Many-electron theory

The wave function for a single electron, i(ri, is a function of the position coordinates of the electron Fi = (xj, y, Zj) and the spin coordinate To simplify the notation, we write this as r(l) = r( i, i). The absolute square of function /, V / (1)V /(1) = v /(l) is the probability density of the electron. As already stated, a function of position in space and spin is called a spin orbital. A function of position only is called an orbital. If we integrate over a volume A, we obtain the probability to find the electron in A. itself can be added to (or superposed on) other wave functions to form a new wave function. Physically, this is equivalent to interference. According to Born, r is probability amplitude. 

In all of the preceding discussion, we have simply assumed that we have some kind of one-particle potential V, which is used to set up the one-particle Hamiltonian matrix. We should now consider the effect of the electron-electron interaction in the discussion. Intuition tells us that since the solutions are mostly dominated by the nuclear Coulomb attraction, things will not change much, if at all. 

Rewriting this in terms of positron and electron indices is more involved, because the two-electron part produces 16 terms. Permutational symmetry and reindexing permits the combining of six of these, and the result in the empty Dirac picture is 

Applying the reinterpretation of the negative-energy states and normal-ordering the result, we get the QED Hamiltonian 

The first, fourth, fifth, and tenth of the two-electron terms all preserve the numbers of particles, and it is these terms that will contribute to the energy. The second and third and the eighth and ninth terms are terms that create or annihilate one pair, and the sixth and seventh terms create and annihilate two pairs, respectively. 

With these principles, the gradients for positive-negative rotations are determined to be 

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Sinanoglu O 1961 Many-electron theory of atoms and molecules Proc. US Natl Acad. Sc/. 47 1217-26... 

Sinanoglu O 1962 Many-electron theory of atoms and moleoules I. Shells, eleotron pairs vs many-eleotron oorrelatlons J. Chem. Phys. 36 706-17... 

Bartlett R J and Purvis G D 1978 Many-body perturbation theory coupled-pair many-electron theory and the importance of quadruple excitations for the correlation problem int. J. Quantum Chem. 14 561-81... 

Sinanoglu, 0. [1961] Many-Electron Theory of Atoms and Molecules, Proceedings of the National Academy of Sciences of the United States of America, 47(8), p. 1217. 

In order to proceed further, we now introduce the language of many-electron theory, and the concept of occupation number. 

Raimes, S. (1972), Many-Electron Theory, North Holland, Amsterdam. Ruckenstein, E. and Huang, Y.S. (1973), J. Catalysis 30, 309. 

Many-Electron Theory of Atoms, Molecules, and their Interactions (Sinanoglu). ... 

C. Some Related Topics Reactivity Indices in Many-Electron Theory... 

The many-electron theory of charge transfer discussed here possesses the versatility needed in order to treat different mechanisms within the same quantum-mechanical framework. However, it remains for future work to decide how successful the present formalism will be in providing a comprehensive many-electron theory of surface charge transfer. 

J. Paldus, J. Cizek, and 1. Shavitt, Correlation problems in atomic and molecular systems. IV. Extended coupled-pair many-electron theory and its application to the BHs molecule. Phys. Rev. A 5, 50 (1972). 

S. Pal, M. D. Prasad, and D. Mukherjee, Use of a size consistent energy functional in many-electron theory for closed shells. Theor. Chim. Acta 62, 523 (1983). 

Paldus, J., Cfzek, J., Takahashi, M. Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory. Phys. Rev. A 1984, 30, 2193-209. 

Smith, J. R. (1968). Self-consistent many-electron theory of electron work functions and surface potential characteristics for selected metals. Phys. Rev. 181, 522-529. 

Atoms and Molecules, Many-Electron Theory of (Sinanoglu) 6 315... 

Lowdin, who contributed in no small measure to the development of formal many-electron theory through his seminal work on electron correlation, reduced density matrices, perturbation theory, etc. many times expressed his concerns about the theoretical aspects of density functional approaches. This short review of the interconnected features of formal many-electron theory in terms of propagators, reduced pure state density matrices, and density functionals is dedicated to the memory of Per-Olov Lowdin. 

In comparing Eq. (13) to the Kohn-Sham equations Eq. (3) one concludes that E(.r, x E), since it is derived from exact many-electron theory [22], is the exact Coulomb (direct) plus exchange-correlation potential. It is non-local and also energy-dependent. In view of this it is hard to see how the various forms of constructed local exchange correlation potentials that are in use today can ever capture the full details of the correlation problem. 

Pu being the charge density or occupancy of orbital i of atom A in the molecule. The second term, a%, a paramagnetic term representing a local correction for the molecular environment, involves the mixing of ground and excited electronic states. This term is extremely difficult to calculate and no exact expression has been found using many-electron theory. Karplus and Pople have represented Op as... 

C. A. Nicolaides, Th. Mercouris, Y. Komninos, Many-electron theory of autoionizing states using complex coordinates The position and the partial and total widths of the Ne+ Is hole state, Int. J. Quantum Chem. 26 (1984) 1017. 

R. J. Bartlett and G. D. Purvis, Int. ]. Quantum Chetn., 14,561 (1978). Many-Body Perturbation Theory, Coupled-Pair Many-Electron Theory, and the Importance of Quadruple Excitations for the Correlation Problem. 

The eigenvectors Ffc determine the oscillator strengths of the excitations. This can be established using the sum-over-states representation of the standard many-electron theory for the dynamic dipole polarizability aav(co) [33]... 

G. Method of Coupled-Pair Many-Electron Theory and Its Results. . 148... 

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