Algorithms McMurchie-Davidson algorithm

Relativistic generalization for G-spinor basis functions of the well-known McMurchie-Davidson algorithm [3] for direct evaluation of interaction integrals. 

The McMurchie-Davidson algorithm [111] is used extensively for the calculation of two electron interaction integrals in nonrelativistic electronic structure calculations. The relativistic generalization [112] can be obtained immediately... 

Electron repulsion integrals may be evaluated by a straightforward generalization of the McMurchie-Davidson algorithm [34], using the definition of the two-spinor charge operator. The Coulomb interaction involves only the Eg-coefficients for q = 0, and results in G-spinor integrals of the form... 

It is here that the simplifications made possible by defining the , -coefficients is most apparent, since integrals over 612 may be be obtained by a simple extension of the McMurchie-Davidson algorithm for electron repulsion integrals. This approach conveys the advantages of simplicity, generality and efficiency when compared with those which exist in the literature [49, 50]. 

By comparing Figures 1 and 2 with the descriptions in Sections 3.7 and 3.9, it becomes immediately apparent that the classical McMurchie-Davidson and Head-Gordon-Pople algorithms correspond to the MD-TTCTC and HGP-TCCTT paths, respectively. 

Whereas the principal concern expressed in the paper by Pople and Hehre [50] was extremely high efficiency for a limited set of integral classes, the main emphasis of McMurchie and Davidson was generality and extendability. Not surprisingly, then, their respective algorithms are, to a large degree, complementary. 

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