We present a new analysis of the nonadiabatic coupling terms in the coupled equations for nuclear motion wave functions when the Born-Oppenheimer (BO) representation is used for the electronic wave function. The new analysis leads to a criterion for truncating the series and neglecting terms in the coupled equations of motion. We show that in general the nonremovable part of the coupling is of the same magnitude as the removable part, except near intersections of the adiabatic states.
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We are grateful to Horst Köppel and D.R. Yarkony for helpful comments; to A. Kuppermann and D.R. Yarkony for allowing us access to the results of  prior to publication; and additionally to A. Kuppermann for similarly allowing us access to  . This work was supported in part by the National Science Foundation under grant no. CHE00-92019. Part of this work was done under the auspices of the US Department of Energy under Project No. 990015 of the Laboratory Directed Research and Development program at Los Alamos under Contract No. W-7405-ENG-36.