Molecular energy at high pressure

Abstract

The effect of molecular interaction at high pressure has been discussed using the approximation that a molecule enclosed by its neighbours may be considered t o be in a box with an infinitely steep potential wall. Tbe calculation has been carried out by the variation method for the hydrogen molecule-ion in a spheroidal box, and the results have been compared with earlier calculations on the hydrogen atom in a spherical box, with a cruder calculation for diatomic molecules, and with experimental results on other gases. The approximation apparently gives results of the correct order of magnitude, but tends to exaggerate the effect of pressure.

Simple wavefunction for an impurity in a parabolic quantum dot

“…A cut-off function of the form (R − r ) has been used previously [26][27][28][29][30] for different confined system problems. The ground-state energy of the system without the impurity can be shown [25] to be…”

Hydrogen molecular ion inside penetrable prolate spheroidal boxes: Electronic and vibrational properties

“…The hydrogen molecular ion (H 2 + ), the simplest molecular system, has served as an important reference to calibrate theoretical approaches in the study of molecular properties and it renders itself as the most suitable system to test new models for the analysis of molecular systems under pressure. In this connection, pressure effects on the ground‐state properties of H 2 + have been examined with the model of confinement in a spheroidal box under different approaches 27–31. Cottrell 27 proposed for the first time the model of H 2 + confinement in a spheroidal box with impenetrable walls using a variational method with a one‐parameter trial wave function suggested by James for the ground‐state free molecule 32 multiplied by a cut‐off factor so that the wave function inside the confining box should vanish at the position of the wall.…”

Properties ofH2under strong compression in a Ne matrix

“…Knowledge of the electronic properties of the H2 molecule in various highly compressed systems ranging from fluid to eventually metal constitutes a valuable data basis set for testing physical-chemistry theories at high pressures. Among them, the quantum-mechanics calculation of H2 + or H2 molecules imprisoned in a spheroidal box of shrinking volume has long served as a compelling model for the study of electronic perturbation induced by pressure [3]. But the hypotheses of this cornerstone theory are too simple for giving a correct analysis of the experimental situation in dense solid H2, mainly because in this case the coupling between the electronic properties of the H2 molecule and that of its surrounding H2 neighbors is very important, as will be demonstrated below.…”