Combined Electrostatically Embedded Multiconfiguration Molecular Mechanics and Molecular Mechanical Method: Application to Molecular Dynamics Simulation of a Chemical Reaction in Aqueous Solution with Hybrid Density Functional Theory

Potential energy interpolation with target-customized weighting coordinates: application to excited-state dynamics of photoactive yellow protein chromophore in water

Interpolation of potential energy surfaces (PESs) can provide a practical route to performing molecular dynamics simulations with a reliability matching a high-level quantum chemical calculation. An obstacle to its widespread use is perhaps the lack of general and optimal interpolation settings that can be applied in a black-box manner for any given molecular system. How to set up the weights for interpolation is one such task, and we still need to diversify the approaches in order to treat various systems. Here, we develop a new interpolation weighting scheme, which allows us to choose the weighting coordinates in a system-specific manner, by amplifying the contribution from specific internal coordinates. The new weighting scheme with an appropriate selection of coordinates is proved to be effective in reducing the interpolation error along the reaction pathway. As a demonstration, we consider the photoactive yellow protein chromophore system, as it constitutes itself as an interesting target that bears long-standing questions related to excited-state dynamics inside protein environments. We build its two-state diabatic interpolated PES with the new weighting scheme. We indeed see the utility of our scheme by conducting nonadiabatic molecular dynamics simulations with the required semi-global PES based on a limited number of data points.

Predicting Solvent Effects on SN2 Reaction Rates: Comparison of QM/MM, Implicit, and MM Explicit Solvent Models

Solvents are one of the key variables in the optimization of a synthesis yield or properties of a synthesis product. In this paper, contemporary solvent models are applied to predict the rates of S_N2 reactions in a range of aqueous and non-aqueous solvents. High-level CCSD(T)/CBS//M06-2X/6-31+G(d) gas phase energies were combined with solvation free energies from SMD, SM12, and ADF-COSMO-RS continuum solvent models, as well as molecular mechanics (MM) explicit solvent models with different atomic charge schemes to predict the rate constants of three S_N2 reactions in eight protic and aprotic solvents. It is revealed that the prediction of rate constants in organic solvents is not necessarily less challenging than in water and popular solvent models struggle to predict their rate constants to within 3 log units of experimental values. Among the continuum solvent models, the ADF-COSMO-RS model performed the best in predicting absolute rate contants while the SM12 model was best at predicting relative rate constants with an average accuracy of about 1.5 and 0.8 log units, respectively. The use of computationally more demanding MM explicit solvent models did not translate to improvements in absolute rate constants but was quite effective at predicting relative rate constants due to systematic error cancellation. Free energy barriers obtained from umbrella sampling with explicit solvent QM/MM simulations led to excellent agreement with experimental values, provided that a validated level of theory is used to treat the QM region.

Free-Energy Landscape of the SN2 Reaction CH3Br + Cl- → CH3Cl + Br- in Different Liquid Environments

This work describes in detail the reaction path of the well-known S_N2 reaction CH₃Br + Cl^- → CH₃Cl + Br^-, whose reaction rate has a huge variation with the solvent in the gas phase and in protic and aprotic liquid environments. We employed the ASEC-FEG method to optimize for minima (reactants and products) and saddle points (transition states) in the in-solution free-energy hypersurface. The method takes atomistic details of the solvent into account. A polarizable continuum model (PCM) has also been employed for comparison. The most perceptive structural changes are noted in aqueous solution by using the ASEC-FEG approach. The activation energies in all solvents, estimated by means of free-energy perturbation calculations, are in good agreement with the experimental data. The total solute-solvent hydrogen bonds play an important role in the increased barrier height observed in water and are therefore crucial to explain the huge decrease in the kinetic constant. It is also found that the hydration shell around the ions breaks itself spontaneously to accommodate the molecule, thus forming minimum energy complexes.

Physics-based, neural network force fields for reactive molecular dynamics: Investigation of carbene formation from [EMIM+][OAc-]

Reactive molecular dynamics simulations enable a detailed understanding of solvent effects on chemical reaction mechanisms and reaction rates. While classical molecular dynamics using reactive force fields allows significantly longer simulation time scales and larger system sizes compared with ab initio molecular dynamics, constructing reactive force fields is a difficult and complex task. In this work, we describe a general approach following the empirical valence bond framework for constructing ab initio reactive force fields for condensed phase simulations by combining physics-based methods with neural networks (PB/NNs). The physics-based terms ensure the correct asymptotic behavior of electrostatic, polarization, and dispersion interactions and are compatible with existing solvent force fields. NNs are utilized for a versatile description of short-range orbital interactions within the transition state region and accurate rendering of vibrational motion of the reacting complex. We demonstrate our methodology for a simple deprotonation reaction of the 1-ethyl-3-methylimidazolium cation with acetate to form 1-ethyl-3-methylimidazol-2-ylidene and acetic acid. Our PB/NN force field exhibits ∼1 kJ mol^-1 mean absolute error accuracy within the transition state region for the gas-phase complex. To characterize the solvent modulation of the reaction profile, we compute potentials of mean force for the gas-phase reaction as well as the reaction within a four-ion cluster and benchmark against ab initio molecular dynamics simulations. We find that the surrounding ionic environment significantly destabilizes the formation of the carbene product, and we show that this effect is accurately captured by the reactive force field. By construction, the PB/NN potential may be directly employed for simulations of other solvents/chemical environments without additional parameterization.

Exchange Repulsion in Quantum Mechanical/Effective Fragment Potential Excitation Energies: Beyond Polarizable Embedding

Hybrid quantum mechanical and molecular mechanical (QM/MM) approaches facilitate computational modeling of large biological and materials systems. Typically, in QM/MM, a small region of the system is modeled with an accurate quantum mechanical method and its surroundings with a more efficient alternative, such as a classical force field or the effective fragment potential (EFP). The reliability of QM/MM calculations depends largely on the treatment of interactions between the two subregions, also known as embedding. The polarizable embedding, which allows mutual polarization between solvent and solute, is considered to be essential for describing electronic excitations in polar solvents. In this work, we employ the QM/EFP model and extend the polarizable embedding by incorporating two short-range terms-a charge penetration correction to the electrostatic term and the exchange-repulsion term-both of which are modeled with one-electron contributions to the quantum Hamiltonian. We evaluate the accuracy of these terms by computing excitation energies across 37 molecular clusters consisting of biologically relevant chromophores surrounded by polar solvent molecules. QM/EFP excitation energies are compared to the fully quantum mechanical calculations with the configuration interaction singles (CIS) method. We find that the charge penetration correction diminishes the accuracy of the QM/EFP calculations. On the other hand, while the effect of exchange-repulsion is negligible for most ππ* transitions, the exchange-repulsion significantly improves description of nπ* transitions with blue solvatochromic shifts. As a result, addition of the exchange-repulsion term improves the overall accuracy of QM/EFP. Performances of QM/EFP models remain similar when excitation energies are modeled with cc-pVDZ and aug-cc-pVDZ basis sets.

QM/MM Calculations for the Cl- + CH3Cl SN2 Reaction in Water Using CM5 Charges and Density Functional Theory

The prototypical S_N2 reaction of chloride ion with methyl chloride has been reinvestigated in aqueous solution using QM/MM methodology featuring MO6-2X/6-31+G(d) calculations with the TIP4P water model, and partial charges were computed with the CM5 method. Though the DFT method yields excellent gas-phase energetics for the reaction, the QM/MM approach is found to yield overestimation of the activation barrier by ca. 12 kcal/mol. The discrepancy is traced to underestimate of the magnitude of the partial charges on the chlorine atoms in the transition structure. When CM1 or CM3 charges based on semiempirical wave functions are used instead, the agreement with experiment is much improved. The findings emphasize the sensitivity of the results of QM/MM calculations to the choice of QM method, the MM force field, and implementation of the QM/MM interface.

Modeling Charge Flux by Interpolating Atomic Partial Charges

Although the charge flux effect or the geometric dependence of the atomic partial charges have been known for a long time, how it can be effectively handled is not yet established. Here, we present a charge interpolation scheme as a new general tool for representing the charge flux in an analytically well-defined manner. By applying it to the anionic GFP chromophore with the diabatically represented atomic charges, we show that the charge interpolation provides a substantial improvement on the accuracy of the geometry-dependent changes in the molecular dipole moments in the gas phase. We also test the scheme toward describing the electrostatic term in the solvation energy in the aqueous environment and observe that it is also improved but that the extent of the improvement is somewhat limited. We show that the remaining errors can be largely corrected by introducing atomic polarizabilities. Overall, our results show that charge interpolation is an amenable approach for describing the charge flux effect and that its description in the condensed phase should be accompanied by proper treatments of polarization effects.

Application of Q2MM to predictions in stereoselective synthesis

Quantum-Guided Molecular Mechanics (Q2MM) can be used to derive transition state force fields (TSFFs) that allow the fast and accurate predictions of stereoselectivity for a wide range of catalytic enantioselective reactions. The basic ideas behind the derivation of TSFFs using Q2MM are discussed and the steps involved in obtaining a TSFF using the Q2MM code, publically available at github.com/q2mm, are shown. The applicability for a range of reactions, including several non-standard applications of Q2MM, is demonstrated. Future developments of the method are also discussed.

Dispersion Interactions in QM/EFP

The dispersion energy term between quantum-mechanical (QM) and classical (represented by effective fragment potentials, EFP) subsystems is developed and implemented. A new formulation is based on long-range perturbation theory and uses dynamic polarizability tensors of the effective fragments and electric field integrals and orbital energies of the quantum-mechanical subsystem. No parametrization is involved. The accuracy of the QM-EFP dispersion energy is tested on a number of model systems; the average mean unsigned error is 0.8 kcal/mol or 13% with respect to the symmetry adapted perturbation theory on the S22 data set of noncovalent interactions. The computational cost of the dispersion energy computation is low compared to the self-consistent field calculation of the QM subsystem. The dispersion energy is sensitive to the level of theory employed for the QM part and to the electrostatic interactions in the system. The latter means that the dispersion interactions in the QM/EFP method are not purely two-body but have more complex many-body behavior.

Theoretical approaches for dynamical ordering of biomolecular systems

BACKGROUND

Living systems are characterized by the dynamic assembly and disassembly of biomolecules. The dynamical ordering mechanism of these biomolecules has been investigated both experimentally and theoretically. The main theoretical approaches include quantum mechanical (QM) calculation, all-atom (AA) modeling, and coarse-grained (CG) modeling. The selected approach depends on the size of the target system (which differs among electrons, atoms, molecules, and molecular assemblies). These hierarchal approaches can be combined with molecular dynamics (MD) simulation and/or integral equation theories for liquids, which cover all size hierarchies.

SCOPE OF REVIEW

We review the framework of quantum mechanical/molecular mechanical (QM/MM) calculations, AA MD simulations, CG modeling, and integral equation theories. Applications of these methods to the dynamical ordering of biomolecular systems are also exemplified.

MAJOR CONCLUSIONS

The QM/MM calculation enables the study of chemical reactions. The AA MD simulation, which omits the QM calculation, can follow longer time-scale phenomena. By reducing the number of degrees of freedom and the computational cost, CG modeling can follow much longer time-scale phenomena than AA modeling. Integral equation theories for liquids elucidate the liquid structure, for example, whether the liquid follows a radial distribution function.

GENERAL SIGNIFICANCE

These theoretical approaches can analyze the dynamic behaviors of biomolecular systems. They also provide useful tools for exploring the dynamic ordering systems of biomolecules, such as self-assembly. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Theoretical estimation of kinetic parameters for nucleophilic substitution reactions in solution: an application of a solution translational entropy model

The kinetic parameters, such as activation entropy, activation enthalpy, activation free-energy, and reaction rate constant, for a series of nucleophilic substitution (SN) reactions in solution, are investigated using both a solution-phase translational entropy model and an ideal gas-phase translational entropy model. The results obtained from the solution translational entropy model are in excellent agreement with the experimental values, while the overestimation of activation free-energy from the ideal gas-phase translational entropy model is as large as 6.9 kcal mol(-1). For some of the reactions studied, such as and in methanol, and and in aqueous solution, the explicit + implicit model, namely, a cluster-continuum type model, should be employed to account for the strong solvent-solute interactions. In addition, the explicit + implicit models have also been applied to the DMSO-H2O mixtures, which would open up a door to investigate the reactions in a mixed solvent using density functional theory (DFT) methods.

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: multi-center molecular Ornstein-Zernike self-consistent field approach

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl(-) + CH3Cl → ClCH3 + Cl(-)) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabatic transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.

Quantum mechanical fragment methods based on partitioning atoms or partitioning coordinates

Conspectus The development of more efficient and more accurate ways to represent reactive potential energy surfaces is a requirement for extending the simulation of large systems to more complex systems, longer-time dynamical processes, and more complete statistical mechanical sampling. One way to treat large systems is by direct dynamics fragment methods. Another way is by fitting system-specific analytic potential energy functions with methods adapted to large systems. Here we consider both approaches. First we consider three fragment methods that allow a given monomer to appear in more than one fragment. The first two approaches are the electrostatically embedded many-body (EE-MB) expansion and the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), which we have shown to yield quite accurate results even when one restricts the calculations to include only electrostatically embedded dimers. The third fragment method is the electrostatically embedded molecular tailoring approach (EE-MTA), which is more flexible than EE-MB and EE-MB-CE. We show that electrostatic embedding greatly improves the accuracy of these approaches compared with the original unembedded approaches. Quantum mechanical fragment methods share with combined quantum mechanical/molecular mechanical (QM/MM) methods the need to treat a quantum mechanical fragment in the presence of the rest of the system, which is especially challenging for those parts of the rest of the system that are close to the boundary of the quantum mechanical fragment. This is a delicate matter even for fragments that are not covalently bonded to the rest of the system, but it becomes even more difficult when the boundary of the quantum mechanical fragment cuts a bond. We have developed a suite of methods for more realistically treating interactions across such boundaries. These methods include redistributing and balancing the external partial atomic charges and the use of tuned fluorine atoms for capping dangling bonds, and we have shown that they can greatly improve the accuracy. Finally we present a new approach that goes beyond QM/MM by combining the convenience of molecular mechanics with the accuracy of fitting a potential function to electronic structure calculations on a specific system. To make the latter practical for systems with a large number of degrees of freedom, we developed a method to interpolate between local internal-coordinate fits to the potential energy. A key issue for the application to large systems is that rather than assigning the atoms or monomers to fragments, we assign the internal coordinates to reaction, secondary, and tertiary sets. Thus, we make a partition in coordinate space rather than atom space. Fits to the local dependence of the potential energy on tertiary coordinates are arrayed along a preselected reaction coordinate at a sequence of geometries called anchor points; the potential energy function is called an anchor points reactive potential. Electrostatically embedded fragment methods and the anchor points reactive potential, because they are based on treating an entire system by quantum mechanical electronic structure methods but are affordable for large and complex systems, have the potential to open new areas for accurate simulations where combined QM/MM methods are inadequate.

Quantum and Molecular Mechanical (QM/MM) Monte Carlo Techniques for Modeling Condensed-Phase Reactions

A recent review (Acc. Chem. Res. 2010, 43:142-151) examined our use and development of a combined quantum and molecular mechanical (QM/MM) technique for modelling organic and enzymatic reactions. Advances included the PDDG/PM3 semiempirical QM (SQM) method, computation of multi-dimensional potentials of mean force (PMF), incorporation of on-the-fly QM in Monte Carlo simulations, and a polynomial quadrature method for rapidly treating proton-transfer reactions. The current article serves as a follow up on our progress. Highlights include new reactions, alternative SQM methods, a polarizable OPLS force field, and novel solvent environments, e.g., "on water" and room temperature ionic liquids. The methodology is strikingly accurate across a wide range of condensed-phase and antibody-catalyzed reactions including substitution, decarboxylation, elimination, isomerization, and pericyclic classes. Comparisons are made to systems treated with continuum-based solvents and ab initio or density functional theory (DFT) methods. Overall, the QM/MM methodology provides detailed characterization of reaction paths, proper configurational sampling, several advantages over implicit solvent models, and a reasonable computational cost.

Concerted hydrogen atom and electron transfer mechanism for catalysis by lysine-specific demethylase

We calculate the free energy profile for the postulated hydride transfer reaction mechanism for the catalysis of lysine demethylation by lysine-specific demethylase LSD1. The potential energy surface is obtained by using combined electrostatically embedded multiconfiguration molecular mechanics (EE-MCMM) and single-configuration molecular mechanics (MM). We employ a constant valence bond coupling term to obtain analytical energies and gradients of the EE-MCMM subsystem, which contains 45 quantum mechanics (QM) atoms and which is parametrized with density functional calculations employing specific reaction parameters obtained by matching high-level wave function calculations. In the MM region, we employ the Amber ff03 and TIP3P force fields. The free energy of activation at 300 K is calculated by molecular dynamics (MD) umbrella sampling on a system with 102,090 atoms as the maximum of the free energy profile along the reaction coordinate as obtained by the weighted histogram analysis method with 17 umbrella sampling windows. This yields a free energy of activation of only 10 kcal/mol, showing that the previously postulated direct hydride transfer reaction mechanism is plausible, although we find that it is better interpreted as a concerted transfer of a hydrogen atom and an electron.

Interpolated mechanics-molecular mechanics study of internal rotation dynamics of the chromophore unit in blue fluorescent protein and its variants

The excited state dynamics of the blue fluorescent protein (BFP) and its variants, azurite, EBFP1.2, and EBFP2.0, are studied using molecular dynamics (MD) simulations on potential energy surfaces (PESs) generated with the interpolated mechanics-molecular mechanics (IM/MM) scheme. This IM/MM strategy adopts the interpolated PES for an important area of the complex and the conventional force field for the remaining part. We focus on the internal rotation dynamics of the chromophore unit, which is directly related to its fluorescence property, and analyze the time evolutions of the nonrotated chromophore fractions based on trajectories over 10 μs of aggregate simulation time. The characteristics obtained from the calculated time progresses of the nonrotated chromophore fractions in BFP and other variants agree well with experimentally observed properties. The results show that the MD simulation with an IM/MM potential is an attractive approach for studying excited state dynamics of fluorescent proteins in consideration of its efficiency and reliability. We also attempt to investigate the detailed roles that the mutated residues play in delaying the excited state chromophore twisting and thus improving the fluorescence property, and discuss the contributions by the Coulombic and the steric interactions between the chromophore and the mutated residues.

Gradient-based multiconfiguration Shepard interpolation for generating potential energy surfaces for polyatomic reactions

This paper describes and illustrates a way to construct multidimensional representations of reactive potential energy surfaces (PESs) by a multiconfiguration Shepard interpolation (MCSI) method based only on gradient information, that is, without using any Hessian information from electronic structure calculations. MCSI, which is called multiconfiguration molecular mechanics (MCMM) in previous articles, is a semiautomated method designed for constructing full-dimensional PESs for subsequent dynamics calculations (classical trajectories, full quantum dynamics, or variational transition state theory with multidimensional tunneling). The MCSI method is based on Shepard interpolation of Taylor series expansions of the coupling term of a 2 x 2 electronically diabatic Hamiltonian matrix with the diagonal elements representing nonreactive analytical PESs for reactants and products. In contrast to the previously developed method, these expansions are truncated in the present version at the first order, and, therefore, no input of electronic structure Hessians is required. The accuracy of the interpolated energies is evaluated for two test reactions, namely, the reaction OH+H(2)-->H(2)O+H and the hydrogen atom abstraction from a model of alpha-tocopherol by methyl radical. The latter reaction involves 38 atoms and a 108-dimensional PES. The mean unsigned errors averaged over a wide range of representative nuclear configurations (corresponding to an energy range of 19.5 kcal/mol in the former case and 32 kcal/mol in the latter) are found to be within 1 kcal/mol for both reactions, based on 13 gradients in one case and 11 in the other. The gradient-based MCMM method can be applied for efficient representations of multidimensional PESs in cases where analytical electronic structure Hessians are too expensive or unavailable, and it provides new opportunities to employ high-level electronic structure calculations for dynamics at an affordable cost.

Quantum tunneling in testosterone 6beta-hydroxylation by cytochrome P450: reaction dynamics calculations employing multiconfiguration molecular-mechanical potential energy surfaces

Testosterone hydroxylation is a prototypical reaction of human cytochrome P450 3A4, which metabolizes about 50% of oral drugs on the market. Reaction dynamics calculations were carried out for the testosterone 6beta-hydrogen abstraction and the 6beta-d(1)-testosterone 6beta-duterium abstraction employing a model that consists of the substrate and the active oxidant compound I. The calculations were performed at the level of canonical variational transition state theory with multidimensional tunneling and were based on a semiglobal full-dimensional potential energy surface generated by the multiconfiguration molecular mechanics technique. The tunneling coefficients were found to be around 3, indicating substantial contributions by quantum tunneling. However, the tunneling made only modest contributions to the kinetic isotope effects. The kinetic isotope effects were computed to be about 2 in the doublet spin state and about 5 in the quartet spin state.