Closed-shell mode

In the next section, we will discuss in some detail the example of bonding between two CN radicals, where the bond between the singly occupied 5a orbitals is heavily influenced by the presence of the fully occupied 4a N lone pair orbital. In this case there is, in contrast to the case of Li2, not only overlap between the singly occupied unpaired electron orbital (2s and 5a, respectively) and the opposite closed shell (Is and 4a, respectively), there is also considerable overlap between the 4a orbitals, contributing strongly to the Pauli repulsion. This Pauli repulsion, as well as the Pauli repulsion with the 5a electrons, will of course be different for the different bonding modes (NC—CN, CN—CN, and CN—NC). A detailed analysis is provided in the next section. 

To investigate the bond between thiophene and M in the S (or 771) mode, DV calculations were performed for the complex ion [Cp (C0)2Fe (17 -T)]+ (Cp=cyclopentadienyl, T=thiophene) [77], Due to the strong covalency between the Fe and the ligands, the electron configuration is a low-spin closed-shell, so that no spin-polarization is present. 

Abstract This chapter reviews some of the recent work about hydrogen-hydrogen bonding (an essentially non-electrostatic closed-shell interaction) and contrasts it with dihydrogen bonding (a predominantly electrostatic closed-shell interaction). These two modes are shown to represent the two extremes of a continuum of closed-shell interactions between pairs of hydrogen atoms in molecules. 

Cluster expansion representation of a wave-function built from a single determinant reference function [1] has been eminently successful in treating electron correlation effects with high accuracy for closed shell atoms and molecules. The cluster expansion approach provides size-extensive energies and is thus the method of choice for large systems. The two principal modes of cluster expansion developments in Quantum Chemistry have been the use of single reference many-body perturbation theory (SR-MBPT) [2] and the non-perturbative single reference Coupled Cluster (SRCC) theory [3,4]. While the former is computationally economical for the first few orders of the perturbation expansion... 

Following the customary terminology, we will call inactive holes the inactive occupied orbitals, doubly filled in every model CSF. The inactive particles will refer to aU the orbitals unoccupied in every CSF. Orbitals which are occupied in some (singly or doubly) but unoccupied in others are the active orbitals. In our spin-free form, the labels are for orbitals only, and not for spin orbitals. From the mode of definition, no active orbital can be doubly occupied in every model CSF. We want to express the cluster operator T, inducing excitations to the virtual functions, in terms of excitations of minimum excitation rank, and at the same time wish to represent them in a manifestly spin-free form. To accomplish this, we take as the vacuum—for excitations out of 4> — the largest closed-shell portion of it, For each such vacuum, we redefine the holes and particles, respectively, as ones which are doubly occupied and unoccupied in < 0 a-The holes are denoted by the labels. .., etc. and the particle orbitals are denoted as a, etc. The particle orbitals are totally unoccupied in any or are necessarily... 

For these three materials, all have nearly equal anion and cation masses, similar closed shell electronic configurations, and nearly the same ratios of anion to cation ionic radii, —1.35 [64]. Yet aside from the RW vibrational modes, the characteristic vibrational patterns differ significantly. This is especially true for the crossing modes which appear to exist across the Brillouin zone only for RbBr and for the optical modes which are seen in NaF but not in KCl and RbBr. The differences certainly lie with the quite different balance of forces, Coulombic versus short-range repulsions, attributable to the range of sizes and polarizabilities of the ions, particularly of the anions. This absence of similarity also illustrates the importance of close collaborations between theoretical and experimental groups in the analysis and interpretation of HAS data. 

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