Reaction paths and generalized valley approximation

The generalized valley approximation has been developed as a method of approximately decoupling one or a few low-frequency nonlinear modes from the remaining higher frequency modes of a multiparticle system. This decoupling will be best when the difference in frequencies is large; this is the case of adiabatic motion. We describe the application of this method to chemical reactions, relying in some measure on our earlier work, and contrast it with reaction-path theories. We give an algorithm for the incorporation of our method in a chemical calculation of the Born–Oppenheimer type. Detailed calculations are reported for several standard models that couple a double well to a harmonic oscillator. The decoupling procedure leads to an effective or renormalized one-dimensional double-well problem. The energy splitting of the lowest doublet in this well is contrasted with the exact splitting obtained by numerical integration of the two-dimensional Schrödinger equation. Results are good when the adiabatic condition is well satisfied. For future applications the most important feature of our theory is that it allows the decoupling of more than one degree of freedom.