Beyond density functional theory: the domestication of nonlocal potentials

Due to efficient scaling with electron number N, density functional theory (DFT) is widely used for studies of large molecules and solids. Restriction of an exact mean-field theory to local potential functions has recently been questioned. This review summarizes motivation for extending current DFT to include nonlocal one-electron potentials, and proposes methodology for implementation of the theory. The theoretical model, orbital functional theory (OFT), is shown to be exact in principle for the general N-electron problem. In practice it must depend on a parametrized correlation energy functional. Functionals are proposed suitable for short-range Coulomb-cusp correlation and for long-range polarization response correlation. A linearized variational cellular method (LVCM) is proposed as a common formalism for molecules and solids. Implementation of nonlocal potentials is reduced to independent calculations for each inequivalent atomic cell.Comment: Accepted for publication in Modern Physics Letters B (2004

Cosmological implications of conformal field theory

Requiring all massless elementary fields to have conformal scaling symmetry removes a conflict between gravitational theory and the quantum theory of elementary particles and fields. Extending this postulate to the scalar field of the Higgs model, dynamical breaking of both gauge and conformal symmetries determines parameters for the interacting fields. In uniform isotropic geometry a modified Friedmann cosmic evolution equation is derived with nonvanishing cosmological constant. Parameters determined by numerical solution are consistent with empirical data for redshifts $z\leq z_*=1090$, including luminosity distances for observed type Ia supernovae and peak structure ratios in the cosmic microwave background (CMB). The theory does not require dark matter.Comment: 8 pages Conclusions about the early universe which must be reexamined have been removed. Manuscript revised and reformatted. Accepted for publication in Modern Physics Letters A (2011

Variational methods in electron-atom scattering theory

The investigation of scattering phenomena is a major theme of modern physics. A scattered particle provides a dynamical probe of the target system. The practical problem of interest here is the scattering of a low­ energy electron by an N-electron atom. It has been difficult in this area of study to achieve theoretical results that are even qualitatively correct, yet quantitative accuracy is often needed as an adjunct to experiment. The present book describes a quantitative theoretical method, or class of methods, that has been applied effectively to this problem. Quantum mechanical theory relevant to the scattering of an electron by an N-electron atom, which may gain or lose energy in the process, is summarized in Chapter 1. The variational theory itself is presented in Chapter 2, both as currently used and in forms that may facilitate future applications. The theory of multichannel resonance and threshold effects, which provide a rich structure to observed electron-atom scattering data, is presented in Chapter 3. Practical details of the computational implementation of the variational theory are given in Chapter 4. Chapters 5 and 6 summarize recent appli­ cations of the variational theory to problems of experimental interest, with many examples of the successful interpretation of complex structural fea­ tures observed in scattering experiments, and of the quantitative prediction of details of electron-atom scattering phenomena

N° 93. — Sur les relations entre les énergies de localisation et les constantes de vitesse des réactions de substitution

On calcule les énergies de localisation électrophile radicalaire et nucléophile pour les atomes non équivalents du benzène, du naphtalène et de l’anthracène. On utilise la méthode de Pariser et Parr dans le cadre de la technique du champ auto-cohérent. Dans le cas électrophile, la comparaison des résultats obtenus avec ceux obtenus par d’autres auteurs selon la même technique, mais avec des paramètres différents, conduit à une relation presque linéaire. Il en est de même pour la comparaison avec les grandeurs expérimentales : dans le cas de l’échange hydrogène-deutérium (électrophile) et celui de la méthylation (radicalaire), on obtient une relation proche de la linéarité entre les énergies de localisation et le logarithme des constantes de vitesse mesurées

Variational principles and methods in theoretical physics and chemistry

This book covers essential ideas and methods behind applications of variational theory in theoretical physics and chemistry