Integrals Required for Computing the Energy of H3 and of H3+

Abstract

Some of the difficult integrals required for the variational method calculation of the energy of the triatomic hydrogen molecule and positive ion were evaluated with the aid of the differential analyzer. The integral ∫ 0πexp (−B(1−A cos θ)12)dθ is tabulated for a complete range of the parameters, A and B. The integral K(c,ab)=(1/π) ∫ rc−1exp(−ra−rb)dτ is tabulated for many configurations of the three electrons or nuclei: a, b, and c. Numerical tables are given of all of the integrals occurring in the Sugiura treatment of the ground state of H2. The values of all of the other integrals used in the calculation of the energy of H3 and of H3+ are given. It is expected that these tables will be useful for many problems of molecular quantum mechanics.

Evaluation of three-center two-electron repulsion integrals over Slater orbitals

“…In 1936 Hirschfelder et al [26,27] solved some cases of two-electron repulsion integrals with equal exponents of 1s-Slater orbitals in calculations of the H 3 molecule. We have extended this method to different exponents, which is usually the case in quantum mechanical calculations.…”

Modified Bond Eigenfunction Method of Constructing Potential Energy Surface of Reaction. II. Application to the Hydrogen Atom-Molecule Reaction

“…In (7) where H is the total Hamiltonian of three electrons in the system and HAB and Ho are the partial ones for molecule AB and atom C, respectively, and so on. Table I.…”