Ab initio calculations of potential energy surfaces in the complex plane. I. General theory and one-electron example

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A general theory for ab initio calculations of potential energy surfaces for complex values of nuclear coordinates, R, is developed. The motivation for this development stems from the interest of the collision theorist in the analytic continuation of potential energy surfaces into the complex R plane. Ab initio calculations at complex R involve the diagonalization of a complex, non-Hermitian, electronic Hamiltonian, which results in biorthogonal eigenvectors. We apply the theory to a simple model system of two potential curves with an avoided crossing for real R, and investigate their crossing and electron distributions in the complex R plane. We carry out ab initio LCAO MO calculations on the one-electron system HeH++, and focus on two particular potential curves with an avoided crossing for real R. We discuss the general problems associated with MO calculations of many-electron polyatomic systems for complex nuclear coordinates.