Gotowe bibliografie tematyczne / Dirac-Fock equations

Gotowa bibliografia na temat „Dirac-Fock equations”

Autor: Grafiati
Data publikacji: 4 czerwca 2021
Data aktualizacji: 20 lutego 2023

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Artykuły w czasopismach na temat "Dirac-Fock equations"

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Jorge, F. E., i A. B. F. Da Silva. "The generator coordinate Dirac–Fock method applied to beryllium-like atomic species". Canadian Journal of Chemistry 74, nr 9 (1.09.1996): 1748–52. http://dx.doi.org/10.1139/v96-193.

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The recently formulated generator coordinate Dirac–Fock method for relativistic closed-shell atoms is applied to the Be atom and Be-like ions Ne6+, Ar14+, and Sn46+ in order to assess its efficacy for light atomic systems. The Dirac–Fock equations are integrated numerically in the generator coordinate Dirac–Fock method so as to generate Gaussian basis sets for the atomic species under study. The results obtained with the application of the generator coordinate Dirac–Fock method in this work for Dirac–Fock–Coulomb and Dirac–Fock–Breit energies for Be-like ions are in excellent agreement with Declaux's benchmark numerical calculations, and are better than the Dirac–Fock–Coulomb and Dirac–Fock–Breit energies obtained with even-tempered Gaussian-type function calculations. For the Be atom, the Dirac–Fock–Coulomb energy result obtained with the generator coordinate Dirac–Fock method is lower than the corresponding value obtained with the Declaux's numerical finite-difference program. Key words: Dirac–Fock–Coulomb energy, Dirac–Fock–Breit energy, Gaussian basis sets, generator coordinate Dirac–Fock method.
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Levitt, Antoine. "Solutions of the multiconfiguration Dirac–Fock equations". Reviews in Mathematical Physics 26, nr 07 (sierpień 2014): 1450014. http://dx.doi.org/10.1142/s0129055x14500147.

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The multiconfiguration Dirac–Fock (MCDF) model uses a linear combination of Slater determinants to approximate the electronic N-body wave function of a relativistic molecular system, resulting in a coupled system of nonlinear eigenvalue equations, the MCDF equations. In this paper, we prove the existence of solutions of these equations in the weakly relativistic regime. First, using a new variational principle as well as the results of Lewin on the multiconfiguration non-relativistic model, and Esteban and Séré on the single-configuration relativistic model, we prove the existence of critical points for the associated energy functional, under the constraint that the occupation numbers are not too small. Then, this constraint can be removed in the weakly relativistic regime, and we obtain non-constrained critical points, i.e. solutions of the multiconfiguration Dirac–Fock equations.
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Esteban, M. J., i E. Séré. "Nonrelativistic Limit of the Dirac-Fock Equations". Annales Henri Poincaré 2, nr 5 (październik 2001): 941–61. http://dx.doi.org/10.1007/s00023-001-8600-7.

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Paturel, Eric. "Solutions of the Dirac-Fock Equations without Projector". Annales Henri Poincaré 1, nr 6 (grudzień 2000): 1123–57. http://dx.doi.org/10.1007/pl00001024.

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Ladik, Janos J. "Four-component Dirac-Hartree-Fock equations for solids; generalization of the relativistic Hartree-Fock equations". Journal of Molecular Structure: THEOCHEM 391, nr 1-2 (luty 1997): 1–14. http://dx.doi.org/10.1016/s0166-1280(96)04791-4.

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Al-Badawi, A., i I. sakalli. "Dirac and Klein–Gordon–Fock equations in Grumiller’s spacetime". International Journal of Geometric Methods in Modern Physics 15, nr 04 (13.03.2018): 1850051. http://dx.doi.org/10.1142/s0219887818500512.

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We study the Dirac and the chargeless Klein–Gordon–Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed.
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Goldman, S. P., i A. Dalgarno. "Finite-Basis-Set Approach to the Dirac-Hartree-Fock Equations". Physical Review Letters 57, nr 4 (28.07.1986): 408–11. http://dx.doi.org/10.1103/physrevlett.57.408.

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Esteban, Maria J., i Eric Séré. "Solutions of the Dirac-Fock Equations for Atoms¶and Molecules". Communications in Mathematical Physics 203, nr 3 (1.06.1999): 499–530. http://dx.doi.org/10.1007/s002200050032.

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Ring, Peter, Sibo Wang, Qiang Zhao i Jie Meng. "Relativistic Brueckner-Hartree-Fock Theory in Infinite Nuclear Matter". EPJ Web of Conferences 252 (2021): 02001. http://dx.doi.org/10.1051/epjconf/202125202001.

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On the way of a microscopic derivation of covariant density functionals, the first complete solution of the relativistic Brueckner-Hartree-Fock (RBHF) equations is presented for symmetric nuclear matter. In most of the earlier investigations, the G-matrix is calculated only in the space of positive energy solutions. On the other side, for the solution of the relativistic Hartree-Fock (RHF) equations, also the elements of this matrix connecting positive and negative energy solutions are required. So far, in the literature, these matrix elements are derived in various approximations. We discuss solutions of the Thompson equation for the full Dirac space and compare the resulting equation of state with those of earlier attempts in this direction.
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Jorge, F. E., i A. B. F. da Silva. "A generator coordinate version of the closed‐shell Dirac–Fock equations". Journal of Chemical Physics 104, nr 16 (22.04.1996): 6278–85. http://dx.doi.org/10.1063/1.471288.

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Rozprawy doktorskie na temat "Dirac-Fock equations"

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Went, Michael Ray, i n/a. "Scattering of Spin Polarized Electrons from Heavy Atoms: Krypton and Rubidium". Griffith University. School of Science, 2003. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20040220.134142.

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This thesis presents a set of measurements of spin asymmetries from the heavy atoms krypton and rubidium. These investigations allow examination of the spin orbit interaction for electron scattering from the target atoms. These measurements utilise spin polarized electrons in a crossed beam experiment to measure the Sherman function from krypton and the A2 parameter from the 52P state of rubidium. The measurements utilise a new spin polarized electron energy spectrometer which is designed to operate in the 20-200 eV range. The apparatus consists of a standard gallium arsenide polarized electron source, a 180 degrees hemispherical electron analyser to detect scattered electrons and a Mott detector to measure electron polarization. A series of measurements of the elastic Sherman function were performed on krypton at incident electron energies of 20, 50, 60, 65, 100, 150 and 200 eV. Scattered electrons are measured over an angular range of 30-130 degrees. These measurements are compared with calculations of the Sherman function which are obtained by solution of the Dirac-Fock equations. These calculations include potentials to account for dynamic polarization and loss of flux into inelastic channels. At the energies 50, 60 and 65 eV, experimental agreement with theory is seen to be extremely dependent on the theoretical model used. Measurement of the A2 parameter from the combined 52P1/2,3/2 state of rubidium are performed at an incident energy of 20 eV. The scattered electrons are measured over an angular range of 30-110 degrees. This measurement represents the first such measurement of this parameter for rubidium. Agreement with preliminary calculations performed using the R-matrix technique are good and are expected to improve with further theoretical development.
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Went, Michael Ray. "Scattering of Spin Polarized Electrons from Heavy Atoms: Krypton and Rubidium". Thesis, Griffith University, 2003. http://hdl.handle.net/10072/365606.

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This thesis presents a set of measurements of spin asymmetries from the heavy atoms krypton and rubidium. These investigations allow examination of the spin orbit interaction for electron scattering from the target atoms. These measurements utilise spin polarized electrons in a crossed beam experiment to measure the Sherman function from krypton and the A2 parameter from the 52P state of rubidium. The measurements utilise a new spin polarized electron energy spectrometer which is designed to operate in the 20-200 eV range. The apparatus consists of a standard gallium arsenide polarized electron source, a 180 degrees hemispherical electron analyser to detect scattered electrons and a Mott detector to measure electron polarization. A series of measurements of the elastic Sherman function were performed on krypton at incident electron energies of 20, 50, 60, 65, 100, 150 and 200 eV. Scattered electrons are measured over an angular range of 30-130 degrees. These measurements are compared with calculations of the Sherman function which are obtained by solution of the Dirac-Fock equations. These calculations include potentials to account for dynamic polarization and loss of flux into inelastic channels. At the energies 50, 60 and 65 eV, experimental agreement with theory is seen to be extremely dependent on the theoretical model used. Measurement of the A2 parameter from the combined 52P1/2,3/2 state of rubidium are performed at an incident energy of 20 eV. The scattered electrons are measured over an angular range of 30-110 degrees. This measurement represents the first such measurement of this parameter for rubidium. Agreement with preliminary calculations performed using the R-matrix technique are good and are expected to improve with further theoretical development.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Science
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Książki na temat "Dirac-Fock equations"

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Dyall, Kenneth G. All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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Dyall, Kenneth G. All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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Dyall, Kenneth G. Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets. [Moffett Field, CA: NASA Ames Research Center, 1990.

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All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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Części książek na temat "Dirac-Fock equations"

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Arai, Asao. "Instability in the Spectral and the Fredholm Properties of an Infinite Dimensional Dirac Operator on the Abstract Boson-Fermion Fock Space". W Partial Differential Equations and Spectral Theory, 1–6. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8231-6_1.

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"Radial Self-consistent Hartree-Fock-Dirac Equations". W Computation of Atomic Processes. Taylor & Francis, 1997. http://dx.doi.org/10.1201/9781420050714.ch5.

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Dyall, Kenneth G., i Knut Faegri. "Basis-Set Expansions of Relativistic Electronic Wave Functions". W Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0017.

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There have been several successful applications of the Dirac–Hartree–Fock (DHF) equations to the calculation of numerical electronic wave functions for diatomic molecules (Laaksonen and Grant 1984a, 1984b, Sundholm 1988, 1994, Kullie et al. 1999). However, the use of numerical techniques in relativistic molecular calculations encounters the same difficulties as in the nonrelativistic case, and to proceed to general applications beyond simple diatomic and linear molecules it is necessary to resort to an analytic approximation using a basis set expansion of the wave function. The techniques for such calculations may to a large extent be based on the methods developed for nonrelativistic calculations, but it turns out that the transfer of these methods to the relativistic case requires special considerations. These considerations, as well as the development of the finite basis versions of both the Dirac and DHF equations, form the subject of the present chapter. In particular, in the early days of relativistic quantum chemistry, attempts to solve the DHF equations in a basis set expansion sometimes led to unexpected results. One of the problems was that some calculations did not tend to the correct nonrelativistic limit. Subsequent investigations revealed that this was caused by inconsistencies in the choice of basis set for the small-component space, and some basic principles of basisset selection for relativistic calculations were established. The variational stability of the DHF equations in a finite basis has also been a subject of debate. As we show in this chapter, it is possible to establish lower variational bounds, thus ensuring that the iterative solution of the DHF equations does not collapse. There are two basically different strategies that may be followed when developing a finite basis formulation for relativistic molecular calculations. One possibility is to expand the large and small components of the 4-spinor in a basis of 2-spinors. The alternative is to expand each of the scalar components of the 4-spinor in a scalar basis. Both approaches have their advantages and disadvantages, though the latter approach is obviously the easier one for adapting nonrelativistic methods, which work in real scalar arithmetic.
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"On the Dirac Equations in General Relativity". W V.A. Fock - Selected Works, 109–12. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643204.ch3c.

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"3 On the Dirac Equations in General Relativity". W V.A. Fock - Selected Works, 121–24. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643204-15.

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Dyall, Kenneth G., i Knut Faegri. "Spin Separation and the Modified Dirac Equation". W Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0022.

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In the preceding chapters, the theory for calculations based on the Dirac equation has been laid out in some detail. The discussion of the methods included a comparison with equivalent nonrelativistic methods, from which it is apparent that four-component calculations will be considerably more expensive than the corresponding nonrelativistic calculations—perhaps two orders of magnitude more expensive. For this reason, there have been many methods developed that make approximations to the Dirac equation, and it is to these that we turn in this part of the book. There are two elements of the Dirac equation that contribute to the large amount of work: the presence of the small component of the wave function and the spin dependence of the Hamiltonian. The small component is primarily responsible for the large number of two-electron integrals which, as will be seen later, contain all the lowest-order relativistic corrections to the electron–electron interaction. The spin dependence is incorporated through the kinetic energy operator and the correction to the electronic Coulomb interaction, and also through the coupling of the spin and orbital angular momenta in the atomic 2-spinors, which form a natural basis set for the solution of the Dirac equation. Spin separation has obvious advantages from a computational perspective. As we will show for several spin-free approaches below, a spin-free Hamiltonian is generally real, and therefore real spin–orbitals may be employed for the large and small components. The spin can then be factorized out and spin-restricted Hartree–Fock methods used to generate the one-electron functions. In the post-SCF stage, where the no-pair approximation is invoked, the transformation of the integrals from the atomic to the molecular basis produces a set of real molecular integrals that are indistinguishable from a set of nonrelativistic MO integrals, and therefore all the nonrelativistic correlation methods may be employed without modification to obtain relativistic spin-free correlated wave functions. In most cases, spin–free relativistic effects dominate the relativistic corrections to electronic structure. We will show later that in a perturbation expansion based on the nonrelativistic wave function, the spin-free effects for a closed-shell system enter in first order, whereas the spin-dependent effects make their first contribution in second order.
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Streszczenia konferencji na temat "Dirac-Fock equations"

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Kambe, Takahide, Tetsuya Katayama i Koichi Saito. "Equation of State for Neutron Star Matter with NJL Model and Dirac–Brueckner–Hartree–Fock Approximation". W Proceedings of the 14th International Symposium on Nuclei in the Cosmos (NIC2016). Journal of the Physical Society of Japan, 2017. http://dx.doi.org/10.7566/jpscp.14.020807.

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