Basis Set Dependence of Optical Rotation Calculations with Different Choices of Gauge

04 March 2022, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


In this work, the basis set dependence of optical rotation (OR) calculations is examined for various choices of gauge/level of theory. The OR is calculated for a set of 50 molecules using B3LYP and CAM-B3LYP, and 17 molecules using coupled cluster with single and double ex- citations (CCSD). The calculations employ the correlation-consistent basis sets, aug-cc-pVζZ with ζ = D, T, Q. An inverse-power extrapolation formula is then utilized to obtain OR values at the complete basis set (CBS) limit. We investigate the basis set convergence for these methods and three choices of gauge: length gauge (with gauge-including atomic orbitals, LG(GIAOs), for DFT), the origin-invariant length gauge [LG(OI)], and the modified velocity gauge (MVG). The results show that all methods converge smoothly to the CBS limit and that the LG(OI) approach has a slightly faster convergence rate than the other choices of gauge. While the DFT methods reach gauge invariance at the CBS limit, CCSD does not. The significant difference between the MVG and LG(OI) results at the CBS limit, 26%, indicates that CCSD is not quite at convergence in the description of electron correlation for this property. On the other hand, gauge invariance at the CBS limit for DFT does not lead to the same OR values for the two density functionals, which is also due to electron correlation incompleteness. A limited comparison to gas-phase experimental OR values for the DFT methods shows that CAM-B3LYP seems more accurate than B3LYP. Overall, this study shows that the LG(OI) approach with the aug-cc-pVTZ basis set for DFT, and with the CBS(DT) extrapolation for CCSD, provides a good cost/accuracy balance.


optical rotation
gauge invariance
complete basis set limit
origin dependence

Supplementary materials

Supporting Information: Basis Set Dependence of Optical Rotation Calculations with Different Choices of Gauge
The Supporting Information includes the OR values for each of the molecules discussed in the main text (Tables S1-S50). Additionally, values for ∆ref are shown in Tables S51-S54, and ∆ref values are given in Tables S55-S58. The handedness of the following molecules was reversed to the enantiomer with positive OR value with the aug-cc-pVQZ basis set, compared to what appears in the study from which the geometry was taken: 1, 2, 7, 9, 10, 11, 12, 13, 20, 21, 22, 23, 26, 27, 28, 30, 32, 42, 45, 47, 48, and 49.


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