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Sergei Manzhos

Publications and source records attributed to Sergei Manzhos.

At least 37 records · Page 2Linked to original sources
arXiv2021

Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for representing multidimensional functions with machine-learned lower-dimensional terms allowing insight with a general method

We present a Python implementation for RS-HDMR-GPR (Random Sampling High Dimensional Model Representation Gaussian Process Regression). The method builds representations of multivariate functions with lower-dimensional terms, either as an expansion over orders of coupling or using terms of only a given dimensionality. This facilitates, in particular, recovering functional dependence from sparse data. The code also allows for imputation of missing values of the variables and for a significant pruning of the useful number of HDMR terms. The code can also be used for estimating relative importance of different combinations of input variables, thereby adding an element of insight to a general machine learning method. The capabilities of this regression tool are demonstrated on test cases involving synthetic analytic functions, the potential energy surface of the water molecule, kinetic energy densities of materials (crystalline magnesium, aluminum, and silicon), and financial market data.

stat.CO↗
arXiv2020

Data-driven kinetic energy density fitting for orbital-free DFT: linear vs Gaussian process regression

We study the dependence of kinetic energy densities (KED) on density-dependent variables that have been suggested in previous works on kinetic energy functionals (KEF) for orbital-free DFT (OF-DFT). We focus on the role of data distribution and on data and regressor selection. We compare unweighted and weighted linear and Gaussian process regressions of KED for light metals and a semiconductor. We find that good quality linear regression resulting in good energy-volume dependence is possible over density-dependent variables suggested in previous literature. This is achieved with weighted fitting based on KED histogram. With Gaussian process regressions, excellent KED fit quality well exceeding that of linear regressions is obtained as well as a good energy-volume dependence which was somewhat better than that of best linear regressions. We find that while the use of the effective potential as a descriptor improves linear KED fitting, it does not improve the quality of the energy-volume dependence with linear regressions but substantially improves it with Gaussian process regression. Gaussian process regression is also able to perform well without data weighting.

physics.comp-ph↗
arXiv2020

Non-parametric Local Pseudopotentials with Machine Learning: a Tin Pseudopotential Built Using Gaussian Process Regression

We present novel non-parametric representation math for local pseudopotentials (PP) based on Gaussian Process Regression (GPR). Local pseudopotentials are needed for materials simulations using Orbital-Free Density Functional Theory (OF-DFT) to reduce computational cost and to allow kinetic energy functional (KEF) application only to the valence density. Moreover, local PPs are important for the development of accurate KEFs for OF-DFT as they are only available for a limited number of elements. We optimize local PPs of tin (Sn) using GP regression to reproduce the experimental lattice constants of α- and \b{eta}-Sn, the energy difference between these two phases as well as their electronic structure and charge density distributions, which are obtained with Kohn-Sham Density Functional Theory employing semi-local PPs. The use of a non-parametric GPR-based PP representation avoids difficulties associated with the use of parametrized functions and has the potential to construct an optimal local PP independent of prior assumptions. The GPR-based Sn local PP results in well-reproduced bulk properties of α- and \b{eta}-tin, and electronic valence densities similar to those obtained with semi-local PP.

cond-mat.mtrl-sci↗
arXiv2019

Machine learning optimization of the collocation point set for solving the Kohn-Sham equation

The rectangular collocation approach makes it possible to solve the Schrödinger equation with basis functions that do not have amplitude in all regions in which wavefunctions have significant amplitude. Collocation points can be restricted to a small region of space. As no integrals are computed, there are no problems due to discontinuities in the potential, and there is no need to use integrable basis functions. In this paper, we show, for the Kohn-Sham equation, that machine learning can be used to drastically reduce the size of the collocation point set. This is demonstrated by solving the Kohn-Sham equations for CO and H2O. We solve the Kohn-Sham equation on a given effective potential which is a critical part of all DFT calculations, and monitor orbital energies and orbital shapes. We use a combination of Gaussian process regression and a genetic algorithm to reduce the collocation point set size by more than an order of magnitude (from about 51,000 points to 2,000 points) while retaining mHartree accuracy.

physics.comp-ph↗
arXiv2019

Revisiting $π$ Backbonding: The Influence of $d$ Orbitals on Metal-CO Bonds and Ligand Red Shifts

The concept of $π$ backbonding is widely used to explain the complex stabilities and CO stretch frequency red shifts of transition metal carbonyls. We theoretically investigate a non-transition metal 18-electron carbonyl complex (Mg(CO)$_8$) and find a pronounced CO red shift without metal-carbon $π$ bonds. Moreover, we use truncated basis sets on the "honorary" and true transition metals Ca and Ti in Ca(CO)$_8$ and [Ti(CO)$_8$]$^{2+}$ complexes to probe the influence of $d$ functions on carbonyl complex stability, C-O bond strength, metal-to-ligand charge transfer and bond order compared to hypothetical complexes without metal-$d$ contributions. We find that the occurrence of metal-ligand $π$ bonds through metal $d$ functions greatly enhances the complex stabilities on one hand but only slightly affects the CO red shift on the other hand. This does not correspond to the classical rationalization of transition metal-CO bonds as synergistic $σ$ donation/$π$ backdonation.

physics.chem-ph↗
arXiv2019

Lithium attachment to C60 and nitrogen- and boron-doped C60: a mechanistic study

Fullerene-based materials including C60 and doped C60 have previously been proposed as anodes for lithium ion batteries. It was also shown earlier that n- and p-doping of small molecules can substantially increase voltages and specific capacities. Here, we study ab initio the attachment of multiple lithium atoms to C60, nitrogen-doped C60 (n-type), and boron doped C60 (p-type). We relate the observed attachment energies (which determine the voltage) to changes in the electronic structure induced by Li attachment and by doping. We compare results with a GGA functional and a hybrid functional and show that while they agree semi-quantitatively with respect to the expected voltages, there are qualitative differences in the electronic structure. We show that, contrary to small molecules, single atom n- and p-doping will not lead to practically useful modulation of the voltage-capacity curve beyond the initial stages of lithiation.

cond-mat.mtrl-sci↗
arXiv2018

A Scheme for Ultrasensitive Detection of Molecules by Using Vibrational Spectroscopy in Combination with Signal Processing

We show that combining vibrational spectroscopy with signal processing can result in a scheme for ultrasensitive detection of molecules. We consider the vibrational spectrum as a signal on the energy axis and apply a matched filter on that axis. On the example of a nerve agent molecule, we show that this allows detecting a molecule by its vibrational spectrum even when the recorded spectrum is completely buried in noise, when conventional spectroscopic detection is impossible. Detection is predicted to be possible with signal-to-noise ratios in recorded spectra as low as 0.1. We study the importance of spectral range used for detection as well as of the quality of the computed spectrum used to program the filter, specifically, the role of anharmonicity, of the exchange correlation functional, and of the basis set. The use of the full spectral range rather than of a narrow spectral window with key vibrations is shown to be advantageous, as well as accounting for anharmonicity.

physics.comp-ph↗
arXiv2018

Kinetic energy densities based on the fourth order gradient expansion: performance in different classes of materials and improvement via machine learning

We study the performance of fourth-order gradient expansions of the kinetic energy density (KED) in semi-local kinetic energy functionals depending on the density-dependent variables. The formal fourth-order expansion is convergent for periodic systems and small molecules but does not improve over the second-order expansion (Thomas-Fermi term plus one-ninth of von Weizsäcker term). Linear fitting of the expansion coefficients somewhat improves on the formal expansion. The tuning of the fourth order expansion coefficients allows for better reproducibility of Kohn-Sham kinetic energy density than the tuning of the second-order expansion coefficients alone. The possibility of a much more accurate match with the Kohn-Sham kinetic energy density by using neural networks trained using the terms of the 4th order expansion as density-dependent variables is demonstrated. We obtain ultra-low fitting errors without overfitting. Small single hidden layer neural networks can provide good accuracy in separate KED fits of each compound, while for joint fitting of KEDs of multiple compounds multiple hidden layers were required to achieve good fit quality. The critical issue of data distribution is highlighted. We also show the critical role of pseudopotentials in the performance of the expansion, where in the case of a too rapid decay of the valence density at the nucleus with some pseudopotentials, numeric instabilities arise.

physics.comp-ph↗
arXiv2018

Using rectangular collocation with finite difference derivatives to solve electronic Schrodinger equation

We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schrödinger equation (ESE). We test the ideas by computing several solutions of the ESE for the H atom and the H2+ cation and several solutions of a Kohn-Sham equation for CO and H2O. In all cases, we achieve millihartree accuracy. Two key advantages of the collocation method we use are: 1) collocation points need not have a particular distribution or spacing and can be chosen to reduce the required number of points; 2) the better the basis, is the less sensitive are the results to the choice of the point set. The ideas of this paper make it possible to use any basis functions and thus open to the door to using basis functions that are not Gaussians or plane waves. We use basis functions that are similar to Slater type orbitals. They are rarely used with the variational method, but present no problems when used with collocation.

physics.comp-ph↗
arXiv2018

Stability of charges in titanium compounds and charge transfer to oxygen in titanium dioxide

We investigate the charge density distribution in titanium dioxide, molecular titanium complexes and a variety of periodic titanium compounds using delocalization indices and Bader charge analysis. Our results are in agreement with previous experimental and theoretical investigations on the charge stability and deviation from formal oxidation states in transition metal compounds. We present examples for practically relevant redox processes, using molecular titanium dioxide model systems, that illustrate the failure of formal oxidation states to account for some redox phenomena. We observe a pronounced charge stability on titanium for trial systems which are expected to be mainly ionic. No environment tested by us is capable to reduce the local titanium charge remainder below one electron.

cond-mat.mtrl-sci↗
arXiv2018

Comparison of three methods to compute optical absorption spectra of organic molecules and solids

We compare the performance of an approach using real frequency dependent polarizability to compute optical absorption spectra to linear-response time-dependent density functional theory (TD-DFT) for small organic dyes, oligomers of different length (oligothiophenes), and molecular clusters representing a molecular crystal (pentacene). For pentacene, the spectra computed with the two methods are also compared to the spectrum computed for clusters and the periodic solid using the dipole approximation. The approach based on real polarizability produces spectra in good agreement with TD-DFT for small molecules. The (artificial) redshift for longer oligomers is more significant with the polarizability-based method than with TD-DFT. For pentacene clusters, TD-DFT produces reasonable spectra with a hybrid functional, but a significant redshift is introduced with a GGA functional due to the presence of charge transfer transitions. This problem is slightly attenuated with the polarizability-based method. The dipole approximation results in spectra much redshifted vs both TD-DFT and the polarizability-based method and in a different trend with cluster size.

cond-mat.mtrl-sci↗
arXiv2018

Influence of the aggregate state on band structure and optical properties of C60 computed with different methods

C60 and C60 based molecules are efficient acceptor and electron transport layers for planar perovskite solar cells. While properties of these molecules are well studied by ab initiomethods, those of solid C60, specifically its optical absorption properties, are not. We present a combined Density Functional Theory - Density Functional Tight Binding study of the effect of solid state packing on bandstructure and optical absorption of C60. The valence and conduction band edge energies of solid C60 differ on the order of 0.1 eV from single molecule frontier orbital energies. We show that calculations of optical properties using linear response TD-DFT(B) or the imaginary part of the dielectric constant (dipole approximation) can result in unrealistically large redshift in the presence of intermolecular interactions compared to available experimental data. We show that optical spectra computed from the frequency-dependent real polarizability better reproduce the effect of C60 aggregation on optical absorption and may be more suited to study effects of molecular aggregation.

cond-mat.mtrl-sci↗
arXiv2017

Dopant-Dopant Interactions in Beryllium doped Indium Gallium Arsenide: an Ab Initio Study

We present an ab initio study of dopant-dopant interactions in beryllium-doped InGaAs. We consider defect formation energies of various interstitial and substitutional defects and their combinations. We find that all substitutional-substitutional interactions can be neglected. On the other hand, interactions involving an interstitial defect are significant. Specially, interstitial Be is stabilized by about 0.9/1.0 eV in the presence of one/two BeGa substitutionals. Ga interstitial is also substantially stabilized by Be interstitials. Two Be interstitials can form a metastable Be-Be-Ga complex with a dissociation energy of 0.26 eV/Be. Therefore, interstitial defects and defect-defect interactions should be considered in accurate models of Be doped InGaAs. We suggest that In and Ga should be treated as separate atoms and not lumped into a single effective group III element, as has been done before. We identified dopant-centred states which indicate the presence of other charge states at finite temperatures, specifically, the presence of Beint+1 (as opposed to Beint+2 at 0K).

cond-mat.mtrl-sci↗
arXiv2017

Ab initio study of Li, Mg and Al insertion into rutile VO2: Fast diffusion and enhanced voltages

Vanadium oxides are among the most promising materials that can be used as electrodes in rechargeable metal-ion batteries. In this work, we systematically investigate thermodynamic, electronic and kinetic properties associated with the insertion of Li, Mg and Al atoms in rutile VO2. Using first-principles calculations, we systematically study the structural evolution and voltage curves of LixVO2, MgxVO2 and AlxVO2 (0<x<1) compounds. The calculated lithium intercalation voltage starts at 3.50 V for single-atom insertion and decreases to 2.23 V for full lithiation, to the LiVO2 compound, which agrees well with experimental results. The Mg insertion features a plateau about 1.6 V up to Mg0.5VO2 and then another plateau-like region at around 0.5 V up to Mg1VO2. The predicted voltage curve for Al insertion starts at 1.98 V, followed by two plateaus at 1.48 V and 1.17 V. The diffusion barrier of Li, Mg and Al in the tunnel structure of VO2 is 0.06, 0.33 and 0.50 eV, respectively. The demonstrated excellent Li, Mg and Al mobility, high structural stability and high specific capacity suggest a promising potential of rutile VO2 electrodes especially for multivalent batteries.

cond-mat.mtrl-sci↗
arXiv2017

The Role of Weak Interactions in Characterizing Peptide Folding Preferences using a QTAIM Interpretation of the Ramachandran Plot (ϕ-ψ)

The Ramachandran plot is a potent way to understand structures of biomolecules, however, the original formulation of the Ramachandran plot only considers backbone conformations. We formulate a new interpretation of the original Ramachandran plot ($ϕ-ψ$) that can include a description of the weaker interactions including both the hydrogen bonds and H$---$H bonds as a new way to derive insights into the phenomenon of peptide folding. We use QTAIM (quantum theory of atoms in molecules) to interpret the Ramachandran plot. Specifically, we show that QTAIM analysis permits identifying key regions of the Ramachandran plot without the need for massive data sets. A highly non-linear relationship is found between the QTAIM vector-derived interpreted Ramachandran plot and the conventional Ramachandran plot ($ϕ-ψ$) demonstrating that this new approach is not a trivial coordinate transformation. An investigation of both the backbone and the weaker bonds within the framework of the QTAIM interpreted Ramachandran plot was found to be in line with physical intuition. The least-preferred directions calculated for the hydrogen bonds and H$---$H bonds were found to coincide with the 'unlikely' regions of the Ramachandran plot.

physics.chem-ph↗
arXiv2017

On the oxidation state of titanium in titanium dioxide

The oxidation state of titanium in titanium dioxide is commonly assumed to be +4. This assumption is used ubiquitously to rationalize phenomena observed with TiO2. We present a comprehensive electronic structure investigation of Ti ions, TiO2 molecules and TiO2 bulk crystals, using different density functional theory and wave function-based approaches, which suggests a lower oxidation state (+3). Specifically, there is evidence of a significant remaining contribution from valence s and d electrons of Ti, including the presence of a nuclear cusp around the Ti core. The charge corresponding to valence s and d states of Ti amounts to 1 e. The commonly assumed picture may therefore have to be revised.

cond-mat.mtrl-sci↗
arXiv2016

A First-Principles Comparative Study of Lithium, Sodium, and Magnesium Storage in Pure and Gallium-Doped Germanium: Competition between Interstitial and Substitutional Sites

Thermodynamics and kinetics of Li, Na, and Mg storage in Ge is studied ab initio. The most stable configurations can consist of tetrahedral, substitutional, or a combination of the two types of sites. In the dilute limit, Li, Na prefer interstitial, while Mg prefers substitutional sites. At higher concentrations of Li, Na, and Mg, there is a combination of interstitial and substitutional sites. This is an important finding, as previous ab initio studies of alloying type electrode materials ignored substitutional sites. Insertion energies computed at dilute concentration (x = 1/64) show that Na and Mg insertion are not thermodynamically favored in Ge vs formation of bulk Na and Mg, as opposed to Li insertion which is favored. We investigate the effect of p-doping of Ge (with Ga) on the thermodynamics and find that it considerably lowers the defect formation energies associated with the insertion of Li/Na/Mg at tetrahedral sites. On the other hand, the energetics associated with Li/Na/Mg insertion at substitutional sites are not significantly affected. In addition, we compute the migration energy barriers for Li/Na/Mg diffusion between two tetrahedral sites (0.38/0.79/0.66 eV), between two substitutional sites (0.77/0.93/1.83 eV), and between two sites of different type (2.15/1.75/0.85 eV).

cond-mat.mtrl-sci↗