On the Quantum-Mechanical Calculation of the Cohesive Energy of Molecules and Crystals. Part I. A General Energy Formula for the Ground State

A simple expression for the energy of the ground state of a molecule or a crystal is derived by starting from a total wave function, which is a Slater determinant of molecular spin orbitals or Bloch spin orbitals, formed by linear combinations of atomic orbitals. By the introduction of the new idea of ``combined atomic orbitals,'' the energy is expressed only in terms of two-center integrals of atomic orbitals, but the formula still includes the bonding and the overlapping between neighbors of all orders, and further, all the three-center and four-center integrals occurring in previous formulas. A simplified expression of the cohesive energy is given for the case the given atomic orbitals belong to the self-consistent field with exchange of the free atoms.