Fundamental relationships between elementary functionals in quantum chemistry. An application for H2 and H2+
| Autor: | Fernando Ruette, Alexander Peraza, Roger Hernández |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
010304 chemical physics
Basis (linear algebra) Chemistry Differential equation Hilbert space Function (mathematics) 010402 general chemistry Condensed Matter Physics 01 natural sciences Biochemistry 0104 chemical sciences Exponential function symbols.namesake Quantum mechanics 0103 physical sciences symbols Molecular Hamiltonian Statistical physics Physical and Theoretical Chemistry Ground state Basis set |
| Zdroj: | Computational and Theoretical Chemistry. 1100:52-60 |
| ISSN: | 2210-271X |
| Popis: | General sets of differential equations have been formulated on the basis sets completeness of the Hilbert space when using operators of the molecular Hamiltonian. In these equations, different relationships between elementary functionals (EF) have been found depending of functions of the overlap, and overlap derivative. Applications of these relationships to simple systems (example: a diatomic molecule with two basis components) were performed. Similarities of early approximations for parametric quantum methods were obtained. The molecular total energy for H2 and H2+ using minimal basis set was found to be as a function of the overlap plus two integration constants. This way, it may be calculated in terms of dissociation energy and equilibrium bond distance of the molecules. Selected trial overlap, as an exponential function, consistently gives values above the exact potential energy curve (PEC) for the ground state. The optimized overlap exponent at each internuclear distance gives better PECs with respect to minimal basis sets. Results suggest an optimal overlap associated to a complete correlated minimal basis set. In particular, a q-exponential function as a model of the overlap gives energy values to a very near exact PEC. |
| Databáze: | OpenAIRE |
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