Self-consistent field formalism

In spite of these gross approximations, the method proved to be extremely useful and was extensively used to correlate the chemical properties of conjugated systems. Several attempts were subsequently made to introduce the repulsions between the n electrons in the calculations. These include the work of Goeppert-Mayer and Sklar 4> on benzene and that of Wheland and Mann 5> and of Streitwieser 6> with the a> technique. But the first general methods of wide application were developed only in 1953 by Pariser and Parr 7> (interaction of configuration) and by Pople 8> (SCF) following the publication by Roothaan of his self-consistent field formalism for solving the Hartree-Fock equation for... 

Determinantal MO s may be obtained by a large number of computational methods based on Roothaan s self-consistent field formalism 94> for solving the Hartree-Fock equation for molecules which differ in degree of sophistication as regards the completeness and kind of the set of starting atomic wave functions, as well as the completeness of the Hamiltonian used 9S>. So a chain of various kinds of approximations is available for calculations starting from different ways of non-empirical ab initio" calculations 96>, viasemiempiricalmethods for all-valence electrons with inclusion of electronic interaction 95-97>98)... 

Pisani C 1978 Approach to the embedding problem in chemisorption in a self-consistent-field-molecular-orbital formalism Phys. Rev. B 17 3143... 

The complete treatment of solvation effects, including the solute selfpolarization contribution was developed in the frame of the DFT-KS formalism. Within this self consistent field like formulation, the fundamental expressions (96) and (97) provide an appropriate scheme for the variational treatment of solvent effects in the context of the KS theory. The effective KS potential naturally appears as a sum of three contributions the effective KS potential of the isolated solute, the electrostatic correction which is identified with the RF potential and an exchange-correlation correction. Simple formulae for these quantities have been presented within the LDA approximation. There is however, another alternative to express the solva-... 

Let us briefly mention some formal aspects of the above-introduced formalism, which have been discussed in detail by Blaizot and Marshalek [218]. First, it is noted that the both the Schwinger and the Holstein-Primakoff representations are not unitary transformations in the usual sense. Nevertheless, a transformation may be defined in terms of a formal mapping operator acting in the fermionic-bosonic product Hilbert space. Furthermore, the interrelation of the Schwinger representation and the Holstein-Primakoff representation has been investigated in the context of quantization of time-dependent self-consistent fields. It has been shown that the representations are related to each other by a nonunitary transformation. This lack of unitarity is a consequence of the nonexistence of a unitary polar decomposition of the creation and annihilation operators a and at [221] and the resulting difficulties in the definition of a proper phase operator in quantum optics [222]. 

Finally, we note that if we retain two-particle operators in the effective Hamiltonian, but restrict A to single-particle form, we recover exactly the orbital rotation formalism of the multiconfigurational self-consistent field. Indeed, this is the way in which we obtain the CASSCF wavefunctions used in this work. 

Within the last five years the development of large-capacity computers has been paralleled by the development of methods for performing allvalence electron calculations including electron interaction for large molecules. In 1964 two papers published independently by Pohl 23> and by Klopman 24) laid out the procedure for such calculations however, they were restricted to small molecules. The self-consistent field (S.C.F.) formalism which is used in these methods was found to be particularly versatile and appropriate for computer use. 

The scientific interests of Huzinaga are numerous. He initially worked in the area of solid-state theory. Soon, however, he became interested in the electronic structure of molecules. He studied the one-center expansion of the molecular wavefunction, developed a formalism for the evaluation of atomic and molecular electron repulsion integrals, expanded Roothaan s self-consistent field theory for open-shell systems, and, building on his own work on the separability of many-electron systems, designed a valence electron method for computational studies on large molecules. 

B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798. 

R. Cammi and J. Tomasi, Nonequilibrium solvation theory for the polarizable continuum model - a new formulation at the SCF level with application to the case of the frequency-dependent linear electric-response function, Int. J. Quantum Chem., (1995) 465-74 B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798-807 R. Cammi, L. Frediani, B. Mennucci, J. Tomasi, K. Ruud and K. V. Mikkelsen, A second-order, quadratically... 

Complete multiconfiguration-self consistent-field (CMC-SCF) technique designates the method where a given occupied molecular orbital of the set is excited to all unoccupied molecular orbitals. If an occupied orbital is excited to one or more, but not all, of the unoccupied orbitals, the technique is described as incomplete MC-SCF (IMC-SCF). The reader is referred to refs. 13 and 14 for details of the derivation. The CMC-SCF formalism differs from most many body techniques presented to date insofar as the Hartree-Fock energy is not assumed to be the zero order energy. 

More recently, an all valence electron, semiempirical molecular orbital theory known as the Complete Neglect of Differential Overlap (CNDO) has been proposed by Pople based on self-consistent field (SCF) formalism (5). Although this method uses a more sophisticated approximation of the wavefunction, it neglects differential overlap. 

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