General Molecules and Molecular Aggregates

In this chapter, the case of general molecules — meaning molecules of arbitrary structure and thus arbitrary external nuclear potential — is considered. We will understand how the numerical solution of mean-field equations for many-electron atoms helps us to solve the molecular problem. The key element is the introduction of analytically known one-particle basis functions rather than an elaborated numerical treatment on a three-dimensional spatial grid, which is feasible but not desirable (a fact that will become most evident in section 10.5). 

Technically, the four-component quantum chemical methods for molecules will turn out to be very much like those known from nonrelativistic quantum chemistry. Historically, the latter based on Schrodinger s one-electron Hamiltonian were developed first. Four-component molecular quantum chemistry 

Relativistic Quantum Chemistry. Markus Reiher and Alexander Wolf 

The development of MOLFDIR came to an end in 2001 and some of the developers of this program joined forces with a new Scandinavian program, Dirac, that emerged in the mid 1990s [518]. Dirac contains an elegant implementation of Dirac-Hartree-Fock theory as a direct SCF method [317] in terms of quaternion algebra [318,319]. For the treatment of electron correla- 

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We should mention that relativistic electronic structure calculations on solid-state systems have been carried out as well. However, our focus here will not be on the special case of translational symmetry as we rather concentrate on molecules and molecular aggregates. The general principles may, of course, be transferred to the special case of crystals, and we may refer the reader for further details to Refs. [390,391,537-544], where four-component and also approximate relativistic Hamiltonians are considered. 

In the preceding two chapters, we dealt with general unitary transformation schemes to produce a one-electron Hamiltonian valid for only the positive-energy part of the Dirac spectrum that governs the electronic bound and continuum states. Evidently, these unitary transformation schemes are elegant but involved. Developments in quantum chemistry always focus on efficient approximations in a sense that the main numerical contribution of some physical effect is reliably captured for any class of molecule or molecular aggregate. The so-called elimination techniques have been very successful in this sense and are therefore discussed in the present chapter. 

The experimental verification of Gibbs theorem. Since the osmotic pressure of a solution is generally difficult to measure, it is simplest to choose a case such that Raoult s law holds good and the concentration of the solution may be used in place of osmotic pressure. The solution should therefore be dilute and should be a true solution the solute, that is, must be dispersed as simple molecules and not as molecular aggregates like soap micelles. These conditions were obtained by Donnan and Barker Proc. 

Several theories have been developed to explain how energy absorbed by one molecule is transferred to a second acceptor molecule of the same or a different species. At first sight exciton theory,20 66 which accounts for excitation transfer in molecular aggregates or crystals and the Davydov splitting effects connected with it, appears to bear little relationship to the treatment of long-range resonance transfer as developed, for example, by Forster.81-32 However, these theories can be shown to arise from the same general considerations treated at different well-defined mathematical limits.33-79... 

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