Space configuration

In the configuration space spanned by (411,1 2, 73), we may then define the vibrational angular momentum k through its classical components, that is, 

I i i(q,01 in configuration space, e.g. as defined by the possible values of the position coordinates q. This motion is given by the time evolution of the wave fiinction i(q,t), defined as die projection ( q r(t)) of the time-dependent quantum state i i(t)) on configuration space. Since the quantum state is a complete description of the system, the wave packet defining the probability density can be viewed as the quantum mechanical counterpart of the classical distribution F(q- i t), p - P t)). The time dependence is obtained by solution of the time-dependent Schrodinger equation 

Let S be any simply connected surface in nuclear configuration space, bounded by a closed-loop L. Then, if 4>(r,R) changes sign when transported adiabatically round L, there must be at least one point on S at which (r, R) is discontinuous, implying that its potential energy surface intersects that of another electronic state. 

The sti ong and weak interaction regions of the internal configuration space is divided into a certain number of spherical hypeiradial shells. The 2D diabatic 

A function T is normalized if the product T integrated over all configuration space is unity. An orthonormal set contains functions that are normalized and orthogonal to each other. 

When two electronie states are degenerate at a particular point in configuration space, the elements of the diabatie potential energy matiix can be modeled as a linear function of the coordinates in the following fonn  

Two functions and are orthogonal if the product integrated over all configuration space, vanishes. 

The values of this (approximate) fi (qx) calculated from this equation are smaller than 0.08 kcal/mol over the entire nuclear configuration space involved, and to a very good approximation can be neglected. 

This method, introduced originally in an analysis of nuclear resonance reactions, has been extensively developed [H, 16 and F7] over the past 20 years as a powerful ab initio calculational tool. It partitions configuration space into two regions by a sphere of radius r = a, where r is the scattered electron coordinate. 

---