Chemical physics without the Born-Oppenheimer approximation: The molecular coupled-cluster method

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Abstract
The Born-Oppenheimer (BO) and Born-Huang (BH) treatments of molecular eigenstates are reexamined. It is argued that in application of the BO approximation to nonrigid molecules and chemical dynamics involving single potential-energy surfaces (PES’s), errors on the order of tens of percents can easily occur in many computed properties. Introduction of a BH expansion (in BO states) will always lead to poor convergence when the BO approximation fails; its diagonal (or adiabatic) approximation will not change this situation. The main problem in the above applications is the absence of well-developed, well-separated minima in the PES (or no minima at all). Inspired by a non-BO view of a molecule by Essén [Int. J. Quantum Chem. 12, 721 (1977)], a molecular coupled-cluster (MCC) method is formulated. An Essén molecule consists of neutral subunits (‘‘atoms’’), weakly interacting (‘‘bonds’’) in some spatial arrangement (‘‘structure’’). The quasiseparation in collective and individual motions within the molecule comes about by virtue of the virial theorem, not the smallness of the electron-to-nuclear mass ratio. The MCC method not only should converge well in the cluster sizes, but it also is capable of describing electronic shell and molecular geometric structures. It can be viewed as the workable formalism for Essén’s physical picture of a molecule. The time-independent and time-dependent versions are described. The latter one is useful for scattering, chemical dynamics, laser chemistry, half-collisions, and any other phenomena that can be described as the time evolution of many-particle wave packets. Close relationship to time-dependent Hartree-Fock theory exists. A few implementational aspects are discussed, such as symmetry, conservation laws, approximations, numerical techniques, as well as a possible relation with a non-BO PES. Appendixes contain mathematical details.

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