Analytic exchange integral for coupled cluster theory in the homogeneous electron gas

A six-dimensional integral occurring in the description of the ground state of the homogeneous electron gas was calculated analytically. This formula, together with the one of a previous work [G.G. Hoffman, Phys. Rev. B 45 (1992) 8730], reduces from seven to one the dimension of the numerical integrations to be performed in the RPA+RPAEX⋆(1) approximation for the correlation energy [R.F. Bishop, K.H. Lührmann, Phys. Rev. B 26 (1982) 5523].Program summaryTitle of program: qexm2em1Catalogue identifier:ADXJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXJ_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandDistribution format: tar.gzComputers: Created using a PC, but can be run on UNIX machinesOperating system under which the program has been tested: LinuxProgramming language used: Mathematica 4.0 (due to versions incompatibility the program does not work with more recent versions like Mathematica 5.1)Memory required to execute with typical data: 151 MbNumber of processors used: 1 Has this code been vectorized or parallelized? noNo. of lines in distributed program, including test data, etc.: 13 415Number of bytes in distributed program, including test data, etc.: 102 988Nature of the physical problem: The program gives an analytical derivation of a six-dimensional exchange integral involved in the calculation of the correlation energy of the electron gas.Method of solution: Changes of variables were gradually introduced in order to decrease the dimensionality of the integral, and eventually an analytical expression was obtained.Restrictions on the complexity of the program: The present version of the program has been designed only for calculating only one integral. Though, the method can be used for other cylindrically-symmetric integrals.Typical running times: file formula.nb: less than 1 s; qexm2em1.nb: 02 mn 02 s; qexm2em1qinf2AA.nb: 09 mn 42 s; qexm2em1qinf2BB.nb: 08 mn 05 s; qexm2em1qinf2AB.nb: 00 mn 43 s; qexm2em1qsup2.nb: 23 mn 26 s on 1 GHz machine.