6 research outputs found
Analysis of The Tailored Coupled-Cluster Method in Quantum Chemistry
In quantum chemistry, one of the most important challenges is the static
correlation problem when solving the electronic Schr\"odinger equation for
molecules in the Born--Oppenheimer approximation. In this article, we analyze
the tailored coupled-cluster method (TCC), one particular and promising method
for treating molecular electronic-structure problems with static correlation.
The TCC method combines the single-reference coupled-cluster (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
one-particle 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 single-reference quantum
chemistry. The analysis covers, in particular, CC methods tailored by
tensor-network states (TNS-TCC 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 Aubin--Nitsche-duality method, a quadratic error
bound valid for TNS-TCC methods is derived, e.g., for linear-tensor-network TCC
schemes using the density matrix renormalization group method
Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory
A wide class of coupled-cluster methods is introduced, based on Arponen's
extended coupled-cluster theory. This class of methods is formulated in terms
of a coordinate transformation of the cluster operators. The mathematical
framework for the error analysis of coupled-cluster methods based on Arponen's
bivariational principle is presented, in which the concept of local strong
monotonicity of the flipped gradient of the energy is central. A general
mathematical result is presented, describing sufficient conditions for
coordinate transformations to preserve the local strong monotonicity. The
result is applied to the presented class of methods, which include the standard
and quadratic coupled-cluster methods, and also Arponen's canonical version of
extended coupled-cluster theory. Some numerical experiments are presented, and
the use of canonical coordinates for diagnostics is discussed.Comment: 11 page
A hybrid stochastic configuration interaction-coupled cluster approach for multireference systems
The development of multireference coupled cluster (MRCC) techniques has
remained an open area of study in electronic structure theory for decades due
to the inherent complexity of expressing a multi-configurational wavefunction
in the fundamentally single-reference coupled cluster framework. The recently
developed multireference coupled cluster Monte Carlo (mrCCMC) technique uses
the formal simplicity of the Monte Carlo approach to Hilbert space quantum
chemistry to avoid some of the complexities of conventional MRCC, but there is
room for improvement in terms of accuracy and, particularly, computational
cost. In this paper we explore the potential of incorporating ideas from
conventional MRCC - namely the treatment of the strongly correlated space in a
configuration interaction formalism - to the mrCCMC framework, leading to a
series of methods with increasing relaxation of the reference space in the
presence of external amplitudes. These techniques offer new balances of
stability and cost against accuracy, as well as a means to better explore and
better understand the structure of solutions to the mrCCMC equations.Comment: 13 pages, 10 figures, 3 table