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

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 ${\displaystyle {\int }_0^{\pi }}\exp \text{(−B(1−A\hspace{0.17em}}\cos {\mathrm{\hspace{0.17em}\theta )}}^{\frac{1}{2}}\mathrm{)d\theta }$ is tabulated for a complete range of the parameters, A and B. The integral $\text{K(c,ab)=(1/π)}{\displaystyle \int }{r}_c^{\text{−1}}\exp {\mathrm{(-r}}_a{\mathrm{-r}}_b\mathrm{)d\tau }$ 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.