, in all cases, better than that achieved previously with KT semiempirical calculations [ 81. It should be, however, stressed that vertical, theoretical IPs do not necessarily correlate with band maxima especially when the bands are highly asymmetric [ 22 1, as is the case for some broad bands of the investigated molecules. Therefore, the detailed assignment provided for all prominent peaks observed in the congested PE spectra should be considered as provisional. As concerns the shifts of the top two n: MOs on passing from NO (one-) to BO
(two-) and BN (three-carbon bridge), the OVGF calculations account satisfactorily for both the progressive stabilization of K_ (out-of-phase or antibonding combination of the semilocalized ethylenic n orbitals) and destabilization of K, (in-phase or bonding combination). Furthermore, the present orbital sequence and corresponding description of the bands in the PE spectrum of NO, which is regarded as a model molecule for dominant TS interactions in contrast to CH, are in full agreement with those reported by von Niessen and Diercksen [ lo] at OVGF level, Bieri et al. [ 111 at extended 2ph-TDA level, and Palmer [ 12 ] at MR CI level. The most peculiar aspect in the UV PE spectra of the examined series of nonconjugated n-electron molecules concerns the pattern of the two lz IPs, whose ordering and splitting have been qualitatively rationalized in terms of the popular concepts of mediated interplay of TS and TB interactions between semilocalized ethylenic orbitals [ 14- 16,23 1. When the longrange TS effects play the stronger role, the x: levels follow the natural sequence n_ > K+, while the predominance of the destabilizing TB interactions between the A and o frameworks leads instead to the inverted sequence. From table 1 it is apparent that the splitting d(n_-x, ) is reproduced satisfactorily along the series: theory: - 1.01 (CH), 1.13 (NO), -1.06 0.79 (BO), -0.16 eV (BN); experiment: (CH), 0.86 (NO), 0.58 (BO), -0.18 eV (BN); this indicates that the OVGF approach accounts reasonably well for the many-body effects in this observable. Therefore, the hyperconjugative TB interactions dominate the TS interactions in the first (CH, zerocarbon bridge) and last (BN, three-carbon bridge) members of the examined series. The opposite situation holds instead in the intermediate members with one- and two-carbon bridges. For the bicycle-alkadienyl systems, the level splitting d can be fitted as a function of the dihedral angle @ between the rings to a quadratic equation: A= uzqj2 + ~,@+a~, where, schematically, the a2 coefficient can be traced back to the destabilizing TB interactions, while the a, coefficient encompasses the stabilizing effect of the TS interactions. In particular, the widening of @ causes an increasing destabilization of n, as a result of an increasingly stronger antibonding mixing of the o orbitals spanning the same symmetry as the II orbitals. By employing the values
V. Galasso/ Nonconjugatedn-electroncyclicsystems Table 1 Vertical IPs of 1+cyclohexadiene Compound CH
and related compounds (in eV )
KT
IP
P
IP,
Compound
Symmetry
KT
IP
P
IP,
9.07 10.02 12.44 13.33 14.50 15.74 15.78 16.52
8.81 9.88 11.07 11.87 13.11 13.95 14.51 14.71
8.82 ‘) 9.88 11.00 11.97 13.32 13.75
NO
8.35 9.48 11.64 12.14 12.43 13.11 13.65 13.66
0.93 0.93 0.93 0.93 0.94 0.94 0.93 0.93
8.69 ” 9.55 11.26 z11.7b’ 12.51 c)
15.32 16.34 16.91 19.20
6bz(= 1 lOal 3a2 6b, 5b Sal 5b, 7al 4b2 3b2 4b, 6al
8.63 9.95 12.76 13.13 13.42 14.18 14.68 14.72
16.67 17.98 18.77 21.56
0.93 0.92 0.92 0.93 0.92 0.89 0.92 0.92 > 0.92 0.90 0.88 0.85
15.75 17.96 18.75 19.50
14.60 16.49 17.31 18.06
0.93 0.89 0.89 0.89
8.68 9.46 10.66 11.26 11.38 13.35 13.42
0.94 0.94 0.95 0.95 0.94 > 0.95 0.95
8.87 ‘) 9.45 10.42
l3ai(x+] 7bz(x-) 9b,
8b, 5bz 3a2
9.07 9.97 11.66 12.19 12.42 14.62 14.31
9.36 9.35 11.73 12.12 12.27 12.38 13.33
8.90 9.06 10.91 11.09 11.46 11.72 12.34
0.95 0.94 0.96 0.95 0.95 0.96 0.94
14.81 14.84 15.90 16.34 17.40 17.74 19.26
13.67 13.77 14.66 15.08 16.21 16.52 17.82
0.94 0.94 0.92 0.93 0.92 0.92 0.89
14.24
13.30
0.95
9ar 7bi 8al 4bz 6br 3bz 7ai
15.15 15.44
14.11 14.27
0.94 0.93
15.48 15.95 16.50 17.81
14.69 14.98 15.29 16.85
0.95 0.94 0.92 0.94
Symmetry 2b,.(x+ ] 1bs,,(x- ] 3b,, 6a, 5b3, 4bz. lb, 3bs. lb,. 4b3. 5% 2bis
BO
233
6bz(x-) llai(x+] 4as 1Oai
14.68 1‘5.6 b) 15.95 16.47 18.58
11.05
1
12.61 *) ... 13.16 ... 13.5 14.30 15.46 15.86 16.97
BN
4a2
12ar 6bz 8bi 1 la,
7b, 5b 3a2
lOa, 4bz 3bz
1
12.75 13.3 13.5 14.24 15.66 16.52 17.16
9.00 =i 9.18 10.4 0
1
10.7 11.1 11.6 12.3 13.5 ‘)
1
... 13.8 ... 14.3 ... 14.8
‘) Ref. [ 11. b, IP estimated from the spectrum in ref. [ 11. C~Thisbandextendsfrom12to14eVwithmaximaat12.51and12.75eVandshou1dersatcl3.3and13.5eV. *) This band extends from 12.2 to 13.9 eV with maxima at 12.61 and 13.16 eV and a shoulder at z 13.5 eV. =) Ref. [4]. ‘) This band extends from 10.2 to 12.0 eV with maxima at ~10.7, ll.l,and 11.6eVandashoulderat z10.4eV. *) This band extends from 13.2 to 15.0 eV with maxima at ca. 13.5, 13.8, and 14.3 eV and a shoulder at s 14.8 eV.
ofN0 (0.86eV, lll’),BO (058eV, BN (-0.18 eV, 130”), weobtain A= -0.004872@+
123.4”),and
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(eV)
(note that the last three digits are retained only for numerical consistency). This equation emphasizes the role of A as an effkient monitor of conformational change. The crossover point, where A=0 and the TB interactions cancel the TS interactions exactly, is found to occur at @= 128.8”, of course at an angle near that shown by BN. Furthermore, applying the above equation to the higher homologue in the series, bicycle [ 4.2.2]deca-7,9diene, with a four-car-
bon bridge and a splitting of - 0.50 eV [ 41, q3is predieted to be 132”, somewhat lower than the 137” value proposed by Heilbronner [ 5 ] on the basis of an HMO perturbational model. Quite recently, on the basis of KT ab initio STQ32 1G calculations, Paddon-Row and Jordan [ 24 ] have claimed 7-silanorbomadiene - a derivative of NO where the >CH2 bridging group is replaced by the >SiH2 group - as an example of norbomadienyl system in which the TB effects play a stronger role than the TS interactions at variance with the parent NO. Bearing in mind both the inherent limitation of the KT approximation and the relatively small calcu-
234
V. Galasso / Nonconjugated n-electron cyclic systems
lated splitting ( -0.16 eV), we have considered worthwhile to check this prediction at many-body level. Use was made of the [ 6s4p] basis set for silicon [ 181 and of the ab initio optimized structure [ 241. The OVGF results for the first IPs (P) are: 8.69 eV (0.93) 12a,, 7c+; 8.88 (0.93) 7b2, rt_; 9.94 (0.94) 7b,; 11.50 (0.93) 3az; 11.88 (0.93) 6b2; 12.49 (0.92) lOa,. Therefore, substitution of the >CH2 group by the more electropositive >SiH2 group in the norbornadienyl skeleton causes a stabilization of A_ by 0.5 eV while a destabilization of x, by 0.8 eV. From these results it can be concluded that the prediction by Paddon-Row and Jordan [ 241 is basically correct, i.e. R+ > rr_, and the spacing between the first two bands in the PE spectrum is expected to be small, of the order of 0.2 eV. As a further example of heteroatom substitution at position 7 in the norbomadiene skeleton, we have also considered the oxaderivative, i.e. 7-oxabicyclo [ 2.11 hepta-2,5-diene. A reasonable geometrical model was built on the basis of the experimental structures of NO [ 191 and 7-oxanorbornane [ 251 with @= 113.5’. The OVGF results for the first vertical IPs (P) are: 9.13 eV (0.92) 6bz, A_; 10.22 (0.93) lOal, x,; 10.41 (0.93) 5b2, no; 11.66 (0.93) 3az; 13.29 (0.92) 9ai; 13.60 (0.92) 6bl; 14.00 (0.94) 5b,; 14.63 (0.93) 8a,. These results show a pattern of the first IPs quite different from that of the 7-sila analogue. Indeed, the following electronic effects are brought about by substitution of the >CH2 bridge with the more electronegative oxygen atom: a nearly equal stabilizing effect of ~0.7 eV occurs for both the II MOs of the parent NO,. the canonical sequence x_ > rc+ is maintained, and the splitting 1.09 eV is quite similar to that of NO. The no MO is expected to fall at higher energy than in the saturated 7-oxanorbomane (9.57 eV) and unsaturated 7-oxanorbornene (9.83 eV) [ 261, as a consequence of both delocalization of no into the o framework and no-n interactions. In order to describe adequately the nature of the low-lying excited electronic states of the examined molecules, knowledge of the exact sequence and splitting of the vacant K*levels is as important as that of the occupied A levels, whose origin stems from the same stereoelectronic factors. Recently, Heinrich et al. [ 27 ] performed a systematic investigation on the correlation of the energies of the lowest unoccupied
MOs with experimentally determined negative EAs resulting from electron-transmission spectra. Despite the well-known shortcomings due to neglection of relaxation and correlation effects, they found that the KT can be used for qualitatively correct estimates of EAs, when theoretical results obtained with small basis sets augmented by only polarization functions are employed. On this ground, the present KT ab initio estimates provide the following splittings d*(R*_--JC:: +0.95 (CH), - 1.84 (NO), -1.50 (BO), and - 1.39 eV (BN). The theoretical results for CH and NO are in satisfactory agreement with both assignments and values of the experimental d(EA)s, +0.92eV [28] and -1.52eV [29],respectively. Note that, in contrast to the n: counterparts, the x* levels in BN still follow the natural sequence, i.e. the TS interactions dominate over the TB. The same pattern is also predicted for 7-silanorbomadiene ( - 1.87 eV) and 7-oxanorbomadiene ( - 1.66 eV). Bearing in mind these relatively large splittings, it is reasonable to expect the many-body corrections to KT estimates not to change the sequence of the IF* MOs, so the present orderings can be considered as definitively settled. If we provisionally use the relation: EA = 0.762OKT + 1.2260 (eV), - empirically fitted to the first two experimental EAs of CH, - 1.75 and -2.67 eV [28], and NO, - 1.04 and -2.56 eV [29] - we obtain for EA(rc?+): -0.98 eV (NO), -1.60 (BO), and -1.56 (BN), and for EA(x!_): -2.39 eV (NO), -2.74 (BO), and -2.62 (BN). The corresponding d*s are: - 1.4 1 eV (NO), - 1.14 (BO), and - 1.06 (BN). Along the bicyclo [ n.2.2 ] alkadiene series, NO (n = 1)) BO (n = 2 ), and BN (n = 3), there are two salient features of the A*S:the natural ordering is always maintained and the net splitting 1A* 1 decreases as does A, which is a further manifestation of progressive compensation of the TB and TS stereoelectronic effects.
Acknowledgement
The author thanks Professor W. von Niessen, University of Brunswick (FRG ) , for making available his OVGF program. This work was supported by the Minister0 della Pubblica Istruzione of Italy.
K Galasso/ Nonconjugatedn-electroncyclicsystems
References [ 1] P. Bischof, J.A. Hashmall, E. Heilbronner and V. Homung, Helv. Chim. Acta 52 (1969) 1745. [2] E. Heilbronner and H.D. Martin, Helv. Chim. Acta 55 (1972) 1490. [ 3 ] G. Bieri, F. Burger, E. Heilbronner and J.P. Maier, Helv. Chim. Acta 60 (1977) 2213. [4] M.J. Goldstein, S. Natowsky, E. Heilbronner and V. Homung, Helv. Chim. Acta 56 (1973) 294. [ 51 E. Heilbronner, Israel J. Chem. 10 (1972) 143. [ 61 E. Heilbronner, F. Brogli and E. Vogel, J. Electron Spectry. 9 (1976) 227. [7] E. Haselbach, L. Neuhaus, R.P. Johnson, KN. Houk and M.N. Paddon-Row, Helv. Chim. Acta 65 ( 1982) 1743. [8] H.J. Chiang and SD. Worley, J. Electron Spectry. 21 (1980) 121. [9] T. Kobayashi, Z. Yoshida, Y. Asako, S. Miki and S. Kate, J. Am. Chem. Sot. 109 (1987) 5103. [ lo] W. von Niessen and G.H.F. Diercksen, J. Electron Spectry. 16 (1979) 351. [ 111 G. Bieri, L. Asbrink and W. von Niessen, J. Electron Spectry. 27 (1982) 129. [ 121 M.H. Palmer, J. Mol. Struct. 161 (1987) 333. [ 131 R. Hoffmann, E. Heilbronner and G. Gleiter, J. Am. Chem. Sot. 92 (1970) 707; R. Hoffmann, P.D. Moliere and E. Heilbronner, J. Am. Chem. Sot. 95 (1973) 4860. [14]M.J.S.DewarandJ.S.Wasson,J.Am.Chem.Soc.92 (1970) 3506. [ 151 H. Bock and B.G. Ramsey, Angew. Chem. Intern. Ed. 12 (1973) 734. [ 161 E. Heilbronner and A. Schmelzer, Helv. Chim. Acta 58 (1975) 936.
235
[ 171 L.S. Cederbaum, J. Phys. B 8 (1975) 290. [ 181 T.H. Dunning Jr., J. Chem. Phys. 53 (1970) 2823; T.H. Dunning Jr. and P.J. Hay, in: Methods in Electronic Structure Theory, ed. H.F. Schaefer III (Plenum Press, New York, 1977) p. 1. [ 19 ] H. Oberhammer and S.H. Bauer, J. Am. Chem. Sot. 9 1 (1969) IO; A. Yokozeki and K. Kuchitsu, Bull. Chem. Sot. Japan 44 (1971) 1783,2356; G.A. Jeffrey, J. Buschmann, C.W. Lehman and P. Luger, J. Am. Chem. Sot. 100 (1988) 7218; H.D. Martin, as quoted in ref. [ IO]. [20] A.J. Baker, A.M. Chalmers, W.W. Fllod, D.D. MacNicol, A.B. Penrose and R.A. Raphael, J. Chem. Sot. Chem. Commun. (1970) 166. [ 2 1 ] W. von Niessen, L.S. Cederbaum, W. Domcke and G.H.F. Diercksen, J. Chem. Phys. 66 (1977) 4893; W. von Niessen, G.H.F. Diercksen and L.S. Cederbaum, J. Chem. Phys. 67 (1977) 4124; W. von Niessen, L.S. Cederbaum, W. Domcke and G.H.F. Diercksen, Chem. Phys. 56 ( 198 1) 43. [22] L.S. Cederbaum and W. Domcke, Advan. Chem. Phys. 36 (1977) 205. [23] M.N. Paddon-Row, Accounts Chem. Res. 15 (1982) 245. [24] M.N. Paddon-Row and KD. Jordan, J. Chem. Sot. Chem. Commun. ( 1988) 1508. [25] K Gyanagi, T. Fukuyama, K. Kuchitsu, R. Bohn and S. Li, Bull. Chem. Sot. Japan 48 ( 1975) 75 1. [26] A.D. Bain, J.C. Biinzli, D.C. Frost and L. Weiler, J. Am. Chem. Sot. 95 (1973) 291. [ 271 N. Heimich, W. Koch and G. Frenking, Chem. Phys. Letters 124 (1986) 20. [28] A. Modelli, D. Jones, S. Rossini and G. Distefano, Chem. Phys. Letters 123 (1986) 375. [ 291 V. Balaji, L. Ng, K.D. Jordan, M.N. Paddon-Row and H.K. Patney, J. Am. Chem. Sot. 109 (1987) 6957.
AB INITIO STUDY OF THE OUTER VALENCE IONIZATION F’OTENTIALS AND ELECTRON AFFINITIES OF NONCONJUGATED n-ELECTRON CYCLIC SYSTEMS
V. GALASSO Dipartimento di Scienze Chimiche, Universitd di Trieste, 34127 Trieste, Italy Received 5 June 1989
Nonempirical calculations using the OVGF approach, which incorporates the main portion of the electron correlation and reorganization effects, are reported for the vertical ionization potentials of 1,4cyclohexadiene, norbomadiene, 7-silanorbomadiene, kxanorbomadiene, bicycle [ 2.2.2]octadiene, and bicyclo[ 3.2.2lnonadiene. The results provide an overall, consistent reproduction of the main features in the photoelectron spectra, in particular of the x bands which are efficient monitors of the competitive through-space and through-bond stereoelectronic effects operating in these molecules. The sequence of the first two negative electron affinities is analysed by using Koopmans’ theorem estimates.
1. Introduction
In recent years the structural parameters and spectroscopic properties, governed by a subtle interplay of stereoelectronic factors, of the nonconjugated IEelectron systems, 1,Ccyclohexadiene ( CH ) , bicyclo [ 2.2.11 hepta-2,5-diene or norbomadiene (NO), bicycle [ 2.2.21 -octa-2,5diene (BO), and bicyclo [ 3.2.2]nona-6,8-diene (BN), have been a topic of continuous experimental and theoretical work.
CH
NO
BO
EN
In particular, the UV photoelectron (PE ) spectra of these compounds have been extensively investigated by Heilbronner and co-workers [ l-4 ] and the corresponding orbital descriptions have been advanced for all molecules [ l-91 but NO [ 1O-12 ] by assuming the validity of Koopmans’ theorem (KT) mainly at the semiempirical level. The major focus of this effort has been devoted to rationalize the ordering and splitting of the uppermost two rt bands. These aspects have also been discussed in great detail by many authors [ l-9,1 3- 16 ] in terms of the classic dissection of in-
tramolecular orbital interactions into throughspace (TS) and through-bond (TB ) components. Nevertheless, only a systematic ab initio analysis, to an accuracy surpassing that afforded by KT, can provide general, quantitative information which reliably complements the available experimental data and further helps in the detailed interpretation of the PE spectra of the bicycle [ n.2.21 alkadiene series. In the present study, we report on ab initio many-body results for the ionization potentials (IPs) according to Cederbaum’s outer-valence Green-function (OVGF) method [ 171, which uses Green functions and includes the effects of electron correlation and reorganization beyond the Hartree-Fock approximation. Furthermore, the consequences of the progressive lengthening of the aliphatic bridge on the first two negative electron affinities (EAs), associated with the IC*MOs, are also examined by appealing to the KT theoretical estimates.
2. Computational details The vertical IPs were calculated at ab initio level according to Cederbaum’s OVGF method [ 17 1, by expanding the self-energy part up to third order and estimating the contributions of higher orders by a renormalization procedure. In order to calculate the
0301-0104/89/$03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
232
V. Galasso / Nonconjugated n-electron cyclic systems
self-energy part, all occupied valence MOs and the 24, 20, 18, and 15 lowest virtual MOs for CH, NO, BO, and BN, respectively, were considered. A similar OVGF calculation has already been reported by von Niessen and Diercksen [ lo] for NO; nevertheless, the calculation was repeated here in order to have, for the entire class of molecules, consistent results achieved with the same computational details. The [ 3s2p ] basis set was used for carbon and a single 1s4G function for hydrogen [ 181. Experimental geometries were used for CH, NO, and BO [ 191. For BN, a geometrical model was built on the basis of that of BO by assuming a CZv symmetry on account of the high conformational mobility in this system [ 201 and by optimizing the flap angle between the rings ( 130” ) with a STO-3G calculation.
3. Results and discussion Before starting the discussion, two preliminar comments are in order. Firstly, the use of the OVGF method relies on the assumption that the one-particle picture of the ionization process holds, i.e. that the Green function is diagonal and the satellite structure of the bands is negligible [ 171. Secondly, as shown by von Niessen et al. [ 2 1 ] highly accurate predictions of the IPs require both very large basis sets and full exhaustion of the particle space, but to meet these requirements is too expensive for such large molecules as the present ones. Therefore, because of the implications of these two factors, the theoretical relevance of the present OVGF results is restricted to an analysis of the main features in the PE spectra. The ab initio OVGF IPs, pole strengths (P) and assignments are shown in table 1 together with the experimental values. The overall agreement with experiment is satisfactory and, in all cases, better than that achieved previously with KT semiempirical calculations [ 81. It should be, however, stressed that vertical, theoretical IPs do not necessarily correlate with band maxima especially when the bands are highly asymmetric [ 22 1, as is the case for some broad bands of the investigated molecules. Therefore, the detailed assignment provided for all prominent peaks observed in the congested PE spectra should be considered as provisional. As concerns the shifts of the top two n: MOs on passing from NO (one-) to BO
(two-) and BN (three-carbon bridge), the OVGF calculations account satisfactorily for both the progressive stabilization of K_ (out-of-phase or antibonding combination of the semilocalized ethylenic n orbitals) and destabilization of K, (in-phase or bonding combination). Furthermore, the present orbital sequence and corresponding description of the bands in the PE spectrum of NO, which is regarded as a model molecule for dominant TS interactions in contrast to CH, are in full agreement with those reported by von Niessen and Diercksen [ lo] at OVGF level, Bieri et al. [ 111 at extended 2ph-TDA level, and Palmer [ 12 ] at MR CI level. The most peculiar aspect in the UV PE spectra of the examined series of nonconjugated n-electron molecules concerns the pattern of the two lz IPs, whose ordering and splitting have been qualitatively rationalized in terms of the popular concepts of mediated interplay of TS and TB interactions between semilocalized ethylenic orbitals [ 14- 16,23 1. When the longrange TS effects play the stronger role, the x: levels follow the natural sequence n_ > K+, while the predominance of the destabilizing TB interactions between the A and o frameworks leads instead to the inverted sequence. From table 1 it is apparent that the splitting d(n_-x, ) is reproduced satisfactorily along the series: theory: - 1.01 (CH), 1.13 (NO), -1.06 0.79 (BO), -0.16 eV (BN); experiment: (CH), 0.86 (NO), 0.58 (BO), -0.18 eV (BN); this indicates that the OVGF approach accounts reasonably well for the many-body effects in this observable. Therefore, the hyperconjugative TB interactions dominate the TS interactions in the first (CH, zerocarbon bridge) and last (BN, three-carbon bridge) members of the examined series. The opposite situation holds instead in the intermediate members with one- and two-carbon bridges. For the bicycle-alkadienyl systems, the level splitting d can be fitted as a function of the dihedral angle @ between the rings to a quadratic equation: A= uzqj2 + ~,@+a~, where, schematically, the a2 coefficient can be traced back to the destabilizing TB interactions, while the a, coefficient encompasses the stabilizing effect of the TS interactions. In particular, the widening of @ causes an increasing destabilization of n, as a result of an increasingly stronger antibonding mixing of the o orbitals spanning the same symmetry as the II orbitals. By employing the values
V. Galasso/ Nonconjugatedn-electroncyclicsystems Table 1 Vertical IPs of 1+cyclohexadiene Compound CH
and related compounds (in eV )
KT
IP
P
IP,
Compound
Symmetry
KT
IP
P
IP,
9.07 10.02 12.44 13.33 14.50 15.74 15.78 16.52
8.81 9.88 11.07 11.87 13.11 13.95 14.51 14.71
8.82 ‘) 9.88 11.00 11.97 13.32 13.75
NO
8.35 9.48 11.64 12.14 12.43 13.11 13.65 13.66
0.93 0.93 0.93 0.93 0.94 0.94 0.93 0.93
8.69 ” 9.55 11.26 z11.7b’ 12.51 c)
15.32 16.34 16.91 19.20
6bz(= 1 lOal 3a2 6b, 5b Sal 5b, 7al 4b2 3b2 4b, 6al
8.63 9.95 12.76 13.13 13.42 14.18 14.68 14.72
16.67 17.98 18.77 21.56
0.93 0.92 0.92 0.93 0.92 0.89 0.92 0.92 > 0.92 0.90 0.88 0.85
15.75 17.96 18.75 19.50
14.60 16.49 17.31 18.06
0.93 0.89 0.89 0.89
8.68 9.46 10.66 11.26 11.38 13.35 13.42
0.94 0.94 0.95 0.95 0.94 > 0.95 0.95
8.87 ‘) 9.45 10.42
l3ai(x+] 7bz(x-) 9b,
8b, 5bz 3a2
9.07 9.97 11.66 12.19 12.42 14.62 14.31
9.36 9.35 11.73 12.12 12.27 12.38 13.33
8.90 9.06 10.91 11.09 11.46 11.72 12.34
0.95 0.94 0.96 0.95 0.95 0.96 0.94
14.81 14.84 15.90 16.34 17.40 17.74 19.26
13.67 13.77 14.66 15.08 16.21 16.52 17.82
0.94 0.94 0.92 0.93 0.92 0.92 0.89
14.24
13.30
0.95
9ar 7bi 8al 4bz 6br 3bz 7ai
15.15 15.44
14.11 14.27
0.94 0.93
15.48 15.95 16.50 17.81
14.69 14.98 15.29 16.85
0.95 0.94 0.92 0.94
Symmetry 2b,.(x+ ] 1bs,,(x- ] 3b,, 6a, 5b3, 4bz. lb, 3bs. lb,. 4b3. 5% 2bis
BO
233
6bz(x-) llai(x+] 4as 1Oai
14.68 1‘5.6 b) 15.95 16.47 18.58
11.05
1
12.61 *) ... 13.16 ... 13.5 14.30 15.46 15.86 16.97
BN
4a2
12ar 6bz 8bi 1 la,
7b, 5b 3a2
lOa, 4bz 3bz
1
12.75 13.3 13.5 14.24 15.66 16.52 17.16
9.00 =i 9.18 10.4 0
1
10.7 11.1 11.6 12.3 13.5 ‘)
1
... 13.8 ... 14.3 ... 14.8
‘) Ref. [ 11. b, IP estimated from the spectrum in ref. [ 11. C~Thisbandextendsfrom12to14eVwithmaximaat12.51and12.75eVandshou1dersatcl3.3and13.5eV. *) This band extends from 12.2 to 13.9 eV with maxima at 12.61 and 13.16 eV and a shoulder at z 13.5 eV. =) Ref. [4]. ‘) This band extends from 10.2 to 12.0 eV with maxima at ~10.7, ll.l,and 11.6eVandashoulderat z10.4eV. *) This band extends from 13.2 to 15.0 eV with maxima at ca. 13.5, 13.8, and 14.3 eV and a shoulder at s 14.8 eV.
ofN0 (0.86eV, lll’),BO (058eV, BN (-0.18 eV, 130”), weobtain A= -0.004872@+
123.4”),and
[email protected]
(eV)
(note that the last three digits are retained only for numerical consistency). This equation emphasizes the role of A as an effkient monitor of conformational change. The crossover point, where A=0 and the TB interactions cancel the TS interactions exactly, is found to occur at @= 128.8”, of course at an angle near that shown by BN. Furthermore, applying the above equation to the higher homologue in the series, bicycle [ 4.2.2]deca-7,9diene, with a four-car-
bon bridge and a splitting of - 0.50 eV [ 41, q3is predieted to be 132”, somewhat lower than the 137” value proposed by Heilbronner [ 5 ] on the basis of an HMO perturbational model. Quite recently, on the basis of KT ab initio STQ32 1G calculations, Paddon-Row and Jordan [ 24 ] have claimed 7-silanorbomadiene - a derivative of NO where the >CH2 bridging group is replaced by the >SiH2 group - as an example of norbomadienyl system in which the TB effects play a stronger role than the TS interactions at variance with the parent NO. Bearing in mind both the inherent limitation of the KT approximation and the relatively small calcu-
234
V. Galasso / Nonconjugated n-electron cyclic systems
lated splitting ( -0.16 eV), we have considered worthwhile to check this prediction at many-body level. Use was made of the [ 6s4p] basis set for silicon [ 181 and of the ab initio optimized structure [ 241. The OVGF results for the first IPs (P) are: 8.69 eV (0.93) 12a,, 7c+; 8.88 (0.93) 7b2, rt_; 9.94 (0.94) 7b,; 11.50 (0.93) 3az; 11.88 (0.93) 6b2; 12.49 (0.92) lOa,. Therefore, substitution of the >CH2 group by the more electropositive >SiH2 group in the norbornadienyl skeleton causes a stabilization of A_ by 0.5 eV while a destabilization of x, by 0.8 eV. From these results it can be concluded that the prediction by Paddon-Row and Jordan [ 241 is basically correct, i.e. R+ > rr_, and the spacing between the first two bands in the PE spectrum is expected to be small, of the order of 0.2 eV. As a further example of heteroatom substitution at position 7 in the norbomadiene skeleton, we have also considered the oxaderivative, i.e. 7-oxabicyclo [ 2.11 hepta-2,5-diene. A reasonable geometrical model was built on the basis of the experimental structures of NO [ 191 and 7-oxanorbornane [ 251 with @= 113.5’. The OVGF results for the first vertical IPs (P) are: 9.13 eV (0.92) 6bz, A_; 10.22 (0.93) lOal, x,; 10.41 (0.93) 5b2, no; 11.66 (0.93) 3az; 13.29 (0.92) 9ai; 13.60 (0.92) 6bl; 14.00 (0.94) 5b,; 14.63 (0.93) 8a,. These results show a pattern of the first IPs quite different from that of the 7-sila analogue. Indeed, the following electronic effects are brought about by substitution of the >CH2 bridge with the more electronegative oxygen atom: a nearly equal stabilizing effect of ~0.7 eV occurs for both the II MOs of the parent NO,. the canonical sequence x_ > rc+ is maintained, and the splitting 1.09 eV is quite similar to that of NO. The no MO is expected to fall at higher energy than in the saturated 7-oxanorbomane (9.57 eV) and unsaturated 7-oxanorbornene (9.83 eV) [ 261, as a consequence of both delocalization of no into the o framework and no-n interactions. In order to describe adequately the nature of the low-lying excited electronic states of the examined molecules, knowledge of the exact sequence and splitting of the vacant K*levels is as important as that of the occupied A levels, whose origin stems from the same stereoelectronic factors. Recently, Heinrich et al. [ 27 ] performed a systematic investigation on the correlation of the energies of the lowest unoccupied
MOs with experimentally determined negative EAs resulting from electron-transmission spectra. Despite the well-known shortcomings due to neglection of relaxation and correlation effects, they found that the KT can be used for qualitatively correct estimates of EAs, when theoretical results obtained with small basis sets augmented by only polarization functions are employed. On this ground, the present KT ab initio estimates provide the following splittings d*(R*_--JC:: +0.95 (CH), - 1.84 (NO), -1.50 (BO), and - 1.39 eV (BN). The theoretical results for CH and NO are in satisfactory agreement with both assignments and values of the experimental d(EA)s, +0.92eV [28] and -1.52eV [29],respectively. Note that, in contrast to the n: counterparts, the x* levels in BN still follow the natural sequence, i.e. the TS interactions dominate over the TB. The same pattern is also predicted for 7-silanorbomadiene ( - 1.87 eV) and 7-oxanorbomadiene ( - 1.66 eV). Bearing in mind these relatively large splittings, it is reasonable to expect the many-body corrections to KT estimates not to change the sequence of the IF* MOs, so the present orderings can be considered as definitively settled. If we provisionally use the relation: EA = 0.762OKT + 1.2260 (eV), - empirically fitted to the first two experimental EAs of CH, - 1.75 and -2.67 eV [28], and NO, - 1.04 and -2.56 eV [29] - we obtain for EA(rc?+): -0.98 eV (NO), -1.60 (BO), and -1.56 (BN), and for EA(x!_): -2.39 eV (NO), -2.74 (BO), and -2.62 (BN). The corresponding d*s are: - 1.4 1 eV (NO), - 1.14 (BO), and - 1.06 (BN). Along the bicyclo [ n.2.2 ] alkadiene series, NO (n = 1)) BO (n = 2 ), and BN (n = 3), there are two salient features of the A*S:the natural ordering is always maintained and the net splitting 1A* 1 decreases as does A, which is a further manifestation of progressive compensation of the TB and TS stereoelectronic effects.
Acknowledgement
The author thanks Professor W. von Niessen, University of Brunswick (FRG ) , for making available his OVGF program. This work was supported by the Minister0 della Pubblica Istruzione of Italy.
K Galasso/ Nonconjugatedn-electroncyclicsystems
References [ 1] P. Bischof, J.A. Hashmall, E. Heilbronner and V. Homung, Helv. Chim. Acta 52 (1969) 1745. [2] E. Heilbronner and H.D. Martin, Helv. Chim. Acta 55 (1972) 1490. [ 3 ] G. Bieri, F. Burger, E. Heilbronner and J.P. Maier, Helv. Chim. Acta 60 (1977) 2213. [4] M.J. Goldstein, S. Natowsky, E. Heilbronner and V. Homung, Helv. Chim. Acta 56 (1973) 294. [ 51 E. Heilbronner, Israel J. Chem. 10 (1972) 143. [ 61 E. Heilbronner, F. Brogli and E. Vogel, J. Electron Spectry. 9 (1976) 227. [7] E. Haselbach, L. Neuhaus, R.P. Johnson, KN. Houk and M.N. Paddon-Row, Helv. Chim. Acta 65 ( 1982) 1743. [8] H.J. Chiang and SD. Worley, J. Electron Spectry. 21 (1980) 121. [9] T. Kobayashi, Z. Yoshida, Y. Asako, S. Miki and S. Kate, J. Am. Chem. Sot. 109 (1987) 5103. [ lo] W. von Niessen and G.H.F. Diercksen, J. Electron Spectry. 16 (1979) 351. [ 111 G. Bieri, L. Asbrink and W. von Niessen, J. Electron Spectry. 27 (1982) 129. [ 121 M.H. Palmer, J. Mol. Struct. 161 (1987) 333. [ 131 R. Hoffmann, E. Heilbronner and G. Gleiter, J. Am. Chem. Sot. 92 (1970) 707; R. Hoffmann, P.D. Moliere and E. Heilbronner, J. Am. Chem. Sot. 95 (1973) 4860. [14]M.J.S.DewarandJ.S.Wasson,J.Am.Chem.Soc.92 (1970) 3506. [ 151 H. Bock and B.G. Ramsey, Angew. Chem. Intern. Ed. 12 (1973) 734. [ 161 E. Heilbronner and A. Schmelzer, Helv. Chim. Acta 58 (1975) 936.
235
[ 171 L.S. Cederbaum, J. Phys. B 8 (1975) 290. [ 181 T.H. Dunning Jr., J. Chem. Phys. 53 (1970) 2823; T.H. Dunning Jr. and P.J. Hay, in: Methods in Electronic Structure Theory, ed. H.F. Schaefer III (Plenum Press, New York, 1977) p. 1. [ 19 ] H. Oberhammer and S.H. Bauer, J. Am. Chem. Sot. 9 1 (1969) IO; A. Yokozeki and K. Kuchitsu, Bull. Chem. Sot. Japan 44 (1971) 1783,2356; G.A. Jeffrey, J. Buschmann, C.W. Lehman and P. Luger, J. Am. Chem. Sot. 100 (1988) 7218; H.D. Martin, as quoted in ref. [ IO]. [20] A.J. Baker, A.M. Chalmers, W.W. Fllod, D.D. MacNicol, A.B. Penrose and R.A. Raphael, J. Chem. Sot. Chem. Commun. (1970) 166. [ 2 1 ] W. von Niessen, L.S. Cederbaum, W. Domcke and G.H.F. Diercksen, J. Chem. Phys. 66 (1977) 4893; W. von Niessen, G.H.F. Diercksen and L.S. Cederbaum, J. Chem. Phys. 67 (1977) 4124; W. von Niessen, L.S. Cederbaum, W. Domcke and G.H.F. Diercksen, Chem. Phys. 56 ( 198 1) 43. [22] L.S. Cederbaum and W. Domcke, Advan. Chem. Phys. 36 (1977) 205. [23] M.N. Paddon-Row, Accounts Chem. Res. 15 (1982) 245. [24] M.N. Paddon-Row and KD. Jordan, J. Chem. Sot. Chem. Commun. ( 1988) 1508. [25] K Gyanagi, T. Fukuyama, K. Kuchitsu, R. Bohn and S. Li, Bull. Chem. Sot. Japan 48 ( 1975) 75 1. [26] A.D. Bain, J.C. Biinzli, D.C. Frost and L. Weiler, J. Am. Chem. Sot. 95 (1973) 291. [ 271 N. Heimich, W. Koch and G. Frenking, Chem. Phys. Letters 124 (1986) 20. [28] A. Modelli, D. Jones, S. Rossini and G. Distefano, Chem. Phys. Letters 123 (1986) 375. [ 291 V. Balaji, L. Ng, K.D. Jordan, M.N. Paddon-Row and H.K. Patney, J. Am. Chem. Sot. 109 (1987) 6957.