Chemical machine learning with kernels: The impact of loss functions

Machine learning promises to accelerate materials discovery by allowing computational efficient property predictions from a small number of reference calculations. As a result, the literature has spent a considerable effort in designing representations that capture basic physical properties. Our work focuses on the less-studied learning formulations in this context in order to exploit inner structures in the prediction errors. In particular, we propose to directly optimize basic loss functions of the prediction error metrics typically used in the literature, such as the mean absolute error or the worst case error. In some instances, a proper choice of the loss function can directly reduce reasonably the prediction performance in the desired metric, albeit at the cost of additional computations during training. To support this claim, we describe the statistical learning theoretic foundations, and provide supporting numerical evidence with the prediction of atomization energies for a database of small organic molecules.     

Machine learning for atomic forces in a crystalline solid: Transferability to various temperatures

Recently, machine learning has emerged as an alternative, powerful approach for predicting quantum‐mechanical properties of molecules and solids. Here, using kernel ridge regression and atomic fingerprints representing local environments of atoms, we trained a machine‐learning model on a crystalline silicon system to directly predict the atomic forces at a wide range of temperatures. Our idea is to construct a machine‐learning model using a quantum‐mechanical dataset taken from canonical‐ensemble simulations at a higher temperature, or an upper bound of the temperature range. With our model, the force prediction errors were about 2% or smaller with respect to the corresponding force ranges, in the temperature region between 300 K and 1650 K. We also verified the applicability to a larger system, ensuring the transferability with respect to system size.     

Benchmarking PES-Learn's machine learning models predicting accurate potential energy surface for quantum scattering

Machine learning (ML) models, neural networks, and Gaussian processes have been used to predict the potential energy surface taking C₂-He (both static and dynamic scenario) and NCCN-He collision systems. The surface is restricted to ∽125 points where traditional spline becomes inefficacious. Quantum dynamics is performed by solving close-coupling equation to compute cross sections benchmarking the performance of the ML models. The current study forms a basis for any future investigation of larger molecules where conventional fitting fails due to sparser ab initio points and cuts down the computational time without compromising on the quality of the surface.     

Serenity: A subsystem quantum chemistry program

We present the new quantum chemistry program Serenity . It implements a wide variety of functionalities with a focus on subsystem methodology. The modular code structure in combination with publicly available external tools and particular design concepts ensures extensibility and robustness with a focus on the needs of a subsystem program. Several important features of the program are exemplified with sample calculations with subsystem density‐functional theory, potential reconstruction techniques, a projection‐based embedding approach and combinations thereof with geometry optimization, semi‐numerical frequency calculations and linear‐response time‐dependent density‐functional theory. © 2018 Wiley Periodicals, Inc.     

Active learning for spectroscopic data regression

In this work, we introduce an active learning approach for the estimation of chemical concentrations from spectroscopic data. Its main objective is to opportunely collect training samples in such a way as to minimize the error of the regression process while minimizing the number of training samples used, and thus to reduce the costs related to training sample collection. In particular, we propose two different active learning strategies developed for regression approaches based on partial least squares regression, ridge regression, kernel ridge regression, and support vector regression. The first strategy uses a pool of regressors in order to select the samples with the greatest disagreements among the different regressors of the pool, while the second one is based on adding samples that are distant from the current training samples in the feature space. For support vector regression, a specific strategy based on the selection of the samples distant from the support vectors is proposed. Experimental results on three different real data sets are reported and discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Quantum chemical electron impact mass spectrum prediction for de novo structure elucidation: Assessment against experimental reference data and comparison to competitive fragmentation modeling

We investigate the success of the quantum chemical electron impact mass spectrum (QCEIMS) method in predicting the electron impact mass spectra of a diverse test set of 61 small molecules selected to be representative of common fragmentations and reactions in electron impact mass spectra. Comparison with experimental spectra is performed using the standard matching algorithms, and the relative ranking position of the actual molecule matching the spectra within the NIST‐11 library is examined. We find that the correct spectrum is ranked in the top two matches from structural isomers in more than 50% of the cases. QCEIMS, thus, reproduces the distribution of peaks sufficiently well to identify the compounds, with the RMSD and mean absolute difference between appropriately normalized predicted and experimental spectra being at most 9% and 3% respectively, even though the most intense peaks are often qualitatively poorly reproduced. We also compare the QCEIMS method to competitive fragmentation modeling for electron ionization, a training‐based mass spectrum prediction method, and remarkably we find the QCEIMS performs equivalently or better. We conclude that QCEIMS will be very useful for those who wish to identify new compounds which are not well represented in the mass spectral databases.     

Rhorix: An interface between quantum chemical topology and the 3D graphics program blender

Chemical research is assisted by the creation of visual representations that map concepts (such as atoms and bonds) to 3D objects. These concepts are rooted in chemical theory that predates routine solution of the Schrödinger equation for systems of interesting size. The method of Quantum Chemical Topology (QCT) provides an alternative, parameter‐free means to understand chemical phenomena directly from quantum mechanical principles. Representation of the topological elements of QCT has lagged behind the best tools available. Here, we describe a general abstraction (and corresponding file format) that permits the definition of mappings between topological objects and their 3D representations. Possible mappings are discussed and a canonical example is suggested, which has been implemented as a Python “Add‐On” named Rhorix for the state‐of‐the‐art 3D modeling program Blender. This allows chemists to use modern drawing tools and artists to access QCT data in a familiar context. A number of examples are discussed. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Development of a new parameter optimization scheme for a reactive force field based on a machine learning approach

Reactive molecular dynamics (MD) simulation is performed using a reactive force field (ReaxFF). To this end, we developed a new method to optimize the ReaxFF parameters based on a machine learning approach. This approach combines the k-nearest neighbor and random forest regressor algorithm to efficiently locate several possible ReaxFF parameter sets. As a pilot test of the developed approach, the optimized ReaxFF parameter set was applied to perform chemical vapor deposition (CVD) of an α-Al₂O₃ crystal. The crystal structure of α-Al₂O₃ was reasonably reproduced even at a relatively high temperature (2000 K). The reactive MD simulation suggests that the (110) surface grows faster than the (0001) surface, indicating that the developed parameter optimization technique could be used for understanding the chemical reaction in the CVD process. © 2019 Wiley Periodicals, Inc.     

Calibration of force-field dependency in free energy landscapes of peptide conformations by quantum chemical calculations

The free energy landscapes of peptide conformations were calibrated by ab initio quantum chemical calculations, after the enhanced conformational diversity search using the multicanonical molecular dynamics simulations. Three different potentials of mean force for an isolated dipeptide were individually obtained by the multicanonical molecular dynamics simulations using the conventional force fields, AMBER parm94, AMBER parm96, and CHARMm22. Each potential of mean force was then calibrated based upon the umbrella sampling algorithm from the adiabatic energy map that was calculated separately by the ab initio molecular orbital method, and all of the calibrated potentials of mean force coincided well. The calibration method was also applied to the simulations of a peptide dimer in explicit water models, and it was shown that the calibrated free energy landscapes did not depend on the force field used in the classical simulations, as far as the conformational space was sampled well. The current calibration method fuses the classical free energy calculation with the quantum chemical calculation, and it should generally make simulations for biomolecular systems much more reliable when combining with enhanced conformational sampling.     

Theoretical evaluation of sensitivity and thermal stability for high explosives based on quantum chemistry methods: A brief review

Over the past 20 years, a number of scientists have conducted numerous fundamental investigations based on quantum chemistry theory into various mechanistic processes that seems to contribute to the sensitivity of energetic materials. A large number of theoretical methods that have been used to predict their mechanical and spark sensitivity are summarized in this article, in which the advantages and disadvantages of these methods, together with their scope of use are clarified. In addition, the theoretical models for thermal stability of explosives are briefly introduced as a supplement. It has been concluded that the current ability to predict sensitivity is merely based on a series of empirical rules, such as simple oxygen balance, molecular properties, and the ratios of C and H to oxygen for different classes of explosive compounds. These are valid only for organic classes of explosives, though some special models have been proposed for inorganic explosives, such as azides. An exact standard for sensitivity should be established experimentally by some new techniques for both energetic compounds and their mixtures. © 2013 Wiley Periodicals, Inc.     

The IR spectrum of supercritical water: Combined molecular dynamics/quantum mechanics strategy and force field for cluster sampling

Supercritical water was analyzed recently as a gas of small clusters of waters linked to each other by intermolecular hydrogen‐bonds, but unexpected “linear” conformations of clusters are required to reproduce the infra‐red (IR) spectra of the supercritical state. Aiming at a better understanding of clusters in supercritical water, this work presents a strategy combining classical molecular dynamics to explore the potential energy landscape of water clusters with quantum mechanical calculation of their IR spectra. For this purpose, we have developed an accurate and flexible force field of water based on the TIP5P 5‐site model. Water dimers and trimers obtained with this improved force field compare well with the quantum mechanically optimized clusters. Exploration by simulated annealing of the potential energy surface of the classical force field reveals a new trimer conformation whose IR response determined from quantum calculations could play a role in the IR spectra of supercritical water. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

ORBKIT: A modular python toolbox for cross‐platform postprocessing of quantum chemical wavefunction data

ORBKIT is a toolbox for postprocessing electronic structure calculations based on a highly modular and portable Python architecture. The program allows computing a multitude of electronic properties of molecular systems on arbitrary spatial grids from the basis set representation of its electronic wavefunction, as well as several grid‐independent properties. The required data can be extracted directly from the standard output of a large number of quantum chemistry programs. ORBKIT can be used as a standalone program to determine standard quantities, for example, the electron density, molecular orbitals, and derivatives thereof. The cornerstone of ORBKIT is its modular structure. The existing basic functions can be arranged in an individual way and can be easily extended by user‐written modules to determine any other derived quantity. ORBKIT offers multiple output formats that can be processed by common visualization tools (VMD, Molden, etc.). Additionally, ORBKIT possesses routines to order molecular orbitals computed at different nuclear configurations according to their electronic character and to interpolate the wavefunction between these configurations. The program is open‐source under GNU‐LGPLv3 license and freely available at https://github.com/orbkit/orbkit/ . This article provides an overview of ORBKIT with particular focus on its capabilities and applicability, and includes several example calculations. © 2016 Wiley Periodicals, Inc.     

A method and program for mass quantum chemical calculations of protein—ligand docking complexes

A new fast computational method for mass calculations of docking complexes by the AM1/PM3 semiempirical methods is proposed. The computation time is shortened by at least an order of magnitude compared to alternative schemes of quantum chemical calculations. The root-mean-square deviation of the AM1 calculated energies of formation of complexes from the results obtained by conventional diagonalization procedure is at most 0.4 kcal mol⁻¹. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 418–420, February, 2008.     

KiSThelP: A program to predict thermodynamic properties and rate constants from quantum chemistry results†

Kinetic and Statistical Thermodynamical Package (KiSThelP) is a cross‐platform free open‐source program developed to estimate molecular and reaction properties from electronic structure data. To date, three computational chemistry software formats are supported (Gaussian, GAMESS, and NWChem). Some key features are: gas‐phase molecular thermodynamic properties (offering hindered rotor treatment), thermal equilibrium constants, transition state theory rate coefficients (transition state theory (TST), variational transition state theory (VTST)) including one‐dimensional (1D) tunnelling effects (Wigner, and Eckart) and Rice‐Ramsperger‐Kassel‐Marcus (RRKM) rate constants, for elementary reactions with well‐defined barriers. KiSThelP is intended as a working tool both for the general public and also for more expert users. It provides graphical front‐end capabilities designed to facilitate calculations and interpreting results. KiSThelP enables to change input data and simulation parameters directly through the graphical user interface and to visually probe how it affects results. Users can access results in the form of graphs and tables. The graphical tool offers customizing of 2D plots, exporting images and data files. These features make this program also well‐suited to support and enhance students learning and can serve as a very attractive courseware, taking the teaching content directly from results in molecular and kinetic modelling. © 2013 Wiley Periodicals, Inc.     

On the possible reaction pathway for the acylation of AChE-catalyzed hydrolysis of ACh: Semiempirical quantum chemical study

The acylation process in the acetylcholinesterase (AChE)-catalyzed hydrolysis of the neurotransmitter, acetylcholine (ACh), has been determined with the semiempirical quantum chemical calculation method AM1 using the model molecules extracted from the X-ray crystal structure of Torpedo Californica AChE. For the sake of identifying the microfeatures of the mechanism of this reaction, two types of possible mechanisms, stepwise mechanism and cooperative mechanisms, were proposed and studied with AM1 methods. All the model molecules for the possible reactants, intermediates, transition states, and products in the reaction pathways of the two mechanisms were obtained. Energy profiles, the structural properties of the transition states, indicate that the acylation of AChE-catalyzed hydrolysis of ACh adopts the cooperative mechanism, i.e., the proton transfer from Ser220 of AChE to His440 occurs simultaneously with the nucleophilic attack of Ser200 to the carbonyl carbon atom of ACh. This result is in agreement with the kinetic data and the secondary isotope effects of AChE-catalyzed reactions. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 515–525, 1998     

Controlled synthesis of CdSe quantum dots by a microwave-enhanced process: a green approach for mass production

A method that does not employ hot-injection techniques has been developed for the size-tunable synthesis of high-quality CdSe quantum dots (QDs) with zinc blende structure. In this environmentally benign synthetic route, which uses less toxic precursors, solvents, and capping ligands, CdSe QDs that absorb visible light are obtained. The size of the as-prepared CdSe QDs and thus their optical properties can be manipulated by changing the microwave reaction conditions. The QDs were characterized by XRD, TEM, UV/Vis, FTIR, time-resolved fluorescence spectroscopy, and fluorescence spectrophotometry. In this approach, the reaction is conducted in open air and at a much lower temperature than in hot-injection techniques. The use of microwaves in this process allows for a highly reproducible and effective synthesis protocol that is fully adaptable for mass production and can be easily employed to synthesize a variety of semiconductor QDs with the desired properties. Possible applications of the CdSe QDs were assessed by deposition on TiO(2) films.     

diSBPred: A machine learning based approach for disulfide bond prediction

The protein disulfide bond is a covalent bond that forms during post-translational modification by the oxidation of a pair of cysteines. In protein, the disulfide bond is the most frequent covalent link between amino acids after the peptide bond. It plays a significant role in three-dimensional (3D) ab initio protein structure prediction (aiPSP), stabilizing protein conformation, post-translational modification, and protein folding. In aiPSP, the location of disulfide bonds can strongly reduce the conformational space searching by imposing geometrical constraints. Existing experimental techniques for the determination of disulfide bonds are time-consuming and expensive. Thus, developing sequence-based computational methods for disulfide bond prediction becomes indispensable. This study proposed a stacking-based machine learning approach for disulfide bond prediction (diSBPred). Various useful sequence and structure-based features are extracted for effective training, including conservation profile, residue solvent accessibility, torsion angle flexibility, disorder probability, a sequential distance between cysteines, and more. The prediction of disulfide bonds is carried out in two stages: first, individual cysteines are predicted as either bonding or non-bonding; second, the cysteine-pairs are predicted as either bonding or non-bonding by including the results from cysteine bonding prediction as a feature.The examination of the relevance of the features employed in this study and the features utilized in the existing nearest neighbor algorithm (NNA) method shows that the features used in this study improve about 7.39 % in jackknife validation balanced accuracy. Moreover, for individual cysteine bonding prediction and cysteine-pair bonding prediction, diSBPred provides a 10-fold cross-validation balanced accuracy of 82.29 % and 94.20 %, respectively. Altogether, our predictor achieves an improvement of 43.25 % based on balanced accuracy compared to the existing NNA based approach. Thus, diSBPred can be utilized to annotate the cysteine bonding residues of protein sequences whose structures are unknown as well as improve the accuracy of the aiPSP method, which can further aid in experimental studies of the disulfide bond and structure determination.