First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

A well-defined notion of chemical compound space (CCS) is essential for gaining rigorous control of properties through variation of elemental composition and atomic configurations. Here, we review an atomistic first principles perspective on CCS. First, CCS is discussed in terms of variational nuclear charges in the context of conceptual density functional and molecular grand-canonical ensemble theory. Thereafter, we revisit the notion of compound pairs, related to each other via "alchemical" interpolations involving fractional nuclear chargens in the electronic Hamiltonian. We address Taylor expansions in CCS, property non-linearity, improved predictions using reference compound pairs, and the ounce-of-gold prize challenge to linearize CCS. Finally, we turn to machine learning of analytical structure property relationships in CCS. These relationships correspond to inferred, rather than derived through variational principle, solutions of the electronic Schr\"odinger equation

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 $\pi$-$\pi$ 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

Structure and band gaps of Ga-(V) semiconductors: The challenge of Ga pseudopotentials

Design of gallium pseudopotentials has been investigated for use in density functional calculations of zinc-blende-type cubic phases of GaAs, GaP, and GaN. A converged construction with respect to all-electron results is described. Computed lattice constants, bulk moduli, and band gaps vary significantly depending on pseudopotential construction or exchange-correlation functional. The Kohn-Sham band gap of the Ga-(V) semiconductors exhibits a distinctive and strong sensitivity to lattice constant, with near-linear dependence of gap on lattice constant for larger lattice constants and Gamma-X crossover that changes the slope of the dependence. This crossover occurs at approximate to 98, 101, and 95% deviation from the equilibrium lattice constant for GaAs, GaP, and GaN, respectively

Alchemical and structural distribution based representation for improved QML

We introduce a representation of any atom in any chemical environment for the generation of efficient quantum machine learning (QML) models of common electronic ground-state properties. The representation is based on scaled distribution functions explicitly accounting for elemental and structural degrees of freedom. Resulting QML models afford very favorable learning curves for properties of out-of-sample systems including organic molecules, non-covalently bonded protein side-chains, (H$_2$O)$_{40}$-clusters, as well as diverse crystals. The elemental components help to lower the learning curves, and, through interpolation across the periodic table, even enable "alchemical extrapolation" to covalent bonding between elements not part of training, as evinced for single, double, and triple bonds among main-group elements

Understanding molecular representations in machine learning: The role of uniqueness and target similarity

The predictive accuracy of Machine Learning (ML) models of molecular properties depends on the choice of the molecular representation. Based on the postulates of quantum mechanics, we introduce a hierarchy of representations which meet uniqueness and target similarity criteria. To systematically control target similarity, we rely on interatomic many body expansions, as implemented in universal force-fields, including Bonding, Angular, and higher order terms (BA). Addition of higher order contributions systematically increases similarity to the true potential energy and predictive accuracy of the resulting ML models. We report numerical evidence for the performance of BAML models trained on molecular properties pre-calculated at electron-correlated and density functional theory level of theory for thousands of small organic molecules. Properties studied include enthalpies and free energies of atomization, heatcapacity, zero-point vibrational energies, dipole-moment, polarizability, HOMO/LUMO energies and gap, ionization potential, electron affinity, and electronic excitations. After training, BAML predicts energies or electronic properties of out-of-sample molecules with unprecedented accuracy and speed

Geometry Relaxation and Transition State Search throughout Chemical Compound Space with Quantum Machine Learning

We use energies and forces predicted within response operator based quantum machine learning (OQML) to perform geometry optimization and transition state search calculations with legacy optimizers. For randomly sampled initial coordinates of small organic query molecules we report systematic improvement of equilibrium and transition state geometry output as training set sizes increase. Out-of-sample S$_\mathrm{N}$2 reactant complexes and transition state geometries have been predicted using the LBFGS and the QST2 algorithm with an RMSD of 0.16 and 0.4 \r{A} -- after training on up to 200 reactant complexes relaxations and transition state search trajectories from the QMrxn20 data-set, respectively. For geometry optimizations, we have also considered relaxation paths up to 5'500 constitutional isomers with sum formula C$_7$H$_{10}$O$_2$ from the QM9-database. Using the resulting OQML models with an LBFGS optimizer reproduces the minimum geometry with an RMSD of 0.14~\r{A}. For converged equilibrium and transition state geometries subsequent vibrational normal mode frequency analysis indicates deviation from MP2 reference results by on average 14 and 26\,cm$^{-1}$, respectively. While the numerical cost for OQML predictions is negligible in comparison to DFT or MP2, the number of steps until convergence is typically larger in either case. The success rate for reaching convergence, however, improves systematically with training set size, underscoring OQML's potential for universal applicability

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.Comment: 13 pages, 8 figure

Popular Kohn-Sham density functionals strongly overestimate many-body interactions in van der Waals systems

We find spuriously large repulsive many-body contributions to binding energies of rare gas systems for the first three rungs of "Jacob's Ladder" within Kohn-Sham density functional theory. While the description of van der Waals dimers is consistently improved by the pairwise London C6 / R6 correction, inclusion of a corresponding three-body Axilrod-Teller C9 / R9 term only increases the repulsive error. Our conclusions based on extensive solid state and molecular electronic structure calculations are particularly relevant for condensed phase van der Waals systems. © 2008 The American Physical Society

FCHL revisited:Faster and more accurate quantum machine learning

We introduce the FCHL19 representation for atomic environments in molecules or condensed-phase systems. Machine learning models based on FCHL19 are able to yield predictions of atomic forces and energies of query compounds with chemical accuracy on the scale of milliseconds. FCHL19 is a revision of our previous work [Faber et al. 2018] where the representation is discretized and the individual features are rigorously optimized using Monte Carlo optimization. Combined with a Gaussian kernel function that incorporates elemental screening, chemical accuracy is reached for energy learning on the QM7b and QM9 datasets after training for minutes and hours, respectively. The model also shows good performance for non-bonded interactions in the condensed phase for a set of water clusters with an MAE binding energy error of less than 0.1 kcal/mol/molecule after training on 3,200 samples. For force learning on the MD17 dataset, our optimized model similarly displays state-of-the-art accuracy with a regressor based on Gaussian process regression. When the revised FCHL19 representation is combined with the operator quantum machine learning regressor, forces and energies can be predicted in only a few milliseconds per atom. The model presented herein is fast and lightweight enough for use in general chemistry problems as well as molecular dynamics simulations