A Length-Gauge Origin-Invariant Approach to Vibrational Circular Dichroism Spectra without Gauge-Including Atomic Orbitals

TL;DR

This work extends the origin-invariant length-gauge (LG(OI)) approach to vibrational circular dichroism (VCD), enabling origin-invariant spectra without gauge-including atomic orbitals (GIAOs). By combining the LG and velocity-gauge (VG) dipole moments through a singular-value decomposition of the mixed LG/VG tensor, the method yields origin-invariant rotational strengths $[R_i']^{\text{LG(OI)}}$, avoiding the traditional origin-dependence of the LG formalism. Comparing LG(OI) with VG and GIAO across HF and DFT calculations for four test molecules shows that, at quadruple-zeta quality bases, LG(OI) reproduces major VCD peaks as well as GIAO, though convergence toward the basis-set limit is slower than GIAO. While LG(OI) offers easier implementation and comparable accuracy for large basis sets, its convergence behavior does not universally exceed VG or GIAO across all systems studied, highlighting both its practical convenience and current limitations.

Abstract

We have extended the origin-invariant length gauge (LG(OI)) approach -- originally developed by Caricato and co-workers for optical rotation (OR) and electronic circular dichroism (ECD) -- to vibrational circular dichroism (VCD). This approach avoids the need for gauge-including atomic orbitals (GIAOs), which are typically required to circumvent the unphysical dependence of the CD rotatory strengths on the arbitrary choice of coordinate origin for length gauge (LG) computations. Benchmark VCD spectra are presented for (P)-hydrogen peroxide, (S)-methyloxirane, (1R, 5R)-α-pinene, and (1R, 4R)-camphor using Hartree-Fock (HF) theory and density functional theory (DFT) methods across a range of basis sets and compared to those obtained from LG, velocity-gauge (VG), and GIAO computations. These analyses show that for VCD the LG(OI) approach does not converge to the basis-set limit as rapidly as the GIAO approach, but does yield similar quality spectra as GIAO for all major VCD peaks for quadruple-zeta-quality basis sets. The LG(OI) and VG VCD spectra are less reliable compared to GIAOs for smaller basis sets.

Figures (6)

• Figure 1: Molecular test set for simulation of LG-, VG-, LG(OI)-, and GIAO-based simulations of VCD spectra including (1) (P)-hydrogen peroxide, (2) (S)-methyloxirane, (3) (1R, 5R)-$\alpha$-pinene, and (4) (1R, 4R)-camphor.
• Figure 2: VCD spectra of (S)-methyloxirane optimized and computed with the HF method using the aug-cc-pVTZ basis set for geometries with the coordinate origin located at (a) the center of mass and (b) translated by 1000 a.u. in each Cartesian direction.
• Figure 3: Basis-set convergence of the rotational strength of each normal mode of (P)-hydrogen peroxide: (a) H$-$O$-$O$-$H torsion, (b) O$-$O stretch, (c) H$-$O$-$O antisymmetric bend, (d) H$-$O$-$O symmetric bend, (e) O$-$H antisymmetric stretch, and (f) O$-$H symmetric stretch.
• Figure 4: VCD spectra of (S)-methyloxirane computed at the (a) B3PW91/aug-cc-pVTZ and (b) B3PW91/aug-cc-pVQZ levels of theory.
• Figure 5: VCD spectra of (1R, 4R)-camphor optimized and computed at the (a) B3PW91/aug-cc-pVTZ and (b) B3PW91/aug-cc-pVQZ levels of theory.