Atomic Calculations Using Generalized Sturmians

The relationship between alternative separable solutions of the Coulomb problem in momentum space is exploited in order to obtain hydrogenic orbitals which are of interest for Sturmian expansions of use in atomic and molecular structure calculations and for the description of atoms in fields. In view of their usefulness in problems where a direction in space is privileged, as when atoms are in an electric or magnetic field, we refer to these sets as to the Stark and Zeeman bases, as an alternative to the usual spherical basis, set. Fock s projection onto the surface of a sphere in the four dimensional hyperspace allows us to establish the connections of the momentum space wave functions with hyperspherical harmonics. Its generalization to higher spaces permits to build up multielectronic and multicenter orbitals. 

Abstract The theory of Sturmians and generalized Sturmians is reviewed. It is shown that when generalized Sturmians are used as basis functions, calculations on the spectra and physical properties of few-electron atoms can be performed with great ease and good accuracy. The use of many-center Coulomb Sturmians as basis functions in calculations on N-electron molecules is also discussed. Basis sets of this type are shown to have many advantages over other types of ETO s, especially the property of automatic scaling. 

In making this table, the basis set used consisted of 63 generalized Sturmians. Singlet and triplet states were calculated simultaneously, 0.5 s of 499 MHz Intel Pentium III time being required for the calculation of 154 states. Experimental values are taken from the NIST tables (http //physics.nist.gov/asd). Discrepancies between calculated and experimental energies for the ions may be due to experimental inaccuracies, since, for an isoelectronic series, the accuracy of the generalized Sturmian method increases with increasing atomic number. 

Having used the generalized Sturmian method to calculate the wave function for an A-electron atom, we are in a position to derive both the corresponding density distribution and the first-order density matrix [36-52], However, because we cannot assume orthonormality between the one-electron spin-orbitals of different configurations, it is necessary to use expressions analogous to the generalized Slater-Condon rules. If we let... 

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