Hermiticity of the Hamiltonian matrix in a discrete variable representation

Application of a discrete variable representation (DVR) to Hamiltonians derived in a nonadiabatic basis or Hamiltonians obtained by making a nonlinear dependent-coordinate transformation, leads to a Hamiltonian matrix which (a) cannot be evaluated without explicitly performing summations, or (b) is not Hermitian. We develop a prescription to avoid these difficulties. Specific examples involving Fourier grid Hamiltonian DVRs are presented.