By Michael Baer, Cheuk-Yiu Ng, Ilya Prigogine, Stuart A. Rice

Nonadiabatic Interactions among power power Surfaces: thought and functions (B. Lengsfield & D. Yarkony).

Diabatic capability power Surfaces for Charge-Transfer methods (V. Sidis).

version power strength Surfaces for Inelastic and Charge-Transfer tactics in Ion-Molecule Collision (F. Gianturco & F. Schneider).

Quantum-Mechanical remedy for Charge-Transfer procedures in Ion-Molecule Collisions (M. Baer).

Semiclassical method of Charge-Transfer methods in Ion-Molecule Collisions (H. Nakamura).

The Semiclassical Time-Dependent method of Charge-Transfer methods (E. Gislason, et al.).

The Classical Trajectory-Surface-Hopping method of Charge-Transfer methods (S. Chapman).

Statistical features of Ion-Molecule Reactions (J. Troe).

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Extra resources for Advances in Chemical Physics: State-Selected and State-To-State Ion-Molecule Reaction Dynamics, Part 2, Theory, Volume 82

Sample text

In particular for the case of a ' I +state of a diatomic molecule orientated along the z axis with internuclear distance R , the adiabatic correction is given by [see Eqs. 11 S)] where 42 BYRON H. LENGSFIELD 111 AND DAVID R . 7a) I(ri) is the orbital angular momentum operator for the ith electron relative to the center of mass of the nuclei, p, the reduced mass, satisfies p-' = M;' My' and the total nuclear mass M = M , M,. In Section I1 D the computational efficiency that can be achieved through the use of Eq.

94)]. Hence, L2"(W) must be reevaluated for distinct mass combinations. This, however, is not a significant limitation since the computational effort required to evaluate L2"( W) is minor compared to that required to evaluate k"(R). E. Avoided and Actual Surface Crossings: Direct Evaluation of the Energy Difference Gradient In Section I I A it was shown that the energy gradient E:(R) and the first derivative nonadiabatic coupling matrix element fi'(R) could be evaluated using a unified density matrix driven procedure.

Denote the operator that generates a translation of all the nuclei along the space-fixed axes as QN and denote as a," the operator that generates a rotation of the nuclei about the body-fixed y axis located at the nuclear center of mass, that is, -V t' = c v: 2 k A and Then Eqs. 1 14) 34 BYRON H. LENGSFIELD 111 A N D DAVID R. 115) where a = x , y , z . Thus, Eqs. 112) are seen to relate derivatives of Born-Oppenheimer electronic wavefunctions with respect to noninternal nuclear degrees of freedom to matrix elements of electronic operators.

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