Session A26: Assigning Structures to Spectra Using Density Functional Theory: Methods and Applications I

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New light sources greatly expand our ability to interrogate the matter, but decoding the message delivered by the spectra is far from trivial. How do we convert the spectra into what the nuclei and electrons are doing? The theoretical modeling provides a way to so. This lecture will discuss new and old challenges faced by the theory in the context of modeling electronic structure in strong fields, high-energy, and non-linear regimes and highlight recent progress in many-body methodology in treating spectroscopic signatures of core-level states.   

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Time-dependent orbital-free density functional theory (TD-OF-DFT) is an efficient method for calculating the dynamic properties of large scale quantum systems due to its linear scaling with system size. We present an in principle exact TD-OF-DFT formalism by mapping the real system of interacting fermions into a fictitious system of non-interacting (NI) bosons. Based on this formalism, we derive a time-dependent Schr\"{o}dinger-like equation for real-time propagation and define the Pauli potential that needs to be approximated for the actual calculation. We also present the linear response form of this formalism with the Dyson equation that relates the NI boson and interacting fermion systems. This formalism yields very accurate oscillator strength on Na clusters and qualitatively accurate results on several metallic and III-V semiconductor nanostructures.   

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Recent developments have shown that density functionals can be derived from semiclassical quantum mechanics in a systematic fashion reminiscent of wavefunction electronic structure. This new technique is completely different from other approaches to functional design (such as the satisfaction of exact conditions or fitting empirical parameters). The Thomas-Fermi kinetic energy functional, which Lieb and Simon showed is exact in the semiclassical limit, is the lowest order term in a semiclassical expansion of the exact kinetic energy functional. We will show, at least in one dimension, how higher order corrections to this series can be obtained by calculating the sums of eigenvalues and then inverting these sums into density functionals. Thus we show how to generate the exact asymptotic expansion of the true kinetic energy functional. We will also demonstrate that boundary terms arise from the turning points/surfaces where the density cannot be slowly varying, which are missed by the traditional gradient expansion. To simplify our analysis we have worked in one dimension but we shall comment on the application of our work to real electronic systems.   

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The adiabatic connection (AC) that has as weak-interaction expansion the Møller-Plesset (MP) perturbation series has been recently shown to have a large coupling-strength expansion in terms of functionals of the Hartree-Fock density [1,2]. Based on these findings, in this work we introduce a new class of functionals that approximate directly the MP AC by interpolating between MP2 and the large-coupling strength limit, which is size consistent for fragments with a non-degenerate ground state [3]. These functionals have the same cost as double hybrids and capture non-covalent interactions (NCI) very accurately, without using dispersion corrections, as will be shown with results for several NCI test sets (S66, CT7, NGD8, DI6 and L7) and dissociation curves ranging from small dimers of noble gases to larger benzene-pyridine dimers.

[1] Seidl, M.; Giarrusso, S.; Vuckovic, S.; Fabiano, E.; Gori-Giorgi, P., J. Chem. Phys. 149, 241101 (2018).
[2] Daas, T. J.; Grossi, J.; Vuckovic, S.; Musslimani, Z. H.; Kooi, D. P.; Seidl, M.; Giesbertz, K. J. H.; Gori-Giorgi, arXiv:2009.04326 (2020).
[3] Vuckovic, S.; Gori-Giorgi, P.; Della Sala, F.; Fabiano, E., J. Phys. Chem. Lett. (2018), 9, 3137–3142.   

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Many theoretical studies of excited state molecules aim to provide accurate solutions to the electronic Schrödinger equation in order to produce energies that can be compared to experiment. However, nuclear quantum motion, which is usually ignored, can also affect exciton energies, as we showed in a recent study [Alvertis et al. Phys. Rev. B, 102, 081122(R) (2020)]. Here we provide an intuitive picture for the effect of nuclear quantum motion on exciton energies and find that zero-point fluctuations can significantly affect the energies of excited states. We compute vibration-induced corrections to exciton energies by combining TDDFT with Monte Carlo sampling techniques based on finite difference methods. We show that incorporating nuclear zero-point energy effects can lead to corrections of up to 1.1 eV on computed exciton energies. We compare our results with the benchmark on the well-known Thiel molecular set, finding that the correction to excited state energies by incorporating nuclear quantum motion, and without any adjustable parameters, leads to vastly improved agreement with experimental results, while maintaining a low computational cost. We therefore establish nuclear quantum motion as a critical factor towards the accurate calculation of exciton energies.   

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A major challenge for Metablomic analyses is obtaining a comprehensive and unambiguous identification of detected metabolites. Among metabolomics techniques, NMR spectroscopy is a sophisticated, powerful and generally applicable spectroscopic tool that can be used to deduce the correct structure of newly isolated biogenic molecules. However, accurate structure prediction using NMR techniques depends on how much conformational space of a particular compound is considered. It is intrinsically challenging to calculate NMR chemical shifts using high level DFT when the conformational space of a metabolite is extensive. In this work, we developed NMR chemical shift calculation protocols using a machine learning model in conjunction with the standard DFT methods. The pipeline encompasses the following steps: (1) conformation generation using a force field (FF) based method, (2) filtering the FF generated conformations using the ASE-ANI machine learning model, (3) clustering of the optimized conformations based on structural similarity to identify chemically unique conformations, (4) DFT structural optimization of the unique conformations and (5) DFT NMR chemical shift calculation. This protocol can calculate the NMR chemical shifts of a set of molecules using any available combination of DFT theory, solvent model, and NMR-active nuclei, using both user-selected reference compounds and/or linear regression methods. Our protocol reduces the overall computational time yet matches experimental structural observations. The complete protocol is designed in such a manner that makes the computation of chemical shifts tractable for large number of conformationally flexible metabolites. Time permotting we will discuss recent work computing collisional cross section (CCS) values obtained from ion mobility coupled to mass spectrometry (IM - MS) studies using a related in silico protocol.   

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The origin of water’s anomalies is still debated, in part, because of the experimental difficulty in measuring the kinetics and thermodynamics at temperatures where key phenomenon are predicted. Recently, we have shown that by transiently heating nanoscale water films at rates on the order of 10¹⁰ K/s, the structural transformation and relaxation of liquid water can be examined in the elusive temperature region known as “no man’s land” (Kringle, et al., Science 369, 1490 (2020)). We observed reversible transformations of water, which are described by a linear combination of high- and low-temperature structural motifs. The temperature-dependent transformation follows a sigmoid function, centered at 210 K. For all temperatures examined, the relaxation to a metastable state occurs prior to crystallization. The relaxation rate is dependent on the initial structural motif, with the higher temperature motif typically relaxing faster, with greater dynamical heterogeneity. The relaxation dynamics can be described by a random two-well model; accounting for the heterogeneity in the context of two-component models.   

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There is a long-standing question about the molecular configuration of interfacial water molecules in the proximity of solid surfaces, particularly carbon atoms which play a crucial role in electrochemistry and biology. In this study, the dielectric, structural and dynamical properties of confined water placed between two parallel graphene walls at different inter distances from the Angstrom scale to few tens of nanometer have been investigated using molecular dynamics. For dielectric properties of water, we show that the perpendicular component of water dielectric constant drastically decreases under sub 2nm spatial confinement. The achieved dielectric constant data through linear response and fluctuation-dissipation theory, are consistent with recent reported experimental results. By determining the charge density as well as fluctuations in the number of atoms, we provide a molecular rationale for the behavior of perpendicular dielectric response function. We also interpret the behavior of the dielectric response in terms of the presence of dangling OH bonds of waters. By examining the residence time and lateral diffusion constant of water under confinement, we reveal that the water molecules tend to keep their hydrogen bond networks at the interface of water-graphene.   

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Confined water and ions mediate the interactions between charged surfaces in a wide range of contexts, from biological membranes and DNA to clays and cements. We use numerical simulations with a semi-atomistic model to study electrolyte solutions (ions, molecular water) confined by uniformly charged planar surfaces. By investigating sodium, calcium, and aluminum ions we find that with increasing ion valency the ion-water coupling grows, changing the structure and dynamics of the ion-water assemblies, which in turn affects the net pressure between the charged surfaces. However, this link is neither linear nor monotonic: instead controlled by the complex interplay of electrostatic, hydration, and entropic effects. In certain conditions, the formation of a highly organized, nearly frozen assembly of water and ions minimizes energy and produces a strong cohesion between surfaces, while in others the presence of large and very stable hydrated structures creates repulsive barriers in the effective interaction potential. By sampling a broad parameter space of ion type, surface charge, and confinement, we determine how these parameters control the structure and dynamics of the confined water/ions and determine the net interactions between the charged surfaces.   

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Cytochrome c is a water-soluble and peripheral membrane protein that has been employed as a model protein in studies on protein hydration and function. The earlier studies encompass a broad range of experimental as well as simulation methods. The earlier studies based on the dielectric relaxation are limited to a narrow frequency region and only partially envelop the hydration water response. We have extensively probed the dielectric response from aqueous cytochrome c at 100 MHz–1.12 THz frequency range. The water molecules within the hydration shells are heterogeneous over a few hydration layers away from the protein surface. Solvation of protein in water significantly alters the relaxation dynamics of water molecules in the immediate neighborhood. Two slower relaxation processes in addition to the bulk water relaxation are observed with the characteristics relaxation times of 35 ± 5 and 330 ± 36 ps. Employing effective medium approximation at terahertz frequencies in combination with molecular dynamics simulations, dielectric response of hydrated cytochrome c could be estimated. The analysis suggests that 310 ± 40 water molecules are tightly bound to cytochrome c and are intermolecularly coupled with protein collective vibrations.   

On Demand

Our protonic bipolar semiconductor model, with protonic self-traps (self-generated proton-prohol traps from dynamic polarization by valence electrons during proton transport in an applied force) in the melted ice periodic lattice, explains the abnormally high electrical mobility of positive protons and negative prohols in pure liquid water. The vibrational frequencies & amplitudes of protons and oxygens on the frozen periodic lattice were computed by us, from the 36x36 dynamical matrix with 6 elastic force constants. Proton transport track on the lattice is modeled by Newton Mechanics of Mass-Spring. Blender software visualizes 3D vibrations of protons and oxygens and 3D proton transport. Blender animations are presented as 2D movie clips to bundle the proton tracks into mass distributed Maxwellian strings with Debye-Waller diameter from the Debye-mode vibrating oxygens and local protons. Self-traps in the transitions of our ABCABC… proton transport model are illustrated via protonic kinetic energy (KE) exchange with the reservoir: A, the 1-step emission-release of a trapped proton by absorbing-capturing its own proton local mode, and B-C: the micro-eV m-steps capture of a forced proton with KE dissipated in each step by emission of a Debye oxygen-proton traveling wave phonon.