Bernard J. Laurenzi

An analytic solution to the Thomas–Fermi equation

A perturbative procedure due to Bender et al. (here referred to as the BMPS procedure) [J. Math. Phys. 30, 1447 (1989)] and useful in solving difficult nonlinear problems, has been used here to solve the Thomas–Fermi (T–F) equation. The present work attempts to balance the ease of the ensuing analysis with the use of an analytic, zero‐order function that already contains a good deal of the nonlinearity of the T–F equation. The initial slope of the T–F potential is computed with 0.35% error in a second‐order application of the theory.

Isoelectronic molecules—The fourteen electron sequence of diatomics

A general theory of isoelectronic diatomic molecules is developed and numerical calculations are performed for the fourteen electron sequence. Calculated values of equilibrium bond distances, force constants, and dissociation energies compare well with experimental values and the global behavior of each quantity is displayed as a function of the nuclear charges. The screening effect of the electrons is seen to play the key role in determining the regions of stability on the nuclear charge plane.

Exact ground and excited state second‐order properties of the hydrogen atom. I. Polarizabilities

Using the exact generalized Greens functions for the first three energy levels of the hydrogen atom, we have computed the static dipole polarizabilities for the S states. The calculations were done analytically and exactly on a digital computer using the list‐processing language LISP.

Isoelectronic Molecules. II. First‐ and Second‐Order Physical Properties

It has been shown that first‐ and second‐order physical properties of isoelectronic molecules are interrelated in a simple way. This follows from the fact that the corresponding first‐ and second‐order operators are homogeneous functions of position and nuclear charge. The results are rigorously true for noninteracting electrons and can be extended to include interelectronic effects as well.

A unified molecular force field via a model theory of isoelectronic diatomic molecules

Electronic energy curves for diatomic molecules come in a wide variety of shapes. More categorically, these correspond to stable, metastable or repulsive states. We propose that a great deal of this apparently diverse behavior might in fact be contained in a single isoelectronic energy surface E(R,Z,Z′). That is, each kind of curve can be thought of as a particular cross section of the surface corresponding to some range of the nuclear charges Z and Z′. Analytic representations for these surfaces have been given and their properties examined. We have found that they are folded and contain critical points. These features put limits on the number of isoelectronic species that can exist in a sequence and interconnect their properties. By this we understand that data gathered on even the repulsive states of one molecule of an isoelectronic sequence contains information about the stable and metastable members of that sequence.

The length of an isoelectronic sequence of molecules

When studying classes of molecules, the isoelectronics are especially attractive since they possess exact interrelationships among their properties. In the work described below the length of an isoelectronic sequence is examined. It is possible to describe an upper and a lower critical charge for a sequence of homonuclear diatomic molecules. Between these critical limits of charge the behavior of the internuclear distance, dissociation energy, and force constant are given as functions of charge.

Isoelectronic Molecules. III. First‐ and Second‐Order Physical Properties for Systems of N‐Interacting Electrons

It is shown that the theory presented in II can be extended to systems of interacting electrons as well, and consequently, isoelectronic species continue to show a systematic variation of their physical properties with nuclear charge.

Isoelectronic molecules: The 13 and 22 electron sequences of diatomics

A theory of isoelectronic molecules [J. Chem. Phys. 74, 1840 (1981)] has been applied to the ground state of an even (22) electron and an odd (13) electron sequence of diatomics. Each of these is compared to the 14 electron sequence which had been studied previously. In the first instance, a striking correspondence in the dissociation energy De(Z,Z′), bond distance R(Z,Z′), and force constant E(2)(Z,Z′) surfaces for isovalent molecules from the 14 and 22 electron systems has become apparent. For the second, gross differences which arise in these surfaces when one electron is removed from 14 electron molecules are explicable in terms of the nature of the electron‐pair bond as opposed to the one‐electron bond. A stability rule which excludes ions with charges greater than plus or minus two units is found to hold for these sequences as well as the 14 electron one.

Green's Functions in Many‐Electron, Second‐Order Calculations

The calculation of second‐order physical properties for many‐electron systems of interacting particles is presented in terms of two‐particle Greens functions and graphs. These Greens functions are known in the atomic case, and therefore practical computations are now possible.

Atomic and molecular model potentials

A constructive theory of atomic and molecular model potentials is developed using the work of Bottcher and Dalgarno as a point of departure. In this theory, all of the terms required by successful, empirical, model potential calculations are obtained from a perturbation theory in which exchange is neglected. We find that valence electrons must be allowed to penetrate into the core regions even in systems with well defined cores and distant valence electrons. Within this theory, exact model potentials for hydrogenlike atoms and H2‐like molecules are obtained and specific, short‐ and long‐range forms of the model potentials are proposed for other atoms and molecules.