Approximation self consistent field

Gerber R B, Buch V and Ratner M A 1982 Simplified time-dependent self consistent field approximation for intramolecular dynamics Chem. Phys. Lett. 91 173... 

Peskin U and Steinberg M 1998 A temperature-dependent Schrodinger equation based on a time-dependent self consistent field approximation J. Chem. Phys. 109 704... 

Kosloff R and Hammerich A D 1991 Nonadiabatic reactive routes and the applicability of multi configuration time dependent self consistent field approximations Feredey Discuss. Chem. Soc. 91 239-47... 

Gerber, R.B., Buch, V., Ratner, M.A. Time-dependent self-consistent field approximation for intramolecular energy transfer. I. Formulation and application to dissociation of van der Waals molecules. J. Chem. Phys. 77 (1982) 3022-3030. 

One approach to the problem of the ri2 temi is a variational self-consistent field approximation. Our treatment here follows that by Rioux (1987), in which he starts... 

Interaction ofthe electrons in the framework of the self-consistent field approximation is accounted for by considering the induced density fluctuations as a response of independent particles to Oext + Poissons equation [2], This means, physically, that collective excitations of the electrons can occur, taken into account via a chain of electron-holeexcitations. These collective excitations show up in S(q, ) as a distinct energy loss feature. Figure 2 shows the shape of the real and imaginary parts of the dielectric function in RPA (er(q, ), Si(q, )) and the resulting dielectric response... 

The description of phase transitions in a two-dimensional dipole system with exact inclusion of long-range dipole interaction and the arbitrary barriers AUv of local potentials was presented in Ref. 56 in the self-consistent-field approximation. The characteristics of these transitions were found to be dependent on AU9 and the number n of local potential wells. At =2, Tc varies from Pj /2 to Pj as AU9... 

Compare these values with 14.25 U and 13.6875 U respectively provided for the two lattice types by the self-consistent-field approximation (2.5.5) at n = 2). 

In the quantitative development of the structure in the self-consistent field approximation (S.C.F.) using the Hartree-Fock method the energy Ei is made up of three terms, one for the mean kinetic energy of the electron in one for its mean potential energy in the field of the nuclei, and a... 

The method of many-electron Sturmian basis functions is applied to molecnles. The basis potential is chosen to be the attractive Conlomb potential of the nnclei in the molecnle. When such basis functions are used, the kinetic energy term vanishes from the many-electron secular equation, the matrix representation of the nnclear attraction potential is diagonal, the Slater exponents are automatically optimized, convergence is rapid, and a solution to the many-electron Schrodinger eqeuation, including correlation, is obtained directly, without the use ofthe self-consistent field approximation. 

Methods are introduced for generating many-electron Sturmian basis sets using the actual external potential experienced by an N-electron system, i.e. the attractive potential of the nuclei. When such basis sets are employed, very few basis functions are needed for an accurate representation of the system the kinetic energy term disappears from the secular equation solution of the secular equation provides automatically an optimal basis set and a solution to the many-electron problem is found directly, including electron correlation, and without the self-consistent field approximation. In the case of molecules, the momentum-space hyperspherical harmonic methods of Fock, Shibuya and Wulfman are shown to be very well suited to the construction of many-electron Sturmian basis functions. 

The Hartree-Fock or self-consistent-field approximation is a simplification useful in the treatment of systems containing more than one electron. It is motivated partly by the fact that the results of Hartree-Fock calculations are the most precise that still allow the notion of an orbital, or a state of a single electron. The results of a Hartree-Fock calculation are interpretable in terms of individual probability distributions for each electron, distinguished by characteristic sizes, shapes and symmetry properties. This pictorial analysis of atomic and molecular wave functions makes possible the understanding and prediction of structures, spectra and reactivities. 

For the H + H2 —H2 + H reaction, for example, the reactive flux requires time evolution of only -25 fs. The requirement of only short-time dynamics does indeed suggest the utility of a variety of approximations, such as the time-dependent self-consistent field approximation. 

The starting point of the creation of the theory of the many-electron atom was the idea of Niels Bohr [1] to consider each electron of an atom as orbiting in a stationary state in the field, created by the charge of the nucleus and the rest of the electrons of an atom. This idea is several years older than quantum mechanics itself. It allows one to construct an approximate wave function of the whole atom with the help of one-electron wave functions. They may be found by accounting for the approximate states of the passive electrons, in other words, the states of all electrons must be consistent. This is the essence of the self-consistent field approximation (Hartree-Fock method), widely used in the theory of many-body systems, particularly of many-electron atoms and ions. There are many methods of accounting more or less accurately for this consistency, usually named by correlation effects, and of obtaining more accurate theoretical data on atomic structure. 

This book explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory, and generalized Sturmian basis functions and introduces methods which may be used to solve many-electron problems directly, without the use of the self-consistent-field approximation. ... 

Now we want to discuss IR optical spectra of the C60H36 synthesized at high-pressure. Results of this study were published in Bazhenov et al. (2008). There are a lot of publications devoted to theoretical and experimental study of C60H36. We should pay attention on the existing discrepancies in the results of theoretical calculations of the dipole-active spectra C60H36, compare, for example, papers Bini et al. (1998) and Bulusheva et al. (2001). There were used different theoretical models. Semiempirical method of the MNDO type (Dewar and Thiel 1977) was used in (Bini et al. 1998). Ab initio Hartree-Fock self-consistent field approximation was used in (Bulusheva et al. 2001). 

The concept of tunneling has recently been invoked to explain the mechanism of photodissociation of matrix-isolated molecules. Previously, photodissociation was customarily accounted for by the fact that transla-tionally hot photofragments escape from the cage and stabilize in separate matrix sites, thereby avoiding recombination. Using the time-dependent self-consistent field approximation for molecular dynamics simulations,... 

The optical properties of organic conductors may be described by the simplest model, which assumes noninteracting electrons (one-electron model). In this approximation the infrared (IR) properties may be derived in the self-consistent field approximation. Assuming a frequency-independent relaxation rate, y, and a background dielectric constant arising from virtual high-frequency transitions, e0, the result takes the Drude form [12] ... 

In the self-consistent field approximation, the equilibrium distribution n( ) can be determined by means of the minimization of F n with the additional condition (4.1). Performing the variational procedure and taking into account Eqs. (5.3) and (5.4), it is easy to find the following equation in complete analogy with the corresponding calculation in Ref.24 ... 

Knochenmuss, R., and Leutwyler, S., Structures and vibrational spectra of water clusters in the self-consistent-field approximation, J. Chem. Phys. 96, 5233-5244 (1992). 

The multi configuration time dependent self consistent field approximation (MCTDSCF)... 

R.B. Gerber, V. Buch and M.A. Ratner, Time-dependent self-consistent field approximation for intramolecular energy transfer. I. Formulation and application to dissociation of van der Waals molecules, J. Chem. Phys., 77 (1982), 3022 M.A. Ratner and R.B. Gerber, Excited vibrational states of polyatomic molcecules the semiclassical self-consistent field approach, J. Phys. Chem., 90 (1986) 20 R.B. Gerber and M.A. Ratner, Mean-field models for molecular states and dynamics new developments, J. Phys. Chem., 92 (1988) 3252 ... 

Ferenczy, G.G., Rivail, J.-L., Surjan, P.R. and Naray-Szabo, G. (1992) NDDO Fragment Self-Consistent Field Approximation for Large Electronic Systems, J. Comput. Chem. 13, 830-837. 

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