Journal ArticleDOI
The Problem of the Normal Hydrogen Molecule in the New Quantum Mechanics
TLDR
The solution of Schroedinger's equation for the normal hydrogen molecule is approximated by the function $C[{e}^{\ensuremath{-}\frac{z({r}_{1}+{p}_{2})}{a}}+{e^{\ensem{-]-{m{e})+{m}−m{n}−n}]$ where m is the distance of one of the electrons to the two nuclei, and r is the distances of one electron to the other electron.Abstract:
The solution of Schroedinger's equation for the normal hydrogen molecule is approximated by the function $C[{e}^{\ensuremath{-}\frac{z({r}_{1}+{p}_{2})}{a}}+{e}^{\ensuremath{-}\frac{z({r}_{2}+{p}_{1})}{a}}]$ where $a=\frac{{h}^{2}}{4{\ensuremath{\pi}}^{2}m{e}^{2}}$, ${r}_{1}$ and ${p}_{1}$ are the distances of one of the electrons to the two nuclei, and ${r}_{2}$ and ${p}_{2}$ those for the other electron. The value of $Z$ is so determined as to give a minimum value to the variational integral which generates Schroedinger's wave equation. This minimum value of the integral gives the approximate energy $E$. For every nuclear separation $D$, there is a $Z$ which gives the best approximation and a corresponding $E$. We thus obtain an approximate energy curve as a function of the separation. The minimum of this curve gives the following data for the configuration corresponding to the normal hydrogen molecule: the heat of dissociation = 3.76 volts, the moment of inertia ${J}_{0}=4.59\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}41}$ gr. ${\mathrm{cm}}^{2}$, the nuclear vibrational frequency ${\ensuremath{\nu}}_{0}=4900$ ${\mathrm{cm}}^{\ensuremath{-}1}$.read more
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Book
Electronic Structure: Basic Theory and Practical Methods
TL;DR: In this paper, the Kohn-Sham ansatz is used to solve the problem of determining the electronic structure of atoms, and the three basic methods for determining electronic structure are presented.
Journal ArticleDOI
Coherent X‐Ray Scattering for the Hydrogen Atom in the Hydrogen Molecule
TL;DR: In this paper, the x-ray form factors for a bonded hydrogen in the hydrogen molecule have been calculated for a spherical approximation to the bonded atom, and the corresponding complex scattering factors have also been calculated.
Book ChapterDOI
Gaussian Basis Sets for Molecular Calculations
Abstract: In the following chapters the electronic structure of molecules will be discussed and the techniques of electronic structure calculations presented. Without exception the molecular electronic wave functions will be expanded in some convenient, but physically motivated, set of one-electron functions. Since the computational effort strongly depends on the number of expansion functions (see, e.g., the following chapters), the set of functions must be limited as far as possible without adversely affecting the accuracy of the wave functions. This chapter will discuss the choice of such functions for molecular calculations.
Journal ArticleDOI
Potential Energy Surface for H3
TL;DR: In this article, an analytic semi-empirical expression for the ground-state potential energy surface of the H3 system was developed using the valence-bond formulation with the inclusion of overlap and three center terms.
Journal ArticleDOI
The theory of electron-molecule collisions
TL;DR: The current state of the theory and its application to low-energy electron-molecule collisions is reviewed in this paper, where the emphasis is on elastic scattering and vibrational and rotational excitation of small diatomic and polyatomic molecules.