Valence pair function

Orbitals within the same parentheses are nonorthogonal. Orbitals in different parentheses are orthogonal.) The valence orbitals y i and (pi and the core orbital 4 are related to

reflection operation. One of the orbitals in a given pair is 5p-hybrid-//fce, the other is Isn-like. In order to develop a hierarchy of models, we find it convenient to write the valence pair functions in the form... 

Diffuse functions are large-size versions of s- and p-type functions (as opposed to the standard valence-size functions). They allow orbitals to occupy a larger region of spgce. Basis sets with diffuse functions are important for systems where electrons are relatively far from the nucleus molecules with lone pairs, anions and other systems with significant negative charge, systems in their excited states, systems with low ionization potentials, descriptions of absolute acidities, and so on. 

When the ionization spheres of two neighbouring atoms interpenetrate, their valence electrons become delocalized over a common volume, from where they interact equally with both atomic cores. The covalent interaction in the hydrogen molecule was modelled on the same assumption in the pioneering Heitler-London simulation, with the use of free-atom wave functions. By the use of valence-state functions this H-L procedure can be extended to model the covalent bond between any pair of atoms. The calculated values of interatomic distance and dissociation energy agree with experimentally measured values. 

The choice of a single function from either set (36) or (37) does not permit such a useful physical interpretation, and may indeed lead to difficulties as the internuclear distance is varied. Thus if one chooses just the perfectly paired function from the set (36), as -R-> 00 one finds each N atom is described by a curious non-stationary state - the so-called valence state of the atom, about which there has been so much discussion in the literature.18 The choice of the set of functions (36) in which orbitals participating in a bond are directly coupled to each other is just the VB theory as proposed by Slater and Pauling,19 whereas the set (37) formed from atoms in specific L-S coupled states corresponds to the spin-valence theory employed by Heitler.20... 

In the general case valence-state functions rather than hydrogenic atomic wave functions feature in the bonding. It has been emphasized that bond formation consists of delocalization of an effective electron pair in the pres-... 

Wilson and Geratt [56] discussed a pair-function model constructing geminals from non-orthogonal one-electron orbitals. Their calculations, performed on the water molecule, supported qualitative valence-shell electron-pair (VSEPR) models [57] of directed valence. 

Hartree -Fock or Self-Consistent Field (SCF) Method Spin Optimized Self-Consistent Field Method Configuration Interaction Iterative Natural Orbital Method Multi-Configuration SCF Many Body Perturbation Theory Valence-Bond Method Pair-Function or Geminal Method... 

A non-empirical alternative supporting a value X Anb close to 0.2 which has been adopted for lone-pair weights in the preceding treatment was presented later [59], using the concept of eccentric functions to enlarge the valence basis set of heteroatoms by means of lone-pair functions (LPF). The NH3 molecule was studied as a test without and with a LPF in the vicinity of nitrogen. A reference calculation with Slater orbitals of exponents = 1-90, ... 

SO that each pair function is defined in a distinct row. The spatial wave function in which all valence orbitals are nonorthogonal has the form... 

The significance of this pairing function is that it is capable of describing the static correlations that are most important when chemical bonds are broken. In most uses, the core orbitals are uncorrelated (c = 0), resulting in the closed shell generalized valence bond (GVB) wave function of Goddard et al. [127]. 

In the procedure of Christiansen and co-workers [33], a Dirac-Fock atomic wave function is used as the starting point. For each pair of l,j indices, the large-component radial function is used [32] to determine the pseudoorbital by the shape-consistent method [36] it is defined to be equal to the valence radial function in the valence region and to decrease smoothly and nodelessly through the core region to the value of zero at the nucleus. The pseudoorbital is then used to define the potential for that pair of /, j indices. The electron repulsion interaction among valence electrons is removed from these potentials. 

ACPF = averaged CPF ANO = atomic natural orbital CCSD(T) = singles and doubles coupled-cluster approach with a perturbational estimate of the triples excitation Cl = configuration interaction CPF = coupled pair functional CPP = core polarization potential CVCI = core-valence Cl FCI = full configuration interaction ICACPF = internally contracted ACPF ICMRCI = internally contracted MRCI MCPF = modified CPF MRCI = multi-reference configuration interaction NHF = numeric Hartree-Fock SDCI = singles plus doubles Cl. 

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