Coupled Perturbation Theory Approach to Dual Basis Sets for Molecules and Solids. 1. General Theory and Application to Molecules

We present a new coupled Hartree–Fock(HF)/Kohn–Sham DFT perturbation method that accounts for the effect of enlarging the basis set in electronic structure calculations. In contrast with previous approaches, our dual basis set treatment yields not only a correction for the total energy but also for the orbital eigenvalues and density. The zeroth order solution is obtained from the projection of the small basis set coefficients. Diagonalization of the full Fock matrix in the large basis set is avoided. In this first paper of a series, we develop the theoretical foundations of our approach for molecules, including the coupled-perturbed equations through second order and the energy expressions through fourth order—as our method complies with Wigner’s 2n + 1 rule. The first-order perturbation equation turns out to be uncoupled, and odd-order terms in the energy expansion vanish. In calculations on simple molecules, our method recovers over 93% (84%) of the missing DFT(HF) energy when going from the cc-pVDZ to the aug-cc-pVDZ basis, and over about 95% in all cases if an energy extrapolation formula is used. Mulliken charges, the orbital eigenvalue spectrum, and HOMO–LUMO gaps of the large basis are well reproduced. Charge density maps show that the differences between the perturbatively corrected density and the reference nearly vanish through second-order.