Energies Of Small Organic Molecules Research Articles

Interpretable delta-learning of GW quasiparticle energies from GGA-DFT

Accurate prediction of the ionization potential and electron affinity energies of small molecules are important for many applications. Density functional theory (DFT) is computationally inexpensive, but can be very inaccurate for frontier orbital energies or ionization energies. The GW method is sufficiently accurate for many relevant applications, but much more expensive than DFT. Here we study how we can learn to predict orbital energies with GW accuracy using machine learning (ML) on molecular graphs and fingerprints using an interpretable delta-learning approach. ML models presented here can be used to predict quasiparticle energies of small organic molecules even beyond the size of the molecules used for training. We furthermore analyze the learned DFT-to-GW corrections by mapping them to specific localized fragments of the molecules, in order to develop an intuitive interpretation of the learned corrections, and thus to better understand DFT errors.

Measurements as a roadblock to near-term practical quantum advantage in chemistry: Resource analysis

Recent advances in quantum computing devices have brought attention to hybrid quantum-classical algorithms like the Variational Quantum Eigensolver (VQE) as a potential route to practical quantum advantage in chemistry. However, it is not yet clear whether such algorithms, even in the absence of device error, could actually achieve quantum advantage for systems of practical interest. We have performed an exhaustive analysis to estimate the number of qubits and number of measurements required to compute the combustion energies of small organic molecules and related systems to within chemical accuracy of experimental values using VQE. We consider several key modern improvements to VQE, including low-rank factorizations of the Hamiltonian. Our results indicate that although these techniques are useful, they will not be sufficient to achieve practical quantum computational advantage for our molecular set, or for similar molecules. This suggests that novel approaches to operator estimation leveraging quantum coherence, such as Enhanced Likelihood Functions [arxiv:2006.09350, arxiv:2006.09349], may be required.

Determining the Adsorption Free Energies of Small Organic Molecules and Intrinsic Ions at the Terrace and Steps of Calcite

Determining the Adsorption Free Energies of Small Organic Molecules and Intrinsic Ions at the Terrace and Steps of Calcite

Computing Charging and Polarization Energies of Small Organic Molecules Embedded into Amorphous Materials with Quantum Accuracy.

The ionization potential, electron affinity, and cation/anion polarization energies (IP, EA, P(+), P(-)) of organic molecules determine injection barriers, charge carriers balance, doping efficiency, and light outcoupling in organic electronics devices, such as organic light-emitting diodes (OLEDs). Computing IP and EA of isolated molecules is a common task for quantum chemistry methods. However, once molecules are embedded in an amorphous organic matrix, IP and EA values change, and accurate predictions become challenging. Here, we present a revised quantum embedding method [Friederich et al. J. Chem. Theory Comput. 2014, 10 (9), 3720-3725] that accurately predicts the dielectric permittivity and ionization potentials in three test materials, NPB, TCTA, and C60, and allows straightforward interpretation of their nature. The method paves the way toward reliable virtual screening of amorphous organic semiconductors with targeted IP/EA, polarization energies, and relative dielectric permittivity.

Learning Atomic Interactions through Solvation Free Energy Prediction Using Graph Neural Networks.

Solvation free energy is a fundamental property that influences various chemical and biological processes, such as reaction rates, protein folding, drug binding, and bioavailability of drugs. In this work, we present a deep learning method based on graph networks to accurately predict solvation free energies of small organic molecules. The proposed model, comprising three phases, namely, message passing, interaction, and prediction, is able to predict solvation free energies in any generic organic solvent with a mean absolute error of 0.16 kcal/mol. In terms of accuracy, the current model outperforms all of the proposed machine learning-based models so far. The atomic interactions predicted in an unsupervised manner are able to explain the trends of free energies consistent with chemical wisdom. Further, the robustness of the machine learning-based model has been tested thoroughly, and its capability to interpret the predictions has been verified with several examples.

Extension and evaluation of the D4 London-dispersion model for periodic systems.

We present an extension of the DFT-D4 model [J. Chem. Phys., 2019, 150, 154122] for periodic systems. The main new ingredients are additional reference polarizabilities for highly-coordinated group 1-5 elements derived from pseudo-periodic electrostatically-embedded cluster calculations. To illustrate the performance of the updated method, several test cases are considered, for which we compare D4 to its predecessor D3(BJ), as well as to a comprehensive set of other dispersion-corrected methods. The largest improvements are observed for solid-state polarizabilities of 16 inorganic salts, where the D4 model achieves an unprecedented accuracy, surpassing its predecessor as well as other, computationally much more demanding approaches. For cell volumes and lattice energies of two sets of chemically diverse molecular crystals, the accuracy gain is less pronounced compared to the already excellently performing D3(BJ) method. For the challenging adsorption energies of small organic molecules on metallic as well as on ionic surfaces, DFT-D4 provides values in good agreement with experimental and/or high-level references. These results suggest the application of the proposed D4 model as a physically improved yet computationally efficient dispersion correction for standard DFT calculations as well as low-cost approaches like semi-empirical or even force-field models.

Adsorption of Amino Acids on Gold: Assessing the Accuracy of the GolP-CHARMM Force Field and Parametrization of Au-S Bonds.

The interaction of amino acids with metal electrodes plays a crucial role in bioelectrochemistry and the emerging field of bionanoelectronics. Here we present benchmark calculations of the adsorption structure and energy of all natural amino acids on Au(111) in vacuum using a van-der-Waals density functional (revPBE-vdW) that showed good performance on the S22 set of weakly bound dimers (mean relative unsigned error (MRUE) wrt CCSD(T)/CBS = 13.3%) and adsorption energies of small organic molecules on Au(111) (MRUE wrt experiment = 11.2%). The vdW-DF results are then used to assess the accuracy of a popular force field for Au-amino acid interactions, GolP-CHARMM, which explicitly describes image charge interactions via rigid-rod dipoles. We find that while the force field underestimates adsorption distances, it does reproduce the binding energy rather well (MRUE wrt revPBE-vdW = 11.3%) with the MRUE decreasing in the order Cys, Met > amines > aliphatic > carboxylic > aromatic. We also present a parametrization of the bonding interaction between sulfur-containing molecules and the Au(111) surface and report force field parameters that are compatible with GolP-CHARMM. We believe the vdW-DF calculations presented herein will provide useful reference data for further force field development, and that the new Au-S bonding parameters will enable improved simulations of proteins immobilized on Au-electrodes via S-linkages.

Bind3P: Optimization of a Water Model Based on Host-Guest Binding Data.

We report a water model, Bind3P (Version 0.1), which was obtained by using sensitivity analysis to readjust the Lennard-Jones parameters of the TIP3P model against experimental binding free energies for six host-guest systems, along with pure liquid properties. Tests of Bind3P against >100 experimental binding free energies and enthalpies for host-guest systems distinct from the training set show a consistent drop in the mean signed error, relative to matched calculations with TIP3P. Importantly, Bind3P also yields some improvement in the hydration free energies of small organic molecules and preserves the accuracy of bulk water properties, such as density and the heat of vaporization. The same approach can be applied to more sophisticated water models that can better represent pure water properties. These results lend further support to the concept of integrating host-guest binding data into force field parametrization.

Automatic selection of atomic fingerprints and reference configurations for machine-learning potentials.

Machine learning of atomic-scale properties is revolutionizing molecular modeling, making it possible to evaluate inter-atomic potentials with first-principles accuracy, at a fraction of the costs. The accuracy, speed, and reliability of machine learning potentials, however, depend strongly on the way atomic configurations are represented, i.e., the choice of descriptors used as input for the machine learning method. The raw Cartesian coordinates are typically transformed in "fingerprints," or "symmetry functions," that are designed to encode, in addition to the structure, important properties of the potential energy surface like its invariances with respect to rotation, translation, and permutation of like atoms. Here we discuss automatic protocols to select a number of fingerprints out of a large pool of candidates, based on the correlations that are intrinsic to the training data. This procedure can greatly simplify the construction of neural network potentials that strike the best balance between accuracy and computational efficiency and has the potential to accelerate by orders of magnitude the evaluation of Gaussian approximation potentials based on the smooth overlap of atomic positions kernel. We present applications to the construction of neural network potentials for water and for an Al-Mg-Si alloy and to the prediction of the formation energies of small organic molecules using Gaussian process regression.

On the performance of time-dependent double-hybrid density functionals for description of absorption and emission spectra of heteroaromatic compounds

Theoretical chemistry provides a panel of powerful tools to investigate the geometries and electronic properties of excited states. However, it is necessary to benchmark the accuracy of existing models to determine the range of their applicability and accountability. In the present work, the performance of two related methodologies in this context, symmetry-adapted cluster-configuration interaction (SAC-CI) and time-dependent double-hybrid density functional theory (TD-DHDFT), is compared in detail for the calculation of absorption and fluorescence energies of small organic molecules and π-conjugated heteroaromatic compounds. Pragmatically, for the SAC-CI calculations the singles and doubles linked excitation operators are considered in the wave functions. On the other hand, for the TD-DHDFT calculations the linear-response Tamm–Dancoff formalism has been imposed. The considered DH density functionals include the approximations from both families of adjusted and non-adjusted models. Our numerical data reveal that of the tested adjusted DHs, B2-PLYP performs the best, while among the category of non-adjusted approximations the PBE0-DH functional outperforms others. Furthermore, the DH density functionals show deviations less than those obtained from SAC-CI method. Putting all the results together, the B2-PLYP and B2GP-PLYP functionals are found to be superior for overall performance. Altogether, the present contribution and recent efforts in this arena point out that besides the ground-state properties the DH approximations have also unquestionably entered into the field of excited-state calculations, where the DHDFT again comes into play and further evidence on the quality of the corresponding models is pronounced.

Machine learning for quantum mechanics in a nutshell

Models that combine quantum mechanics (QM) with machine learning (ML) promise to deliver the accuracy of QM at the speed of ML. This hands‐on tutorial introduces the reader to QM/ML models based on kernel learning, an elegant, systematically nonlinear form of ML. Pseudocode and a reference implementation are provided, enabling the reader to reproduce results from recent publications where atomization energies of small organic molecules are predicted using kernel ridge regression. © 2015 Wiley Periodicals, Inc.

Toward high-throughput predictions of the hydration free energies of small organic molecules from first principles

In this work we examine a multiscale procedure for predicting the solvation free energies of small organic molecules in liquid water at ambient conditions. The experimental database consists of thermodynamic data for 2583 neutral organic molecules, one of the largest sets available in the molecular modeling community. Using the extensive experimental data for hydration free energies as a benchmark, we find that the theoretical predictions are sensitive not only to water models but also to quantum-mechanical calculations for determining the molecular configurations and the atomic charges of solute molecules, and to the assignment of the non-bonded force-field parameters for different organic functional groups. Considering the computational cost of multiscale modeling for large-scale free-energy calculations from first principles, we maintain that the classical density functional theory provides a valuable alternate to conventional molecular simulation methods. The theoretical procedure will be important for future development of semi-empirical force fields and, in particular, for applications of multiscale modeling methods to practical problems that require high-throughput free-energy calculations.

Quantitative molecular orbital energies within a G0W0 approximation

Using many-body perturbation theory within the $G_0W_0$ approximation, we explore routes for computing the ionization potential (IP), electron affinity (EA), and fundamental gap of three gas-phase molecules -- benzene, thiophene, and (1,4) diamino-benzene -- and compare with experiments. We examine the dependence of the IP on the number of unoccupied states used to build the dielectric function and the self energy, as well as the dielectric function plane-wave cutoff. We find that with an effective completion strategy for approximating the unoccupied subspace, and a converged dielectric function kinetic energy cutoff, the computed IPs and EAs are in excellent quantitative agreement with available experiment (within 0.2 eV), indicating that a one-shot $G_0W_0$ approach can be very accurate for calculating addition/removal energies of small organic molecules. Our results indicate that a sufficient dielectric function kinetic energy cutoff may be the limiting step for a wide application of $G_0W_0$ to larger organic systems.

Basis set convergence of molecular correlation energy differences within the random phase approximation

The basis set convergence of energy differences obtained from the random phase approximation (RPA) to the correlation energy is investigated for a wide range of molecular interactions. For dispersion bound systems the basis set incompleteness error is most pronounced, as shown for the S22 benchmark [P. Jurecka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The use of very large basis sets (> quintuple-zeta) or extrapolation to the complete basis set (CBS) limit is necessary to obtain a reliable estimate of the binding energy for these systems. Counterpoise corrected results converge to the same CBS limit, but counterpoise correction without extrapolation is insufficient. Core-valence correlations do not play a significant role. For medium- and short-range correlation, quadruple-zeta results are essentially converged, as demonstrated for relative alkane conformer energies, reaction energies dominated by intramolecular dispersion, isomerization energies, and reaction energies of small organic molecules. Except for weakly bound systems, diffuse augmentation almost universally slows down basis set convergence. For most RPA applications, quadruple-zeta valence basis sets offer a good balance between accuracy and efficiency.

Improving Implicit Solvent Models with Differential Geometry

Implicit solvent models are popular for their high computational efficiency and simplicity over explicit solvent models. Hence, there has been significant interest in testing and improving these models for their ability to accurately compute the thermodynamic properties of a wide range of chemicals and macromolecules. One such model is a differential geometry-based solvation model where a generalized geometric flow (GF) equation and a generalized Poisson-Boltzmann (PB) equation are self-consistently solved to compute a smooth dielectric profile, and the polar and non-polar solvation free energies. The GF equation contains the polar energetic terms defined by the PB equation, and non-polar energetic terms describing the pressure-volume work to create a cavity in the solvent, energy to create a solute-solvent interface, and solute-solvent attractive dispersion interactions. The solution to the GF equation is a characteristic function that describes a smooth solute-solvent boundary. This function defines the smooth dielectric profile used in the PB equation to compute the electrostatic potential. Therefore, the main parameters of the model are the solute/solvent dielectric, solvent pressure, surface tension, solvent density, and molecular force-field parameters. As for other solvation models, these parameters have to be determined by experimental conditions or optimized against experimental solvation energy data before the model can be applied for new molecules. However, it is not clearly understood how different choices of the model parameters are coupled with force field choice to affect the computed results. In this work, we have performed a parametric study on the GF-based solvation model to investigate how changes in the pressure, surface tension and use of different force fields affect the optimal solutions to the solvation free energies of small organic molecules. Results of this model will be presented for a set of 17 small organic molecules using three different force fields.

Predicting binding affinities of host-guest systems in the SAMPL3 blind challenge: the performance of relative free energy calculations

Relative free energy calculations based on molecular dynamics simulations are combined with available experimental binding free energies to predict unknown binding affinities of acyclic Cucurbituril complexes in the blind SAMPL3 competition. The predictions yield root mean square errors between 2.6 and 3.2 kcal/mol for seven host-guest systems. Those deviations are comparable to results for solvation free energies of small organic molecules. However, the standard deviations found in our simulations range from 0.4 to 2.4 kcal/mol, which indicates the need for better sampling. Three different approaches are compared. Bennett's Acceptance Ratio Method and thermodynamic integration based on the trapezoidal rule with 12 λ-points exhibit a root mean square error of 2.6 kcal/mol, while thermodynamic integration with Simpson's rule and 11 λ-points leads to a root mean square error of 3.2 kcal/mol. In terms of absolute median errors, Bennett's Acceptance Ratio Method performs better than thermodynamic integration with the trapezoidal rule (1.7 vs. 2.9 kcal/mol). Simulations of the deprotonated forms of the guest molecules exhibit a poorer correspondence to experimental results with a root mean square error of 5.2 kcal/mol. In addition, a decrease of the buffer concentration by approximately 20 mM in the simulations raises the root mean square error to 3.8 kcal/mol.

Parameterization of PACE Force Field for Membrane Environment and Simulation of Helical Peptides and Helix-Helix Association.

The recently developed PACE force field was further parametrized so that it can be applied to the studies of membrane systems. Parameters for the interactions between united-atom protein particles and lipid hydrophobic tails were developed by reproducing the solvation free energies of small organic molecules in hexadecane. Interactions between protein particles and lipid heads were parametrized by fitting the potential of mean force of the corresponding all-atom simulation. The force field was applied to the study of five helical peptides in membrane environments. The calculated tilt angles of WALP and GWALP and their mutations are in good agreement with experimental data. The association of two glycophorin A (GpA) helices was simulated for 6 μs. Root-mean-square-deviation of the simulated dimer from the nuclear magnetic resonance structure was found to be 0.272 nm, better than all results obtained so far. These findings demonstrate the high accuracy and applicability of the PACE force field in studying membrane proteins.

Solvation effect on conformations of 1,2:dimethoxyethane: charge-dependent nonlinear response in implicit solvent models.

The physical content of and, in particular, the nonlinear contributions from the Langevin-Debye model are illustrated using two applications. First, we provide an improvement in the Langevin-Debye model currently used in some implicit solvent models for computer simulations of solvation free energies of small organic molecules, as well as of biomolecular folding and binding. The analysis is based on the implementation of a charge-dependent Langevin-Debye (qLD) model that is modified by subsequent corrections due to Onsager and Kirkwood. Second, the physical content of the model is elucidated by discussing the general treatment within the LD model of the self-energy of a charge submerged in a dielectric medium for three different limiting conditions and by considering the nonlinear response of the medium. The modified qLD model is used to refine an implicit solvent model (previously applied to protein dynamics). The predictions of the modified implicit solvent model are compared with those from explicit solvent molecular dynamics simulations for the equilibrium conformational populations of 1,2-dimethoxyethane (DME), which is the shortest ether molecule to reproduce the local conformational properties of polyethylene oxide, a polymer with tremendous technological importance and a wide variety of applications. Because the conformational population preferences of DME change dramatically upon solvation, DME is a good test case to validate our modified qLD model. The present analysis of the modified qLD model provides the motivation and tools for studying a wide variety of other interesting systems with heterogeneous dielectric properties and spatial anisotropy.

The SGB/NP hydration free energy model based on the surface generalized born solvent reaction field and novel nonpolar hydration free energy estimators.

The development and parameterization of a solvent potential of mean force designed to reproduce the hydration thermodynamics of small molecules and macromolecules aimed toward applications in conformation prediction and ligand binding free energy prediction is presented. The model, named SGB/NP, is based on a parameterization of the Surface Generalized Born continuum dielectric electrostatic model using explicit solvent free energy perturbation calculations and a newly developed nonpolar hydration free energy estimator motivated by the results of explicit solvent simulations of the thermodynamics of hydration of hydrocarbons. The nonpolar model contains, in addition to the more commonly used solvent accessible surface area term, a component corresponding to the attractive solute-solvent interactions. This term is found to be important to improve the accuracy of the model, particularly for cyclic and hydrogen bonding compounds. The model is parameterized against the experimental hydration free energies of a set of small organic molecules. The model reproduces the experimental hydration free energies of small organic molecules with an accuracy comparable or superior to similar models employing more computationally demanding estimators and/or a more extensive set of parameters.

Prediction of Solvation Free Energies of Small Organic Molecules: Additive-Constitutive Models Based on Molecular Fingerprints and Atomic Constants

Solvation free energy is an important molecular characteristic useful in drug discovery because it represents the desolvation cost of a ligand binding to a receptor. Most of the recent developments in the estimation of solvation free energy require the use of molecular mechanics and dynamics calculations. Group contribution methods have been rarely used in the past for calculating solvation free energy because automated prediction methods have not been developed in this regard. As an aid to combinatorial library design, we explored rapid and accurate means of computing solvation free energies from the covalent structures of organic molecules and compared the results on a test set with the GB/SA solvation model. Two independent additive-constitutive QSPR methods have been developed for the computation of solvation free energy. The first is a QSPR model (HLOGS) derived using a technique that uses the counts of distinct/similar fragments and substructures for each molecule as variables in a PLS regression. T...