Analytic Computation of Vibrational Circular Dichroism Spectra Using Second-Order Møller–Plesset Perturbation Theory

We present the first analytic-derivative-based formulation of vibrational circular dichroism (VCD) atomic axial tensors for second-order Mo̷ller-Plesset (MP2) perturbation theory. We compare our implementation to our recently reported finite-difference approach and find close agreement, thus validating the new formulation. The new approach is dramatically less computationally expensive than the numerical derivative method with an overall computational scaling of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math>. In addition, we report the first fully analytic VCD spectrum for (<i>S</i>)-methyloxirane at the MP2 level of theory.