A semiempirical quantum polarization model for water

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.

The MOD-QM/MM Method: Applications to Studies of Photosystem II and DNA G-Quadruplexes

Quantum mechanics/molecular mechanics (QM/MM) hybrid methods are currently the most powerful computational tools for studies of structure/function relations and catalytic sites embedded in macrobiomolecules (eg, proteins and nucleic acids). QM/MM methodologies are highly efficient since they implement quantum chemistry methods for modeling only the portion of the system involving bond-breaking/forming processes (QM layer), as influenced by the surrounding molecular environment described in terms of molecular mechanics force fields (MM layer). Some of the limitations of QM/MM methods when polarization effects are not explicitly considered include the approximate treatment of electrostatic interactions between QM and MM layers. Here, we review recent advances in the development of computational protocols that allow for rigorous modeling of electrostatic interactions in biomacromolecules and structural refinement, beyond the common limitations of QM/MM hybrid methods. We focus on photosystem II (PSII) with emphasis on the description of the oxygen-evolving complex (OEC) and its high-resolution extended X-ray absorption fine structure spectra (EXAFS) in conjunction with Monte Carlo structural refinement. Furthermore, we review QM/MM structural refinement studies of DNA G4 quadruplexes with embedded monovalent cations and direct comparisons to NMR data.

Quantum wavepacket ab initio molecular dynamics: generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics (QWAIMD) method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD (xLag-QWAIMD) and diabatic extended Lagrangian-QWAIMD (DxLag-QWAIMD). In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.

Accounting for water molecules in drug design

IMPORTANCE OF THE FIELD

Water molecules often appear around ligands in protein crystal structures. Reliable prediction of the effects of water on ligand binding remains a challenge. Solvation effects are crucial for lead optimization where a 100-fold difference in binding affinity is significant but correspond to only ∼3 kcal/mol in binding free energy. Well-known examples, such as nonpeptidic urea inhibitors of HIV protease, prove that careful examination of water molecules and their energetics can contribute significantly to a successful drug design campaign.

AREAS COVERED IN THIS REVIEW

In this review, we examine methods to account for the effect of water in ligand binding at two stages of drug discovery: lead identification via docking calculations and lead optimization. We provide a survey of the models and techniques available to account for water in drug design.

WHAT THE READER WILL GAIN

The reader will become aware of common practices and pitfalls in dealing with water molecules in structure-based drug design.

TAKE HOME MESSAGE

Although solvation effects are not fully understood, some pragmatic recommendations at the end of the article provide guidance for modelers in this area as well as new practitioners.

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.

Excited state properties of liquid water

In this paper, we give an overview of the state of the art in calculations of the electronic band structure and absorption spectra of water. After an introduction to the main theoretical and computational schemes used, we present results for the electronic and optical excitations of water. We focus mainly on liquid water, but spectroscopic properties of ice and vapor phase are also described. The applicability and the accuracy of first-principles methods are discussed, and results are critically presented.

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.

On the performance of molecular polarization methods. I. Water and carbon tetrachloride close to a point charge

The three main methods to implement molecular polarization (point dipoles, fluctuating charges, and shell model) are tested against high level ab initio calculations for a molecule (water, carbon tetrachloride) close to a point charge (at the distance of a lithium or magnesium ion). The goal is to check whether an approximation (linear polarization) strictly valid at large intermolecular distances is sufficiently accurate for liquid state molecular dynamics simulations, where strong polarization effects are to be expected at short separations. The monitored observable is the molecular dipole moment as a function of the charge-molecule distance for selected molecular orientations. Analytic formulas are derived for the components of the molecular polarization tensor, facilitating the optimization of the performance for each polarization method as a function of its underlying parameters. Overall, the methods studied provide a remarkably good representation of the induced dipole, with no divergences appearing even at the shortest distances. For water close to a monovalent point charge the point dipole model, implemented with one or three dipoles, accurately reproduces the water dipole moment at all distances. Deficiencies appear as the molecular polarizability and/or charge increase: basically, the ab initio induced moments grow faster at intermediate distances than the linear increase characteristic of the phenomenological polarization methods, suggesting that nonlinear effects (hyperpolarizability) cannot be neglected in these cases. Regarding the capabilities of each method, the point dipole method is the one that performs best overall, with the shell model achieving acceptable results in most instances. The fluctuating charge method shows some noticeable limitations for implementations of comparable complexity (in terms of the number of sites required).