On energy calculation for Coulomb systems

The problem of energy calculation for a Coulomb atomic-molecular system with arbitrary number N of particles is studied. The exponential wave functions explicitly depending on all N(N-1)/2 interparticle separations and taking into account the effects of correlation and nonadiabaticity are used. Straightforward use of these functions in many-particle systems with N > 3 is faced by time-consuming calculations of various multidimensional integrals with nonseparable variables. The number of these integrals increases as N3. This main obstacle can be obviated in the approach developed, based on the model Schroedinger equation combined with the virial and Hellmann-Feynman theorems. In this way the number of integrals in the expression for the matrix element of the many-particle Coulomb system Hamiltonian is significantly reduced: indeed, for a system with N = 4 particles only 7 instead of 43 integrals must be evaluated, for N = 5 only 10 instead of 101 integrals, etc. The number of different types of integral is also reduced. For a calculation of the energy of a 4-particle Coulomb system it is sufficient to calculate only 6 integrals of interparticle Coulomb interaction and the normalization integral. The results obtained offer a practical possibility for high-precision calculations of many-particle atomic-molecular systems with a detailed account of correlation and nonadiabaticity. 9 refs