Implementation of Nuclear Velocity Perturbation and Magnetic Field Perturbation Theory in CP2K and Their Application to Vibrational Circular Dichroism

Abstract

We present the implementation of nuclear velocity perturbation theory (NVPT), using a pioneering combination of atom-centered (velocity-dependent) Gaussian basis functions and plane waves in the CP2K package. The atomic polar tensors (APTs) and atomic axial tensors (AATs) are evaluated in the velocity representation using efficient density functional perturbation theory. The presence of nonlocal pseudopotentials, the representation of potentials on numerical integration grids, and effects arising from the basis functions being centered on the atoms have been considered in the implementation. The Magnetic Field Perturbation Theory (MFPT) using gauge-including atomic orbitals is implemented in the same code and compared to the NVPT. Our implementation is the first to compare both approaches (MFPT and NVPT) in the same code. The implementation has been verified via sum rules and by investigating the gauge origin dependence of the AATs for a set of small molecules, oxirane, and fluoro-oxirane. We also present vibrational circular dichroism spectra that are related to the APTs and AATs, applying both theories.

Vibrational Circular Dichroism from DFT Molecular Dynamics: The AWV Method

“…Velocities and accelerations are readily available at each time step of the trajectory. Widespread QM codes, such as Gaussian, 22 ADF, 23 and Cp2k, 24 allow the computing of APTs and AATs in the gas phase and periodic systems. However, evaluating them at each time step would be quite computationally expensive.…”

“…The dynamic spectra discussed in section have been computed using eq . The DFT-MD trajectories on the liquid phase of the S-PO molecule have been run with the Cp2k code . Born–Oppenheimer molecular dynamics were used, i.e., at each time step, the electronic wave function was converged, imposing a threshold for the energy difference between two SCF cycles of 3.0 × 10 –7 Hartree/cell.…”

“…The DFT-MD trajectories on the liquid phase of the S-PO molecule have been run with the Cp2k code. 24 Born–Oppenheimer molecular dynamics were used, i.e., at each time step, the electronic wave function was converged, imposing a threshold for the energy difference between two SCF cycles of 3.0 × 10 –7 Hartree/cell. The classical Newton equations of motion for the nuclei were integrated through the velocity Verlet algorithm with a time step of 0.4 fs.…”

“…Standard quantum chemistry software packages ,− can nowadays compute VCD static spectra (i.e., of equilibrium structures) in the double harmonic approximation. Efforts have been made to go beyond the harmonic approximation, and approaches have been implemented to account for anharmonic effects .…”

How Crystal Symmetry Dictates Non‐Local Vibrational Circular Dichroism in the Solid State

“…[41,55,56] Very recently, MFPT and NVPT have also been implemented into the CP2K package and a direct comparison of the two methods is provided. [57] On the other hand, anharmonicity or the extension of structural models to mimic bulk scenarios are becoming practicable. [10,56,[58][59][60][61][62][63][64] In particular, ab initio molecular dynamics (AIMD), though relying on classical nuclear mechanics, offer a workable route to post-harmonic studies of bulk phase systems, including crystals.…”