Space configuration

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

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. 

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... 

Figure A3.13.9. Probability density of a microcanonical distribution of the CH cliromophore in CHF within the multiplet with cliromophore quantum nmnber V= 6 (A. g = V+ 1 = 7). Representations in configuration space of stretching and bending (Q coordinates (see text following (equation (A3.13.62)1 and figure A3.13.10). Left-hand side typical member of the microcanonical ensemble of the multiplet with V= 6...

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. 

MD, one needs to use multiple time step methods to ensure proper handling of the sprmg vibrations, and there is a possible physical bottleneck in the transfer of energy between the spring system and the other degrees of freedom which must be handled properly [199]. In MC, one needs to use special methods to sample configuration space efficiently [200, 201]. 

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 ... 

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. 

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... 

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. 

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,... 

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