Localized orbitals in nonmetallic ring systems

Abstract

Localized molecular Hartree᎐Fock orbitals have been determined by means of an iterative procedure consisting of orthogonalization and configuration interaction employing single excitations. For ring systems the rotational symmetry has been included explicitly to obtain Wannier-like orbitals suited for a posteriori correlation calculations using only the most important contributions within a limited region around one reference ring segment. Applications involving different estimates of the correlation Ž . energy include as model systems H , the ionic Li H , and a weakly bound 2 2nq1 n n Ž . beryllium ring as well as the strongly covalent molecule CH forming a closed ring. 36In all cases, the localized and canonical MP2 results are close, and the localized Epstein᎐Nesbet second-order gives a good estimate of more expensive MP4 or CEPA-0 values.

Ab initio correlation corrections to the Hartree-Fock quasi band-structure of periodic systems employing Wannier-type orbitals

“…r CÀC 0X1536 nm, r CÀH 0X1083 nm, CÀCÀC 112X7 Y and HÀCÀH 106X8 . Details of the algorithm employed to obtain the HF solution in local orbitals and examples of applications both for HF and for correlation calculations are given in papers I and II ( [27] and [28]). …”

“…16, since the repetition of the state jli would go through the -space, an event which is not allowed by the Bloch equations without changing the diagram type by invoking backfold diagrams. The same kind of summation was used for the ground-state energy calculations in papers I and II ( [27] and [28]). Additionally the Epstein-Nesbet (EN) corrections [43] were applied, using the diagonal of the exact Hamiltonian r as zeroth-order Hamiltonian r 0 rather than the diagonal of the Fock operator p , i.e.…”

“…The present paper being the third one in a series on ring molecules, we will henceforth denote [27] and [28] as papers I and II. The implementation described in these articles is used to obtain HF orbitals, and is the basis for the programming of the module used to calculate the correlated band structures presented here.…”

Theory and calculation of excited-state wave functions and properties

“…In this section we summarize results of some of our recent work on this topic [3]. BSC are also discussed elsewhere in these proceedings [35]. (I) The decay of the nonstationary atomic state and the definition of its energy.…”

Fragment-Localized Kohn−Sham Orbitals via a Singles Configuration-Interaction Procedure and Application to Local Properties and Intermolecular Energy Decomposition Analysis

“…The fact that the construction of Hartree-Fock orbitals through the singles-CI method is useful has been demonstrated several times since its proposition, in particular for periodic systems. 19,37,61 The derivation of the singles-CI equations through the minimization of the Rayleigh quotient with respect to the expansion coefficients in the space of determinant may be found in standard textbooks. 62 What remains in this section is to show that the minimization of the DFT energy functional with respect to a multideterminantal wave function leads to similar expressions for the matrix elements of the CI matrix.…”