VBSCF

The VBSCF and EH-MOVB potential energy surfaces for the nucleophilic substitution reaction of HS and CH3CI are depicted in Figure 4-2. The energy contours determined using the EH-MOVB method (Figure 4-2A) are found to be in good accord... 

However, using the newly developed nonorthogonal Valence Bond SCF (VBSCF) method these VB structures can be constructed directly from purely carbene localized orbitals, without the uncertainty introduced by the orthogonality tails15,16. The orthogonal LMO analysis described above (OVB) is more convenient computationally, but a limited number of real VB calculations need to be carried out on actual heteronuclear doublebond systems to compare with and to validate the LMO results. This analysis has been carried out here using ab initio VBSCF computer codes. 

For the OVB and VBSCF theory levels it remains to define the set of structures that comprise the wave function. If the two variably occupied orbitals on each carbene fragment [CF1(A) and XH(A)] are labeled 11, 12, rl and r2 (1 = left and r = right), then Table 1 gives the orbital distribution of all the structures that can be composed by distributing 4 electrons among the 4 orbitals. These structures can be classified as covalent, with two electrons on each carbene irrespective of spin coupling, and charge transfer (CT) in either the 1 - r or r —> 1 directions with an uneven number of electrons on each carbene... 

In the VBSCF method the wave function is expanded as a linear combination of the 20 structures described in Table 1. Since the orbitals are nonorthogonal, the sum of the squares of the structure expansion coefficients (C,) don t add up to one. However, a measure of the importance of each structure s wave function ( I, ) can be obtained from the formula in equation 1 for the weight, tV,l38) ... 

Table 4 also contains an analogous analysis of the saturated CH3—XH3 systems for X = C - Pb, for comparison purposes. The optimized geometries were taken from CAS (2,2) calculations on CH3—XH3 using the CEP-DZP basis set. VBSCF calculations were then carried out on the CH3—XH3 set using the usual 3 VB structures one covalent (CH3 XH3) and two ionic (CII3 XI[3 and CH3-XH3+)39. 

We will now discuss the heteronuclear double-bonded systems in light of the carbene S-T gaps and the weight analysis of the contributing VB electronic structures to the total wave function. The VBSCF and OVB structure weights summed by category are set out in Tables 7 and 8. For a somewhat different approach, analysis and discussion of these aspects the reader is referred elsewhere14. 

Figure 6 shows a Hess cycle which links benzene (b) to its reference molecule (R), such that the energies of the steps sum up to the Dewar resonance energy of benzene, DRE(b). At the VBSCF/6-31G level,111 the DRE(b) value is 20.4 kcal/mol, which is within 1 kcal/mol of the experimentally derived value27 based on heats of formation of benzene and cyclohexatriene (the latter value is determined from an additivity scheme). Our older value in the original literature,5 DRE(b) = 31 kcal/mol, was determined with the Kollmar method,157 which is less accurate than the VBSCF method111 used here. Since, our VB-derived DRE(b) value matches the unanimously... 

Shaik, S. Hiberty, P. C. Shurki, A. Wu, W. Danovich, D. Unpublished VB calculations on 3-electron—3-center, 4-electron— 4-center, and 6-electron—6-center species. These VB calculations which are cited in this study were performed at the VBSCF/6-31G level. A bond in a localized structure is expressed with bond-distorted orbitals as explained by Mo et al.149... 

J. H. van Lenthe, F. Dijkstra, W. A. Havenith, in Valence Bond Theory, D. L. Cooper, Ed., Elsevier, Amsterdam, The Netherlands, 2002, pp. 79-116. TURTLE—A Gradient VBSCF Program Theory and Studies of Aromaticity. 

The second output for HF was calculated using VBSCF/STO-3G, with the program XMVB (7), and is displayed in Output 2.2. The relevant output information begins again with the symbolic representation of the structures, which are written in the same manner as before, 4 5 , 4 4 , and 5 5 , and represent the HL and ionic structures of the H—F bond, as sketched in Scheme 2.1. The number labels of the orbitals are 4 for the bond hybrid of F, and 5 for the AO of H. The rest of the valence electrons are kept in doubly occupied orbitals on fluorine, and the filled subshell is labeled as 1 1 2 2 3 3 . This subshell accompanies all the structures. The core electrons are not mentioned specifically, although they are included in the calculations. 

W. Wu, S. Shaik, W. H. Saunders, Jr., J. Phys. Chem. A 106, 11616 (2002). Comparative Study of Identity Proton Transfer Reactions Between Simple Atoms or Groups by VBSCF Methods. 

The Valence Bond Self-Consistent Field (VBSCF) method has been devised by Balint-Kurti and van Lenthe (32), and was further modified by Verbeek (6,33) who also developed an efficient implementation in a package called TURTLE (11). Basically, the VBSCF method is a multiconfiguration SCF procedure that allows the use of nonorthogonal orbitals of any type. The wave function is given as a linear combination of VB structures, (Eq. 9.7). 

The VBSCF method permits complete flexibility in the definition of the orbitals used for constructing the VB structures, d>A-. The orbitals can be allowed to delocalize freely during the orbital optimization (resulting in... 

OEOs), thereby performing GVB or SCVB calculations. The orbitals can also be defined by pairs that are allowed to delocalize on only two centers (BDOs), or they can be defined as strictly localized on a single center or fragment (see below). The VBSCF method is implemented in the TURTLE module (now being a part of GAMESS—UK) and in the XMVB package. 

The flexibility of the valence bond self-consistent field (VBSCF) method can be exploited to calculate VB wave functions based on orbitals that are purely localized on a single atom or fragment. In such a case, the VBSCF wave function takes a classical VB form, which has the advantage of giving a very detailed description of an electronic system, as, for example, the interplay between the various covalent and ionic structures in a reaction. On the other hand, since covalent and ionic structures have to be explicitly considered for... 

Consider, for example, the dissociation of an A-B bond, where A and B are two polyelectronic fragments. Including the two HAOs that are involved in the bond in the active space, and the adjacent orbitals and electrons in the spectator space, the VBSCF wave function reads as follows ... 

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