A software implementation of analytic geometric derivatives of electron-repulsion integrals up to second order is presented for the modeling of vibrational spectroscopies at the level of first-principles Kohn–Sham density functional theory (DFT). In line with the general goals of the VeloxChem program, it targets efficient execution in high-performance computing environments with a hybrid MPI/OpenMP parallelization model and is based on the technique of automatic C++ code generation for high versatility. Gradient calculations scale identically with conventional Fock matrix constructions, and also with the prefactor taken into account, the computational cost of the gradient is significantly lower than that of the self-consistent field (SCF) optimization of the reference state. The Hessian calculation shows a scaling of N3.5 with N being the number of contracted Gaussian basis functions. The computational bottleneck in the Hessian calculation is the solving of the coupled-perturbed Kohn–Sham equations that with VeloxChem can be offloaded to GPU-accelerated nodes. The large-scale virtues of the presented software module are demonstrated by the DFT/B3LYP calculation of the IR spectrum of the entire ubiquitin protein with 1,152 atoms in the quantum mechanical (QM) region and TIP3P water in the molecular mechanics (MM) region. The simulated amide I band shows to be in excellent agreement with experiment.

Nuclear spin-induced circular dichroism (NSCD) is a molecular effect of differential absorption of left- and right-circularly polarized light due to nuclear spins in the molecule. In this work, new tools for its calculation are presented. Specifically, analytic expressions for the computation of the 000000001111110000 000001110000001100 000010000000110110 000010001001100010 000100001011000100 000010010011001100 000001100110110000 000000001110001000 011000001100011000 011100011100011000 000010110100110000 000011100011100000 K term of NSCD have been derived and implemented for the second-order coupled cluster singles and doubles (CC2) model. NSCD results obtained thereby for three derivatives of azobenzenes have been compared with results from time-dependent density functional theory (TD-DFT). The complementary information that could be obtained from NSCD measurements compared to NMR for these three species is discussed. Due to its sensitivity to the local electronic structure, nuclear spin-induced circular dichroism can be used to gain insight into properties of excited states. New computational tools for its calculation are presented.