Waller–Hartree spin‐free method

Abstract

AbstractIn this paper we show that with the equivalent transformation Pr = (−1)P(Pσ)−1 the spin function dependent methods such as Slater's method without group theory or Goddard's method with group theory differ only in different antisymmetric requirements from the present Waller‐Hartree spin function free method. There exists a one‐to‐one correspondence between Slater's determinantal wave function and the Waller–Hartree double determinantal wave function. Explicit expressions for the S2 operator, Löwdin's spin projector, matric basis and several different forms of spin‐projected functions are given for the Waller–Hartree formalism. The results are compared with other methods including those of Slater, Matsen, Gallup, Goddard and Segal. The differences are quite significant. New spin operators are worked out using creation‐destruction operators. A knowledge of group theory is not required in this Waller–Hartree method. We have also shown that the Waller–Hartree method is more convenient than Slater's method with spin functions especially in the evaluation of the functional ℋ︁Ψ/Ψ. The advantages and disadvantages in the use of a linear combination of N! Hartree products and linear combinations of all possible double determinants are discussed. In addition, a formula for the calculation of the Sanibel coefficients C(S, M, i) is obtained.