Basis Set Effects with Nuclear-Orbital Apporaches

Born-Oppenheimer (BO) approximation is one of the fundaments of “practical” quantum-mechanical calculations on various systems like isolated molecules, clusters and condensed matter. It is based on the separation of nuclear and electronic wave functions (adiabatic expansion) and further neglect of the nonadiabatic (NA) coupling terms in the resulting molecular Schrödinger equation (SE). The latter is commonly solved within Harmonic approximation, involving second derivatives (with respect to nuclear coordinates) of the electronic potential energy surfaces (PES) depending on the nuclear positions parametrically. In spite of the clear success in many areas, BO approximation has certain limitations. For example it is not applicable anymore in the situations when two or more adiabatic PES corresponding to different electronic states approach to each other. Correction of this failure introduces complicated techniques, requiring computation of NA couplings. Another alternative to Born-Oppenheimer approximation is the electron-nuclear orbital (ENO) approaches. The molecular wave function in these approaches is constructed as a product of electronic, nuclear and/or electron-nuclear orbitals (geminals), taking to account proper symmetry with respect to the permutations of electrons and nuclei. The molecular SE is then solved by means of the same computational methodologies as the electronic SE. In theory, the approach is capable to solve the entire molecular problem without complications introduced by BO. In the forthcoming talk, a brief overview of the available ENO-based methodologies will be presented. A special attention will be paid to the basis-set effects with the ENO approaches.