Addition theorem of Slater-type orbitals:: Application to H2+ in a strong magnetic field

The C-matrix representation of the two-range addition theorem of Slater-type functions (STFs) proved to be very useful especially when using a computer algebra system. However, for intensive numerical work it was found advantageous to use the G- (or T-) matrix representation for the apart of STFs while the remaining term is expanded with the help of the addition theorem of solid spherical harmonics. Two major advantages are to be related to this procedure. On the one hand, the new C matrices are symmetric and most important can be generated recursively. On the other hand, this procedure allows one to generalize and to unify the previous E-and F-matrix expansions. Indeed, the new T-matrix form allows one to avoid the calculation-of C-matrix elements and much more important to use a recursive scheme in order to generate their elements. As an application of these formulas, we address in the last part of this work the study of the electronic structure of H2+ when subjected to a strong magnetic field. Our calculation shows that the expansion in terms of spherical harmonics (i.e., STFs) becomes slowly convergent for large values of the magnetic field.