John Avery

Dimensional scaling in chemical physics

I: Basic Aspects. 1. Introduction. 2. Tutorial. II: The Research Frontier. 3. large-D Limit for N-Electron Atoms. 4. Low D Regime. 5. Hyperspherical Symmetry. 6. Hypercylindrical Symmetry. 7. General Computational Strategies. 8. Two-Electron Excited States. 9. Large-D Limit for Metalic Hydrogen. 10. D-Interpolation of Virial Coefficients. III: Related Methods. 11. Nonseparable Dynamics. 12. Pseudomolecular Electron Correlation in Atoms. Index.

New Methods in Quantum Theory

Dimensional Saling J.G. Loeser, D.R. Herschbach. Subhamiltonian Methods J.G. Loeser. Dimensional Renormalization For Electronic Structure Calculations S. Kais, R. Bleil. Generalized Self-Consistent-Field Approximations D.Z. Goodson. Dimensional Expansions for Atomic Systems D.K. Watson, et al. The Manifestation of Chaotic Behaviour of the Hydrogen Atom in the Presence of Uniform Electric Field R. Damburg, B. Baranovsky. Multielectron, Multichannel Problems and Their Solution to All-Orders Via the Diagonalization of State-Specific Complex Eigenvalue Schrodinger Equations C.A. Nicolaides, et al. Large Orders of 1/n-Expansion in Quantum Mechanics and Atomic Physics V.S. Popov. Size-Extensive Brillouin-Wigner Perturbation Theory. Size-Extensive Brillouin-Wigner Coupled Cluster Theory I. Hubac. Least Motion, Hyperspherical Co-ordinates, And Polytopes J. Linderberg. Evolution of Atom-Molecular Eigenstates U. Fano, J.L. Bohn. Hyperangular Momentum: Applications to Atomic and Molecular Science V. Aquilanti, et al. Quantum and Semi-Classical Methods in Reactive Scattering G.D. Billing. Multidimensional Angular Function Methods in Theoretical and Applied Physics A.A. Sadovoy, Yu.A. Simonov. Hyperspherical Sturmian Basis Functions in Reciprocal Space J.S. Avery. Inelastic Scattering With Coulomb Forces: A Semiclassical S-Matrix Approach J.-M. Rost. Cusp Conditions and Electron Correlation J.D. Morgan III. Local-Scaling Many-Electron Density Functional Theory E.S. Kryachko. Density Functional Theory: Improving the Functionals, Extending the Applications D.R. Salahub, et al. Electron Correlation and the Structure of the Exchange-Correlation Potential and the Correlation Energy Density in Density Functional Theory E.J. Baerends, et al. Relativistic Pseudopotentials and Nonlocal Effects W.C. Ermler, M.M. Marino. One Centre Expansion in Quantum Mechanical Molecular Calculations R.J. Rakauskas, J. Sulskus. Distributed Gaussian Basis Sets: Some Recent Results and Prospects S. Wilson. Exact Ab Initio Quantum Chemistry J.B. Anderson. Comments on Computational Chemistry, In General and Quantum Chemistry, In Particular E. Clementi, G. Corongiou. Hyperspherical Co-ordinates in Reactive Scattering Theory A. Kuppermann.

Generalized potential harmonics and contracted sturmians

Abstract A formalism is described for choosing computationally manageable Sturmian basis sets which are automatically adapted to the requirements of particular physical problems. The method is a generalization and improvement of the potential harmonic technique of Fabre de la Ripelle, which is extensively used in nuclear and atomic physics. The present generalization is not restricted to hyperspherical coordinates, and the basis functions are characterized by a physically motivated grand principal quantum number, rather than the grand angular momentum quantum number. As an illustration, the simple example of a two-electron atom is presented.

Many-particle Sturmians

The weighted orthonormality relations for many-particle Sturmian basis functions are derived both in momentum space and in position space. It is shown that when these functions are used as a basis, the kinetic energy term disappears from the Schrödinger equation. A general method is developed for constructing many-electron Sturmian basis sets from one-electron Sturmians. This method is illustrated by applications to atoms and ions and to the H2 molecule. It is shown that the direct solution of the Schrödinger equation using many-particle Sturmianbasis functions offers a useful alternative to the Hartree–Fock approximation and configuration interaction; and it is shown that the Sturmian method leads to an automatic optimization of the orbital exponents.

A FORMULA FOR ANGULAR AND HYPERANGULAR INTEGRATION

A formula is derived which allows angular or hyperangular integration to be performed on any function of the coordinates of a D-dimensional space, provided that it is possible to expand the function as a polynomial in the coordinates x1,x2,...,xd. The expansion need not be carried out for the formula to be applied.

A fully retarded expression for the rotatory strength

Abstract Theoretical expressions are derived for the ellipticity and for the rotatory strength of an electronic transition in an oriented molecule using the fully retarded vector potential for the electromagnetic field. The resulting expression for the retarded rotatory strength is shown to reproduce the Rosenfeld-Condon expression in the electric dipole-magnetic dipole approximation.

Sturmian expansions for quantum mechanical many-body problems, and hyperspherical harmonics

Abstract Generalized Sturmian basis sets make it possible to solve the many-particle Schrodinger equation directly, without the use of the SCF approximation. The functions in such a basis set are solutions to the many-particle Schrodinger equation with a weighted “basis potential”, βvV0(x), the weighting factor βv being chosen in such a way as to make all the functions in the set correspond to the same energy. For a many-electron system, it is shown that when V0(x) is chosen to be the nuclear attraction potential, rapidly convergent solutions can be obtained directly from a secular equation from which the kinetic energy term has vanished. The close relationship between generalized Sturmian basis functions and hyperspherical harmonics is discussed, as well as the relationship between all the matrix elements of the theory, such as the Shibuya-Wulfman integrals, the generalized Wigner coefficients of angular momentum theory, and the Hahn polynomials of modern numerical analysis.

Some properties of electronic non-adiabatic coupling terms

Analytical expressions are obtained for the Born-Oppenheimer non-adiabatic coupling terms formed by a given distribution of conical intersections. The gauge-dependent formulae contain explicitly the boundary conditions that have to be obtained by ab initio calculations performed along a circle in the close vicinity of each conical intersection.

The Generalized Sturmian Method for Calculating Spectra of Atoms and Ions

The properties of generalized Sturmian basis sets are reviewed, and functions of this type are used to perform direct configuration interaction calculations on the spectra of atoms and ions. Singlet excited states calculated in this way show good agreement with experimentally measured spectra. When the generalized Sturmian method is applied to atoms, the configurations are constructed from hydrogenlike atomic orbitals with an effective charge which is characteristic of the configuration. Thus, orthonormality between the orbitals of different configurations cannot be assumed, and the generalized Slater–Condon rules must be used. This aspect of the problem is discussed in detail. Finally spectra are calculated in the presence of a strong external electric field. In addition to the expected Stark effect, the calculated spectra exhibit anomalous states. These are shown to be states where one of the electrons is primarily outside the atom or ion, with only a small amplitude inside.

Many-Electron Sturmians as an Alternative to the SCF-CI Method

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.