Numerical self-consistent field method for polyatomic molecules

A method for non-relativistic self-consistent field (SCF) electronic structure calculations for polyatomic molecules is described, which retains the linear combination of atomic orbitals ansatz for molecular orbitals (MO-LCAO), but replaces the usual algebraic expansion of atom-centred radial parts in terms of basis functions (usually some kind of Gauss-type functions) by a numerical representation on a set of radial grid points around each centre. The radial parts are optimized, according to the variation principle, until self-consistency is achieved. Even though Fourier integral transform techniques are used the method works completely in ordinary space. Intermediate quantities defined in momentum space are evaluated in closed form.     

Quasiharmonic approximation for a crystal in the self-consistent field method

An equation of state is derived for fcc crystals on the basis of earlier studies, and the stability of the crystalline phase and polymorphic transitions are discussed.Translated from lzvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol.12, No. 1, pp. 18–23, January, 1969.     

Diagrammatic review and implications of the self-consistent field theory method

Some of the most intriguing and important phenomena in modern many-body physics are explainable in terms of self-consistent quantum mechanical field theory. This is the powerful theory developed by Umezawa and co-workers and modified by Benson and Hatch in applications to ferromagnetism. It is usually lengthy and involved mathematically. Thus, it is very helpful and meaningful to see its overall step-by-step progress in simple, diagrammatic flow starting from basic principles, with a ferromagnetic model as an example. As one immediately notes, there are two paths leading to very powerful physical conclusions and implications, and something most interesting is that each path implies the other. Many useful examples of applications of these methods are noted and some future possible applications are cited.     

A self-consistent approach to linear and nonlinear transport in an electric field

The Boltzmann equation for charge carriers (obeying any statistics) is solved analytically in terms of electric-field-dependent relaxation times for a model collision operator. This operator is a linear, rotationally invariant one, which reduces to a multiplicative operator in each irreducible tensor subspace. The relaxation times are given by a self-consistency requirement. This gives (i) an exact solution of the Boltzmann equation for energy-independent multiplicative factors and (ii) exact asymptotic solutions for low- and high-field situations. Ohm's law is shown to hold exactly in case (i). Furthermore, a number of simple models is shown to be exactly soluble. For more complicated cases, perturbative and iterative methods of solution are discussed.     

A self-consistent method of constructing an effective rotational Hamiltonian

Methods have become widely used in molecular spectroscopy that involve the construction of effective rotational Hamiltonians [1, 2]. One of these methods has been developed by one of us over several years [3, 4]. A simple basis is provided for this method and it is shown that the scheme for constructing the effective operator for the rotational energy is substantially self-consistent.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 68–72, May, 1981.     

Nuclear level densities in self-consistent field approximation

The effect of two-body nature of the nuclear shell model potential on the recent numerical calculations of the nucleai level density has been examined. For the two most widely used single particle energy level schemes based on harmonic oscillator and Woods-Saxon potential, this effect is shown to significantly modify the excitation energy dependence of the level densisties.     

Unstable particles in a self-consistent field theory

We indicate how unstable particles can be introduced into the self-consistent field theory formulation of Umezawa where the equal-time commutation relations for Heisenberg fields are derived and not assumed. The Lee model is used to illustrate the results.     

Modified model of self-consistent field for an electron solvated in a polar liquid

The self-consistent field model is modified to take into account the effect of orientation correlations on the behavior of an electron solvated in a polar liquid. This model is used as the basis for calculating the maximum of the absorption spectrum as well as the temperature dependence of this maximum for an electron sol-vated in water and ammonium. The results are in accord with experimental data and with the results of calcu-lation by the quantum molecular dynamics method.     

A parallel multi-configuration self-consistent field algorithm

A scalable multi-configuration self-consistent field (MCSCF) algorithm is described. The method for optimizing the orbital and configurational parameters is based upon the two-step Newton–Raphson approach with an augmented orbital Hessian matrix. A single copy of the two-electron integrals in the molecular orbital basis is distributed over the memory of all processors. Storage of the augmented Hessian is avoided by re-computing its elements as needed. A replicated data approach is used to parallelize the configuration interaction step. Scalability to 1024 processors is demonstrated.     

A self-consistent field theory of crystals

A self-consistent theory of crystals is presented. The classical phenomenological theory of crystals is derived by means of the boson transformation method.     

A new mixed self-consistent field procedure

A new approach for the calculation of three-centre electronic repulsion integrals (ERIs) is developed, implemented and benchmarked in the framework of auxiliary density functional theory (ADFT). The so-called mixed self-consistent field (mixed SCF) divides the computationally costly ERIs in two sets: far-field and near-field. Far-field ERIs are calculated using the newly developed double asymptotic expansion as in the direct SCF scheme. Near-field ERIs are calculated only once prior to the SCF procedure and stored in memory, as in the conventional SCF scheme. Hence the name, mixed SCF. The implementation is particularly powerful when used in parallel architectures, since all RAM available are used for near-field ERI storage. In addition, the efficient distribution algorithm performs minimal intercommunication operations between processors, avoiding a potential bottleneck. One-, two- and three-dimensional systems are used for benchmarking, showing substantial time reduction in the ERI calculation for all of them. A Born–Oppenheimer molecular dynamics calculation for the Na⁺₅₅ cluster is also shown in order to demonstrate the speed-up for small systems achievable with the mixed SCF.     

Calculation of properties of the ozone molecule by the multiconfigurational self-consistent field method

For the ground state of the ozone molecule, by using the multiconfigurational self-consistent field method, we calculated the electric and magnetic properties — quadrupole moment, polarizability, tensor of magnetic susceptibility, nuclear quadrupole interaction constant, and the rotational g-factor. Qualitative agreement between the calculated parameters and experimental values was obtained. The tensors of chemical shielding in the spectrum of the nuclear magnetic resonance for the ¹⁷O isotopes have also been predicted (without allowance for the contribution made by the spin of the electrons). __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 713–716, November–December, 2005.     

Dynamics of self-consistent planar axisymmetric motions of an electron beam in a magnetic field

The dynamics of self-consistent planar axisymmetric motions of a cylindrical electron beam is investigated analytically. The beam electrons move under the action of an unneutralized space-charge field against an immobile ion background or in a vacuum in the presence of a magnetic field. The electric field strength and the electron density and velocity are determined as functions of the distance traveled by the beam electrons.     

Fully self-consistent ion-drag-force calculations for dust in collisional plasmas with an external electric field

The ion drag force on a spherical dust particle immersed in a flowing plasma with an external electric field is self-consistently calculated using the particle-in-cell code SCEPTIC in the entire range of charge-exchange collisionality. Our results, not based on questionable approximations, extend prior analytic calculations valid only in a few limiting regimes. Particular attention is given to the force direction, shown never to be directed opposite to the flow except in the continuum limit, where other forces are of a much stronger magnitude.     

A partially self-consistent phenomenological nuclear mean field

A version of a partially self-consistent phenomenological mean field of a nucleus that considers the effect of nucleon density polarization due to particle-hole interaction is proposed. Allowing for this effect enables us to fit the calculated charge radius of the nucleus and the energies of isobaric analog resonance to the corresponding observed magnitudes without using any additional parameters.     

Development of an improved spatial reconstruction technique for the HLL method and its applications

The integral form of the conventional HLL fluxes are presented by taking integrals around the control volume centred on each cell interface. These integrals are demonstrated to reduce to the conventional HLL flux through simplification by assuming spatially constant conserved properties. The integral flux expressions are then modified by permitting the analytical inclusion of spatially linearly varying conserved quantities. The newly obtained fluxes (which are named HLLG fluxes for clarification, where G stands for gradient inclusion) demonstrate that conventional reconstructions at cell interfaces are invalid and can produce unstable results when applied to conventional HLL schemes. The HLLG method is then applied to the solution of the Euler Equations and Shallow Water Equations for various common benchmark problems and finally applied to a 1D fluid modeling for an argon RF discharge at low pressure. Results show that the correct inclusion of flow gradients is shown to demonstrate superior transient behavior when compared to the existing HLL solver and conventional spatial reconstruction without significantly increasing computational expense.     

A new method of calculating the spectrum and the self-consistent field of negative ions

A new method is suggested for negative ion calculations, based on perturbation theory with a model zeroth approximation and a polarization potential formalism. The binding energy of an electron in an Na^– ion is calculated as a test, and is found to agree with experiment.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 41–46, September, 1990.In conclusion, the author is grateful to E. P. Ivanova for her interest, to V. V. Flambaum and V. K. Ivanov for supplying preprints of [8, 9], and to V. V. Filatov for help in the numerical calculations.