Non-Resonant Raman Optical Activity From Phase-Space Electronic Structure Theory

TL;DR

This work develops a phase-space electronic structure theory (PS) framework to compute nonresonant ROA without relying on BO Berry-curvature corrections. By explicitly coupling electronic structure to nuclear momentum via a carefully constructed one-electron operator $\hat{\boldsymbol\Gamma}$ and a distributed-origin scheme, the authors express the ROA tensor $G'$ through derivatives with respect to nuclear momentum, generating gauge-origin invariant predictions for magic-angle CID. The approach is benchmarked on (R)-methyloxirane, showing reasonable agreement with experiment and offering potential computational advantages over traditional Berry-curvature ROA calculations. The results demonstrate robustness of the PS method, outline practical parameterizations, and discuss future extensions to external magnetic fields and more complex systems, highlighting the PS framework as a versatile tool for chiroptical spectroscopy beyond BO limitations.

Abstract

In order to model experimental non-resonant Raman optical activity, chemists must compute a host of second-order response tensors, (e.g. the electric-dipole magnetic-dipole polarizability) and their nuclear derivatives along a set of vibrational modes. While these response functions are almost always computed within a Born-Oppenheimer (BO) framework, here we provide a natural interpretation of the electric-dipole magnetic-dipole polarizability within phase space electronic structure theory, a beyond-BO model whereby the electronic structure depends on nuclear momentum (P) in addition to nuclear position (R). By coupling to nuclear momentum, phase space electronic structure theory is able to capture the asymmetric response of the electronic properties to an external field, in sofar as for a vibrating (non-stationary) molecule, dmu/dB \ne dm/dF, where mu and m are the electrical linear and magnetic dipoles, and F and B are electric and magnetic fields. As an example, for a prototypical methyloxirane molecule, we show that phase space electronic structure theory is able to deliver a reasonably good match with experimental results in a manner that is invariant to gauge origin G0.

Figures (4)

• Figure 1: Calculated (a) magic-angle ($\Delta(*)$), (b) polarized ($\Delta(x)$), and depolarized CIDs ($\Delta(z)$) for (R)-methyloxirane using perturbation theory based on BO states (shown in orange) and PS theory (shown in blue, locality parameters, $\sigma=\eta = 1.5$ Bohr and $\beta = 9$ Bohr) compared to experimental values (shown in black). The results shown here were calculated with aug-cc-pVTZ basis set. The magic-angle and polarized experimental results were reported in Ref. bose_ab_1990. For the depolarized experimental results, we used the experimental data from a later experiment in Ref. polavarapu_vibrational_1993 that matched the same signs with the previous reported signals in Ref. bose_ab_1990. Experimentally reported frequencies were used to label x-axis.
• Figure 2: Calculated (a) magic-angle ($\Delta(*)$), (b) polarized ($\Delta(x)$), and depolarized CIDs ($\Delta(z)$) for (R)-methyloxirane using perturbation theory based on BO states (shown in orange) and PS theory (shown in blue, Eq. \ref{['eq:ROA_PS3']}, the locality parameters $\sigma=\eta=2$ Bohr and $\beta = 9$ Bohr) compared to experimental values (shown in black). The results shown here were calculated with aug-cc-pVTZ basis set. The magic-angle and polarized experimental results were reported in Ref. bose_ab_1990. For the depolarized experimental results, we used the experimental data from a later experiment in Ref. polavarapu_vibrational_1993 that matched the same signs with the previous reported signals in Ref. bose_ab_1990. Experimentally reported frequencies were used to label x-axis. PS results give reasonable agreement with experimental signals with the gauge center at the center of charge.
• Figure 3: Calculated (a) magic-angle ($\Delta(*)$), (b) polarized ($\Delta(x)$), and depolarized CIDs ($\Delta(z)$) for (R)-methyloxirane using perturbation theory based on BO states (shown in orange), PS theory with the distributed origin scheme (shown in blue, Eqs. \ref{['eq:final_original_do']}-\ref{['eq:final_original2_do']}), PS theory with a common gauge origin (shown in purple, Eq. \ref{['eq:ROA_PS3']}) at different translated gauge origins. The locality parameters take the values $\sigma=\eta=2$ Bohr and $\beta = 9$ Bohr. The labels with subscript x,y,z refer to translating the molecule with 1 Å along x-, y-, or z-direction. The results shown here were calculated with aug-cc-pVTZ basis set. The CIDs computed with the BO approach and the PS approach within the distributed gauge origin scheme are not sensitive to the choice of gauge origins, despite the gauge dependence of the electric-dipole-electric-quadrupole polarizability $\bm A$, which are relevant for polarized and depolarized CID calculations.
• Figure 4: Calculated (a) magic-angle ($\Delta(*)$), (b) polarized ($\Delta(x)$), and depolarized CIDs ($\Delta(z)$) for (R)-methyloxirane using different reference frames for electronic pseudomomentum in the PS theory compared to experimental values (shown in black). See text for the definitions of the curves with other colors. The results shown here were calculated with aug-cc-pVTZ basis set. The magic-angle and polarized experimental results were reported in Ref. bose_ab_1990. For the depolarized experimental results, we used the experimental data from a later experiment in Ref. polavarapu_vibrational_1993 that matched the same signs with the previous reported signals in Ref. bose_ab_1990. Experimentally reported frequencies were used to label x-axis. This data makes clear that some locality (but not strict locality) is best for establishing a reference frame.