218 research outputs found
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 - 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, (HO)-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 S2 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 CHO
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, 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 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
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