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

Abstract

In this work, we describe a simple approach to select the most important molecular orbitals (MOs) to compute the optical rotation tensor through linear response (LR) Kohn‐Sham density functional theory (KS‐DFT). Taking advantage of the iterative nature of the algorithms commonly used to solve the LR equations, we select the MOs with contributions to the guess perturbed density that are larger than a certain threshold and solve the LR equations with the selected MOs only. We propose two criteria for the selection, and two definitions of the selection threshold. We then test the approach with two functionals (B3LYP and CAM‐B3LYP) and two basis sets (aug‐cc‐pVDZ and aug‐cc‐pVTZ) on a set of 51 organic molecules with specific rotation spanning five orders of magnitude, 100–104 deg (dm−1 (g/mL)−1). We show that this approach indeed can provide very accurate values of specific rotation with estimated speedup that ranges from 2 to 8× with the most conservative selection criterion, and up to 20 to 30× with the intermediate criterion.

Gauge Dependence of the S̃ Molecular Orbital Space Decomposition of Optical Rotation

“…If these significant transitions could be determined a priori, one could greatly reduce the cost of an OR calculation. Aharon and Caricato proposed truncating the MO space based on the S̃ ia values computed using the initial guess perturbed density . Using this criterion for a set of 51 organic molecules (including molecules 1 – 5 ), they estimated a speedup of 2–8× depending on the size of the basis, with a mean unsigned error of <1% for the computed OR.…”

“…Aharon and Caricato proposed truncating the MO space based on the S ̃ia values computed using the initial guess perturbed density. 32 Using this criterion for a set of 51 organic molecules (including molecules 1−5), they estimated a speedup of 2−8× depending on the size of the basis, with a mean unsigned error of <1% for the computed OR. side of each plot, only the largest contributors are included.…”

“…We also test the quantitative convergence of each definition, as we have previously shown that small fractions of the total number of transitions can be used to approximate the specific rotation. Demonstrating this for other definitions of S̃ would aid in the development of reduced cost methods to compute OR …”

“…Demonstrating this for other definitions of S ̃would aid in the development of reduced cost methods to compute OR. 32…”

Full optical rotation tensor at coupled cluster with single and double excitations level in the modified velocity gauge

“…The molecules used in the test set are reported in Figure 1. The geometries were taken from Stephens et al 42 for molecules 1 and 2, from Srebro et al 43 for molecules 3-7, 12, 13, 15, and 18-20, from Aharon and Caricato 44 for molecules 8-11, 16, and 17, and from Caricato 36 for molecules 14, 21, and 22. TheB calculations were performed with the MVG approach as discussed in the previous section at the sodium D line: 589.3 nm, because this is a typical wavelength used in experiment and it is far from resonance for all molecules.…”