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

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.