Perturbation theory self-consistent

If we add a perturbation A then the self-consistency is destroyed and we need to re-do the iterative HF-LCAO calculation. The idea of self-consistent perturbation theory is to seek solutions of the perturbed HF-LCAO equations... 

This is similar to self-consistent perturbation theory, except that we just solve the modified HF-LCAO equations... 

Self-Consistent Perturbation Theory of Diamagnetism 1. A Gauge-Invariant... 

Ditchfield, R. Self-consistent perturbation theory of diamagnetism. I. A gage-invariant LCAO(linear combination of atomic orbitals) method for NMR chemical shifts, Mol. Phys. 1974, 27, 789-807. 

R. Ditchfield, Mol. Phys., 27, 789 (1974). Self-Consistent Perturbation Theory of Diamagnetism. I. A Gauge-Invariant LCAO Method for NMR Chemical Shifts. 

In this chapter we consider the most widely used method of the second type the so-called self-consistent perturbation theory. Before developing and implementing the theory it is necessary to put the SCF equation into a new form. 

The equations for time-independent self-consistent perturbation theory are of very similar form to those time-dependent ones we have just studied, but the interpretation of the case of infinitesimal perturbations is, if an)d hing, more problematical. What is the meaning of the fact that there eire non-trivial solutions of the time-independent equations for arbitrarily small perturbations ... 

The effect of small changes in the molecular Hamiltonian due to interactions of the molecule with external fields, solvents and other molecules are often too small to be included directly in the SCF process. Perturbation theory provides a suitable tool for the investigation of these effects since they can be computed directly rather than as small differences between large numbers. If we insist on retaining the single-determinant form of the wavefunction while allowing the orbitals to change and retain electron interaction self-consistency, the self-consistent perturbation theory is obtained. 

Much more enigmatically, the first-order time-dependent self-consistent field approximation is also widely called the Random Phase Approximation (RPA). This terminology is entrenched and so, although the name time-dependent self-consistent perturbation theory is more descriptive and preferable to both time-dependent Hartree-Fock and RPA all are used more or less interchangeably. The evolution of the concept and phrase random phase approximation is sketched in Appendix 27.A to this chapter. 

More important from the point of view of the cormection with self-consistent perturbation theory, the approximation, when translated back into ordinary Coulomb repulsion language, has the physical interpretation of retaining only the electron repulsion in the mean, which is just the classical equivalent of the physics of the single-determinant model. Thus the approximation of neglecting these terms in a (classical) time-dependent treatment has the same physical interpretation as the single-determinant model. 

A self-consistent perturbation theory which leads to similar results has also been developed, e.g., Kuramoto (1983) and Kojima et al. (1984). A different variational approach has been used by Gunnarson and Schonhammer (1983, 1987) to discuss high-energy properties like photoemission spectra. 

Ditchfield R (1974) Self-consistent perturbation theory of diamagnetism. Mol Phys 27 789-807... 

Ditchfield R (1974) Self-consistent perturbation theory of diamagnetism 1. A gauge-invariant LCAO method for NMR chemical shifts. Molec Phys 27 789-807 Duncan TM, Douglass DC (1984) On the P chemical shift anisotropy in condensed phosphates. Chem Phys 87 339-349... 

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