Covalent wavefunction

The extension of this method to the case of a molecule of the form ABn, taking into account several valence electrons on the central atom, is straightforward. We consider q such valence electrons stemming from a configuration ( /) on atom A (Kg<2/+ 1). The set of covalent wavefunctions are now written as... 

A VB formulation of CASSCF wavefunctions is attractive because as chemists we believe that we can attach physical significance to the various VB covalent configurations. However, we would also like to introduce an other aspect. VB wavefunctions can always be written as eigenfunctions of what is known as a Heisenberg spin hamiltonian. The parameters of this hamiltonian have a simple physical interpretation and this provides a very useful way of Modelling MC-SCF results. Let us introduce the idea with a 2 electron 2 orbital system again. Using a covalent wavefunction... 

For the one-center valence contribution, there are essentially three factors that control its value (a) the radial wavefunction of the 3d orbitals, (b) the covalent dilution of the 3d orbitals with ligand orbitals, and (c) the occupation pattern of the 3d shell. An additional factor may be low-symmetry induced 3d/4p mixing. We will focus on the first three factors here. 

A natural starting point for modem valence bond applications lies in the optimization of the spin-coupled wavefunction [28], which consists of a single covalent configuration of N singly occupied orbitals ... 

A two-configuration MCSCF-MI wavefunction corresponding to the covalent -A -I- BH - and ionic - AH -i- - systems is constructed in the form ... 

Clearly, the three Z CSFs retain purely covalent R —> °° character even in the heteronuclear case. The Z, lZ, and JZ (all three of which can undergo Cl mixing now) possess one covalent and two ionic components of the form sxa Sy(3 + sya sx(3, sxa sx(3, and sya sy(3. The three singlet CSFs therefore can be combined to produce a singlet covalent product function sxa Sy(3 + sya sx(3 as well as both X + Y 2 and X + Y ionic product wavefunctions... 

Figure 7 should serve to illustrate the text, concerning our opinion of how this reversal comes about. For terms internal to the set, there occurs only a relatively small nephelauxetic reduction in excitation energies with materials of advancing covalency. However the differential effects between the f and d levels are, it is evident, quite large, and not monotonic. Advanced p/d mixing inhibits further expansion of the f wavefunctions. How the energy of the final state optically excited d-electron should be correlated with the bands on Fig. 1 is dealt with in the main text. 

R. S. Mulliken,/. Chem. Phys., 23, 1833, 1841 (1955). Electronic Population Analysis on LCAO-MO Molecular Wavefunctions. I. (no subtitle). II. Overlap Populations, Bond Orders, and Covalent Bond Energies. 

With establishment of the crystal structure, three major features concerning the electronic structure of the blue copper site can be addressed. These features are 1) the nature of the thiolate and thioether bonds, 2) the nature of the ground state wavefunction and 3) the extent of covalency. We have also become strongly involved in using photoelectron spectroscopy as a powerful approach toward determining covalency in transition metal complexes. These will be discussed in turn. 

In some cases, the HF wavefunction does not describe the molecular wavefunction well, even to a first approximation, and MP2 and CCSD(T) methods are also usually inappropriate. This happens especially often when two electrons are nominally paired but in practice are partially decoupled, as in a molecule with a covalent bond that is partly broken. This can happen if the bond is stretched (H2 at long bond lengths is a classic case where HF fails). 

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