Exploring the accuracy of relative molecular energies with local correlation theory

Local coupled-cluster singles–doubles theory (LCCSD) is a theorist’s attempt to capture electron–electron correlation in a fast amount of time and with chemical accuracy. Many of the difficult computational hurdles have been navigated over the last twenty years, including how to construct a linear scaling algorithm and how to produce smooth potential energy surfaces. Nevertheless, there remains the question of just how accurate a local correlation model can be, and what are the chemical limits within which local models are largely applicable. Here, we investigate how accurately can LCCSD approximate full CCSD for cases of atomization energies, isomerization energies, conformational energies, barrier heights and electron affinities. Our conclusion is that LCCSD computes relative energies that are correct to within 1–2 kcal mol−1 of the CCSD energy using relatively aggressive cutoffs and over a broad range of different molecular environments—alkane isomers, dipeptide conformations, Diels–Alder transition states and electron attachment in charge delocalized systems. These findings should push the reach of local correlation applications into new research terrain, including molecules on metal cluster surfaces or perhaps even metal–molecule–metal clusters. (Some figures in this article are in colour only in the electronic version) 1. Local CCSD: a small review 1.1. Historical overview Over the past two decades, computational physicists and chemists by and large have succeeded in producing linear scaling algorithms, capable of capturing the electronic structure of large atomic systems at the mean-field level. Today, density functional (DFT) calculations are routinely done on systems with more than a thousand atoms, yielding valuable information about the band structure of large systems [1]. Nevertheless, the problem of measuring electron– electron correlation remains a daunting problem. On the one hand, if one seeks to construct the formal wavefunction for the ground state of a molecule, the computational problem scales exponentially with the number of electrons [2] and converges very slowly with basis set size, making the complete solution (full configuration interaction [CI]) unfeasible for systems with more than 10 electrons or so. On the other hand, while DFT formally solves the problem of energy levels for interacting electrons around a nuclear potential quickly and without huge basis set effects, because the exact exchange– correlation potential is unknown, DFT cannot treat highly correlated systems, it cannot be systematically improved and it does not easily yield information about magnetic field interactions. Our purpose in this paper is to review and assess the accuracy of one wavefunction-based method for overcoming the problem of exponential scaling and quickly measuring electron–electron correlation: local coupled-cluster singles–doubles theory (LCCSD). Just as for large mean-field calculations, the basic idea of local coupled-cluster theory (CCSD) [3–11] is to invoke the locality of individual electronic orbitals in order to achieve 0953-8984/08/294211+13$30.00 © 2008 IOP Publishing Ltd Printed in the UK 1 J. Phys.: Condens. Matter 20 (2008) 294211 J E Subotnik and M Head-Gordon a huge speed-up in computational time within the context of a CCSD calculation. The coupled-cluster approach [12–15] towards calculating electronic correlation is to make the ansatz that the n-electron fully correlated ground state has the following form: CCSD = e 0. (1) Here, 0 is a single Slater determinant, often the Hartree–Fock (HF) ground state, and T̂ is an excitation operator accounting for electronic correlation. We now denote the occupied orbitals of the HF or mean-field calculation as i jkl and the virtual orbitals as abcd , where the virtual orbitals are what remain of our original basis after we have projected out the occupied basis. Then, for the case of coupled-cluster singles–doubles (CCSD) calculation, T̂ assumes the form T̂ = ∑ia t i a† aai + ∑ i jab t ab i j a † aa † bai a j . At low order, the CCSD ansatz is