The position operator problem in periodic calculations with an emphasis on theoretical spectroscopy.

In this article, we present the challenges that arise when carrying out spectroscopic simulations within periodic boundary conditions. We present approaches which were proposed in the literature for the calculation of the extension of the electric dipole moment to periodic systems. Further, we describe the challenges arising for the simulation of magnetic properties within periodic boundary conditions and for the simulation of nuclear magnetic resonance shielding tensors and related quantities. Furthermore, issues arising in periodic implementations of vibrational circular dichroism spectroscopy are described, especially for the case of atom-centered basis functions and nuclear velocity perturbation theory.

Vibrational circular dichroism spectra of natural products by means of the nuclear velocity perturbation theory.

We present the application of the recently implemented nuclear velocity perturbation theory, using the combined Gaussian and plane waves approach in CP2K, to the vibrational circular dichroism (VCD) spectra of a set of natural products. Even though the calculations were carried out for isolated molecules in the gas-phase limit, neglecting inter-molecular interactions and anharmonic effects, the match between simulated and experimental spectra is reasonable. We also study the influence of different density functionals on the conformational search and the resulting VCD spectra via group coupling matrices (GCMs). The GCM analysis reveals that the VCD signal can in some cases arise from moieties which are close to each other and in other cases from moieties far from each other. Differences in spectra obtained using different exchange-correlation density functionals can be attributed to interaction terms between different moieties in the molecules changing their sign.

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

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.

Analytic calculation and analysis of atomic polar tensors for molecules and materials using the Gaussian and plane waves approach.

The evaluation of atomic polar tensors and Born Effective Charge (BEC) tensors from Density Functional Perturbation Theory (DFPT) has been implemented in the CP2K code package. This implementation is based on a combination of the Gaussian and plane wave approach for the description of basis functions and arising potentials. The presence of non-local pseudo-potentials has been considered, as well as contributions arising from the basis functions being centered on the atoms. Simulations of both periodic and non-periodic systems have been implemented and carried out. Dipole strengths and infrared absorption spectra have been calculated for two isomers of the tripeptide Ser-Pro-Ala using DFPT and are compared to the results of standard vibrational analyses using finite differences. The spectra are then decomposed into five subsets by employing localized molecular orbitals/maximally localized Wannier functions, and the results are discussed. Moreover, group coupling matrices are employed for visualization of results. Furthermore, the BECs and partial charges of the surface atoms of a periodic (101) anatase (TiO2) slab have been investigated in a periodic framework.

Massive Dirac Fermion Behavior in a Low Bandgap Graphene Nanoribbon Near a Topological Phase Boundary.

Graphene nanoribbons (GNRs) have attracted much interest due to their largely modifiable electronic properties. Manifestation of these properties requires atomically precise GNRs which can be achieved through a bottom-up synthesis approach. This has recently been applied to the synthesis of width-modulated GNRs hosting topological electronic quantum phases, with valence electronic properties that are well captured by the Su-Schrieffer-Heeger (SSH) model describing a 1D chain of interacting dimers. Here, ultralow bandgap GNRs with charge carriers behaving as massive Dirac fermions can be realized when their valence electrons represent an SSH chain close to the topological phase boundary, i.e., when the intra- and interdimer coupling become approximately equal. Such a system has been achieved via on-surface synthesis based on readily available pyrene-based precursors and the resulting GNRs are characterized by scanning probe methods. The pyrene-based GNRs (pGNRs) can be processed under ambient conditions and incorporated as the active material in a field effect transistor. A quasi-metallic transport behavior is observed at room temperature, whereas at low temperature, the pGNRs behave as quantum dots showing single-electron tunneling and Coulomb blockade. This study may enable the realization of devices based on carbon nanomaterials with exotic quantum properties.