Hylleraas-CI method

In the Hylleraas-CI method. the Hylleraas idea has been exploited when designing a method for larger systems. The electronic wave function is proposed as a linear combination of Slater determinants, and in front of each determinant , (1,2,3,..., N), we insert, next to the variational coefficient c,-, correlational factors with some powers (v, m ) of the interelectronic... 

G. Pestka, M. Byhcki, J. KarwowskL Ap-phcation of the camplex-coordinate ro-tahon to the relativistic Hylleraas-CI method a case study. /. Phys. B, 39(14) (2006)2979-2987. 

Therefore only two-electron integrals, as in the case of the Cl method, and triangle integrals have to be computed. This fact will be extremely helpful when extending the application of Hy-CI method to larger systems. In our code, the same computer memory is needed for Cl and Hy-CI calculations. Note, that in the Hylleraas-CI method for any electron number no higher order integrals than four-electron ones appear. 

This characteristic is commonly referred to as the bracketing theorem (E. A. Hylleraas and B. Undheim, Z. Phys. 759 (1930) J. K. E. MacDonald, Phys. Rev. 43, 830 (1933)). These are strong attributes of the variational methods, as is the long and rich history of developments of analytical and computational tools for efficiently implementing such methods (see the discussions of the CI and MCSCF methods in MTC and ACP). 

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