On the virial of quasi-stationary molecular systems

Abstract

For quasi-stationary complex-energy states, the fundamental quantum mechanical relationships are formulated: complex form of Heisenberg's equation of motion, hypervirial theorem, and Hellmann-Feynman theorems. Particular attention is focused on molecular dynamics of complex-energy states; at the equilibrium geometry on the Born-Oppenheimer adiabatic potential energy surface, it is found that the complex virial theorem is consonant with the theorem for the entire molecular system. Furthermore, the complex-coordinate method is developed particularly for the application to the molecular dynamics of complex-energy states. An example of the problem of molecular dynamics on complex potential energy surfaces is also given: ²σ _u ⁺ transient H₂ ^- ion formed as an intermediate species in a dissociative attachment reaction.