Toward exact quantum chemistry: High-level coupled-cluster energetics by Monte Carlo sampling and moment expansions

Abstract:  One of the main goals of electronic structure theory is precise ab initio description of increasingly complex polyatomic systems. It is generally accepted that size extensive methods based on the exponential wave function ansatz of coupled-cluster (CC) theory are excellent candidates for addressing this goal. Indeed, when applied to molecular properties and chemical reaction pathways, the CC hierarchy, including CCSD, CCSDT, CCSDTQ, etc., rapidly converges to the limit of the exact, full configuration interaction (CI) diagonalization of the Hamiltonian, allowing one to capture the relevant many-electron correlation effects in a conceptually straightforward manner through particle-hole excitations from a single Slater determinant. One of the key challenges has been how to incorporate higher-than-two-body components of the cluster operator, needed to achieve a quantitative description, without running into prohibitive computational costs of CCSDT, CCSDTQ, and similar schemes, while eliminating failures of the more practical perturbative approximations of the CCSD(T) type in multi-reference situations, such as chemical bond breaking. A similar challenge applies to other areas of many-body theory, where CC methods have demonstrated considerable promise and where higher-than-two-body clusters are important, such as nuclear physics. In this talk, I will discuss a radically new way of obtaining accurate energetics equivalent to high-level CC calculations, even when electronic quasi-degeneracies and higher–than–two-body clusters become significant, at the small fraction of the computational cost, while preserving the black-box character (minimum input information) of conventional single-reference computations. The key idea is a merger of the deterministic formalism, abbreviated as CC(P;Q) [1-4], with the stochastic CI [5,6] and CC [7–9] Monte Carlo approaches [10,11]. The advantages of the proposed methodology will be illustrated by a few molecular examples, where the goal is to recover highly accurate full CCSDT and CCSDTQ energetics, including bond breaking in F2 and H2O and automerization of cyclobutadiene. [1] J. Shen and P. Piecuch, Chem. Phys. 401, 180 (2012). [2] J. Shen and P. Piecuch, J. Chem. Phys. 136, 144104 (2012). [3] J. Shen and P. Piecuch, J. Chem. Theory Comput. 8, 4968 (2012). [4] N.P. Bauman, J. Shen, and P. Piecuch, Mol. Phys. 115, 2860 (2017). [5] G.H. Booth, A.J.W. Thom, and A. Alavi, J. Chem. Phys. 131, 054106 (2009). [6] D. Cleland, G.H. Booth, and A. Alavi, J. Chem. Phys. 132, 041103 (2010). [7] A.J.W. Thom, Phys. Rev. Lett. 105, 263004 (2010). [8] R.S.T. Franklin, J.S. Spencer, A. Zoccante, and A.J.W. Thom, J. Chem. Phys. 144, 044111 (2016). [9] J. S. Spencer and A. J. W. Thom, J. Chem. Phys. 144, 084108 (2016). [10] J.E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017). [11] J.E. Deustua, J. Shen, and P. Piecuch, in preparation.