Analysis of The Tailored CoupledCluster Method in Quantum Chemistry
Abstract
In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schrödinger equation for molecules in the BornOppenheimer approximation. In this article, we analyze the tailored coupledcluster method (TCC), one particular and promising method for treating molecular electronicstructure problems with static correlation. The TCC method combines the singlereference coupledcluster (CC) approach with an approximate reference calculation in a subspace [complete active space (CAS)] of the considered Hilbert space that covers the static correlation. A oneparticle spectral gap assumption is introduced, separating the CAS from the remaining Hilbert space. This replaces the nonexisting or nearly nonexisting gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital usually encountered in standard singlereference quantum chemistry. The analysis covers, in particular, CC methods tailored by tensornetwork states (TNSTCC methods). The problem is formulated in a nonlinear functional analysis framework, and, under certain conditions such as the aforementioned gap, local uniqueness and existence are proved using Zarantonello's lemma. From the AubinNitscheduality method, a quadratic error bound valid for TNSTCC methods is derived, e.g., for lineartensornetwork TCC schemes using the density matrix renormalization group method.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.05699
 Bibcode:
 2018arXiv180205699F
 Keywords:

 Mathematics  Numerical Analysis;
 Condensed Matter  Strongly Correlated Electrons;
 Physics  Chemical Physics;
 Physics  Computational Physics;
 Quantum Physics
 EPrint:
 doi:10.1137/18M1171436