Many-electron configuration interaction calculations have been carried out on a system of six hydrogen atoms arranged in a regular hexagonal array with a variable lattice spacing. The approximate wave functions for this system have been expressed as linear combinations of the (2×6)!(6!)2=924 determinantal functions which can be formed from atomic 1s functions. In this manner, the effects of ionic configurations containing as many as three pairs of doubly filled orbitals have been introduced into the calculations. All three- and four-center integrals have been taken into account. The nonorthogonality of hydrogenic 1s orbitals localized about different atomic sites has been removed by transforming to a set of orthonormal Wannier functions. The principal result of these calculations is the fact that the effects of configuration interaction can be represented quite accurately at large internuclear separations in terms of a parameter J' (analogous to a nearest-neighbor exchange integral) which assumes a negative value in a nonferromagnetic system such as this one. This provides a justification for the use of the Heisenberg exchange operator, -2J'(isi.si+1-14), to describe the magnetic interaction at large separations in this system. In addition, these results show that this system of hydrogen atoms is bound with respect to six separated atoms, but not with respect to three molecules. The ground-state wave function is a singlet at all internuclear separations. The general form of the curves representing energy as a function of internuclear separation show a striking similarity to those obtained for the hydrogen molecule.