Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory

Abstract

The frozen-virtual natural-orbital (NO) approach, whereby the unoccupied-orbital space is constructed using a correlated density such as that from many-body perturbation theory, has proven to yield compact wave functions for determining ground-state correlation energies and associated properties, with corresponding occupation numbers providing a guide to the truncation of the virtual space. In this work this approach is tested for the first time for the calculation of higher-order response properties, particularly frequency-dependent dipole polarizabilities using coupled-cluster theory. We find that such properties are much more sensitive to the truncation of virtual space in the NO basis than in the original canonical molecular orbital (CMO) basis, with truncation errors increasing linearly with respect to the number of frozen virtual NOs. The reasons behind this poor performance include the more diffuse nature of NOs with low occupation numbers as well as the reduction in sparsity of the perturbed singles amplitudes in the NO basis and the neglect of orbital response. We tested a number of approaches to improve the performance of the NO space, including the use of a field-perturbed density to define the virtual orbitals and various external-space corrections. The truncation of the CMO space, on the other hand, yields errors in coupled-cluster dipole polarizabilities of less than 2% even after removing as much as 50% of the full virtual space. We find that this positive performance of the CMO space results from a cancellation of errors due to the truncation of the unperturbed and perturbed amplitudes, as well as sparsity of the singles amplitudes. We introduce a simple criterion called a dipole amplitude to use as a threshold for truncating the CMO basis for such property calculations.

Correlated natural transition orbital framework for low-scaling excitation energy calculations (CorNFLEx)

“…Finally, we note that computational savings can be obtained by simply truncating the virtual orbital space in the canonical orbital basis. 50,51 In a previous publication, we have introduced a local framework for calculating CC excitation energies (LoFEx), 49 which provides a general approach for calculating excitation energies at a reduced computational cost. The orbital space in the LoFEx approach is a mixed space containing natural transition orbitals (NTOs) determined from a timedependent Hartree-Fock (TDHF) calculation and localized molecular orbitals (LMOs).…”

Reduced‐scaling coupled cluster response theory: Challenges and opportunities

“…While the FVNO method has been used successfully within the context of coupled‐cluster theory for correlation energies, ionization energies, geometry optimizations, and so forth, its utility for response properties was only recently considered, specifically in the context of dynamic polarizabilities. Figure compare the impact of freezing virtual orbitals on CCSD correlation energies vs. polarizabilities (using hydrogen peroxide as an example system), where CMOs are removed starting from the highest‐energy orbitals and virtual NOs starting from the lowest occupation numbers.…”

“…However, Figure b reveals a complete reversal of this trend for polarizabilities: the virtual NOs that play an insignificant role in describing electron correlation can be essential for describing the response to the electric field; on the other hand, due in part to fortuitous error cancellations, high‐energy CMOs play no role in this regard, a finding consistent with those of Sundholm and co‐workers . Similar trends can be observed for molecules such as dimethylallene, and methyloxirane (as well as these compounds interacting with explicit solvent molecules) and with diffuse‐augmented basis sets like aDZ, d‐aDZ, aTZ, and so forth …”

Reduced-cost linear-response CC2 method based on natural orbitals and natural auxiliary functions

“…50,51 Although the literature of local correlation methods is intensively growing, applications to excited states are relatively scarce. The first excited-state local approach was proposed by Crawford et al, 52,53 who generalized the ground-state local CCSD method of Werner and co-workers 54 to EOM-CCSD. Subsequently several excited-state CC methods utilizing local approximations were published by Korona, Schütz, and their associates.…”

“…In this method, a one-particle density matrix is constructed using a more approximate correlation method, the matrix is diagonalized, and the orbitals with small occupation number, i.e., eigenvalue, are dropped from the resulting NO basis. [67][68][69] While the approach is extensively used for ground-state CCSD and higher-order CC calculations, [70][71][72][73] only a couple of applications have been reported for excited states, 53,74 and, to the best of knowledge, no attempt has been made so far to accelerate CC2 calculations with frozen NO approximations. Motivated by the NO technique, a related approach was recently put forward by one of us for the reduction of the auxiliary function basis set employed in DF methods.…”