An accurate representation of ion solvation in aqueous solution is critical for meaningful computer simulations of a broad range of physical and biological processes. Polarizable models based on classical Drude oscillators are introduced and parametrized for a large set of monoatomic ions including cations of the alkali metals (Li + , Na + , K + , Rb + and Cs + ) and alkaline earth elements (Mg 2+ , Ca 2+ , Sr 2+ and Ba 2+ ) along with Zn 2+ and halide anions (F − , Cl − , Br − and I − ). The models are parameterized, in conjunction with the polarizable SWM4-NDP water model [Lamoureux et al., Chem. Phys. Lett. 418, 245 (2006)], to be consistent with a wide assortment of experimentally measured aqueous bulk thermodynamic properties and the energetics of small ion-water clusters. Structural and dynamic properties of the resulting ion models in aqueous solutions at infinite dilution are presented.

Computation based on molecular models is playing an increasingly important role in biology, biological chemistry, and biophysics. Since only a very limited number of properties of biomolecular systems is actually accessible to measurement by experimental means, computer simulation can complement experiment by providing not only averages, but also distributions and time series of any definable quantity, for example, conformational distributions or interactions between parts of systems. Present day biomolecular modeling is limited in its application by four main problems: 1) the force-field problem, 2) the search (sampling) problem, 3) the ensemble (sampling) problem, and 4) the experimental problem. These four problems are discussed and illustrated by practical examples. Perspectives are also outlined for pushing forward the limitations of biomolecular modeling.

The standard self-consistent-charge density-functional-tight-binding (SCC-DFTB) method (Phys. Rev. B 1998, 58, 7260) is derived by a second-order expansion of the density functional theory total energy expression, followed by an approximation of the charge density fluctuations by charge monopoles and an effective damped Coulomb interaction between the atomic net charges. The central assumptions behind this effective charge-charge interaction are the inverse relation of atomic size and chemical hardness and the use of a fixed chemical hardness parameter independent of the atomic charge state. While these approximations seem to be unproblematic for many covalently bound systems, they are quantitatively insufficient for hydrogen-bonding interactions and (anionic) molecules with localized net charges. Here, we present an extension of the SCC-DFTB method to incorporate third-order terms in the charge density fluctuations, leading to chemical hardness parameters that are dependent on the atomic charge state and a modification of the Coulomb scaling to improve the electrostatic treatment within the second-order terms. These modifications lead to a significant improvement in the description of hydrogen-bonding interactions and proton affinities of biologically relevant molecules.

Motivated by the long-term goal of understanding vectorial biological processes such as proton transport (PT) in biomolecular ion pumps, a number of developments were made to establish combined quantum mechanical/molecular mechanical (QM/MM) methods suitable for studying chemical reactions involving significant charge separation in the condensed phase. These developments were summarized and discussed with representative problems. Specifically, free energy perturbation and boundary potential methods for treating long-range electrostatics were implemented to test the robustness of QM/MM results for protein systems. It was shown that consistent models with sufficient sampling were able to produce quantitatively satisfactory results, such as pK a for titritable groups in the interior of T4-lysozyme, while an inconsistent treatment of electrostatics or lack of sufficient sampling may produce incorrect results. Modifications were made to an approximate density functional theory (SCC-DFTB) to improve the description of proton affinity and hydrogen-bonding, which are crucial for the treatment of PT in polar systems. Test calculations on water autoionization showed clearly that both improvements are necessary for quantitatively reliable results. Finally, the newly established SCC-DFTB/MM-GSBP protocol was used to explore mechanistic issues in carbonic anhydrase (CA). Preliminary results suggest that PT in CA occurs mainly through short water wires containing two water molecules in a thermally activated fashion. Although longer water wires occur with similar frequencies, PT along those pathways, on average, has substantially higher barriers, a result not expected based on previous studies. The fluctuations of water molecules peripheral to the water wire were found to make a larger impact on the PT energetics compared to polar protein residues in the active site, which are largely pre-organized and therefore have less tendency to reorganize during the reaction.

The charge-on-spring method is used to develop a rigid, three-site, polarizable water model, a noniterative and a self-consistent version. In this method, the polarizability is taken into account by a variable separation of charges on selected polarizable centers. One of the pair of polarization charges resides on a polarizable center, while the other one is treated as an additional particle attached to the polarizable center by a parabolic restraint potential. The separation is calculated in response to the instantaneous electric field. We parametrized two models which are based on noniterative and self-consistent versions of the method, respectively. We computed several liquid-phase and gas-phase properties and compared with data available from experiment and ab initio calculations. The condensed-phase properties of both models are in reasonable accord with experiment, apart from discrepancies in electrostatic properties consistent with a slightly too large liquid-state dipole. The charge-on-spring method is used to develop a rigid, three-site, polarizable water model, a noniterative and a self-consistent version. In this method, the polarizability is taken into account by a variable separation of charges on selected polarizable centers. One of the pair of polarization charges resides on a polarizable center, while the other one is treated as an additional particle attached to the polarizable center by a parabolic restraint potential. The separation is calculated in response to the instantaneous electric field. We parametrized two models which are based on noniterative and self-consistent versions of the method, respectively. We computed several liquid-phase and gas-phase properties and compared with data available from experiment and ab initio calculations. The condensed-phase properties of both models are in reasonable accord with experiment, apart from discrepancies in electrostatic properties consistent with a slightly too large liquid-state dipole.

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The properties of two improved versions of charge-on-spring �COS� polarizable water models (COS/G2 and COS/G3) that explicitly include nonadditive polarization effects are reported. In COS models, the polarization is represented via a self-consistently induced dipole moment consisting of a pair of separated charges. A previous polarizable water model (COS/B2), upon which the improved versions are based, was developed by Yu, Hansson, and van Gunsteren �J. Chem. Phys. 118, 221 �2003��. To improve the COS/B2 model, which overestimated the dielectric permittivity, one additional virtual atomic site was used to reproduce the water monomer quadrupole moments besides the water monomer dipole moment in the gas phase. The molecular polarizability, residing on the virtual atomic site, and Lennard-Jones parameters for oxygen-oxygen interactions were varied to reproduce the experimental values for the heat of vaporization and the density of liquid water at room temperature and pressure. The improved models were used to study the properties of liquid water at various thermodynamic states as well as gaseous water clusters and ice. Overall, good agreement is obtained between simulated properties and those derived from experiments and ab initio calculations. The COS/G2 and COS/G3 models may serve as simple, classical, rigid, polarizable water models for the study of organic solutes and biopolymers. Due to its simplicity, COS type of polarization can straightforwardly be used to introduce explicit polarization into (bio)molecular force fields. The properties of two improved versions of charge-on-spring ͑COS͒ polarizable water models (COS/G2 and COS/G3) that explicitly include nonadditive polarization effects are reported. In COS models, the polarization is represented via a self-consistently induced dipole moment consisting of a pair of separated charges. A previous polarizable water model (COS/B2), upon which the improved versions are based, was developed by Yu, Hansson, and van Gunsteren ͓J. Chem. Phys. 118, 221 ͑2003͔͒. To improve the COS/B2 model, which overestimated the dielectric permittivity, one additional virtual atomic site was used to reproduce the water monomer quadrupole moments besides the water monomer dipole moment in the gas phase. The molecular polarizability, residing on the virtual atomic site, and Lennard-Jones parameters for oxygen-oxygen interactions were varied to reproduce the experimental values for the heat of vaporization and the density of liquid water at room temperature and pressure. The improved models were used to study the properties of liquid water at various thermodynamic states as well as gaseous water clusters and ice. Overall, good agreement is obtained between simulated properties and those derived from experiments and ab initio calculations. The COS/G2 and COS/G3 models may serve as simple, classical, rigid, polarizable water models for the study of organic solutes and biopolymers. Due to its simplicity, COS type of polarization can straightforwardly be used to introduce explicit ...

Phosphate chemistry is involved in many key biological processes yet the underlying mechanism often remains unclear. For theoretical analysis to effectively complement experimental mechanistic analysis, it is essential to develop computational methods that can capture the complexity of the underlying potential energy surface and allow for sufficient sampling of the configurational space. To this end, we report the parameterization of an approximate density functional theory, SelfConsistent-Charge Density-Functional Tight-Binding (SCC-DFTB) method for systems containing phosphorus. Compared to high-level density functional theory and ab initio (MP2 and G3B3) results, the standard second-order parameterization is shown to give reliable structures for a diverse set of phosphate compounds but inaccurate energetics. With the on-site third-order terms included, referred to as SCC-DFTBPA, calculated proton affinities of phosphate compounds are substantially improved, although it remains difficult to obtain reliable proton affinity for both phosphates and compounds that do not contain phosphorus, indicating that further improvement in the formulation of SCC-DFTB is still a challenge to meet. To make SCC-DFTB applicable to phosphate reactions in the current (on-site-third-order-only) formulation, a "reaction-specific" parameterization, referred to as SCC-DFTBPR, is developed based on hydrolysis reactions of model phosphate species. Benchmark calculations in both the gas-phase and solution-phase indicate that SCC-DFTBPR gives reliable structural properties and semi-quantitative energetics for phosphate hydrolysis reactions. Since the number of reaction-specific parameters is small, it is likely that SCC-DFTBPR is applicable to a broad set of phosphate species. Indeed, for 56 reaction exothermicities and 47 energy barriers related to RNA catalysis model reactions collected from the QCRNA database, which involve molecules rather different from those used to parameterize SCC-DFTBPR, the corresponding rootmean-square difference between SCC-DFTBPR and high-level DFT results is only 5.3 kcal/mol. We hope that the parameterized SCC-DFTB models will complement NDDO based reaction-specific models (e.g., AM1-d/PhoT) and high-level ab initio QM/MM methods in better understanding the mechanism of phosphate chemistry in condensed phase, particularly biological systems.