Abstract
We present a basis set correction scheme for the coupled-cluster singles and doubles (CCSD) method. The scheme is based on employing frozen natural orbitals (FNOs) and diagrammatically decomposed contributions to the electronic correlation energy, which dominate the basis set incompleteness error (BSIE). As recently discussed in the work of Irmler et al. [Phys. Rev. Lett. 123, 156401 (2019)], the BSIE of the CCSD correlation energy is dominated by the second-order Møller-Plesset (MP2) perturbation energy and the particle-particle ladder term. Here, we derive a simple approximation to the BSIE of the particle-particle ladder term that effectively corresponds to a rescaled pair-specific MP2 BSIE, where the scaling factor depends on the spatially averaged correlation hole depth of the coupled-cluster and first-order pair wavefunctions. The evaluation of the derived expressions is simple to implement in any existing code. We demonstrate the effectiveness of the method for the uniform electron gas. Furthermore, we apply the method to coupled-cluster theory calculations of atoms and molecules using FNOs. Employing the proposed correction and an increasing number of FNOs per occupied orbital, we demonstrate for a test set that rapidly convergent closed and open-shell reaction energies, atomization energies, electron affinities, and ionization potentials can be obtained. Moreover, we show that a similarly excellent trade-off between required virtual orbital basis set size and remaining BSIEs can be achieved for the perturbative triples contribution to the CCSD(T) energy employing FNOs and the (T*) approximation.
Highlights
Traditional quantum chemical theories approximate the manyelectron wavefunction by a linear combination of Slater determinants constructed from one-electron orbitals
V B, we show that this behavior persists for most quantities computed from the total energies including reaction energies, atomization energies, ionization potentials, and electron attachment energies
We introduced a new coupled-cluster singles and doubles (CCSD) basis set correction scheme that employs frozen natural orbitals (FNOs) and exhibits an excellent tradeoff between the virtual orbital basis set size and remaining basis set incompleteness error (BSIE)
Summary
Traditional quantum chemical theories approximate the manyelectron wavefunction by a linear combination of Slater determinants constructed from one-electron orbitals. Most importantly, we introduce approximations to the electron pair wavefunctions appearing in the expression for the PPL term, making it possible to compute BSIE corrections with low computational cost but high accuracy To this end, we develop a pair-specific mean-field ansatz that exhibits an average correlation hole depth that agrees with the spatially averaged correlation hole depth of the coupled-cluster or first-order wavefunction in a finite basis set. Our work corroborates the success of CCSD basis set corrections that are based on rescaling MP2 BSIEs. We note that the averaged pair-specific correlation hole depth can be computed from the electronic transition structure factor, which introduces the need for two-electron integrals employing the δ(r12) kernel. We demonstrate that the introduced BSIE correction yields CCSD correlation energies that converge rapidly with respect to the number of frozen natural orbitals
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