Polyelectronic theory

Th. Mercouris, C.A. Nicolaides, Polyelectronic theory of atoms in strong laser fields. C02-laser seven-photon ionisation of H, ]. Phys. B 21 (1988) L285. 

The equation determining the optimum orbitals of polyelectronic systems in the case of the SCF and MCSCF theories can be written in the form ... 

The theory of chemical shifts of the nuclei of polyelectronic atoms is complicated and certainly does not yet produce results in quantitative agreement with theory. It is conceivable that a more qualitative use of these parameters might be more appropriate to the problem in hand and an example of this sort is illustrated in Fig. 8, due to Lauterbur (75), where the chemical shifts of the Si and nuclei in analogous com-... 

The aim of molecular orbital theory is to provide a complete description of the energies of electrons and nuclei in molecules. The principles of the method are simple a partial differential equation is set up, the solutions to which are the allowed energy levels of the system. However, the practice is rather different, and, just as it is impossible (at present) to obtain exact solutions to the wave equations for polyelectronic atoms, so it is not possible to obtain exact solutions for molecular species. Accordingly, the application of molecular orbital theory to molecules is in a regime of successive approximations. Numerous rigorous mathematical methods have been utilised in the effort to obtain ever more accurate solutions to the wave equations. This book is not concerned with the details of the methods which have been used, but only with their results. 

Equation (2.1) cannot be solved exactly for a polyelectronic atom A because of complications resulting from interelectronic repulsions. We therefore use approximate solutions which are obtained by replacing A with a fictitious atom having the same nucleus but only one electron. For this reason, atomic orbitals are also called hydrogen-like orbitals and the orbital theory the monoelectronic approximation. 

However, even though it is formulated rather easily, this problem cannot be solved exactly. The difficulty is the same as that encountered in dealing with polyelectronic atoms—the electron correlation problem. Since we cannot account for the details of the electron movements, we cannot deal with the electron-electron interactions in a specific way. We need to make approximations that allow the solution of the problem but that do not destroy the model s physical integrity. The success of these approximations can be measured only by comparing predictions from the theory with experimental observations. In this case we will see that the simplified model works well. 

Spin-orbit coupling is an addition to the Schrodinger equation but it is a natural feature in Dirac s theory which associates relativity theory with quantum mechanics. There are, however, other relativistic effects in the electronic structure of polyelectronic atoms which can be related to changes in the electron mass with velocity (for a review on relativistic effects in structural chemistry, see ref. 62). 

In QSAR of enzyme inhibition reactions, quantum-chemically calculated electrostatic or MO-related descriptors have been widely used. The former are expected to describe the complex formation between enzyme and the substrate, whereas the latter reflect the chemical reactivity of the substrate at the site. Already in 1967, Klopman and Hudson [83] developed a polyelectronic perturbation theory, according to which the drug-receptor interactions can be under either charge or orbital control. Thus the net atomic... 

M. Bylicki, S.l. Themelis, C.A. Nicolaides, State-specific theory and computation of a polyelectronic atomic state in a magnetic field. Application to doubly excited states of H-, J. Phys. B 27 (1994) 2741. 

The Schrodinger equation is not exactly soluble for polyelectronic systems due to the electron-electron interaction. In order to solve approximately the Schrodinger equation, different methods are available. The most traditional way is based on the Hartree-Fock (HF) method. An alternative treatment is based on the Density-Functional Theory (DFT). 

The importance of the hydrogen molecule ion for the theory of diatomic molecules is similar to the importance of the hydrogen atom for our understanding of atoms both H and H2 are one-electron systems for which the Schrbdinger equation can be solved exactly. The exact solution of the one-electron species is then used as a starting point for the discussion of polyelectron species for which exact solutions of the Schrodinger are unavailable. 

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