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# Research

# Theoretical Spectroscopy of Condensed-Phase Systems

### Vibrational spectroscopy is a powerful and sensitive tool to study structure and dynamics of many condensed-phase systems. For example, OH stretching vibration frequency of a water molecule depends on its local hydrogen-bonding environment, and vibrational frequencies of peptide groups are also sensitive to the secondary structure of a protein. In spite of the rich information provided by such methods the complexity and congestion of the experimental spectra in many ways limited the utility of these methods in answering detailed structural questions. Theoretical methods have become an integral tool in interpreting and guiding experiments. Our group develops new and improves existing theoretical methods for linear and nonlinear infrared, sum-frequency generation, and Raman spectroscopies of condensed-phase systems of biological and technological importance such as liquid water, ice, ionic liquids, proteins in solution, on surfaces and at the interfaces. We investigate the importance of various non-trivial effects such as vibrational couplings, Fermi resonances, nuclear quantum effects, and self-trapped vibrational states in linear and nonlinear spectroscopy. Additionally, we apply spectral processing algorithms such as multivariate curve resolution to the theoretical spectra in order to investigate solute-induced perturbations of the solvent. Such methods are particularly important for understanding of emergent phenomena in multicomponent and crowded systems.

# Nonadiabatic Dynamics

### Nonadiabatic dynamics involves nuclear motion on several potential energy surfaces and is a manifestation of the breakdown of Born-Oppenheimer approximation. Nonadiabatic transitions play a pivotal role in photochemistry, vibrational and electronic spectroscopy, electrochemical reactions, and quantum computing. Our ability to accurately solve the time-dependent Schrodinger equation in the presence of nonadiabatic transitions is limited to low dimensional systems. This has motivated the development of various semiclassical and mixed quantum-classical methods. For example, in mixed quantum-classical methods the total system is partitioned into an “important” subsystem which is treated quantum-mechanically and the rest of the system (environment) is treated classically via molecular dynamics simulations. Different methods treat parts of the total system differently e.g., using path-integral, wave function theory or classical trajectories, but no single method is known to satisfy all mathematical constrains and, at the same time, can be routinely applied to general multilevel quantum systems without convergence issues. We develop new mixed quantum-classical and semiclassical methods and apply them to study various interesting phenomena such as coupled electron-proton transfer reactions, magnetization dynamics in ferromagnetic metals, electronic and vibrational quantum Zeno and anti-Zeno effects, interference between chemical reaction paths, entanglement, and decoherence of qubits.

# Density Functional Theory

### Kohn–Sham density functional theory (DFT) is the most widely used computational tool to study the ground-state properties of molecular and condensed-matter systems. Despite its overall success, usual density functional approximations often produce qualitatively wrong predictions. Mixing local and semilocal exchange-correlation (XC) functionals with the wave function theory often successfully corrects some deficiencies of a standard DFT. Such range-separated hybrid functionals describe short-range electron-electron interactions using standard XC functionals, while the long-range electron-electron interactions are described by the many-body wave function theory. Our interest in DFT is twofold. Firstly, we develop range-separated hybrids by combining new and promising XC functionals with Green’s function theory. Our target applications include systems with pronounced noncovalent interactions such as condensed-phase water and proteins as well as semiconductors such as silicon. We are also interested in further developing potential-driven DFT, a type of DFT which instead of searching for better XC functionals develops approximations to a more fundamental quantity—the XC potential.

# Noncovalent Interactions and Hydrogen Bonding

### The importance of intermolecular forces in nature is very difficult to overestimate. The very existence of liquids and solids is due to intermolecular interactions. The attractive intermolecular forces, known as van der Waals or dispersion forces are a key to the structure and function of molecules and materials. Due to their pure quantum-mechanical origin, dispersion interactions are notoriously difficult to deal with both conceptually and computationally. We develop new range-separated density functionals and use existing electronic-structure methods such as CCSD(T) and Symmetry-adapted perturbation theory to study van der Waals interactions in a variety of systems ranging from water and polypeptides to van der Waals heterostructures such as graphene and 2D atomic crystals of MoS_{2}, BN, and many others. Of special interest is the hydrogen bonding in water, noncovalent aqua materials, also known as aqua plastics, and noncovalent nanobelts which use hydrogen bonds to permit charge transport between electrodes in molecular junction devices. We also combine electronic-structure methods with machine learning to develop potential energy surfaces (force fields) for molecular dynamics simulations of polymers and polymer composites whose properties are governed by the van der Waals forces. Examples of such systems include polyethylene, polypropylene, and aramides (e.g., Kevlar) which are used in aerospace and military applications in high-impact materials.

# Machine Learning

### Data-driven machine learning algorithms are being applied at an unprecedented rate in physics, chemistry, biology, engineering, and social science. Our group develops various machine learning approaches to a multitude of problems in atomic and molecular physics. Specifically, we utilize neural networks to establish structure-property relationships for theoretical spectroscopy, and in many-electron perturbation theory as well as for analyzing the diffraction data. We also use recurrent neural networks to study reduced dynamics of open quantum systems, autoencoders to design improved descriptors of molecular and solid-state systems, kernel ridge regression for interpolation of Born-Oppenheimer potential energy surfaces, and generative adversarial networks to study electronic correlation. Additionally, we leverage non-gradient based methods such as genetic algorithms in various tasks ranging from developing basis sets for electronic structure calculations to parametrizing force fields for molecular dynamics simulations. Clustering algorithms are developed and applied to dissect experimental and theoretical spectra to study reaction mechanisms and complex multicomponent condensed-phase systems.