Abstract
Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/Lα two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol–1. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approaches require additional MP2 calculations with basis sets of up to QZ quality. We also assess the performance of the basis-set extrapolations and additivity schemes for a set of 20 basis-set limit CCSD atomization energies of larger molecules including amino acids, DNA/RNA bases, aromatic compounds, and platonic hydrocarbon cages. We obtain the following RMSDs for the above methods: 10.2 (global extrapolation), 5.7 (system-dependent extrapolation), and 2.9 (additivity scheme) kJ mol–1.
Highlights
Coupled-cluster theory is one of the most reliable, yet computationally affordable, methods for solving the nonrelativistic electronic Schrödinger equation.[1]
We assess the performance of a number of approaches for obtaining calculations with all single and double excitations (CCSD) correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets
We have shown that extrapolating the CCSD energy from the A′VDZ and A′VTZ basis sets using system-dependent basis set extrapolations cuts the RMSD by over50% relative to the global basis set extrapolations.We turn to CCSD extrapolations in conjunction with the larger A′VTZ and A′VQZ basis sets
Summary
Coupled-cluster theory is one of the most reliable, yet computationally affordable, methods for solving the nonrelativistic electronic Schrödinger equation.[1] Coupled-cluster theory entails a hierarchy of approximations that can be systematically improved towards the exact quantum mechanical solution, providing a roadmap for highly accurate chemical properties.[2,3,4,5,6,7,8] In particular, the CCSD(T) method (coupled-cluster with single, double, and quasiperturbative triple excitations) has been found to be a cost-effective approach for the calculation of reliable thermochemical and kinetic data(e.g. reaction energies and barrier heights) as well as molecular properties based on energy derivatives (e.g. equilibrium/transition structures, vibrational frequencies, and electrical properties).[9,10,11,12,13,14] one of the greatest weaknesses of the CCSD(T) method is that it converges exceedingly slowly to the complete basis set (CBS) limit This is true for the double excitations, as they reflect dynamical rather than static electron correlation effects..
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