Calculations of Hartree-Fock polarizabilities for some simple atoms and molecules, and their practicality

Hartree-Fock electric polarizabilities have been calculated for H2, He, Li, Be, LiH, and N2. Perturbation theory with all the coupling terms was employed variationally for the first five, using a variety of basis sets for each. Each basis for the perturbation calculations was composed of a zero-order set, plus a first-order set (appropriate to the direction of polarization, for the molecules). The two sets are disjoint to ensure identical zero-order functions for the two molecular polarizability components and, hence, reliable anisotropy values. Nonorthogonal theory as formulated by Das and Duff [Phys. Rev. 168, 43 (1968)], assuming exact zero-order orbitals, was used for LiH. For practical reasons, the nitrogen molecule was treated by the fully self-consistent approach which does not distinguish orders of perturbation. The results for all six species are in very good agreement with experiment, reflecting both a reliable choice of polarization functions and, more significantly, the basic accuracy of the Hartree-Fock method for the static charge distributions, both unperturbed and perturbed by an electric field

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3. Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H2, He, Li, Be, LiH, and N2 by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities. Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H2-H2 collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.</p

Calculation of transition probabilities for collinear atom–diatom and diatom–diatom collisions with Lennard-Jones interaction

Numerical integration of the close coupled scattering equations is performed to obtain vibrational transition probabilities for three models of the electronically adiabatic H2-H2 collision. All three models use a Lennard-Jones interaction potential between the nearest atoms in the collision partners. The results are analyzed for some insight into the vibrational excitation process, including the effects of anharmonicities in the molecular vibration and of the internal structure (or lack of it) in one of the molecules. Conclusions are drawn on the value of similar model calculations. Among them is the conclusion that the replacement of earlier and simpler models of the interaction potential by the Lennard-Jones potential adds very little realism for all the complication it introduces

Non-Lambertian Corrected Albedo and Vegetation Index for Estimating Land Evapotranspiration in a Heterogeneous Semi-Arid Landscape

The application of energy balance algorithms to remotely sensed imagery often fails to account for surface roughness variation with diverse land cover, resulting in poor resolution of evapotranspiration (ET) variations. Furthermore, the assumption of a horizontally homogeneous Lambertian surface reflecting energy equally in all directions affects the calculations of albedo and vegetation index. The primary objective of this study is to improve the accuracy of the estimation and discrimination of ET among different land cover types in Southern New Mexico from ASTER datasets, by formulating the spatial variation of non-Lambertian reflectance using a wavelength-dependent Minnaert function