Application of the Q-DFT Fully Correlated Approximation to the Hydrogen Molecule

Abstract

We now turn our attention from atoms to the simplest molecule containing an electron-pair bond viz. the Hydrogen molecule (H₂). In this chapter, we study the properties of this molecule from the perspective of Q-DFT, i.e. from the view point of the representation of all different electron correlations present in terms of the corresponding quantal sources, and of the resulting fields, potential energies and total energy components.We apply [1] the Q-DFT Fully Correlated Approximation to map the Hydrogen molecule in its ground state to an equivalent-density noninteracting fermion model S system “molecule” that is also in its ground state with configuration.(σ_g1s)². We thereby consider correlations due to the Pauli principle, Coulomb repulsion, and Correlation-Kinetic effects. The application of this Q-DFT approximation to H₂ can be performed in a manner similar to that described in Chap. 15 for the mapping of the Helium atom. As such, for our approximate ground state wave function ψ ^approx(X), we employ the accurate correlated wave function of Kolos and Roothaan [2]. Also, as the spins of the two model fermions are opposite, the single-particle molecular orbitals of the S system are known exactly in terms of the density, and therefore do not have to be determined in a numerically self-consistent manner. Hence, all the properties of the Q-DFT description of the H₂ molecule determined are essentially exact. As this description of the H₂ molecule differs in many ways from the conventional description [3], a considerable degree of new physics is gleaned. However, beyond the new understandings achieved, another attribute of these calculations is the knowledge that the structure of the corresponding Q-DFT properties for other diatomic molecules in their ground states will be qualitatively the same. Furthermore, these “exact” properties can be used as the basis for comparison and testing of other Q-DFT approximation methods prior to their application to more complex molecules.