Systematic Improvement of Empirical Energy Functions in the Era of Machine Learning

The impact of targeted replacement of individual terms in empirical force fields is quantitatively assessed for pure water, dichloromethane (DCM), and solvated K$^+$ and Cl$^-$ ions. For the electrostatics, point charges (PCs) and machine learning (ML)based minimally distributed charges (MDCM) fitted to the molecular electrostatic potential are evaluated together with electrostatics based on the Coulomb integral. The impact of explicitly including second-order terms is investigated by adding a fragment molecular orbital (FMO)-derived polarization energy to an existing force field, in this case CHARMM. It is demonstrated that anisotropic electrostatics reduce the RMSE for water (by 1.6 kcal/mol), DCM (by 0.8 kcal/mol) and for solvated Cl$^-$ clusters (by 0.4 kcal/mol). An additional polarization term can be neglected for DCM but notably improves errors in pure water (by 1.1 kcal/mol) and in Cl$^-$ clusters (by 0.4 kcal/mol) and is key to describing solvated K$^+$, reducing the RMSE by 2.3 kcal/mol. A 12-6 Lennard-Jones functional form is found to perform satisfactorily with PC and MDCM electrostatics, but is not appropriate for descriptions that account for the electrostatic penetration energy. The importance of many-body contributions is assessed by comparing a strictly 2-body approach with self-consistent reference data. DCM can be approximated well with a 2-body potential while water and solvated K$^+$ and Cl$^-$ ions require explicit many-body corrections. The present work systematically quantifies which terms improve the performance of an existing force field and what reference data to use for parametrizing these terms in a tractable fashion for ML fitting of pure and heterogeneous systems

Q-Force:Quantum Mechanically Augmented Molecular Force Fields

The quality of molecular dynamics simulations strongly depends on the accuracy of the underlying force fields (FFs) that determine all intra- and intermolecular interactions of the system. Commonly, transferable FF parameters are determined based on a representative set of small molecules. However, such an approach sacrifices accuracy in favor of generality. In this work, an open-source and automated toolkit named Q-Force is presented, which augments these transferable FFs with molecule-specific bonded parameters and atomic charges that are derived from quantum mechanical (QM) calculations. The molecular fragmentation procedure allows treatment of large molecules (&gt;200 atoms) with a low computational cost. The generated Q-Force FFs can be used at the same computational cost as transferable FFs, but with improved accuracy: We demonstrate this for the vibrational properties on a set of small molecules and for the potential energy surface on a complex molecule (186 atoms) with photovoltaic applications. Overall, the accuracy, user-friendliness, and minimal computational overhead of the Q-Force protocol make it widely applicable for atomistic molecular dynamics simulations.</p

Prediction of Electronic Properties of Radical-Containing Polymers at Coarse-Grained Resolutions

The properties of soft electronic materials depend on the coupling of electronic and conformational degrees of freedom over a wide range of spatiotemporal scales. Description of such properties requires multiscale approaches capable of, at the same time, accessing electronic properties and sampling the conformational space of soft materials. This could in principle be realized by connecting the coarse-grained (CG) methodologies required for adequate conformational sampling to conformationally-averaged electronic property distributions via backmapping to atomistic-resolution level models and repeated quantum-chemical calculations. Computational demands of such approaches, however, have hindered their application in high-throughput computer-aided soft materials discovery. Here, we present a method that, combining machine learning and CG techniques, can replace traditional backmapping-based approaches without sacrificing accuracy. We illustrate the method for an emerging class of soft electronic materials, namely non-conjugated, radical-containing polymers, promising materials for all-organic energy storage. Supervised machine learning models are trained to learn the dependence of electronic properties on polymer conformation at CG resolutions. We then parametrize CG models that retain electronic structure information, simulate CG condensed phases, and predict the electronic properties of such phases solely from the CG degrees of freedom. We validate our method by comparing it against a full backmapping-based approach, and find good agreement between both methods. This work demonstrates the potential of the proposed method to accelerate multiscale workflows, and provides a framework for the development of CG models that retain electronic structure information

Development and Validation of the Quantum Mechanical Bespoke Protein Force Field.

Molecular mechanics force field parameters for macromolecules, such as proteins, are traditionally fit to reproduce experimental properties of small molecules, and thus, they neglect system-specific polarization. In this paper, we introduce a complete protein force field that is designed to be compatible with the quantum mechanical bespoke (QUBE) force field by deriving nonbonded parameters directly from the electron density of the specific protein under study. The main backbone and sidechain protein torsional parameters are rederived in this work by fitting to quantum mechanical dihedral scans for compatibility with QUBE nonbonded parameters. Software is provided for the preparation of QUBE input files. The accuracy of the new force field, and the derived torsional parameters, is tested by comparing the conformational preferences of a range of peptides and proteins with experimental measurements. Accurate backbone and sidechain conformations are obtained in molecular dynamics simulations of dipeptides, with NMR J coupling errors comparable to the widely used OPLS force field. In simulations of five folded proteins, the secondary structure is generally retained, and the NMR J coupling errors are similar to standard transferable force fields, although some loss of the experimental structure is observed in certain regions of the proteins. With several avenues for further development, the use of system-specific nonbonded force field parameters is a promising approach for next-generation simulations of biological molecules

System-specific parameter optimization for non-polarizable and polarizable force fields

The accuracy of classical force fields (FFs) has been shown to be limited for the simulation of cation-protein systems despite their importance in understanding the processes of life. Improvements can result from optimizing the parameters of classical FFs or by extending the FF formulation by terms describing charge transfer and polarization effects. In this work, we introduce our implementation of the CTPOL model in OpenMM, which extends the classical additive FF formula by adding charge transfer (CT) and polarization (POL). Furthermore, we present an open-source parameterization tool, called FFAFFURR that enables the (system specific) parameterization of OPLS-AA and CTPOL models. The performance of our workflow was evaluated by its ability to reproduce quantum chemistry energies and by molecular dynamics simulations of a Zinc finger protein.Comment: 62 pages and 25 figures (including SI), manuscript to be submitted soo

Coarse-grained peptide models: conformational sampling, peptide association and dynamical properties for peptides

In dieser Arbeit wird ein vergröbertes (engl. coarse-grained, CG) Simulationsmodell für Peptide in wässriger Lösung entwickelt. In einem CG Verfahren reduziert man die Anzahl der Freiheitsgrade des Systems, so dass manrngrössere Systeme auf längeren Zeitskalen untersuchen kann. Die Wechselwirkungspotentiale des CG Modells sind so aufgebaut, dass die Peptid Konformationen eines höher aufgelösten (atomistischen) Modells reproduziert werden.rnIn dieser Arbeit wird der Einfluss unterschiedlicher bindender Wechsel-rnwirkungspotentiale in der CG Simulation untersucht, insbesondere daraufhin,rnin wie weit das Konformationsgleichgewicht der atomistischen Simulation reproduziert werden kann. Im CG Verfahren verliert man per Konstruktionrnmikroskopische strukturelle Details des Peptids, zum Beispiel, Korrelationen zwischen Freiheitsgraden entlang der Peptidkette. In der Dissertationrnwird gezeigt, dass diese “verlorenen” Eigenschaften in einem Rückabbildungsverfahren wiederhergestellt werden können, in dem die atomistischen Freiheitsgrade wieder in die CG-Strukturen eingefügt werden. Dies gelingt, solange die Konformationen des CG Modells grundsätzlich gut mit der atomistischen Ebene übereinstimmen. Die erwähnten Korrelationen spielen einerngrosse Rolle bei der Bildung von Sekundärstrukturen und sind somit vonrnentscheidender Bedeutung für ein realistisches Ensemble von Peptidkonformationen. Es wird gezeigt, dass für eine gute Übereinstimmung zwischen CG und atomistischen Kettenkonformationen spezielle bindende Wechselwirkungen wie zum Beispiel 1-5 Bindungs- und 1,3,5-Winkelpotentiale erforderlich sind. Die intramolekularen Parameter (d.h. Bindungen, Winkel, Torsionen), die für kurze Oligopeptide parametrisiert wurden, sind übertragbarrnauf längere Peptidsequenzen. Allerdings können diese gebundenen Wechselwirkungen nur in Kombination mit solchen nichtbindenden Wechselwirkungspotentialen kombiniert werden, die bei der Parametrisierung verwendet werden, sind also zum Beispiel nicht ohne weiteres mit einem andere Wasser-Modell kombinierbar. Da die Energielandschaft in CG-Simulationen glatter ist als im atomistischen Modell, gibt es eine Beschleunigung in der Dynamik. Diese Beschleunigung ist unterschiedlich für verschiedene dynamische Prozesse, zum Beispiel für verschiedene Arten von Bewegungen (Rotation und Translation). Dies ist ein wichtiger Aspekt bei der Untersuchung der Kinetik von Strukturbildungsprozessen, zum Beispiel Peptid Aggregation.rnA bottom-up coarse-graining (CG) procedure for peptides in aqueous solutionrnis studied in this thesis. The coarse-graining procedure reduces the numberrnof degrees of freedom of the system, enabling us to investigate larger systemsrnand due to the smoother energy landscape one can get faster a better sam-rnpling of the system. The interaction potentials in our coarse-grained modelrnare constructed in a such way, that the coarse-grained peptide reproducesrnconformations according to a high-resolution (atomistic) model.rnIn this work the influence of differently constructed bonded potentials onrnthe reproduction of atomistic characteristics in structure-based CG simula-rntion was investigated. In the coarse-graining procedure one loses by constuc-rntion microscopic structural details of the peptide. This can be for examplerncorrelations between degrees of freedom. In the thesis it is presented thatrnthose “lost” properties can be recovered in a backmapping procedure whichrnreintroduces atomistic degrees of freedom into CG structures – as long asrnthe overall conformational sampling of the molecule is correctly representedrnin the CG level of resolution. These correlations play an important role inrnsecondary structure formation. Therefore they are crucial for a realistic con-rnformational ensemble of the peptide. It is shown that for an exact agreementrnof the CG conformations with the atomistic reference additional bonded po-rntentials are required such as 1-5 bond and 1,3,5-angle potentials.rnIt is shown that the intramolecular parameters (i.e. bonds, angles, tor-rnsions) determined for short oligopeptides are transferable to longer peptidernsequences. But one has to be aware that bonded potentials should be usedrnonly in combination with those nonbonded interaction potentials, with whichrnthey were parametrized. So, they cannot necessarily be combined with otherrnnonbonded interactions, for example a different water model.rnSince the energy landscape is smoother in CG simulations, there is thernacceleration in time and in principle the CG time does not corresponds onernto one to the atomistic time any more. The dynamical properties of thernpeptide in water on the atomistic and CG levels were investigated in order tornget an estimate for the speed-up of the dynamics in the CG model comparedrnto the atomistic one. We found that these scaling factors are different forrndifferent dynamical properties and concluded that there is different “speed-rnup” for different types of motions (for example rotation and translation).rnThis is an important observation for the kinetics of processes such as peptidernaggregation.r

Potential energy surfaces: from force fields to neural networks

Almost a century ago, Paul A. M. Dirac remarked that the Schrödinger equation (SE) contains all that is necessary to describe chemical phenomena. Unfortunately, solving the SE, even approximately, remains a time-intensive task and is possible only for systems containing a few atoms. For this reason, potential energy surfaces (PESs) are used to circumvent the solution of the SE altogether: They estimate the energy of a chemical system by evaluating an analytical function. For example, so-called force fields (FFs) model chemical bonds as "springs", i.e. with harmonic potentials. While this is computationally efficient, it limits the accuracy of FFs. A promising alternative are machine learning (ML) methods, such as kernel ridge regression (KRR) and artificial neural networks (NNs), which allow the construction of a PES without assuming a functional form. In the first part of this thesis, FFs are described in more detail and the minimal distributed charge model (MDCM) is introduced as a way to increase their accuracy. Applications to several challenging molecules are used to demonstrate the utility of this method. In the second part, KRR is reviewed and ways to improve its computational efficiency for PES construction are discussed. Further, the reproducing kernel Hilbert space (RKHS) toolkit is introduced, which largely automates the construction of efficient and accurate PESs for small systems. In the last part, a brief overview of NNs and their historic development is given. The use of NNs to construct PESs is explored and two alternatives are described in more detail. Both variants are applied to various benchmark datasets in order to demonstrate their versatility and accuracy