Hamiltonian Matrix Elements from a Symmetric Wave Function

The matrix elements of a c.m. transformed molecular Hamiltonian for a wave function constructed from a symmetrized product of one-particle orthonormal spin functions are given in terms of the integrals over the coordinates of the particles. These matrix elements are necessary to study the structure of deuterated molecules such as ${\mathrm{D}}_2$O, N${\mathrm{D}}_3$, C${\mathrm{D}}_4$, etc. The integrals are the same as those found for antisymmetric wave functions with the exception of the two-particle integrals of the form $\int {g_i}^{*}\mathrm{}\left(1\right)\mathrm{}{g_i}^{*}\mathrm{}\left(2\right)\mathrm{} {\left(r_{12}\right)}^{-1\mathrm{}}{g}_j\mathrm{}\left(1\right)\mathrm{}{g}_j\mathrm{}\left(2\right)\mathrm{} \mathrm{dV}$, when two bosons occupy the same spin function. There are, however, significant differences in the matrix elements.