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Anders S. Christensen

Publications and source records attributed to Anders S. Christensen.

18 recordsLinked to original sources
arXiv2024

NeuralPLexer3: Accurate Biomolecular Complex Structure Prediction with Flow Models

Structure determination is essential to a mechanistic understanding of diseases and the development of novel therapeutics. Machine-learning-based structure prediction methods have made significant advancements by computationally predicting protein and bioassembly structures from sequences and molecular topology alone. Despite substantial progress in the field, challenges remain to deliver structure prediction models to real-world drug discovery. Here, we present NeuralPLexer3 -- a physics-inspired flow-based generative model that achieves state-of-the-art prediction accuracy on key biomolecular interaction types and improves training and sampling efficiency compared to its predecessors and alternative methodologies. Examined through newly developed benchmarking strategies, NeuralPLexer3 excels in vital areas that are crucial to structure-based drug design, such as physical validity and ligand-induced conformational changes.

cs.LG↗
arXiv2022

Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry

Predicting electronic energies, densities, and related chemical properties can facilitate the discovery of novel catalysts, medicines, and battery materials. By developing a physics-inspired equivariant neural network, we introduce a method to learn molecular representations based on the electronic interactions among atomic orbitals. Our method, OrbNet-Equi, leverages efficient tight-binding simulations and learned mappings to recover high fidelity quantum chemical properties. OrbNet-Equi models a wide spectrum of target properties with an accuracy consistently better than standard machine learning methods and a speed orders of magnitude greater than density functional theory. Despite only using training samples collected from readily available small-molecule libraries, OrbNet-Equi outperforms traditional methods on comprehensive downstream benchmarks that encompass diverse main-group chemical processes. Our method also describes interactions in challenging charge-transfer complexes and open-shell systems. We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly.

cs.LG↗
arXiv2021

OrbNet Denali: A machine learning potential for biological and organic chemistry with semi-empirical cost and DFT accuracy

We present OrbNet Denali, a machine learning model for electronic structure that is designed as a drop-in replacement for ground-state density functional theory (DFT) energy calculations. The model is a message-passing neural network that uses symmetry-adapted atomic orbital features from a low-cost quantum calculation to predict the energy of a molecule. OrbNet Denali is trained on a vast dataset of 2.3 million DFT calculations on molecules and geometries. This dataset covers the most common elements in bio- and organic chemistry (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, I) as well as charged molecules. OrbNet Denali is demonstrated on several well-established benchmark datasets, and we find that it provides accuracy that is on par with modern DFT methods while offering a speedup of up to three orders of magnitude. For the GMTKN55 benchmark set, OrbNet Denali achieves WTMAD-1 and WTMAD-2 scores of 7.19 and 9.84, on par with modern DFT functionals. For several GMTKN55 subsets, which contain chemical problems that are not present in the training set, OrbNet Denali produces a mean absolute error comparable to those of DFT methods. For the Hutchison conformers benchmark set, OrbNet Denali has a median correlation coefficient of R^2=0.90 compared to the reference DLPNO-CCSD(T) calculation, and R^2=0.97 compared to the method used to generate the training data (wB97X-D3/def2-TZVP), exceeding the performance of any other method with a similar cost. Similarly, the model reaches chemical accuracy for non-covalent interactions in the S66x10 dataset. For torsional profiles, OrbNet Denali reproduces the torsion profiles of wB97X-D3/def2-TZVP with an average MAE of 0.12 kcal/mol for the potential energy surfaces of the diverse fragments in the TorsionNet500 dataset.

physics.chem-ph↗
arXiv2020

An assessment of the structural resolution of various fingerprints commonly used in machine learning

Atomic environment fingerprints are widely used in computational materials science, from machine learning potentials to the quantification of similarities between atomic configurations. Many approaches to the construction of such fingerprints, also called structural descriptors, have been proposed. In this work, we compare the performance of fingerprints based on the Overlap Matrix(OM), the Smooth Overlap of Atomic Positions (SOAP), Behler-Parrinello atom-centered symmetry functions (ACSF), modified Behler-Parrinello symmetry functions (MBSF) used in the ANI-1ccx potential and the Faber-Christensen-Huang-Lilienfeld (FCHL) fingerprint under various aspects. We study their ability to resolve differences in local environments and in particular examine whether there are certain atomic movements that leave the fingerprints exactly or nearly invariant. For this purpose, we introduce a sensitivity matrix whose eigenvalues quantify the effect of atomic displacement modes on the fingerprint. Further, we check whether these displacements correlate with the variation of localized physical quantities such as forces. Finally, we extend our examination to the correlation between molecular fingerprints obtained from the atomic fingerprints and global quantities of entire molecules.

physics.comp-ph↗
arXiv2020

On the role of gradients for machine learning of molecular energies and forces

The accuracy of any machine learning potential can only be as good as the data used in the fitting process. The most efficient model therefore selects the training data that will yield the highest accuracy compared to the cost of obtaining the training data. We investigate the convergence of prediction errors of quantum machine learning models for organic molecules trained on energy and force labels, two common data types in molecular simulations. When training and predicting on different geometries corresponding to the same single molecule, we find that the inclusion of atomic forces in the training data increases the accuracy of the predicted energies and forces 7-fold, compared to models trained on energy only. Surprisingly, for models trained on sets of organic molecules of varying size and composition in non-equilibrium conformations, inclusion of forces in the training does not improve the predicted energies of unseen molecules in new conformations. Predicted forces, however, also improve about 7-fold. For the systems studied, we find that force labels and energy labels contribute equally per label to the convergence of the prediction errors. Choosing to include derivatives such as atomic forces in the training set or not should thus depend on, not only on the computational cost of acquiring the force labels for training, but also on the application domain, the property of interest, and the desirable size of the machine learning model. Based on our observations we describe key considerations for the creation of datasets for potential energy surfaces of molecules which maximize the efficiency of the resulting machine learning models.

physics.chem-ph↗
arXiv2020

ML Models of Vibrating H$_2$CO: Comparing Reproducing Kernels, FCHL and PhysNet

Machine Learning (ML) has become a promising tool for improving the quality of atomistic simulations. Using formaldehyde as a benchmark system for intramolecular interactions, a comparative assessment of ML models based on state-of-the-art variants of deep neural networks (NN), reproducing kernel Hilbert space (RKHS+F), and kernel ridge regression (KRR) is presented. Learning curves for energies and atomic forces indicate rapid convergence towards excellent predictions for B3LYP, MP2, and CCSD(T)-F12 reference results for modestly sized (in the hundreds) training sets. Typically, learning curve off-sets decay as one goes from NN (PhysNet) to RKHS+F to KRR (FCHL). Conversely, the predictive power for extrapolation of energies towards new geometries increases in the same order with RKHS+F and FCHL performing almost equally. For harmonic vibrational frequencies, the picture is less clear, with PhysNet and FCHL yielding respectively flat learning at $\sim$ 1 and $\sim$ 0.2 cm$^{-1}$ no matter which reference method, while RKHS+F models level off for B3LYP, and exhibit continued improvements for MP2 and CCSD(T)-F12. Finite-temperature molecular dynamics (MD) simulations with the same initial conditions yield indistinguishable infrared spectra with good performance compared with experiment except for the high-frequency modes involving hydrogen stretch motion which is a known limitation of MD for vibrational spectroscopy. For sufficiently large training set sizes all three models can detect insufficient convergence (``noise'') of the reference electronic structure calculations in that the learning curves level off. Transfer learning (TL) from B3LYP to CCSD(T)-F12 with PhysNet indicates that additional improvements in data efficiency can be achieved.

physics.chem-ph↗
arXiv2020

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.

physics.chem-ph↗
arXiv2019

Neural networks and kernel ridge regression for excited states dynamics of CH$_2$NH$_2^+$: From single-state to multi-state representations and multi-property machine learning models

Excited-state dynamics simulations are a powerful tool to investigate photo-induced reactions of molecules and materials and provide complementary information to experiments. Since the applicability of these simulation techniques is limited by the costs of the underlying electronic structure calculations, we develop and assess different machine learning models for this task. The machine learning models are trained on {\emph ab initio} calculations for excited electronic states, using the methylenimmonium cation (CH$_2$NH$_2^+$) as a model system. For the prediction of excited-state properties, multiple outputs are desirable, which is straightforward with neural networks but less explored with kernel ridge regression. We overcome this challenge for kernel ridge regression in the case of energy predictions by encoding the electronic states explicitly in the inputs, in addition to the molecular representation. We adopt this strategy also for our neural networks for comparison. Such a state encoding enables not only kernel ridge regression with multiple outputs but leads also to more accurate machine learning models for state-specific properties. An important goal for excited-state machine learning models is their use in dynamics simulations, which needs not only state-specific information but also couplings, i.e., properties involving pairs of states. Accordingly, we investigate the performance of different models for such coupling elements. Furthermore, we explore how combining all properties in a single neural network affects the accuracy. As an ultimate test for our machine learning models, we carry out excited-state dynamics simulations based on the predicted energies, forces and couplings and, thus, show the scopes and possibilities of machine learning for the treatment of electronically excited states.

physics.chem-ph↗
arXiv2019

Operator quantum machine learning: Navigating the chemical space of response properties

The identification and use of structure property relationships lies at the heart of the chemical sciences. Quantum mechanics forms the basis for the unbiased virtual exploration of chemical compound space (CCS), imposing substantial compute needs if chemical accuracy is to be reached. In order to accelerate predictions of quantum properties without compromising accuracy, our lab has been developing quantum machine learning (QML) based models which can be applied throughout CCS. Here, we briefly explain, review, and discuss the recently introduced operator formalism which substantially improves the data efficiency for QML models of common response properties.

physics.chem-ph↗
arXiv2019

A Universal Density Matrix Functional from Molecular Orbital-Based Machine Learning: Transferability across Organic Molecules

We address the degree to which machine learning can be used to accurately and transferably predict post-Hartree-Fock correlation energies. Refined strategies for feature design and selection are presented, and the molecular-orbital-based machine learning (MOB-ML) method is applied to several test systems. Strikingly, for the MP2, CCSD, and CCSD(T) levels of theory, it is shown that the thermally accessible (350 K) potential energy surface for a single water molecule can be described to within 1 millihartree using a model that is trained from only a single reference calculation at a randomized geometry. To explore the breadth of chemical diversity that can be described, MOB-ML is also applied to a new dataset of thermalized (350 K) geometries of 7211 organic models with up to seven heavy atoms. In comparison with the previously reported $Δ$-ML method, MOB-ML is shown to reach chemical accuracy with three-fold fewer training geometries. Finally, a transferability test in which models trained for seven-heavy-atom systems are used to predict energies for thirteen-heavy-atom systems reveals that MOB-ML reaches chemical accuracy with 36-fold fewer training calculations than $Δ$-ML (140 versus 5000 training calculations).

physics.chem-ph↗
arXiv2018

Operators in Machine Learning: Response Properties in Chemical Space

The role of response operators is well established in quantum mechanics. We investigate their use for universal quantum machine learning models of response properties in molecules. After introducing a theoretical basis, we present and discuss numerical evidence based on measuring the potential energy's response with respect to atomic displacement and to electric fields. Prediction errors for corresponding properties, atomic forces and dipole moments, improve in a systematic fashion with training set size and reach high accuracy for small training sets. Prediction of normal modes and IR-spectra of some small molecules demonstrates the usefulness of this approach for chemistry.

physics.chem-ph↗
arXiv2017

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.

physics.chem-ph↗
arXiv2015

Inferential protein structure determination and refinement using fast, electronic structure based backbone amide chemical shift predictions

This report covers the development of a new, fast method for calculating the backbone amide proton chemical shifts in proteins. Through quantum chemical calculations, structure-based forudsiglese the chemical shift for amidprotonen in protein has been parameterized. The parameters are then implemented in a computer program called Padawan. The program has since been implemented in protein folding program Phaistos, wherein the method andvendes to de novo folding of the protein structures and to refine the existing protein structures.

physics.chem-ph↗
arXiv2015

Improving intermolecular interactions in DFTB3 using extended polarization from chemical-potential equalization

Semi-empirical quantum mechanical methods traditionally expand the electron density in a minimal, valence-only electron basis set. The minimal-basis approximation causes molecular polarization to be underestimated, and hence intermolecular interaction energies are also underestimated, especially for intermolecular interactions involving charged species. In this work, the third-order self-consistent charge density functional tight-binding method (DFTB3) is augmented with an auxiliary response density using the chemical-potential equalization (CPE) method and an empirical dispersion correction (D3). The parameters in the CPE and D3 models are fitted to high-level CCSD(T) reference interaction energies for a broad range of chemical species, as well as dipole moments calculated at the DFT level; the impact of including polarizabilities of molecules in the parameterization is also considered. Parameters for the elements H, C, N, O and S are presented. The RMSD interaction energy is improved from 6.07 kcal/mol to 1.49 kcal/mol for interactions with one charged specie, whereas the RMSD is improved from 5.60 kcal/mol to 1.73 for a set of 9 salt bridges, compared to uncorrected DFTB3. For large water clusters and complexes that are dominated by dispersion interactions, the already satisfactory performance of the DFTB3-D3 model is retained; polarizabilities of neutral molecules are also notably improved. Overall, the CPE extension of DFTB3-D3 provides a more balanced description of different types of non-covalent interactions than NDDO type of semi-empirical methods (e.g., PM6-D3H4) and PBE-D3 with modest basis sets.

physics.chem-ph↗
arXiv2013

Protein structure validation and refinement using amide proton chemical shifts derived from quantum mechanics

We present the ProCS method for the rapid and accurate prediction of protein backbone amide proton chemical shifts - sensitive probes of the geometry of key hydrogen bonds that determine protein structure. ProCS is parameterized against quantum mechanical (QM) calculations and reproduces high level QM results obtained for a small protein with an RMSD of 0.25 ppm (r = 0.94). ProCS is interfaced with the PHAISTOS protein simulation program and is used to infer statistical protein ensembles that reflect experimentally measured amide proton chemical shift values. Such chemical shift-based structural refinements, starting from high-resolution X-ray structures of Protein G, ubiquitin, and SMN Tudor Domain, result in average chemical shifts, hydrogen bond geometries, and trans-hydrogen bond (h3JNC') spin-spin coupling constants that are in excellent agreement with experiment. We show that the structural sensitivity of the QM-based amide proton chemical shift predictions is needed to refine protein structures to this agreement. The ProCS method thus offers a powerful new tool for refining the structures of hydrogen bonding networks to high accuracy with many potential applications such as protein flexibility in ligand binding.

physics.chem-ph↗
arXiv2013

Hybrid RHF/MP2 geometry optimizations with the Effective Fragment Molecular Orbital Method

The frozen domain effective fragment molecular orbital method is extended to allow for the treatment of a single fragment at the MP2 level of theory. The approach is applied to the conversion of chorismate to prephenate by chorismate mutase, where the substrate is treated at the MP2 level of theory while the rest of the system is treated at the RHF level. MP2 geometry optimization is found to lower the barrier by up to 3.5 kcal/mol compared to RHF optimzations and ONIOM energy refinement and leads to a smoother convergence with respect to the basis set for the reaction profile. For double zeta basis sets the increase in CPU time relative to RHF is roughly a factor of two.

physics.chem-ph↗
arXiv2013

Interface of the polarizable continuum model of solvation with semi-empirical methods in the GAMESS program

An interface between semi-empirical methods and the polarized continuum model (PCM) of solvation successfully implemented into GAMESS following the approach by Chudinov et al (Chem. Phys. 1992, 160, 41). The interface includes energy gradients and is parallelized. For large molecules such as ubiquitin a reasonable speedup (up to a factor of six) is observed for up to 16 cores. The SCF convergence is greatly improved by PCM for proteins compared to the gas phase.

physics.chem-ph↗