Chapter 10 A Computer-Algebraic Approach to the Derivation of Feynman–Goldstone Perturbation Expansions for Open-Shell Atoms and Molecules (original) (raw)

Many-body aspects of the parameterization of the hyperfine and other atomic interactions

Zeitschrift f�r Physik D Atoms, Molecules and Clusters, 1987

The idea of the parametrization of atomic interactions, such as the hyperfine interaction, the spin-orbit interaction and the isotopic field shift, is reviewed from the point of view of atomic many-body theory. The close analogy between Goldstone perturbation diagrams and the angular-momentum diagrams of Jucys et al. is used extensively in the analysis. In the non-relativistic limit, when only electrostatic perturbations are considered, it is verified that the hyperfine interaction can be exactly described by the effective onebody operator, introduced by Harvey, provided LS-dependent parameters are used. When relativity is considered, it is shown that the consideration of effective one-body effects leads to the theory of Sandars and Beck, with LS-independent parameters, while the remaining effects can be represented by LS-dependent one-body operators of higher tensor ranks.

Many-Body Theory for Hyperfine Effects in Atoms and Molecules

Journal de physique. Colloque, 1970

RCsumC.-Comnle exemple d'application de la theorie des perturbations A N-corps, nous avons etudie le probleme de la constante J~r n de couplage spin-spin nucleaire indirect dans la molCcule HD. L'ensenible cornplet d'etats utilise est exactement celui des etats des spectres discret et continu de I'ion moleculaire H;, avec la mCme separation internucleaire que pour la molecule HZ. Notre valeur calculee de J H D par le mecanisme d'interaction de contact de Ferrni est 42,57 Hz, alors que la plus recente valeur experimentale est de 42,l : 0,l Hz.

Relativistic quantum mechanics of many-electron systems

Journal of Molecular Structure: THEOCHEM, 2001

The present review surveys the single-and multicon®guration matrix Dirac±Fock self-consistent ®eld methods and their many-body theoretical re®nements developed in our group over the last decade. Implementation with analytic basis sets of Gaussian spinors is discussed in detail. q (Y. Ishikawa). Y. Ishikawa, M.J. Vilkas / Journal of Molecular Structure (Theochem) 573 (2001) 139±169 Fig. 1. 1s 1=2 relativistic wave functions, 1=2P 1s 1=2 r; of gold representing the nucleus as a point and a ®nite sphere of uniform proton charge. Nonrelativistic 1s orbital of Au is also displayed for comparison.

Foundations of the relativistic theory of many-electron bound states

International Journal of Quantum Chemistry, 1984

Most of the existing calculations of relativistic effects in many-electron atoms or molecules are based on the Dirac-Coulomb Hamiltonian HDc. However, because the electron-electron interaction mixes positive-and negative-energy states, the operator HDc has no normalizable eigenfunctions.

The Two-Component Quantum Theory of Atoms in Molecules (TC-QTAIM): Foundations

Theoretical Chemistry Accounts

In this contribution, pursuing our research program extending the atoms in molecules analysis into unorthodox domains, another key ingredient of the two-component quantum theory of atoms in molecules (TC-QTAIM) namely, the theory of localization/delocalization of quantum particles, is disclosed. The unified proposed scheme is able not only to deal with the localization/delocalization of electrons in/between atomic basins, but also to treat nuclei as well as exotic particles like positrons and muons equally. Based on the general reduced second order density matrices for indistinguishable quantum particles, the quantum fluctuations of atomic basins are introduced and then used as a gauge to quantify the localization/delocalization introducing proper indexes. The explicit mass-dependence of the proposed indexes is demonstrated and it is shown that a single localization/delocalization index is capable of being used for all kind of quantum particles regardless of their masses or charge content. For various non-Born-Oppenhiemer (non-BO) wavefunctions, including Hartree-product as well as singlet and triplet determinants, the indices are calculated and then employed to rationalize the localization/delocalization of particles in a series of fourbody model systems consist of two electrons and two positively charged particles with variable mass. The ab initio FV-MC_MO derived non-BO wavefunctions for the four-body series are used for a comprehensive computational TC-QTAIM analysis, including topological analysis as well as basin integrations, in a wide mass regime, e e m m m 13 10 10 − = (m e stands for electron mass), disclosing various traits in these series of species that are unique to the TC-QTAIM. On the other hand, it is demonstrated that in the large mass extreme the TC-QTAIM analysis reduces to the one performed within context of the orthodox QTAIM with two clamped positive particles revealing the fact that the TC-QTAIM encompasses the orthodox QTAIM as an asymptote. Finally, it is concluded that the proposed localization/delocalization scheme is capable of quantifying quantum tunneling of nuclei for systems containing delocalized protons. Such capability promises novel applications for the TC-QTAIM as well as its extended multi-component version (MC-QTAIM) introduced recently.

Computational approaches of relativistic models in quantum chemistry

2003

This chapter is a review of some methods used for the computation of relativistic atomic and molecular models based on the Dirac equation. In the linear case, we briefly describe finite basis set approaches, including ones that are generated numerically, perturbation theory and effective Hamiltonians procedures, direct variational methods based on nonlinear transformations, min-max formulations and constrained minimizations. In the atomic case, we describe the MCDF method and some ways to solve numerically the homogeneous and inhomogeneous Dirac-Fock equations. Finally, we describe also some numerical methods relevant to the case of molecules.

A new operator formulation of the many-electron problem for molecules

Theoretical and Experimental Chemistry, 1989

An n-electron operator ~, called a wave operator, is associated with a 2n-electron molecular wave function. Electron densities and energy are written in terms of ~ An equation defining an exact wave operator is found. Thus, a 2n-electron vector problem (for the wave function) is rigorously reduced to an n-electron operator problem. Conditions are formulated which guarantee that ~ corresponds to a state with a given spin. The" configuration-interaction problem is considered and methods of approximate construction of ~,~ are discussed. In particular, a matrix algorithm is proposed for calculations in the two-body approximation. A generalizaton of the approach to the case of systems with an odd number of electrons is given. The waveoperator model developed forms a general basis for construction of covariant electron models of molecules.

Many-Body Perturbation Theory for Molecules Based on a United Atom Model

Physical Review Letters, 1970

PHYSI CAL REVIEW LETTERS 27 JULY 1970 electrons ordinarily exist only up to microwave frequencies. However, Eq. (8) indicates that electrons modulated by a laser will give rise to fields at discrete frequencies far beyond T It seems plausible that the optical radiation observed by Schwarz and Hora' is due to the presence of these classical fields. The justification of the use of the classical calculation at frequencies»T ' must await a full quantum mechanical treatment of the problem. Further investigation is needed to determine the details of the modulation process, the extent of the modulation, the details of the radiation mechanism, and the resulting intensities.