arXiv subjects

O. Anatole von Lilienfeld

Publications and source records attributed to O. Anatole von Lilienfeld.

99 records · Page 6Linked to original sources

arXiv2015

Many Molecular Properties from One Kernel in Chemical Space

We introduce property-independent kernels for machine learning modeling of arbitrarily many molecular properties. The kernels encode molecular structures for training sets of varying size, as well as similarity measures sufficiently diffuse in chemical space to sample over all training molecules. Corresponding molecular reference properties provided, they enable the instantaneous generation of ML models which can systematically be improved through the addition of more data. This idea is exemplified for single kernel based modeling of internal energy, enthalpy, free energy, heat capacity, polarizability, electronic spread, zero-point vibrational energy, energies of frontier orbitals, HOMO-LUMO gap, and the highest fundamental vibrational wavenumber. Models of these properties are trained and tested using 112 kilo organic molecules of similar size. Resulting models are discussed as well as the kernels' use for generating and using other property models.

physics.chem-ph↗

arXiv2015

Big Data meets Quantum Chemistry Approximations: The $Δ$-Machine Learning Approach

Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k constitutional isomers of C$_7$H$_{10}$O$_2$ we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semi-empirical quantum chemistry and machine learning models trained on 1 and 10\% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy.

physics.chem-ph↗

arXiv2014

Machine learning for many-body physics: The case of the Anderson impurity model

Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are investigated; a representation in terms of Legendre polynomials is found to be superior due to its limited number of coefficients and its applicability to state of the art methods of solution. The dependence of the errors on the size of the training set is determined. The results indicate that a machine learning approach to dynamical mean-field theory may be feasible.

cond-mat.str-el↗

arXiv2014

Toward transferable interatomic van der Waals interactions without electrons: The role of multipole electrostatics and many-body dispersion

We estimate polarizabilities of atoms in molecules without electron density, using a Voronoi tesselation approach instead of conventional density partitioning schemes. The resulting atomic dispersion coefficients are calculated, as well as many-body dispersion effects on intermolecular potential energies. We also estimate contributions from multipole electrostatics and compare them to dispersion. We assess the performance of the resulting intermolecular interaction model from dispersion and electrostatics for more than 1,300 neutral and charged, small organic molecular dimers. Applications to water clusters, the benzene crystal, the anti-cancer drug ellipticine---intercalated between two Watson-Crick DNA base pairs, as well as six macro-molecular host-guest complexes highlight the potential of this method and help to identify points of future improvement. The mean absolute error made by the combination of static electrostatics with many-body dispersion reduces at larger distances, while it plateaus for two-body dispersion, in conflict with the common assumption that the simple $1/R^6$ correction will yield proper dissociative tails. Overall, the method achieves an accuracy well within conventional molecular force fields while exhibiting a simple parametrization protocol.

physics.chem-ph↗

arXiv2014

Modeling Electronic Quantum Transport with Machine Learning

We present a Machine Learning approach to solve electronic quantum transport equations of one-dimensional nanostructures. The transmission coefficients of disordered systems were computed to provide training and test datasets to the machine. The system's representation encodes energetic as well as geometrical information to characterize similarities between disordered configurations, while the Euclidean norm is used as a measure of similarity. Errors for out-of-sample predictions systematically decrease with training set size, enabling the accurate and fast prediction of new transmission coefficients. The remarkable performance of our model to capture the complexity of interference phenomena lends further support to its viability in dealing with transport problems of undulatory nature.

cond-mat.mes-hall↗

arXiv2013

Machine Learning of Molecular Electronic Properties in Chemical Compound Space

The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compounds that are synthetically accessible. Here, we present a machine learning (ML) model, trained on a data base of \textit{ab initio} calculation results for thousands of organic molecules, that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity, and excitation energies. The ML model is based on a deep multi-task artificial neural network, exploiting underlying correlations between various molecular properties. The input is identical to \emph{ab initio} methods, \emph{i.e.} nuclear charges and Cartesian coordinates of all atoms. For small organic molecules the accuracy of such a "Quantum Machine" is similar, and sometimes superior, to modern quantum-chemical methods---at negligible computational cost.

physics.chem-ph↗

arXiv2013

Force correcting atom centered potentials for generalized gradient approximated density functional theory: Approaching hybrid functional accuracy for geometries and harmonic frequencies in small chlorofluorocarbons

Generalized gradient approximated (GGA) density functional theory (DFT) typically overestimates polarizability and bond-lengths, and underestimates force constants of covalent bonds. To overcome this problem we show that one can use empirical force correcting atom centered potentials (FCACPs), parameterized for every nuclear species. Parameters are obtained through minimization of a penalty functional that explicitly encodes hybrid DFT forces and static polarizabilities of reference molecules. For hydrogen, fluorine, chlorine, and carbon the respective reference molecules consist of H$_2$, F$_2$, Cl$_2$, and CH$_4$. The transferability of this approach is assessed for harmonic frequencies in a small set of chlorofluorocarbon molecules. Numerical evidence, gathered for CF$_4$, CCl$_4$, CCl$_3$F, CCl$_2$F$_2$, CClF$_3$, ClF, HF, HCl, CFH$_3$, CF$_2$H$_2$, CF$_3$H, CHCl$_3$, CH$_2$Cl$_2$, CH$_3$Cl indicates that the GGA+FCACP level of theory yields harmonic frequencies that are significantly more consistent with hybrid DFT values, as well as slightly reduced molecular polarizability.

physics.chem-ph↗

arXiv2011

Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schrödinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross-validation over more than seven thousand small organic molecules yields a mean absolute error of ~10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves.

physics.chem-ph↗

arXiv2005

Coarse-grained interaction potentials for polyaromatic hydrocarbons

Using Kohn-Sham density functional theory (KS-DFT), we have studied the interaction between various polyaromatic hydrocarbon molecules. The systems range from mono-cyclic benzene up to hexabenzocoronene (hbc). For several conventional exchange-correlation functionals potential energy curves of interaction of the $π$-$π$ stacking hbc dimer are reported. It is found that all pure local density or generalized gradient approximated functionals yield qualitatively incorrect predictions regarding structure and interaction. Inclusion of a non-local, atom-centered correction to the KS-Hamiltonian enables quantitative predictions. The computed potential energy surfaces of interaction yield parameters for a coarse-grained potential, which can be employed to study discotic liquid-crystalline mesophases of derived polyaromatic macromolecules.

cond-mat.soft↗