Forces in Molecules. II. A Differential Equation for the Potentialhyphen;Energy Function

摘要

A secondhyphen;order, linear, homogeneous, differential equation for the diatomic molecular potentialhyphen;energy function,Un(R), is derived. Several aspects of this equation are studied in detail. The solutions of an approximate form of the equation suggest an empirical function that slowly oscillates in the complete interval 0le;Rle;infin;. This function is fit about the optimum minimum for 23 molecules. An approximate differential equation is derived for the functiongij(R)equiv;Ui(R)mdash;Uj(R), whereUiandUjare any two potentialhyphen;energy curves for different electronic states. This equation is valid in an interval for whichgijis smallmdash;that is, for near degeneracies. An application to two states of H2+is given.