Vibrational Circular Dichroism Achieves Origin-Invariant Spectra Without Gauge-Including Atomic Orbitals

Vibrational circular dichroism (VCD) spectroscopy offers a powerful method for determining the absolute configuration of chiral molecules, yet accurate computational modelling of VCD spectra remains a significant challenge. Brendan M. Shumberger, James R. Cheeseman, Marco Caricato, and T. Daniel Crawford have now extended an origin-invariant length gauge approach , previously successful in modelling rotation and electronic circular dichroism , to the calculation of VCD spectra. Their work, originating from the Department of Chemistry at Virginia Tech and the University of Kansas, alongside contributions from Gaussian, Inc., circumvents the need for computationally demanding gauge-including atomic orbitals. This new methodology promises to provide a more efficient and reliable pathway to predicting VCD spectra, as demonstrated through benchmark calculations on a variety of chiral molecules including hydrogen peroxide, methyloxirane, α-pinene, and camphor.

Vibrational Frequencies and Rotational Strength Data

This is a table of vibrational frequencies (in cm⁻¹) and associated data, likely from a computational chemistry calculation. Higher frequencies correspond to faster vibrations, and the values in the columns likely relate to the intensity of these vibrational modes. This data is used for interpreting vibrational spectra, performing normal mode analysis, validating theoretical calculations, and is particularly relevant to vibrational circular dichroism (VCD) calculations for chiral molecules.

Origin-Invariant Gauge for Vibrational Circular Dichroism

Scientists have extended the origin-invariant length gauge (LG(OI)) approach, previously successful in modelling rotation and electronic circular dichroism, to the calculation of vibrational circular dichroism (VCD). This methodology avoids the need for computationally demanding gauge-including atomic orbitals (GIAOs), which are conventionally used to address the artificial dependence of rotatory strengths on the chosen coordinate origin. Benchmark VCD spectra were generated for hydrogen peroxide, methyloxirane, α-pinene, and camphor, utilising Hartree-Fock (HF) and density functional theory (DFT) methods.

The research demonstrates that while the LG(OI) approach doesn’t converge as quickly as the GIAO method, it delivers comparable spectral quality for major VCD peaks when using quadruple-zeta-quality basis sets. Measurements confirm that LG(OI) and velocity-gauge VCD spectra exhibit reduced reliability compared to GIAO calculations with smaller basis sets, emphasising the importance of basis set selection. This new approach provides a pathway for simulating VCD spectra without the computational demands of GIAOs, potentially increasing accessibility to this analytical technique.

The study meticulously calculated rotational strengths, the imaginary component of the dot product of electric and magnetic vibrational transition dipole moments, to assess the accuracy of the LG(OI) method. Results show that the LG(OI) formulation effectively combines molecular orientations to diagonalise the mixed length/velocity gauge dipole strength tensor, eliminating origin dependence in the rotational strength calculation. A singular value decomposition (SVD) of the mixed LG/VG dipole strength tensor streamlined the process and enhanced computational efficiency, allowing for simulations previously limited to HF, multiconfigurational self-consistent field (MCSCF), and DFT methods reliant on GIAOs.

Until now, rotational strengths derived from the velocity gauge representation of Stephens’s formulation for VCD have remained unreported at any level of theory. This breakthrough delivers a new tool for theoretical simulation, validated through spectral analyses of four test compounds, paving the way for more efficient and accurate VCD calculations.

LG(OI) for Accurate Vibrational Circular Dichroism

This work successfully extends the origin-invariant length gauge (LG(OI)) approach, previously established for rotation and electronic circular dichroism, to the calculation of vibrational circular dichroism spectra. Researchers demonstrated the method’s ability to yield origin-invariant results, comparable to the widely used gauge-including atomic orbitals (GIAO) approach, for systems including hydrogen peroxide, methyloxirane, α-pinene, and camphor. Calculations were performed using both Hartree-Fock and density functional theory with varying basis sets to assess performance.

The study reveals that while LG(OI) and velocity-gauge approaches converge towards similar rotational strengths as basis set quality increases, they do not exhibit significantly faster convergence than the GIAO method for the molecules tested. The principal benefit of LG(OI) lies in its relative ease of implementation, requiring only modifications to existing atomic polar tensor codes, and may prove particularly useful in advanced VCD calculations incorporating dynamic electron correlation. Further investigation is warranted to understand the observed lack of faster convergence, potentially through exploring the behaviour of LG(OI) with a wider range of molecular systems and computational methods.

The authors also highlight the potential for insights into basis set balance through singular value decomposition of the relevant polarizability tensors, suggesting a direction for theoretical development. These findings contribute to the ongoing refinement of computational methods for predicting and interpreting VCD spectra, a technique valuable in determining molecular chirality and structure.