Block-localized wavefunction

Alternatively, the height of the crossing point can be calculated with any MO-based method, by determining the energy of the reactant wave function at zero iteration (see Appendix 23A), by constrained optimization of block-localized wavefunctions [44], or by an energy decomposition scheme of the Morokuma-analysis type [45]. Lastly, the height of the crossing point can be computed by means of molecular mechanical methods [46], or related empirical VB calculations [47,48]. 

NBO)-based approaches (iv) aromatic fluctuation index (FLU) by M. Sola and coworkers (v) block-localized wavefunction (BLW) method by P. v. R. Schleyer and Y. Mo and (vi) energy decomposition analysis (EDA) by F. M. Bickelhaupt and coworkers. 

Block localized wavefunction (BLW) method s The electron delocalization to the cationic carbon and neutral boron center can be estimated by removing the vacant p-orbitals from the expansion space of molecular orbitals. Although this simple orbital deletion procedure (ODP) technique is limited to the analysis of positive hyperconjugation in carbocations and boranes, it has been generalized and extended to the block localized wavefunction (BLW) method. ... 

Figure 6.40 B3LYP geometries and block localized wavefunction (BLW) estimates of delocalization energies in...

Mo Y, Song L, Lin Y (2007) Block-localized wavefunction (blw) method at the density functional theory (dft) level. J Phys Chem A 111(34) 8291-8301. dol 10.1021/jp0724065... 

The BLW method combines the MO and VB theories. In this method, the wavefunction for a localized (diabatic) state is defined by limiting the expansion of each MO (called block-localized MO) to a predefined subspace. Block-localized MOs belonging to different subspaces are generally non-orthogonal. A conceptual advantage of this method is that the BLWs for diabatic states are optimized self-consistently, and the adiabatic state is a combination of a few (usually two or three) diabatic state wavefunctions. 

The symmetry projection of the wavefunction is equivalent to a particular orbital transformation among the occupied orbitals of the wavefunction. If the CSF expansion is full within these sets of symmetry-related orbitals, no new CSFs will be generated by this orbital transformation. This type of wavefunction could have been computed directly in terms of symmetry orbitals with no loss of generality. (In fact, the CSF expansion expressed in terms of symmetry orbitals will usually result in fewer expansion terms because the symmetry blocking of the individual CSFs allows those of the incorrect symmetries to be deleted from the expansion.) However, if the CSF expansion is not full within these orbital sets, it is possible that the symmetry transformation of the orbitals will generate new CSF expansion terms. The coefficients of these new CSF expansion terms are determined by the old expansion coefficients and the symmetry transformation coefficients. For example, consider the case of two H2 molecules, described in terms of localized orbitals, separated by a reflection plane. Assume that the localized description of the two H2 molecules is of the form... 

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