Machine learning of solvent effects on molecular spectra and reactions

Fast and accurate simulation of complex chemical systems in environments such as solutions is a long standing challenge in theoretical chemistry. In recent years, machine learning has extended the boundaries of quantum chemistry by providing highly accurate and efficient surrogate models of electronic structure theory, which previously have been out of reach for conventional approaches. Those models have long been restricted to closed molecular systems without accounting for environmental influences, such as external electric and magnetic fields or solvent effects. Here, we introduce the deep neural network FieldSchNet for modeling the interaction of molecules with arbitrary external fields. FieldSchNet offers access to a wealth of molecular response properties, enabling it to simulate a wide range of molecular spectra, such as infrared, Raman and nuclear magnetic resonance. Beyond that, it is able to describe implicit and explicit molecular environments, operating as a polarizable continuum model for solvation or in a quantum mechanics/molecular mechanics setup. We employ FieldSchNet to study the influence of solvent effects on molecular spectra and a Claisen rearrangement reaction. Based on these results, we use FieldSchNet to design an external environment capable of lowering the activation barrier of the rearrangement reaction significantly, demonstrating promising venues for inverse chemical design.

A machine learning approach for modeling the influence of external environments and fields on molecules has been developed, which allows the prediction of various types of molecular spectra in vacuum and under implicit and explicit solvation.     

Halogen bonding in ligand-receptor systems in the framework of classical force fields

Halogen bond is an important non-covalent interaction which is receiving a growing attention in the study of protein-ligand complexes. Many drugs are halogenated molecules and it has been recently shown that many halogenated ligands establish halogen bonds with biomolecules. As the halogen bond nature is due to an anisotropy of the electrostatic potential around halogen atoms, it is not possible to use traditional force fields based on a set of atom-centred charges to study halogen bonds in biomolecules. We show that the introduction of pseudo-atoms on halogens permits us to correctly describe the anisotropy of the electrostatic potential and to perform molecular dynamics simulations on complexes of proteins with halogenated ligands that reproduce experimental values. The results are compared with crystallographic data and with hybrid quantum mechanics/molecular mechanics calculations.     

Recent applications and developments of charge equilibration force fields for modeling dynamical charges in classical molecular dynamics simulations

With the continuing advances in computational hardware and novel force fields constructed using quantum mechanics, the outlook for non-additive force fields is promising. Our work in the past several years has demonstrated the utility of polarizable force fields, in our hands those based on the charge equilibration formalism, for a broad range of physical and biophysical systems. We have constructed and applied polarizable force fields for small molecules, proteins, lipids, and lipid bilayers and recently have begun work on carbohydrate force fields. The latter area has been relatively untouched by force field developers with particular focus on polarizable, non-additive interaction potential models. In this review of our recent work, we discuss the formalism we have adopted for implementing the charge equilibration method for phase-dependent polarizable force fields, lipid molecules, and small-molecule carbohydrates. We discuss the methodology, related issues, and briefly discuss results from recent applications of such force fields.     

Accurate conformation‐dependent molecular electrostatic potentials for high‐throughput in silico drug discovery

The atom‐centered partial charges‐approximation is commonly used in current molecular modeling tools as a computationally inexpensive alternative to quantum mechanics for modeling electrostatics. Even today, the use of partial charges remains useful despite significant advances in improving the efficiency of ab initio methods. Here, we report on new parameters for the EEM and SFKEEM electronegativity equalization‐based methods for rapidly determining partial charges that will accurately model the electrostatic potential of flexible molecules. The developed parameters cover most pharmaceutically relevant chemistries, and charges obtained using these parameters reproduce the B3LYP/cc‐pVTZ reference electrostatic potential of a set of FDA‐approved drug molecules at best to an average accuracy of 13 ± 4 kJ mol^?1; thus, equipped with these parameters electronegativity equalization‐based methods rival the current best non‐quantum mechanical methods, such as AM1‐BCC, in accuracy, yet incur a lower computational cost. Software implementations of EEM and SFKEEM, including the developed parameters, are included in the conformer‐generation tool BALLOON , available free of charge at http://web.abo.fi/fak/mnf/bkf/research/johnson/software.php . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Development of a polarizable force field for proteins via ab initio quantum chemistry: first generation model and gas phase tests

We present results of developing a methodology suitable for producing molecular mechanics force fields with explicit treatment of electrostatic polarization for proteins and other molecular system of biological interest. The technique allows simulation of realistic-size systems. Employing high-level ab initio data as a target for fitting allows us to avoid the problem of the lack of detailed experimental data. Using the fast and reliable quantum mechanical methods supplies robust fitting data for the resulting parameter sets. As a result, gas-phase many-body effects for dipeptides are captured within the average RMSD of 0.22 kcal/mol from their ab initio values, and conformational energies for the di- and tetrapeptides are reproduced within the average RMSD of 0.43 kcal/mol from their quantum mechanical counterparts. The latter is achieved in part because of application of a novel torsional fitting technique recently developed in our group, which has already been used to greatly improve accuracy of the peptide conformational equilibrium prediction with the OPLS-AA force field.1 Finally, we have employed the newly developed first-generation model in computing gas-phase conformations of real proteins, as well as in molecular dynamics studies of the systems. The results show that, although the overall accuracy is no better than what can be achieved with a fixed-charges model, the methodology produces robust results, permits reasonably low computational cost, and avoids other computational problems typical for polarizable force fields. It can be considered as a solid basis for building a more accurate and complete second-generation model.     

Macromodel—an integrated software system for modeling organic and bioorganic molecules using molecular mechanics

An integrated molecular modeling system for designing and studying organic and bioorganic molecules and their molecular complexes using molecular mechanics is described. The graphically controlled, atom-based system allows the construction, display and manipulation of molecules and complexes having as many as 10,000 atoms and provides interactive, state-of-the-art molecular mechanics on any subset of up to 1,000 atoms. The system semiautomates the graphical construction and analysis of complex structures ranging from polycyclic organic molecules to biopolymers to mixed molecular complexes. We have placed emphasis on providing effective searches of conformational space by a number of different methods and on highly optimized molecular mechanics energy calculations using widely used force fields which are supplied as external files. Little experience is required to operate the system effectively and even novices can use it to carry out sophisticated modeling operations. The software has been designed to run on Digital Equipment Corporation VAX computers interfaced to a variety of graphics devices ranging from inexpensive monochrome terminals to the sophisticated graphics displays of the Evans & Sutherland PS300 series.     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

Classical aspects emerging from local control of energy and particle transfer in molecules

The question in how far classical mechanics can be used to describe coherent control processes in molecules is addressed within the framework of local control theory. Therefore, quantum and classical calculations are compared for a model proton transfer process and also for the multi-photon infrared dissociation of the HOD molecule. It is shown that control fields can be derived classically as long as wave packet dispersion is not too large. This hints at further applications which might be helpful to devise control fields for complex molecular systems being present in biological processes.     

Limiting assumptions in molecular modeling: electrostatics

Molecular mechanics attempts to represent intermolecular interactions in terms of classical physics. Initial efforts assumed a point charge located at the atom center and coulombic interactions. It is been recognized over multiple decades that simply representing electrostatics with a charge on each atom failed to reproduce the electrostatic potential surrounding a molecule as estimated by quantum mechanics. Molecular orbitals are not spherically symmetrical, an implicit assumption of monopole electrostatics. This perspective reviews recent evidence that requires use of multipole electrostatics and polarizability in molecular modeling.     

Efficient parametrization of complex molecule–surface force fields

We present an efficient scheme for parametrizing complex molecule–surface force fields from ab initio data. The cost of producing a sufficient fitting library is mitigated using a 2D periodic embedded slab model made possible by the quantum mechanics/molecular mechanics scheme in CP2K. These results were then used in conjunction with genetic algorithm (GA) methods to optimize the large parameter sets needed to describe such systems. The derived potentials are able to well reproduce adsorption geometries and adsorption energies calculated using density functional theory. Finally, we discuss the challenges in creating a sufficient fitting library, determining whether or not the GA optimization has completed, and the transferability of such force fields to similar molecules. © 2015 Wiley Periodicals, Inc.     

Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide

Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree–Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by “breaking” bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. Results from tests of the method to find relative conformational energies and geometries of alanine dipeptides and alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1468–1494, 1999     

Generation of Molecular Fields, Quantum Similarity Measures and Related Questions

A straightforward discussion on how to generate molecular fields is developed within the postulates of quantum mechanics. The theoretical formalism points towards the generalization and extension of the well-known molecular field forms, associated to density function and electrostatic molecular potential (EMP), including another category of fields associated to quantum molecular similarity measures. The results show that the new formalism can be easily applied to obtain an unlimited number of new information about molecular behavior.     

Nonuniform charge scaling (NUCS): a practical approximation of solvent electrostatic screening in proteins

In molecular mechanics calculations, electrostatic interactions between chemical groups are usually represented by a Coulomb potential between the partial atomic charges of the groups. In aqueous solution these interactions are modified by the polarizable solvent. Although the electrostatic effects of the polarized solvent on the protein are well described by the Poisson--Boltzmann equation, its numerical solution is computationally expensive for large molecules such as proteins. The procedure of nonuniform charge scaling (NUCS) is a pragmatic approach to implicit solvation that approximates the solvent screening effect by individually scaling the partial charges on the explicit atoms of the macromolecule so as to reproduce electrostatic interaction energies obtained from an initial Poisson--Boltzmann analysis. Once the screening factors have been determined for a protein the scaled charges can be easily used in any molecular mechanics program that implements a Coulomb term. The approach is particularly suitable for minimization-based simulations, such as normal mode analysis, certain conformational reaction path or ligand binding techniques for which bulk solvent cannot be included explicitly, and for combined quantum mechanical/molecular mechanical calculations when the interface to more elaborate continuum solvent models is lacking. The method is illustrated using reaction path calculations of the Tyr 35 ring flip in the bovine pancreatic trypsin inhibitor.     

Quantum molecular mechanics—a noniterative procedure for the fast Ab Initio calculation of closed shell systems

In this article, we advance the foundations of a strategy to develop a molecular mechanics method based not on classical mechanics and force fields but entirely on quantum mechanics and localized electron‐pair orbitals, which we call quantum molecular mechanics (QMM). Accordingly, we introduce a new manner of calculating Hartree–Fock ab initio wavefunctions of closed shell systems based on variationally preoptimized nonorthogonal electron pair orbitals constructed by linear combinations of basis functions centered on the atoms. QMM is noniterative and requires only one extremely fast inversion of a single sparse matrix to arrive to the one‐particle density matrix, to the electron density, and consequently, to the ab initio electrostatic potential around the molecular system, or cluster of molecules. Although QMM neglects the smaller polarization effects due to intermolecular interactions, it fully takes into consideration polarization effects due to the much stronger intramolecular geometry distortions. For the case of methane, we show that QMM was able to reproduce satisfactorily the energetics and polarization effects of all distortions of the molecule along the nine normal modes of vibration, well beyond the harmonic region. We present the first practical applications of the QMM method by examining, in detail, the cases of clusters of helium atoms, hydrogen molecules, methane molecules, as well as one molecule of HeH⁺ surrounded by several methane molecules. We finally advance and discuss the potentialities of an exact formula to compute the QMM total energy, in which only two center integrals are involved, provided that the fully optimized electron‐pair orbitals are known. © 2012 Wiley Periodicals, Inc.     

Prediction of the mechanisms of enzyme-catalysed reactions using hybrid quantum mechanical/molecular mechanical methods

The use of hybrid methods, involving both quantum mechanics and molecular mechanics, to model the mechanism of enzyme-catalysed reactions, is discussed. Two alternative approaches to treating the electrostatic interactions between the quantum mechanical and molecular mechanical regions are studied, involving either the inclusion of this term in the electronic Hamiltonian (QM/MM), or evaluating it purely classically (MO + MM). In the latter scheme, possible problems of using force fields that are standard for macromolecular modelling are identified. The use of QM/MM schemes to investigate the mechanism of the enzymes thymidine phosphorylase (ThdPase) and protein tyrosine phosphatase (PTP) is described. For both systems, transition states have been identified using a PM3 Hamiltonian. For ThdPase, concerted motion of the enzyme during the course of the reaction is suggested and, for PTP, a two-step dephosphorylation reaction is indicated, both with quite low barriers.     

Electrostatic and covalent contributions in the coordination bonds of transition metal complexes

To develop a molecular mechanics force field for modeling complexes of transition metals and organic ligands, the electrostatic and covalent contributions in the coordination bonds were investigated using quantum mechanical density functional theory and model complexes of glyoxal diimine and the 2+ cations of the first row transition metals. The VDD and Hirshfeld charges are found to be closely correlated with the extent of the electron transfer between the ligands and the cations. Assuming the electrostatic contribution can be represented by the atomic partial charges, the covalent contributions in the coordination bonds are estimated to be in a range of 54-92% for the systems calculated. A simple force field was parametrized to validate the partial charge representation.     

Molecular modeling of sigma receptor ligands: A model of binding based on conformational and electrostatic considerations

We have performed molecular modeling studies on four representative sigma receptor specific ligands, (+)haloperidol, (+)3-PPP, (+)pentazocine and progesterone, to develop a model for sigma receptor-ligand binding. The modeling studies have investigated the conformational and electrostatic properties of the ligands. Based on the complementarity of the conformational and electrostatic properties of the ligands, a model of binding has been proposed which shows that the four ligands can fit a common receptor sit. Unlike the binding model for haloperidol that was previously proposed by Manallack and Andrews, our model binds haloperidol in the gauche conformation. The first site binds the fluorophenyl group and the second site the lone pair of the piperidine nitrogen. This pharmacophore can be presented by (+)3-PPP and (+)pentazocine, but for progesterone the binding model requires the ring junction of the cyclohexenyl ring A and ring B to fit the fluorophenyl region, while the lone pair of the acetylcarbonyl oxygen at ring D emulates the nitrogen lone pair of the piperidine ring. Calculations were performed using RCG5 for generating conformations, molecular mechanics for calculating steric energies, quantum mechanical methods for generating charges, and ARCHEM for calculating electrostatic potentials on the Van der Waals surface.     

Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.     

Derivation of class II force fields: V. Quantum force field for amides,peptides, and related compounds

As the field of biomolecular structure advances, there is an ever-growing need for accurate modeling of molecular energy surfaces to simulate and predict the properties of these important systems. To address this need, a second generation amide force field for use in simulations of small organics as well as proteins and peptides has been derived. The critical question of what accuracy can be expected from calculations in general, and with this class II force field in particular, is addressed for structural, dynamic, and energetic properties. The force field is derived from a recent methodology we have developed that involves the systematic use of quantum mechanical observables. Systematic ab initio calculations were carried out for numerous configurations of 17 amide and related compounds. Relative energies and first and second derivatives of the energy of 638 structures of these compounds resulted in 140,970 ab initio quantum mechanical observables. The class II peptide quantum mechanical force field (QMFF), containing 732 force constants and reference values, was parameterized against these observables. A major objective of this work is to help establish the role of anharmonicity and coupling in improving the accuracy of molecular force fields, as these terms have not yet become an agreed upon standard in the ever more extensive simulations being used to probe biomolecular properties. This has been addressed by deriving a class I harmonic diagonal force field (HDFF), which was fit to the same energy surface as the QMFF, thus providing an opportunity to quantify the effects of these coupling and anharmonic contributions. Both force field representations are assessed in terms of their ability to fit the observables. They have also been tested by calculating the properties of 11 stationary states of these amide molecules. Optimized structures, vibrational frequencies, and conformational energies obtained from the quantum calculations and from both the QMFF and the HDFF are compared. Several strained and derivatized compounds including urea, formylformamide, and butyrolactam are included in these tests to assess the range of applicability (transferability) of the force fields. It was found that the class II coupled anharmonic force field reproduced the structures, energies, and vibrational frequencies significantly more faithfully than the class I harmonic diagonal force field. An important measure, rms energy deviation, was found to be 1.06 kcal/mol with the class II force field, and 2.30 kcal/mol with the harmonic diagonal force field. These deviations represent the error in relative configurational energy differences for strained and distorted structures calculated with the force fields compared with quantum mechanics. This provides a measure of the accuracy that might be expected in applications where strain may be important such as calculating the energy of a system as it approaches a (rotational) barrier, in ligand binding to a protein, or effects of introducing substituents into a molecule that may induce strain. Similar results were found for structural properties. Protein dynamics is becoming of ever-increasing interest, and, to simulate dynamic properties accurately, the dynamic behavior of model compounds needs to be well accounted for. To this end, the ability of the class I and class II force fields to reproduce the vibrational frequencies obtained from the quantum energy surface was assessed. An rms deviation of 43 cm⁻¹ was achieved with the coupled anharmonic force field, as compared to 105 cm⁻¹ with the harmonic diagonal force field. Thus, the analysis presented here of the class II force field for the amide functional group demonstrates that the incorporation of anharmonicity and coupling terms in the force field significantly improves the accuracy and transferability with regard to the simulation of structural, energetic, and dynamic properties of amides. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 430–458, 1998