A Comparison of Three Approaches to the Reduced-Scaling Coupled Cluster Treatment of Non-Resonant Molecular Response Properties

Abstract

We have investigated the performance of the reduced-scaling coupled cluster method based on projected atomic orbitals (PAOs), pair natural orbitals (PNOs), and orbital specific virtuals (OSVs) for the prediction of linear response properties. These methods introduce different degrees of controllable sparsity in the ground-state and perturbed coupled cluster wave functions, leading to localization errors in properties such as dynamic polarizabilities and specific optical rotations. Using a series of chiral test compounds, we find that the inherent costs associated with computing response properties are significantly greater than those for determining the ground-state energy. As the dimensionality of the molecular system increases-from (pseudo)linear structures, such as fluoroalkanes, to cagelike structures, such as β-pinene-the crossover point between canonical-orbital and localized-orbital algorithms increases substantially. Furthermore, both the OSV and PNO methods provide greater reduction in cost (as measured by the size of the double-excitation space) than do PAOs, and PNOs provide the greatest level of sparsity for the systems examined here. Single-excitation truncation induces much larger errors than corresponding doubles truncation due to the fact that the first-order contribution to the one-electron perturbed wave function appears in the singles amplitudes. Both the PNO and OSV methods perform reasonably well for frequency-dependent polarizabilities provided appropriate thresholds are used for the occupation-number and weak-pair cutoffs on which each method depends. Specific rotations, however, are very sensitive to wave function truncation, to the extent that aggressive thresholds can yield the incorrect sign of the rotation, due to the delicate balance of positive and negative wave function contributions to the mixed electric-/magnetic-field response.

A molecular orbital selection approach for fast calculations of specific rotation with density functional theory

“…Crawford et al extended the local correlation idea of Pulay and Saebø to response properties and then later implemented it for [ α ] ω calculations . This method uses localized orbitals and neglects interactions between distant orbitals, thus reducing the cost of the correlation part of the calculation . While this method is successful for smaller systems, the authors show that for larger systems the need for tighter thresholds outweighs the benefits of neglecting parts of the wave function …”

“…25 This method uses localized orbitals and neglects interactions between distant orbitals, thus reducing the cost of the correlation part of the calculation. 26,27 While this method is successful for smaller systems, the authors show that for larger systems the need for tighter thresholds outweighs the benefits of neglecting parts of the wave function. 25 In this work, we present a different approach to reduce the cost of [α] ω calculations with Kohn-Sham DFT (KS-DFT), based on the selection of the molecular orbitals (MOs) that are likely to contribute the most to this property and discarding the rest.…”

CC2 oscillator strengths within the local framework for calculating excitation energies (LoFEx)

“…projected atomic orbitals (PAOs) or pair natural orbitals (PNOs)) is widely used to reduce the total number of wave function parameters and it has been applied to the calculation of excitation energies, [19][20][21][22][23][24][25][26] transition strengths, 23,27 and other molecular properties. 23,[27][28][29][30] The incremental scheme in which the quantities of interest are expanded in a many-body series has also been applied to the calculation of CC excitation energies 31 and dipole polarizabilities. 32 Another recent development is the multilevel CC theory in which different CC models are used to treat different parts of the system.…”

Molecular Dipole Moments within the Incremental Scheme Using the Domain-Specific Basis-Set Approach

“…Significant contribution in this area was done by Werner, Schütz and coworkers, [29][30][31][32][33][34][35][36] who utilized the 3 Pulay-Saebø approach, 24,25 as well as by Neese et al, who realized the local pair-naturalorbital (LPNO) approach. [37][38][39][40][41][42] Other methods are based on fragmentation schemes, which divide the whole system into parts [66][67][68][69] and frequency-dependent polarizabilities. 6,69 In this work the incremental scheme of is used for the calculation of molecular dipole moments.…”

“…[37][38][39][40][41][42] Other methods are based on fragmentation schemes, which divide the whole system into parts [66][67][68][69] and frequency-dependent polarizabilities. 6,69 In this work the incremental scheme of is used for the calculation of molecular dipole moments. The fundamental idea behind the incremental scheme was introduced in quantum chemistry by Nesbet 73-75 as a generalized Bethe-Goldstone expansion.…”