We minimize the energy of a quantum Hamiltonian on the tensor product of two Hilbert spaces within the class of product states. This yields a nonlinear Schrodinger equation, whose ground state may bifurcate, producing symmetry breaking. We describe a procedure for computing the ground states numerically, and prove that it converges. We argue that the nonlinear Schrodinger equation has relevance to the issue of molecular structure in quantum chemistry, and study an exactly soluble example in detail to support this claim. The paper concludes with a brief discussion of other approaches to molecular structure.