Bonding in molecules and complexes

we have defined electronic states with energies that will be functions of the nuclear positions. These functions, (Ra,Rq) are often referred to as interatomic potentials. A molecule will have a number of electronic states (RA,Rg) but for most geochemical problems we are only interested in the lowest energy (ground) electronic state. 

We would next like an equation for the motion of the atomic nuclei. Without going into the mathematical arguments, we can use the adiabatic approximation to separate our molecular wavefunction into nuclear and electronic wavefunctions  

The Schrodinger equation for the nuclear motion wavefunction i (Ra,Rb) takes the form  

Physically, this means that we will have a set of vibrational and rotational quantum levels (W,) associated with a given electronic state E (Fig. 1). For nearly all systems of geochemical relevance, the adiabatic approximation is perfectly reliable. Two systems where it will fail, however, are Cu and Mn complexes. For these cations, there is a large coupling between the electronic and nuclear motions via the Jahn-Teller effect. This makes difficult to do dynamical simulations of Cu and Mn complexes using simple two-body classical potentials. 

Density functional codes can use a much more flexible range of basis sets. The Amsterdam Density functional (ADF) code (te Velde and Baerends 1992 te Velde 1995), for example, uses both numerical functions and analytic Slater functions to represent atomic orbitals. It is very convenient to set up a density functional calculation by expressing the molecular orbitals as a summation of plane waves. This is used, in particular, in implementation of the Car-Parinello scheme discussed later. 

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In the course of investigating multiple bonds in molecules and complexes by the valence bond approach, we have recently found that such multiple bonds are more accurately described as bent bonds rather than as a and tt bonds (7-5). In order to understand the potential implications of these results for multiple metal-metal bonds, it is important to brieffy review the basic assumptions of the valence bond model and compare them to those of the more familiar molecular orbital model of bonding. 

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