PPP-VB method

We overview our valence bond (VB) approach to the ir-electron Pariser-Parr-Pople (PPP) model Hamiltonians referred to sis the PPP-VB method. It is based on the concept of overlap enhanced atomic orbitals (OEAOs) that characterizes modern ab initio VB methods and employs the techniques afforded by the Clifford algebra unitary group approach (CAUGA) to carry out actual computations. We present a sample of previous results, sis well sis some new ones, to illustrate the ability of the PPP-VB method to provide a highly correlated description of the ir-electron PPP model systems, while relying on conceptusilly very simple wave functions that involve only a few covalent structures. 

The primary objective of most applications carried out so far was to assess the performance of the PPP-VB method for diverse alternant and nonaltemant -electron systems of aromatic, nonaromatic or antiaromatic character, both electrically neutral and charged. The main emphasis was on ground states of different spin multiplicity, even though some preliminary calculations were also carried out for excited states. The PPP-VB codes were also employed to provide the approximate three- and four-body connected cluster components for the so-called VB-corrected coupled cluster (CC) approach [71]. In the following, we briefly point out the most important aspects of the PPP-VB method and illustrate them with a few typical results. 

To assess the effectiveness of the PPP-VB method in describing the correlated ground states of various w-electron systems, we have examined a set of 70 relatively small molecules... 

We can thus conclude that the PPP-VB method, employing a simple one- or two-parameter OEAO basis and relying on a few covalent (mostly Kekule type) structures, provides an excellent approximation that accounts for a large part of correlation effects. 

We can thus conclude that states of different spin multiplicity (singlets, doublets, triplets, quartets, etc.) of very diverse jr-electron systems (Kekule or non-Kekule, alternant or nonalternant, aromatic, nonaromatic or antiaromatic) can be satisfactorily described by the PPP-VB method with a severely truncated set of covalent or maximally covalent structures using the same simple OEAO basis set hi. In contrast, the MO description requires a different handling of closed and open shell cases and the amount of correlation recovered in states of different multiplicity may be rather unbalanced. 

So far we carried out only a very preliminary study of the excited states [62] for four typical 7r-electron systems CBT, benzene, hexatriene and naphthalene. In all cases we found that the PPP-VB method can successfully describe the low lying excited states using only a small subset of VB structures. For states of a predominantly covalent character, the same OEAO basis as for the ground state can be used. However, for higher lying states with significant ionic character, a re-optimized OEAO basis is preferable. 

As a final illustration of the PPP-VB method we present some new results on the ionization potentials (IPs) and electron aiffinities (EAs) of cyclic polyenes C H with am odd number of sites N = 2n + 1, n = 1,2, -. We compute these quaintities as the difference between the energy of the appropriate ion aind of the pairent molecule. 

Figure 1. The IPs and EAs obtained with the PPP-VB method, employing both the optimal (opt) and average (ave) 61 OEAO basis and involving N VB structures, are compared with the exact FCI results.

A comparison of the exact FCI total jr-electron energies E(FCI) (in eV) with those obtained by the PPP-VB method, employing either the optimal [E(VB, e opt )] or average [U(VB, e( v ))] OEAO 61 basis set and the minimum number N of VB structures, for the ground states of cyclic polyenes C rH r with an odd number of sites N, N = 2n + 1, and of their ions. The degeneracy (Deg.) of these states is indicated by the type of the symmetry species involved (E for doubly degenerate and A for totally symmetric nondegnerate ones). 

We thus believe that the PPP-VB approach represents a viable and useful alternative even for the excited states which, to this day, were invariably treated by MO methods. Particularly in photochemical processes, the insight afforded by the VB formalism may be very useful. 

The above presented examples amply demonstrate that even the simplest version of the proposed PPP-VB scheme, employing a single parameter OEAO 61 basis, represents a viable, very efficient and transparent method that provides highly correlated description of low lying states of jr-electron systems. Moreover, the required 61 basis is readily... 

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