Sturmian approach

Aquilanti V, Caligiana A (2002) Sturmian approach to one-electron many-center systems integrals and iteration schemes. Chem Phys Lett 366 157-164... 

The problem of evaluating matrix elements of the interelectron repulsion part of the potential between many-electron molecular Sturmian basis functions has the degree of difficulty which is familiar in quantum chemistry. It is not more difficult than usual, but neither is it less difficult. Both in the present method and in the usual SCF-CI approach, the calculations refer to exponential-type orbitals, but for the purpose of calculating many-center Coulomb and exchange integrals, it is convenient to expand the ETO s in terms of a Cartesian Gaussian basis set. Work to implement this procedure is in progress in our laboratory. 

There have been several papers published on a(co) and y(co) for the hydrogen atom[85]-[90]. Shelton[89] used an expansion in Sturmian functions to obtain y values for Kerr, ESHG, THG and DFWM at a number of frequencies. A more straightforward and simpler method is to use the SOS approach and a pseudo spectral series based on the wavefunctions formed by the linear combinations ... 

V. Aquilanti, S. Cavalli, C. Coletti, D. Di Domenico, and G. Grossi, Hyperspherical harmonics as sturmian orbitals in momentum space a systematic approach to the few-body coulomb problem. Int. Rev. in Phys. Chem., 20 673-709, 2001. 

Apart from these one-particle effects , additional complications arise in the case of two electrons, which may dissolve from a bound state to the positronic and electronic continua. A mathematically rigorous approach to avoid this so-called continuum dissolution is to use as basis functions the relativistic Coulomb Sturmians... 

Recent applications of generalized Sturmians as a basis set for atomic structure calculations have been presented, also including the effects of external fields. There has been a treatment of the Sturmian formalism applied to one-electron molecules according to the MO-LCAO method [9], and also a method for exploiting Sturmians in a valence bond approach to the study of molecules [10]. 

By comparing experimental or accurate theoretical results with others based on approximate models, it is possible to determine which among those models offers the best approximate constants of the motion and quantum numbers to describe particular states. This approach is used to evaluate and compare the extent of validity of independent-particle, Hartree-Fock and collective, molecule-like descriptions of atoms with two valence electrons. The comparisons are made on the basis of overlaps, oscillator strengths, momentum correlation and quadrupole moments. The criterion for each evaluation is the extent of agreement with results obtained from well-converged Sturmian Configuration Interaction wave functions. 

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