Simulations from Ab Initio Approaches:

Structure and Dynamics from Quantum Mechanics

# Research

In the following, we list and discuss some of the research lines followed in the group (under construction). We develop and use techniques based on density-functional theory, path integral methods, machine learning, and concepts of statistical mechanics to study the following subjects:

## Anharmonic and nuclear quantum effects in H-bonded systems

## Nuclear quantum effects in dynamical observables

A few approximate methods based on path integral molecular dynamics for the inclusion of nuclear quantum effects on dynamical observables such as reaction rates, diffusion coefficients, and vibrational spectra have been proposed over the years, such as ring polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). We augmented first augmented the RPMD method by attaching optimally damped white noise Langevin thermostats to the internal modes of the ring polymers, and thus coined this method thermostated ring polymer molecular dynamics (TRPMD) TRPMD is a method that heals the artificial resonances observed in vibrational spectra calculated with RPMD, that is more ergodic than RPMD, and allows the use of time steps for integrating the equations of motion that are much larger than the ones allowed by methods like CMD. It remains, however, just an approximation to quantum real time correlation functions, and inherits all other limitations of the original RPMD method. Nevertheless, it is a very good approximation especially when treating larger systems or approaching condensed phases – and surely the most efficient of its kind to be used together with ab initio methods. Recently we have further exploited the freedom in attaching different kinds of thermostats to the internal modes of the ring polymer and obtained much sharper vibrational spectra for molecules and low-temperature solid phases than with the original TRPMD. Developments in this area continue in our group.

## Vibrational Raman Spectroscopy

Complementary to IR spectroscopy, Raman spectroscopy can be used for a detailed structural characterization of nanostructures. With more recent experimental techniques that can enhance the Raman signal, like surface enhanced or tip enhanced Raman spectroscopy (SERS and TERS), and that can be conducted in very low temperature and ultra-high vacuum, as well as in solution, this technique has become a fundamental and versatile technique to obtain structural fingerprints. These spectroscopic techniques can probe molecular time scales of the order of femto- to picoseconds, which are within reach of current quantum mechanical techniques. The simulation of Raman spectroscopy from a first-principles perspective involves the calculation of the (zero-frequency) dipole polarizability tensor of a system from an electronic structure calculation. While it is possible to calculate such a quantity for smaller molecules with a finite differences approach, for larger and periodic systems density functional perturbation theory (DFPT) is the method of choice. In the all electron, numerical localized orbitals code FHI-aims, we have currently extended and optimized an all-electron, real-space-based DFPT implementation for the response to electric fields.

Anharmonic Raman intensities can be calculated through the Fourier transform of time correlation functions involving the static polarizability tensor. We currently apply our implementation for the structural characterization of molecular crystals at finite temperatures and are exploiting ways based on machine learning techniques to make polarizability-tensor calculations cheaper.

## Structure search for biomolecules in non-biological environments

Relatively reliable empirical potentials exist to describe of peptides in solution or isolated organic molecules, but in order to study their interactions with inorganic surfaces with predictive accuracy, it is mandatory to design new empirical models based on electronic structure calculations. For that, it is necessary to obtain a thorough exploration of the first-principles potential energy surface. A especially challenging aspect is to model reliably the surface-(bio)molecule interaction, accounting for the correct level alignments and charge rearrangements. We develop genetic algorithms that act on internal degrees of freedom and optimize them for use with ab initio potential energy surfaces. In order to analyze and explore efficiently the free energy landscape, we exploit enhance machine learning clustering techniques and venues for cheaper potential energy evaluation. Our goal is to reach longer time and length scales involved that allow the modeling of self-assembly of bio-organic molecules on surfaces.