Analytic Computation of Vibrational Circular Dichroism Spectra Using Configuration Interaction Methods

TL;DR

This work delivers the first analytic-gradient formulation for atomic axial tensors (AATs) within CID and CISD, enabling accurate vibrational circular dichroism (VCD) simulations that include dynamic electron correlation. The authors implement non-canonical perturbed orbitals and frozen-core in a second-quantized, CI-based framework, achieving $O(N^5)$ scaling via intermediates and validating the approach against finite-difference derivatives. Across a test set of five chiral molecules, they observe substantial differences between HF/MP2 and CID/CISD rotatory strengths, with singly excited determinants notably impacting high-frequency and axial-chiral modes and sometimes causing sign changes. The results highlight the importance of CI-coefficient optimization for VCD predictions and pave the way for more reliable interpretation of experimental VCD spectra in complex systems, while also identifying gauge-origin dependence as an area for future improvement.

Abstract

In this work, we present the first derivation and implementation of analytic gradient methods for the computation of the atomic axial tensors (AATs) required for simulations of vibrational circular dichroism (VCD) spectra using configuration interaction methods including double (CID) and single and double (CISD) excitations. Our new implementation includes the use of non-canonical perturbed orbitals to improve the numerical stability of the gradients in the presence of orbital near-degeneracies, as well as frozen-core capabilities. We validated our analytic CID and CISD formulations against two new finite-difference approaches. Using this new implementation, we investigated the significance of singly excited determinants and the role of CI-coefficient optimization in VCD simulations by comparisons among Hartree-Fock (HF) theory, second-order Møller-Plesset perturbation (MP2) theory, CID, and CISD theories. For our molecular test set including (P )-hydrogen peroxide, (S )-methyloxirane, (R)-3-chloro-1-butene, (R)-4-methyl-2-oxetanone, and (M )-1,3-dimethylallene we noted sign discrepancies between the HF and MP2 methods compared to that of the new CID and CISD methods for four of the five molecules as well as similar discrepancies between the CID and CISD methods for (M )-1,3-dimethylallene.

Figures (6)

• Figure 1: Molecular test set for comparisons of HF, MP2, CID, and CISD VCD spectra including (1) (P)-hy-dro-gen per-ox-ide, (2) (S)-meth-yl-ox-i-rane, (3) (R)-3-chlo-ro-1-bu-tene, (4) (R)-4-meth-yl-2-ox-et-a-none, and (5) (M)-1,3-di-meth-yl-all-ene.
• Figure 2: VCD spectra of (P)-hy-dro-gen per-ox-ide computed at the HF, MP2, and CISD levels of theory with aug-cc-pVDZ using a common optimized geometry and Hessian obtained at the MP2/aug-cc-pVDZ level of theory. Artificial shifts of 5 cm$^{-1}$, 10 cm$^{-1}$, and 15 cm$^{-1}$ for MP2, CID, and CISD, respectively, have been introduced into the spectrum to distinguish the peaks more easily.
• Figure 3: VCD spectra of (S)-meth-yl-ox-i-rane computed at the HF, MP2, and CISD levels of theory with aug-cc-pVDZ using a common optimized geometry and Hessian obtained at the MP2/aug-cc-pVDZ level of theory. Artificial shifts of 5 cm$^{-1}$, 10 cm$^{-1}$, and 15 cm$^{-1}$ for MP2, CID, and CISD, respectively, have been introduced into the spectrum to distinguish the peaks more easily.
• Figure 4: VCD spectra of (R)-3-chlo-ro-1-bu-tene computed at the HF, MP2, and CISD levels of theory with aug-cc-pVDZ using a common optimized geometry and Hessian obtained at the MP2/aug-cc-pVDZ level of theory. Artificial shifts of 5 cm$^{-1}$, 10 cm$^{-1}$, and 15 cm$^{-1}$ for MP2, CID, and CISD, respectively, have been introduced into the spectrum to distinguish the peaks more easily.
• Figure 5: VCD spectra of (R)-4-meth-yl-2-ox-et-a-none computed at the HF, MP2, and CISD levels of theory with aug-cc-pVDZ using a common optimized geometry and Hessian obtained at the MP2/aug-cc-pVDZ level of theory. Artificial shifts of 5 cm$^{-1}$, 10 cm$^{-1}$, and 15 cm$^{-1}$ for MP2, CID, and CISD, respectively, have been introduced into the spectrum to distinguish the peaks more easily.