Polyelectronic systems

Had we been dealing with a polyelectron system, there would have been extra terms in the total Hamiltonian to take account of the electron-electron repulsion. These would have also been collected into Hg. 

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

Quantum mechanics has made important contributions to the development of theoretical chemistry, e.g. the concept of quantum mechanical resonance in the interpretation of the perturbation in the excited states of polyelectronic systems, the concept of exchange in the formation of a covalent bond, the concept of non-localized bonds (though, in my view, unsatisfactory and only arising from a neglect of electronic repulsions), the concept of dispersion forces etc., but it is noteworthy that all these ideas owe their success and justification to their ability to account qualitatively for previously unexplained experimental facts rather than to their quantitative mathematical aspect. 

The above rule can readily be extended to other polyelectronic systems, like the tt system of benzene (6), or to molecules bearing lone pairs as in formamide (7). In this latter case, calling n, c, and o, respectively, the tt atomic orbitals of nitrogen, carbon, and oxygen, the VB wave function describing the neutral covalent structure is given by Equation 3.10 ... 

It was Pauling and his collaborators who generalized the Heitler-London treatment of the hydrogen molecule to general polyelectronic systems and gave the rules for evaluating the Hamiltonian matrix elements [3,4], which could also... 

Pre-lab 5.2 Electronic Spectra of Metal Complexes—Polyelectronic Systems... 

The Hamiltonian, H, for polyelectronic systems (atom or molecule) is given by Eq. (1.110). It can be divided into three terms HR, a term intrinsic to the radiation field, HM, a term intrinsic to the molecular field, and Hh a term for the interaction between the radiation and the molecular fields. The term //, is further divided into first and second order terms of the vector potential, A, for the quantified operators, p-A = A p, using Vvl = 0. 

The orbital picture has proved invaluable for providing insight and qualitative interpretations into the nature of the bonding in and reactivity of chemical systems. It is one which we would like to retain for polyelectronic systems to provide a unifying theme that links the simplest systems with much more complicated ones. 

We now turn to the general case. What is an appropriate functional form of the wavefunction for a polyelectronic system (not necessarily an atom) with N electrons that satisfies the antisymmetry principle First, we note that the following functional form of the wavefunction is inappropriate ... 

Indeed, the techniques of repeated diagonalization of the Hamiltonian on a large basis set and the search for resonance states from the numerical features of the roots upon variation of the function space may lead to reliable conclusions for models or for certain cases of ground shape resonances or of low-lying states of simple systems for which the chosen function space happens to describe the inner part of the resonance accurately. However, it was evident in the late 1960s that such methods had (have) certain limitations when it comes to the MEP in complex, polyelectronic systems. For example, for complex spectra of polyelectronic systems the root-identification criteria may not always lead to physically correct results, even qualitatively. Thus, in spite of careful (and computationally costly) examination, resonance states may be missed or roots may be wrongly attributed to resonances that do not exist. 

Y. Komninos, Th. Mercouris, G.A. Nicolaides, Ab initio calculation of time-dependent control dynamics in polyelectronic systems involving bound and resonance states Application to a quartet spectrum of He , Phys. Rev. A 77 (2008) 013412. 

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). 

With the above introduction to excited state electronic structure and having established the notation conventions to be used from now on, we can begin to deal with state manifolds of polyelectronic systems. Before we proceed to do so, we note parenthetically the lucid discussion and ingenius utilization of the "two electron-... 

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