A new intrinsic localization algorithm is suggested based on a recently developed mathematical measure of localization. No external criteria are used to define a priori bonds, lone pairs, and core orbitals. It is shown that the method similarly to Edmiston–Ruedenberg’s localization prefers the well established chemical concept of σ–π separation, while on the other hand, works as economically as Boys’ procedure. For the application of the new localization algorithm, no additional quantities are to be calculated, the knowledge of atomic overlap intergrals is sufficient. This feature allows a unique formulation of the theory, adaptable for both ab initio and semiempirical methods, even in those cases where the exact form of the atomic basis functions is not defined (like in the EHT and PPP calculations). The implementation of the procedure in already existing program systems is particularly easy. For illustrative examples, we compare the Edmiston–Ruedenberg and Boys localized orbitals with those calculated b...

A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions

Maximally-localized Wannier functions for disordered systems: application to amorphous silicon

The fundamental band gap and the exciton binding energies of t‐PA have been evaluated with the aid of ab initio Hartree–Fock plus Mo/ller–Plesset perturbation theoretical calculations. The irreducible self‐energy part has been expanded up to third order and the irreducible vertex part has been expanded up to second order. The results support one of several controversial assignments of the ∼2 eV peak in the experimental absorption spectrum of trans‐polyacetylene, namely that to interband transitions.

Ab initio calculations of correlation effects in trans‐polyacetylene

Recent advances in the quantum theory of polymers : proceedings of the workshop held in Namur (Belgium), February 11-14, 1979

A mathematically well-defined measure of localization is presented based on Mulliken's orbital populations. It is shown that this quantity equals 1 for core- and lone-pair orbitals, 2 for two-atomic bonds, 6 for benzene rings, etc., and it is applicable for delocalized canonical HF orbitals as well. The definition of this quantity is general in the sense that ab initio MOS with overlapping AO expansion, and semiempirical wave functions using the ZDO approximation as well, can be treated. The localization quantity is essentially “intrinsic,” i.e., no subdivision of the molecule is required. For N-electron wave functions, mean delocalization can be defined. This measure is not invariant to unitary transformations of the one-electron orbitals, characterizing in this way the localized or extended representation of the N-electron wave function. It can be proven, however, that for unitary transformed wave functions a maximum delocalization exists which depends only on the physical (N-electron) properties of the molecule. It is shown that inhomogeneous charge distribution can cause strong electron localization in molecular systems. The delocalization of the canonical Hartree–Fock orbitals, the Parr–Chen circulant orbitals, and the optimum delocalized orbitals is studied by numerical calculations in extended systems.

Localization measure and maximum delocalization in molecular systems

Ab initio crystal orbital calculations with extended basis sets and model potentials are performed for one-dimensional periodic systems. The results of restricted Hartree–Fock-type calculation for all-trans polyacetylene (CH)n and linear and bent hydrogen-bonded poly(hydrogen fluoride) (HF)n are mainly reported. The results, in particular total energies per unit cell, are shown to be much more dependent upon the basis sets than on the method of lattice-sum truncation, number of k points, or order of neighbor interactions.

Ab initio crystal orbital calculations on (CH)n and (HF)n with extended basis sets

A "pseudo-potential"study on Roothaan's open-shell system

Optimization with a direct search for orbital localization

The method of orthonormality-constrained variation is extended using a dual-basis set instead of a single orthonormal basis. The complete and the partial variation methods are discussed and applied to electronic systems. It is found that the present formulation leads to the most general equation in the coupling operator method.

Susumu Narita

Papers

Ab initio crystal orbital calculations on (CH)n and (HF)n with extended basis sets

A "pseudo-potential"study on Roothaan's open-shell system

Optimization with a direct search for orbital localization

Dual‐basis orthonormality‐constrained variation method