Rotational-invariant Sturmian-FaddeevAnsatzfor the solution ofH2+: A general approach to molecular three-body problems

Using a rotational-invariant Faddeev Ansatz for the electronic two-center wave function that is written as a sum of terms involving hydrogenic Sturmians and appropriate spherical harmonics coupled to total angular momentum J and parity P, we are able to diagonalize the two-center Hamiltonian to obtain the 1s${\sigma }_g$, 2s${\sigma }_g$, 2p${\sigma }_u$, 2p${\pi }_u$, and 3d${\sigma }_g$ electronic energy curves. For 36 Sturmians in the wave function we get energy states that are accurate to six to nine digits for 0$a_0$. All adiabatic corrections are calculated for the 1s${\sigma }_g$ state and the results compared with previous work by W. Kolos [Acta Phys. Acad. Sci. Hung. 27, 241 (1969)] and C. L. Beckel, B. D. Hausen, and J. M. Peek [J. Chem. Phys. 53, 3681 (1970)]. Using the ideas of R. T. Pack and J. O. Hirschfelder [J. Chem. Phys. 49, 4009 (1968); 52, 521 (1970); 52, 4198 (1970)] we calculate the avoided crossing energy gap Δɛ between 2s${\sigma }_g$ and 3d${\sigma }_g$ curves. For a 36-term Sturmian basis set we get Δɛ=3.27 ${\mathrm{cm}}^{\mathrm{-}1}$ at R=4.053 52$a_0$. Our work allows for a general approach to the solution of any molecular three-body problem that is applicable independently of the light-particle–heavy-particle interaction and the masses of the two heavier particles.