Valence bond function

Calculations of nuclear spin-spin couplings by Karplus and co-workers (60) using valence bond functions have been gratifyingly successful. It was to be expected that valence bond functions would be more accurate than LCAO MO functions for this purpose since the former include explicitly effects of spin correlation. For interactions between nonbonded nuclei such as occur, for example, between the hydrogen atoms of CH4 or NH4+, structures of the forms (61)... 

The Slater valence-bond function leads to an energy expression that contains the single exchange integrals between bonded orbitals, such as a and b, with the coefficient +1. These integrals are usually negative,... 

P. C. Hiberty, J. P. Flament, E. Noizet, Chem. Phys. Lett. 189, 259 (1992). Compact and Accurate Valence Bond Functions with Different Orbitals for Different Configurations Application to the Two-Configuration Description of F2. 

P. C. Hiberty, S. Humbel, C. P. Byrman, J. H. van Lenthe, J. Chem. Phys. 101, 5969 (1994). Compact Valence Bond Functions with Breathing Orbitals Application to the Bond Dissociation Energies of F2 and FH. 

When the new orbitals are determined, the Valence Bond function is redetermined using Eq. (2), and the procedure is repeated until convergence is obtained, i.e. all by s in Eq. (6) are zero and the Generalised Brillouin theorem (Eq. (4)) is satisfied. 

Using the hydrogen Is orbitals with optimised f parameters shows that there is not much to choose between these two approaches neither is particularly good. It is, however, possible to obtain a better description, even confining attention to the lsa and ist atomic orbitals. First, following Parr [10], we note that the valence bond function (6.94) represents a covalent structure, with the electrons shared between the two atoms. Alternatively, a function which places both electrons on the same atom,... 

Term in brackets is the valence-bond function for the bond. The remaining terms represent contributions from ionic structures and H H+ with both electrons on the same hydrogen atom. 

Flo. 43-4.—Energy curves for the hydrogen molecule (in units es/2ao) A, for an extreme molecular-orbital wavo function B, for an extreme valence-bond wave function and C, for a valence-bond function with partial ionic character (Weinbaum). 

Is it necessary or desirable always to start from a one-determinant SCF function, to be improved by Cl or other expansion methods Would another starting point be better e.g. a valence-bond function, which is essentially of many-determinant form) ... 

Before going on to IA2, let us express the Heitler-London valence-bond functions for H2 as Slater determinants. The ground-state Heitler-London function (13.101) can be written as... 

Under what conditions are the molecular-orbital and valence-bond descriptions of the c bonding in an octahedral complex equivalent Derive the valence-bond functions shown in Fig. 9-7 from the general molecular-orbital functions. 

The multi-state empirical valence bond (MS-EVB) model elaborated by Voth and his group is more flexible since the valence bond functions are optimized at each step of the molecular dynamics calculation.This model is well adapted for the study of diffusion processes and proton transport chains."... 

In practice, chemists who need to compute the more accurate behavior of a valence bond function usually achieve this by mixing together different MO configurations. In the case just discussed, for example, we can obtain the VB... 

Accurate Valence Bond Functions with Different Orbitals for Different Configurations Application to the Two-Configuration Description of F2. 

Compact Valence Bond Functions with Breathing Orbitals Application to the Bond Dissociation Energies of F2 and FH. 

Orbital wave functions are not the only type of approximate molecular wave functions. In 1927 Heitler and London introduced the valence-bond function ... 

The simple LCAOMO wave function gives the ionic terms equal weight with the covalent terms while the simple valence-bond function omits them completely. A better result is obtained by including the ionic terms with reduced weight. Amodified valence-bond wave function is ... 

A bonding factor corresponds to a single covalent bond, so the bond order for the wave function in Example 20.7 is equal to 2, as in the LCAOMO description of Example 20.6. This wave function does not include ionic terms, but ionic terms can be added to each bonding factor in the wave function to make an improved valence-bond function. 

Actual calculations made with these valence bond functions cannot be expected to lead to accurate values of bond energies, nor could they be expected to lead to any results not given by the above qualitative procedure. The above procedure must be looked upon as a quantum-mechanical description of covalent bond formation based largely on a previous knowledge of experimental fact. In the next chapter we will find that it is possible to treat many problems in a more quantitative manner we will here largely limit ourselves to this descriptive method. 

To improve further the molecular orbital wave-function, we may invoke configuration interaction (C.I.), i.e. linearly combine the bonding configuration Vab(l)Vab(2) with the antibonding configuration )/ (1) )/ (2). Covalent-ionic resonance improves the Heitler-London valence-bond function, This resonance involves linearly combining the covalent wave-function a(l)b(2) + b(l)a(2) with the wave-functions a(l)a(2) and b(l)b(2) for the ionic valence-bond structures A B" and A B . For Hj, the appropriate ionic wave-function is... 

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