Evaluation of spectral and other experimental parameters using Hartree-Fock-Roothaan calculations

Evaluation of spectral and other experimental parameters using Hartree-Fock-Roothaan calculations 

Hartree-Fock-Roothaan methods have often been quite successful in the calculation of properties despite the fact that the variational principle upon which they are based ensures only the best total energy. In particular, other energetic properties such as force constants and charge-distribution properties such as electron-density distributions and electric-field gradients are well reproduced. 

Many of the properties described in Chapter 2 can be rather routinely evaluated from ground-state wave functions for the equilibrium geometry. Such properties, P, can be expressed as a sum over molecular orbitals i as  

One set of quantities often evaluated from the ground-state wave function that are not quantum-mechanical observables are the various components of the Mulliken population analysis (Mulliken, 1955, 1962). For example, we could define the net Mulliken charge on an atom A as  

There are also properties for which the magnitude is dependent upon transition intensity and for which accurate results can be obtained only with perturbation theory examples occur in currently much studied areas like NMR spectroscopy (described in Chapter 2), but also involve other properties like magnetic susceptibilities and refractive indices, which are not much studied from an electronic structure point of view (although we would argue that, due to advances in theory, such experimental techniques are ripe for further exploration). Within a Hartree-Fock approach the perturbation of a molecule by electric or magnetic fields can be calculated at a number of levels of theory. Coupled Hartree-Fock perturbation theory (Lipscomb, 1966 Ditchfield, 1974), which arrives at a self- 

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