A Multistate Empirical Valence Bond Approach to a Polarizable and Flexible Water Model

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.

Multistate Reactive Molecular Dynamics Simulations of Proton Diffusion in Water Clusters and in the Bulk

The molecular mechanics with proton transfer (MMPT) force field is combined with multistate adiabatic reactive molecular dynamics (MS-ARMD) to describe proton transport in the condensed phase. Parametrization for small protonated water clusters based on electronic structure calculations at the MP2/6-311+G(2d,2p) level of theory and refinement by comparing with infrared spectra for a protonated water tetramer yields a force field which faithfully describes the minimum energy structures of small protonated water clusters. In protonated water clusters up to (H₂O)₁₀₀H⁺, the proton hopping rate is around 100 hops/ns. This rate converges for 21 ≤ n ≤ 31, and no further speedup in bulk water is found. This indicates that bulklike behavior requires the solvation of a Zundel motif by ∼25 water molecules, which corresponds to the second solvation sphere. For smaller cluster sizes, the number of available states (i.e., the number of proton acceptors) is too small and slows down proton-transfer rates. The cluster simulations confirm that the excess proton is typically located on the surface. The free-energy surface as a function of the weights of the two lowest states and a configurational parameter suggests that the "special pair" plays a central role in rapid proton transport. The barriers between this minimum-energy structure and the Zundel and Eigen minima are sufficiently low (∼1 kcal/mol, consistent with recent experiments and commensurate with a hopping rate of ∼100/ns or 1 every 10 ps), leading to a highly dynamic environment. These findings are also consistent with recent experiments which find that Zundel-type hydration geometries are prevalent in bulk water.

Specific Reaction Path Hamiltonian for Proton Transfer in Water: Reparameterized Semiempirical Models

The semiempirical MNDO-based AM1 and PM3 methods and the orthogonalization-corrected OM1, OM2, and OM3 models were reparameterized to improve their description of bulk water and of proton transfer in water. Reference data included the gas-phase geometries and energies of the water molecule, small water clusters, the hydronium ion, and small hydronium ion-water clusters, as well as the gas-phase potential energy surface for proton transfer between the two water molecules in a Zundel ion, all calculated at the MP2/aug-cc-pVTZ level of theory. Combined QM/MM molecular dynamics simulations were carried out for bulk water and for a proton solvated in water using large cluster models. Both the authentic and reparameterized semiempirical models were employed in the simulations. The reparameterization led to significantly better results in all cases. The new set of OM3 parameters gave the best overall results for the structural and dynamic properties of water and the hydrated proton, with a small but finite barrier of 0.1-0.2 kcal/mol in the potential of mean force for proton transfer, in agreement with ab initio path-integral molecular dynamics simulations. The reparameterized OM3 model is expected to be useful for efficient modeling of proton transfer in aqueous solution.

Multiscale reactive molecular dynamics

Many processes important to chemistry, materials science, and biology cannot be described without considering electronic and nuclear-level dynamics and their coupling to slower, cooperative motions of the system. These inherently multiscale problems require computationally efficient and accurate methods to converge statistical properties. In this paper, a method is presented that uses data directly from condensed phase ab initio simulations to develop reactive molecular dynamics models that do not require predefined empirical functions. Instead, the interactions used in the reactive model are expressed as linear combinations of interpolating functions that are optimized by using a linear least-squares algorithm. One notable benefit of the procedure outlined here is the capability to minimize the number of parameters requiring nonlinear optimization. The method presented can be generally applied to multiscale problems and is demonstrated by generating reactive models for the hydrated excess proton and hydroxide ion based directly on condensed phase ab initio molecular dynamics simulations. The resulting models faithfully reproduce the water-ion structural properties and diffusion constants from the ab initio simulations. Additionally, the free energy profiles for proton transfer, which is sensitive to the structural diffusion of both ions in water, are reproduced. The high fidelity of these models to ab initio simulations will permit accurate modeling of general chemical reactions in condensed phase systems with computational efficiency orders of magnitudes greater than currently possible with ab initio simulation methods, thus facilitating a proper statistical sampling of the coupling to slow, large-scale motions of the system.

Empirical valence bond models for reactive potential energy surfaces: a parallel multilevel genetic program approach

We describe a new method for constructing empirical valence bond potential energy surfaces using a parallel multilevel genetic program (PMLGP). Genetic programs can be used to perform an efficient search through function space and parameter space to find the best functions and sets of parameters that fit energies obtained by ab initio electronic structure calculations. Building on the traditional genetic program approach, the PMLGP utilizes a hierarchy of genetic programming on two different levels. The lower level genetic programs are used to optimize coevolving populations in parallel while the higher level genetic program (HLGP) is used to optimize the genetic operator probabilities of the lower level genetic programs. The HLGP allows the algorithm to dynamically learn the mutation or combination of mutations that most effectively increase the fitness of the populations, causing a significant increase in the algorithm's accuracy and efficiency. The algorithm's accuracy and efficiency is tested against a standard parallel genetic program with a variety of one-dimensional test cases. Subsequently, the PMLGP is utilized to obtain an accurate empirical valence bond model for proton transfer in 3-hydroxy-gamma-pyrone in gas phase and protic solvent.

A wave-function based approach for polarizable charge model: Systematic comparison of polarization effects on protic, aprotic, and ionic liquids

We first describe a wave-function based formalism of polarizable charge model by starting from the Hartree product ansatz for the total wave function and making the second-order expansion of individual molecular energies with the use of partial charge operators. The resulting model is shown to be formally equivalent to the charge response kernel model that starts from the linear-response approximation to partial charges, and also closely related to a family of fluctuating charge models that are based on the electronegativity equalization principle. We then apply the above model to a systematic comparison of polarization effects on qualitatively different liquids, namely, protic solvents (water and methanol), an aprotic polar solvent (acetonitrile), and imidazolium-based ionic liquids. Electronic polarization is known to decelerate molecular motions in conventional solvents while it accelerates them in ionic liquids. To obtain more insights into these phenomena, we consider an effective decomposition of total polarization energy into molecular contributions, and show that their statistical distribution is well-correlated with the acceleration/deceleration of molecular motions. In addition, we perform effective nonpolarizable simulations based on mean polarized charges, and compare them with fully polarizable simulations. The result shows that the former can reproduce structural properties of conventional solvents rather accurately, while they fail qualitatively to reproduce acceleration of molecular motions in ionic liquids.

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.

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.

Self-consistent polarization neglect of diatomic differential overlap: application to water clusters

Semiempirical self-consistent field (SCF) methods based on the neglect of diatomic differential overlap (NDDO) formalism have the ability to treat the formation and breaking of chemical bonds but have been found to poorly describe hydrogen bonding and weak electrostatic complexes. In contrast, most empirical potentials are not able to describe bond breaking and formation but have the ability to add missing elements of hydrogen bonding by using classical electrostatic interactions. We present a new method which combines aspects of both NDDO-based SCF techniques and classical descriptions of polarization to describe the diffuse nature of the electronic wavefunction in a self-consistent manner. We develop the "self-consistent polarization neglect of diatomic differential overlap" (SCP-NDDO) theory with the additional description of molecular dispersion developed as a second-order perturbation theory expression. The current study seeks to model water-water interactions as a test case. To this end, we have parametrized the method to accurate ab initio complete basis set limit estimates of small water cluster binding energies of Xantheas and co-workers [J. Chem. Phys. 116, 1493 (2002); 120, 823 (2004)]. Overall agreement with the ab initio binding energies (n=2-6, and 8) is achieved with a rms error of 0.19 kcal/mol. We achieve noticeable improvements in the structure, vibrational frequencies, and energetic predictions of water clusters (n< or =21) relative to standard NDDO-based methods.

Are many-body electronic polarization effects important in liquid water?

Many-body electronic polarization effects may be important for an accurate description of aqueous environments. As a result, numerous polarizable water models have been developed to include explicit polarization effects in intermolecular potential functions. In this paper, it is shown for liquid water at ambient conditions that such many-body polarization interactions can be decomposed into effective pairwise contributions using the force-matching (FM) method [Izvekov et al., J. Chem. Phys. 120, 10896 (2004)]. It is found that an effective pairwise water model obtained by the FM method can accurately reproduce various bulk structural and thermodynamic properties obtained from an accurate fully polarizable water model. In addition, the effective pairwise water model also provides a reasonable description of the water liquid-vapor interface, thus exhibiting a degree of transferability to heterogeneous environments. These results suggest that the role and importance of many-body electronic polarization effects in aqueous systems might be fruitfully explored relative to the best possible pairwise decomposable bulk phase model as the reference state.

Ab initio molecular-dynamics simulation of aqueous proton solvation and transport revisited

The solvation and transport of the hydrated excess proton is studied using the Car-Parrinello molecular-dynamics (CPMD) simulation method. The simulations were performed using BLYP and HCTH gradient-corrected exchange-correlation energy functionals. The fictitious electronic mass was chosen to be small enough so that the underlying water structural and dynamical properties were converged with respect to this important CPMD simulation parameter. An unphysical overstructuring of liquid water in the CPMD simulations using the BLYP functional resulted in the formation of long-lived hydrogen-bonding structures involving the excess proton and a particular (special) water oxygen. The excess proton was observed to be attracted to the special oxygen through the entire length of the BLYP CPMD simulations. Consequently, the excess proton diffusion was limited by the mobility of the special oxygen in the slowly diffusing water network and, in turn, the excess proton self-diffusion coefficient was found to be significantly below the experimental value. On the other hand, the structural properties of liquid water in the HCTH CPMD simulation were seen to be in better agreement with experiment, although the water and excess proton diffusions were still well below the experimental value.

Energy landscapes for water clusters in a uniform electric field

The behavior of small water clusters, (H2O)n, n=2-5 and n=8, in a uniform electric field is investigated for three related rigid-body models. Changes in the properties of the low-lying potential energy minima and the rearrangement pathways between them are examined. Results for certain structural transitions are compared with recent ab initio calculations. The models are found to give qualitatively similar trends, and there is some evidence that as the applied field strength is increased the quantitative differences between the models are also reduced.

Effects of Solute Electronic Polarizability on Solvation in a Room-Temperature Ionic Liquid

The effects of solute polarizability on solvation and solute transport in the room-temperature ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI+PF(6)-) are investigated via molecular dynamics simulations. A valence-bond description is employed to account for the instantaneous adjustment of the solute electronic charge distribution to the fluctuating solvent environment. It is found that the ultrafast inertial component of solvation dynamics becomes slower as the solute polarizability grows. Moreover, its contribution to overall solvent relaxation becomes reduced with increasing polarizability, especially in the case of nonequilibrium solvation dynamics. Overall, the inclusion of the solute electronic polarizability in the simulations improves the agreement with time-dependent Stokes shift measurements.

Effective force fields for condensed phase systems from ab initio molecular dynamics simulation: a new method for force-matching

A novel least-squares fitting approach is presented to obtain classical force fields from trajectory and force databases produced by ab initio (e.g., Car-Parrinello) molecular dynamics (MD) simulations. The method was applied to derive effective nonpolarizable three-site force fields for liquid water at ambient conditions from Car-Parrinello MD simulations in the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure includes a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The various parameterizations of the water force field differ by an enforced smooth cut-off applied to the short-ranged interaction term. These were obtained by fitting to the trajectory and force data produced by Car-Parrinello MD simulations of systems of 32 and 64 H(2)O molecules. The new water force fields were developed assuming both flexible or rigid molecular geometry. The simulated structural and self-diffusion properties of liquid water using the fitted force fields are in close agreement with those observed in the underlying Car-Parrinello MD simulations. The resulting empirical models compare to experiment much better than many conventional simple point charge (SPC) models. The fitted potential is also shown to combine well with more sophisticated intramolecular potentials. Importantly, the computational cost of the new models is comparable to that for SPC-like potentials.

Extended treatment of charge response kernel comprising the density functional theory and charge regulation procedures

We propose an extended treatment of the charge response kernel (CRK), (partial differential Q(a)/partial differential V(b)), which describes the response of partial charges on atomic sites to external electrostatic potential, on the basis of the density functional theory (DFT) via the coupled perturbed Kohn-Sham equations. The present CRK theory incorporates regulation procedures in the definition of partial charges to avoid unphysical large fluctuation of the CRK on "buried" sites. The CRKs of some alcohol and organic molecules, methanol, ethanol, propanol, butanol, dimethylsulfoxide (DMSO), and tetrahydrofuran (THF) were calculated, demonstrating that the new CRK model at the DFT level has greatly improved the performance of accuracy in comparison with that at the Hartree-Fock level previously proposed. The CRK model was also applied to investigate spatial nonlocality of the charge response through alkyl chain sequences. The CRK model at the DFT level enables us to construct a nonempirical strategy for polarizable molecular modeling, with practical reliability and robustness.

Making ATP

We present a mesoscopic model for ATP synthesis by F(1)F(o) ATPase. The model combines the existing experimental knowledge of the F(1) enzyme into a consistent mathematical model that illuminates how the stages in synthesis are related to the protein structure. For example, the model illuminates how specific interactions between the gamma, epsilon, and alpha(3)beta(3) subunits couple the F(o) motor to events at the catalytic sites. The model also elucidates the origin of ADP inhibition of F(1) in its hydrolysis mode. The methodology we develop for constructing the structure-based model should prove useful in modeling other protein motors.

Polarizable Solute in Polarizable and Flexible Solvents: Simulation Study of Electron Transfer Reaction Systems

A polarizable solute model, based on the empirical valence bond approach, is developed and applied to electron transfer (ET) reactions in polarizable and flexible water solvents. The polarization effect is investigated in comparison with a nonpolarizable solute and solvent model. With free energy curves constructed by a molecular dynamics simulation, the activation energy barrier and the reorganization energy related to ET processes are investigated. The present simulation results show that the activation energy barrier becomes larger in the polarizable model than in the nonpolarizable model and that this makes the ET rate slower than that with the nonpolarizable model. It is shown that the effect of the electronic energy difference of solute molecule on free energy profiles is remarkable and that, corresponding to this effect, the reorganization energy is significantly modified. These results indicate that the process of solvent polarization by the polarized solute to enhance the solute-solvent interaction is a key factor and that treating the polarization of both solute and solvent at the same time is essential. Also, the polarization effect on the diffusive motion of the solute molecule in the polarization solvent is studied. The polarized solute molecule shows slower diffusive motion compared with that in the nonpolarizable model.

A polarizable multistate empirical valence bond model for proton transport in aqueous solution

A multistate empirical valence bond model for proton transport in water, which explicitly includes solvent polarization, is presented. Polarization is included for each valence-bond state via induced point dipoles, and the model is parametrized to be used with an effective path integral derived potential surface, so as to include quantum effects of the transferring proton. The new model is shown to reproduce ab initio geometries and energetics for small protonated clusters. It is also shown that the new model gives a diffusion constant for the excess proton in water, which is in good agreement with experiment, and that the qualitative features of ab initio path integral simulations [D. Marx, M. E. Tuckerman, J. Hutter, and M. Parrinello, Nature (London) 397, 601 (1999)] are well reproduced.

Protonated water clusters described by an empirical valence bond potential

The properties of low-lying stationary points on the potential energy surfaces of singly protonated water clusters (H(2)O)(n)H(+), are investigated using an empirical valence bond potential. Candidate global minima are reported for n=2-4, 8, and 20-22. For n=8, the variation in the energies and structures of low-lying minima with the number of valence bond states included in the model is studied. For n=4 and 8, disconnectivity graphs are also reported and are compared to results for the equivalent neutral water clusters as described by the rigid TIP3P potential. For the larger clusters, n=20-22, the structural properties of the low energy minima are compared with recently published spectroscopic data on these systems. The observed differences between the n=20 and n=21 systems are qualitatively reproduced by the model potential, but the similarities between the n=21 and n=22 systems are not.