On the Use of the Exact Exchange Optimized Effective Potential Method for Static Response Properties

摘要

In the present work, we question the notion that the modified Kohn-Sham orbital energies and smaller HOMO-LUMO gaps, produced from the exact exchange optimized effective potential (EXX-OEP) method, might significantly improve the paramagnetic contribution to the NMR chemical shifts compared with the regular Hartree-Fock (HF) scheme. First of all, it is shown analytically that if there is such a local potential that produces the HF energy, and the Kohn-Sham orbitals are obtained as a result of separate rotations of the occupied and virtual HF orbitals, any static magnetic property obtained from the coupled perturbed HF method will be identical to that obtained from the EXX-OEP approach. In fact the EXX-OEP method is equivalent to the improved virtual orbitals (IVO) scheme in which the energies of the virtual orbitals are modified by an effective potential. It is shown that the IVO procedure leaves static response properties unchanged. To test our analysis numerically we have employed several variants of the EXX-OEP method, based on the expansion of the local exchange potential into a linear combination of fit functions. The different EXX-OEP schemes have been used to calculate the NMR chemical shifts for a set of small molecules containing C, H, N, O, and F atoms. Comparison of the deviation between experimental and calculated chemical shifts from the HF, the EXX-OEP, and the common energy denominator approximation (CEDA) approximation to the EXX-OEP methods has shown that for carbon, hydrogen, and fluorine the EXX-OEP methods do not yield any improvement over the HF method. For nitrogen and oxygen we have found that the EXX-OEP performs better than the HF method. However, in the limit of infinite fit basis set and, as a consequence of it, a perfect fit of the HF potential the EXX-OEP and the HF methods would afford the same chemical shifts according to our theoretical analysis. Unfortunately, without a perfect fit the chemical shifts from the EXX-OEP method strongly depend on the fit convergence. In our opinion, the EXX-OEP method should not be used for response properties as it is numerically unstable. Thus, any apparent improvement of the EXX-OEP method over the HF scheme for a finite fit basis set must be considered spurious.