On nonadiabatic SCF calculations of molecular properties

We argue that the dynamic extended molecular orbital (DEMO) method may be less accurate than expected because the motion of the center of mass was not properly removed prior to the SCF calculation. Under such conditions the virial theorem is a misleading indication of the accuracy of the wavefunction. The first step in any quantum–mechanical treatment of atomic and molecular systems is the separation of the motion of the center of mass. The nonrelativistic Hamiltonian operator with only Coulomb interactions between the constituent particles for such systems is of the form ĤT = T̂ + V , where T̂ is the total kinetic–energy operator and V is the sum of all the Coulomb interactions between the charged particles. By means of a straightforward linear combination of variables one rewrites the kinetic–energy operator as T̂ = T̂CM + T̂rel, where T̂CM and T̂rel are the operators for the kinetic energies of the center of mass and relative motion, respectively. Then one solves the Schrödinger equation for the internal Hamiltonian Ĥ = T̂rel + V [1–3]. 1 e–mail: [email protected] Preprint submitted to Elsevier 3 August 2009 It is well known that the eigenfunctions of ĤT are not square integrable. For this reason, it is at first sight striking that Tachikawa et al [4, 5] carried out their dynamic extended molecular orbital (DEMO) method on the total Hamiltonian operator ĤT . A question therefore arises: how does this omission affect the results of the nonadiabatic calculation of molecular properties?. In this letter we will try to answer it. Suppose that we try to approximate the energy of the system by minimization of the variational energy W = 〈 ĤT 〉 = 〈φ| ĤT |φ〉 / 〈φ| φ〉 as in the DEMO method of Tachikawa et al [4, 5]. If φ depends only on translation–invariant coordinates then W = Wrel = 〈