The Spin-Coupled Valence Bond SCVB Approach

2 The spin-coupled valence bond (SCVB) approach 

In its simplest form (6), spin-coupled theory is based on a single product of N singly occupied nonorthogonal orbitals (Jy for the N active electrons  

At convergence of a single-configuration spin-coupled calculation, the active orbitals tv satisfy separate orbital equations based on (A-l)-electron operators from which the particular occupied orbital has been excluded (9)  

In this way, we obtain for each active electron a stack of fairly compact orthonormal virtual orbitals that correspond closely to the physical situation in actual excited states. Virtual orbitals in different stacks may of course overlap with one another. 

In order to solve the scattering problem, it proves convenient to avoid the sharp changes in the nonadiabatic couplings by transforming to the so-called p-diabatic representation in which the matrix elements of d/dR are zero. Explicitly, we carry out a unitary transformation using the matrix W(R) which satisfies  

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The latter was developed as a single-configuration method, complemented by non-orthogonal configuration-interaction calculations exploiting virtual orbitals in the Spin-Coupled Valence Bond (SCVB) approach [5] (for a review, see e.g. Ref. [6]). More recently, the use of perturbative virtuals has been introduced, giving rise to the SCVB variant of the method [7] [8]. There are further accounts of SCVB in this volume. 

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