SCVB wavefunction

We are especially interested in calculating accurate intermolecular potentials to be used with classical and quantum dynamics programs. Particularly for systems with larger numbers of valence electrons, we need to be able to obtain very accurate SCVB wavefunction by means of even smaller numbers of structures. To accomplish this we have devised a new approach in order to generate one or more optimal virtual orbitals for each occupied SC orbital [10]. We concentrate here on the case of a single properly optimized virtual orbital for each SC occupied orbital < r... 

Ultimately, the SC occupied orbitals and the optimized virtuals are used to construct the final, variational SCVB wavefunctions. These take the form ... 

The interaction between a helium atom and the LiH molecule has been described using a SCVB wavefunction built up using just 25 structures. Interaction energies, computed along different approaches of the two moieties, compare extremely well with a corresponding traditional SCVB calculation using many more structures. Even a very small energy minimum of about 0.01 mHartree is perfectly reproduced for He at a distance of 7 =11 bohr from the centre of mass of the LiH molecule (collinear approach of He to H—Li). 

Psc Tf P j ), etc. It should be mentioned that eqn (3.26) is slightly more general than the expression reported in refs. 62-64 which is valid only if the reference SC wavefunction is normalised, i.e. for >Soo = 1- The optimal virtual orbitals are calculated through minimisation of E. The final SCVB wavefunction is constructed as a non-orthogonal Cl expansion including all single and double excitations l/ l/ ... 

A SCVB wavefunction incorporating just 25 structures has been shown to produce highly accurate results for the He- -LiH van der Waals system, with marked improvements over a SCVB treatment making use of a much larger number of structures. 

Excited configurations may be constructed by replacing one or more occupied SC orbitals with a virtual orbital, frequently taken from the same stack as the occupied orbital, in which case it is referred to as a vertical excitation. If the occupied orbital is replaced with a virtual from a different stack, then this is referred to as a cross excitation. A linear combination of the reference SC configuration and the excited configurations described above constitutes a so-called spin-coupled valence bond (SCVB) wavefunction. We use the term configuration to denote a particular orbital product, with all possible modes of coupling... 

The resulting orbitals are then used in a standard nonorthogonal Cl expansion (single and double vertical excitations) in order to relax the spincoupling coefficients and to find a variational bound for the energy. We refer to such an expansion as an SCVB wavefunction. In order to improve the description of one-electron properties, we may choose to include, at very little additional cost, configurations with double occupancy of the occupied and/or virtual orbitals. 

Ab initio modem valence bond theory, in its spin-coupled valence bond (SCVB) form, has proved very successful for accurate computations on ground and excited states of molecular systems. The compactness of the resulting wavefunctions allows direct and clear interpretation of correlated electronic structure. We concentrate in the present account on recent developments, typically involving the optimization of virtual orbitals via an approximate energy expression. These virtuals lead to higher accuracy for the final variational wavefunctions, but with even more compact functions. Particular attention is paid here to applications of the methodology to studies of intermolecular forces. 

The right-hand panel of Figure 1 compares the excited curve obtained from the final MR-SCVB (or, MRVB for short) calculation with that from the full Cl. In this study, starting with the double-reference SC functions, we optimized a set of 4 pairs of virtuals for each reference and, at the end, we built a VB wavefunction consisting of 84 spatial configurations for a total of only 125 VB structures. This... 

Another alternative to the SCVB approach is provided by the SCVB treatment,in which one generates one or more optimal virtual orbitals for each occupied SC orbital and then employs these virtuals to construct a non-orthogonal Cl expansion. The simplest case involves the calculation of one optimal virtual orbital for each SC orbital i/. If the SC wavefunction (3.9) is augmented with all vertical double excitations into these virtuals. 

Analogous calculations were performed for Li2, for which the SC wave-function overestimates the value of Re by 9.8% and recovers only 42% of the experimental value of De. The SCVB -4 wavefunction, however, represents a significant further improvement, overestimating Re by only 0.7% and recovering 91.5% of De. FVCAS calculations in the same basis set recover 94% of De (a 0.03 eV improvement), while 2-electron FCI calculations produce a further energy lowering of less than 0.004 eV. 

We have indicated the ability of spin-coupled valence bond (SCVB) calculations to provide compact, though accurate, nonorthogonal configuration interaction expansions for ground and excited states. These wavefunctions can be made even more compact using the SCVB method, which starts from direct... 

In this paper we shall follow this line of reasoning, to show there are some symmetry conditions to be obeyed in order to represent the wavefunction of a molecule as a superposition of waveflinctions of resonance hybrids. Although some of the results to be presented may drastically differ from the classical VB picture, all the predictions are fiilly supported by calculations using modem VB methods, such as GVB (Generalized VB) and SCVB (Spin-Coupled VB), which consider explicit optimization of the singly-occupied orbitals, as suggested by Coulson and Fisher . 

Generalized valence bond perfect pairing (GVB/PP) and spin-coupled valence bond (SCVB) calculations for tri- and polyatomic molecules use multicentre, delocalized orbitals (i.e. 3-centre or many-centre orbitals) to accommodate the active space electrons. To quote Ref 27 The GVB/PP wavefimctions are antisymmetrized products of paired orbitals and represent a single valence bond structure.. .. The SC method is based on a single configuration in which each electron is described by a distinct orbital. The complete spin state is utilized. For example, a 4-electron 3-centre SC wavefunction involves four non-orthogonal 3-centre or-... 

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