The isotropic nuclear magnetic shielding constants of acetone in supercritical water: a sequential Monte Carlo/quantum mechanics study including solute polarization

The nuclear isotropic shielding constants sigma((17)O) and sigma((13)C) of the carbonyl bond of acetone in water at supercritical (P=340.2 atm and T=673 K) and normal water conditions have been studied theoretically using Monte Carlo simulation and quantum mechanics calculations based on the B3LYP6-311++G(2d,2p) method. Statistically uncorrelated configurations have been obtained from Monte Carlo simulations with unpolarized and in-solution polarized solute. The results show that solvent effects on the shielding constants have a significant contribution of the electrostatic interactions and that quantitative estimates for solvent shifts of shielding constants can be obtained modeling the water molecules by point charges (electrostatic embedding). In supercritical water, there is a decrease in the magnitude of sigma((13)C) but a sizable increase in the magnitude of sigma((17)O) when compared with the results obtained in normal water. It is found that the influence of the solute polarization is mild in the supercritical regime but it is particularly important for sigma((17)O) in normal water and its shielding effect reflects the increase in the average number of hydrogen bonds between acetone and water. Changing the solvent environment from normal to supercritical water condition, the B3LYP6-311++G(2d,2p) calculations on the statistically uncorrelated configurations sampled from the Monte Carlo simulation give a (13)C chemical shift of 11.7+/-0.6 ppm for polarized acetone in good agreement with the experimentally inferred result of 9-11 ppm.     

A sequential molecular mechanics/quantum mechanics study of the electronic spectra of amides

We report gas-phase electronic spectra of formamide, N-methyformamide, acetamide, and N-methylacetamide at 300 K calculated using a combination of classical molecular dynamics and time-dependent density functional theory (TDDFT). In comparison to excitation energies computed using the global minima structures, the valence npi* and pi(nb)pi* states show a significant red-shift of 0.1-0.35 eV, while smaller shifts are found for the n3s and pi(nb)3s Rydberg states. In this work, we have identified the physical origin of these shifts arising from variations of the molecular structure. We present simple relationships between key geometrical parameters and spectral shifts. Consequently, electronic spectra can be generated directly from ground-state structures, without additional quantum chemical calculations. The electronic spectrum of formamide in aqueous solution is computed using TDDFT using an explicit solvent model. This provides a quantitative determination of the condensed-phase spectrum. In general, this study shows that temperature effects can change the predicted excitation energies significantly and demonstrates how electronic spectra at elevated temperatures can be computed in a computationally efficient way.     

Structure and electronic properties of hydrated mesityl oxide: a sequential quantum mechanics/molecular mechanics approach

The hydration of mesityl oxide (MOx) was investigated through a sequential quantum mechanics/molecular mechanics approach. Emphasis was placed on the analysis of the role played by water in the MOx syn–anti equilibrium and the electronic absorption spectrum. Results for the structure of the MOx–water solution, free energy of solvation and polarization effects are also reported. Our main conclusion was that in gas-phase and in low-polarity solvents, the MOx exists dominantly in syn-form and in aqueous solution in anti-form. This conclusion was supported by Gibbs free energy calculations in gas phase and in-water by quantum mechanical calculations with polarizable continuum model and thermodynamic perturbation theory in Monte Carlo simulations using a polarized MOx model. The consideration of the in-water polarization of the MOx is very important to correctly describe the solute–solvent electrostatic interaction. Our best estimate for the shift of the π–π^* transition energy of MOx, when it changes from gas-phase to water solvent, shows a red-shift of −2,520 ± 90 cm⁻¹, which is only 110 cm⁻¹ (0.014 eV) below the experimental extrapolation of −2,410 ± 90 cm⁻¹. This red-shift of around −2,500 cm⁻¹ can be divided in two distinct and opposite contributions. One contribution is related to the syn → anti conformational change leading to a blue-shift of ~1,700 cm⁻¹. Other contribution is the solvent effect on the electronic structure of the MOx leading to a red-shift of around −4,200 cm⁻¹. Additionally, this red-shift caused by the solvent effect on the electronic structure can by composed by approximately 60 % due to the electrostatic bulk effect, 10 % due to the explicit inclusion of the hydrogen-bonded water molecules and 30 % due to the explicit inclusion of the nearest water molecules.     

Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model

A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By separating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described.     

Polarization energy gradients in combined quantum mechanics, effective fragment potential, and polarizable continuum model calculations

A method that combines quantum mechanics (QM), typically a solute, the effective fragment potential (EFP) discrete solvent model, and the polarizable continuum model is described. The EFP induced dipoles and polarizable continuum model (PCM) induced surface charges are determined in a self-consistent fashion. The gradients of these two energies with respect to molecular coordinate changes are derived and implemented. In general, the gradients can be formulated as simple electrostatic forces and torques among the QM nuclei, electrons, EFP static multipoles, induced dipoles, and PCM induced charges. Molecular geometry optimizations can be performed efficiently with these gradients. The formulas derived for EFPPCM can be generally applied to other combined molecular mechanics and continuum methods that employ induced dipoles and charges.     

Structure and ultrafast dynamics of liquid water: a quantum mechanics/molecular mechanics molecular dynamics simulations study

A quantum mechanics/molecular mechanics molecular dynamics simulation was performed for liquid water to investigate structural and dynamical properties of this peculiar liquid. The most important region containing a central reference molecule and all nearest surrounding molecules (first coordination shell) was treated by Hartree-Fock (HF), post-Hartree-Fock [second-order Moller-Plesset perturbation theory (MP2)], and hybrid density functional B3LYP [Becke's three parameter functional (B3) with the correlation functional of Lee, Yang, and Parr (LYP)] methods. In addition, another HF-level simulation (2HF) included the full second coordination shell. Site to site interactions between oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen atoms of all ab initio methods were compared to experimental data. The absence of a second peak and the appearance of a shoulder instead in the gO-O graph obtained from the 2HF simulation is notable, as this feature has been observed so far only for pressurized or heated water. Dynamical data show that the 2HF procedure compensates some of the deficiency of the HF one-shell simulation, reducing the difference between correlated (MP2) and HF results. B3LYP apparently leads to too rigid structures and thus to an artificial slow down of the dynamics.     

Nuclear magnetic shielding constants of liquid water: insights from hybrid quantum mechanics/molecular mechanics models

We present a gauge-origin independent method for the calculation of nuclear magnetic shielding tensors of molecules in a structured and polarizable environment. The method is based on a combination of density functional theory (DFT) or Hartree-Fock wave functions with molecular mechanics. The method is unique in the sense that it includes three important properties that need to be fulfilled in accurate calculations of nuclear magnetic shielding constants: (i) the model includes electron correlation effects, (ii) the model uses gauge-including atomic orbitals to give gauge-origin independent results, and (iii) the effect of the environment is treated self-consistently using a discrete reaction-field methodology. The authors present sample calculations of the isotropic nuclear magnetic shielding constants of liquid water based on a large number of solute-solvent configurations derived from molecular dynamics simulations employing potentials which treat solvent polarization either explicitly or implicitly. For both the (17)O and (1)H isotropic shielding constants the best predicted results compare fairly well with the experimental data, i.e., they reproduce the experimental solvent shifts to within 4 ppm for the (17)O shielding and 1 ppm for the (1)H shielding.     

Solvent effects on the UV-visible absorption spectrum of benzophenone in water: a combined Monte Carlo quantum mechanics study including solute polarization

The entire ultraviolet-visible absorption spectrum of benzophenone in water is studied and compared with the same spectrum in gas phase. Five transitions are considered, and the corresponding solvatochromic shifts are obtained and compared to experiment. Using a sequential procedure of Monte Carlo simulations and quantum mechanical calculations, liquid configurations were generated and an averaged spectrum of the solution was calculated. The solute polarization was included by an iterative procedure where the atomic charges of the solute were obtained as an average with the solvent distribution. The calculated average dipole moment of benzophenone in water, with MP26-31++G(d,p), converges to the value of 5.84+/-0.05 D, 88% larger than the gas-phase value of 3.11 D. Using 100 statistically uncorrelated configurations and solvation shells with 235 explicit water molecules selected by a minimum-distance distribution of solvent shells, instead of the usual radial distribution, the excitation energies were obtained from solute-solvent all-valence-electron INDO/CIS calculations. The shift of the weak n-pi(*) transition is obtained as 2045+/-40 cm(-1) and the strong and broad pi-pi(*) shift as -1790+/-30 cm(-1). These results are in good agreement with the experimental values of 2200 and -1600 cm(-1), respectively. Standard procedure used by common force fields to generate atomic charges to describe the electrostatic moments of the solute, with HF6-31G(d), gives a dipole moment of 3.64 D. Using these standard charges in the simulation, the average shifts are calculated as 1395+/-35 and -1220+/-25 cm(-1), both about 600 cm(-1) smaller in magnitude than those obtained with the average converged fully polarized solute. The influence of the solute polarization in the solute-solvent interaction and, in particular, in solute-solvent hydrogen bonds is analyzed.     

Effective modeling of intrinsic and environmental effects on the structure and electron plaramagnetic resonance parameters of nitroxides by an integrated quantum mechanical/molecular mechanics/polarizable continuum model approach

 Experimental and density functional theory geometries have been used to extend the AMBER force field to nitroxides. An optimum set of transferable atomic charges for the calculation of electrostatic interactions both in vacuo and in aqueous solution has been obtained by averaging the charges obtained by a restrained electrostatic potential fitting of representative compounds. Besides reliable structural data, our implementation allows the computation of accurate spectromagnetic properties by single-point B3LYP computations on geometries optimized at the AMBER level. Solvent shifts in aqueous solution can be reproduced quantitatively by a mixed model in which specific solvent effects are described by two water molecules strongly coordinated to the nitroxide oxygen, while bulk effects are described by the polarizable continuum model. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 29 June 2000     

Geometry optimization of molecular structures in solution by the polarizable continuum model

A new implementation of analytical gradients for the polarizable continuum model is presented, which allows Hartree-Fock and density functional calculations taking into account both electrostatic and nonelectrostatic contributions to energies and gradients for closed and open shell systems. Simplified procedures neglecting the derivatives of the cavity surface and/or using single spheres for XH_n groups have also been implemented and tested. The solvent-induced geometry relaxation has been studied for a number of representative systems in order to test the efficiency of the procedure and to investigate the role of different contributions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 404–417, 1998     

Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

A combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a self-consistent scheme linear in the solvent polarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the density-functional theory (DFT) and the Hartree-Fock (HF) theory. Sample calculations presented for ground-state energies, first-order ground-state properties, excitation energies, first-order excited state properties, polarizabilities, first-hyperpolarizabilities, and two-photon absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to high-level theory, such as coupled-cluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for ground-state and first-order properties. However, to obtain such accuracy an exchange-correlation functional capable of describing the diffuse Rydberg states must be chosen.     

Binding of D- and L-captopril inhibitors to metallo-beta-lactamase studied by polarizable molecular mechanics and quantum mechanics

The bacterial Zn2+ metallo-beta-lactamase from B. fragilis is a zinc-enzyme with two potential metal ion binding sites. It cleaves the lactam ring of antibiotics, thus contributing to the acquired resistance of bacteria against antibiotics. The present study bears on the binuclear form of the enzyme. We compare several possible binding modes of captopril, a mercaptocarboxamide inhibitor of several zinc-metalloenzymes. Two diastereoisomers of captopril were considered, with either a D- or an L-proline residue. We have used the polarizable molecular mechanics procedure SIBFA (Sum of Interactions Between Fragments ab initio computed). Two beta-lactamase models were considered, encompassing 104 and 188 residues, respectively. The energy balances included the inter and intramolecular interaction energies as well as the contribution from solvation computed using a continuum reaction field procedure. The thiolate ion of the inhibitor is binding to both metal ions, expelling the bridging solvent molecule from the uncomplexed enzyme. Different competing binding modes of captopril were considered, either where the inhibitor binds in a monodentate mode to the zinc cations only with its thiolate ion, or in bidentate modes involving additional zinc binding by its carboxylate or ketone carbonyl groups. The additional coordination by the inhibitor's carboxylate or carbonyl group always occurs at the zinc ion, which is bound by a histidine, a cysteine, and an aspartate side chain. For both diastereomers, the energy balances favor monodentate binding of captopril via S-. The preference over bidentate binding is small. The interaction energies were recomputed in model sites restricted to captopril, the Zn2+ cations, and their coordinating end side chains from beta-lactamase (98 atoms). The interaction energies and their ranking among competing arrangements were consistent with those computed by ab initio HF and DFT procedures.     

Effective generation of molecular cavities in polarizable continuum model by DefPol procedure

A new computational strategy for the building of molecular cavities (named DefPol) has been linked to the most recent implementation of the polarizable continuum model (PCM) for the representation of solvent effects on physicochemical properties of large molecules. Free energies, analytical gradients, and Hessians can be computed in this framework in the rigid cavity approximation. Coupling DefPol cavities with a number of other recent improvements of the standard algorithm (e.g., effective use of symmetry, iterative procedures with linear scaling) significantly enlarges the dimensions of systems amenable to refined computations and strongly reduces the gap between computations for isolated molecules and in solution. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1693–1701, 1999     

Surface properties of the polarizable Baranyai-Kiss water model

The water surface properties using the Baranyai-Kiss (BK) model [A. Baranyai and P. T. Kiss, J. Chem. Phys. 133, 144109 (2010)] are studied by molecular dynamics simulation, and compared to popular rigid water potentials, namely to the extended simple point charge (SPC/E) and the transferable interaction potential with 4 points (TIP4P) models. The BK potential is a polarizable model of water with three Gaussian charges. The negative charge is connected to its field-free position by a classical harmonic spring, and mechanical equilibrium is established between this spring force and the force due to the charge distribution of the system. The aim of this study is, on the one hand, to test the surface properties of the new model, and on the other hand, to identify differences between the models listed above. The obtained results reveal that the BK model reproduces very well a number of properties corresponding to liquid-vapor equilibrium, such as the coexisting liquid and vapor densities, saturated vapor pressure or surface tension. Further, this model reproduces excellently the critical point of water even in comparison with a large number of widely used polarizable and nonpolarizable models. The structural properties of the liquid surface of BK water turns out to be very similar to that of the SPC/E model, while the surface of TIP4P water is found to be somewhat less ordered. This finding is related to the fact that the critical temperature of the TIP4P model is lower than that of either SPC/E or BK.     

Solvation of N3- at the water surface: the polarizable continuum model approach

We present a new quantum mechanical model to introduce Pauli repulsion interaction between a molecular solute and the surrounding solvent in the framework of the Polarizable Continuum Model. The new expression is derived in a way to allow naturally for a position-dependent solvent density. This development makes it possible to employ the derived expression for the calculation of molecular properties at the interface between two different dielectrics. The new formulation has been tested on the azide anion (N3-) for which we have calculated the solvation energy, the dipole moment, and the static polarizability at the interface as a function of the ion position. The calculations have been carried out for different ion-surface orientations, and the results have also been compared with the parallel electrostatic-only solvation model.     

Energy gradients in combined fragment molecular orbital and polarizable continuum model (FMO/PCM) calculation

The analytic energy gradients for the combined fragment molecular orbital and polarizable continuum model (FMO/PCM) method are derived and implemented. Applications of FMO/PCM geometry optimization to polyalanine show that the structures obtained with the FMO/PCM method are very close to those obtained with the corresponding full ab initio PCM methods. FMO/PCM (RHF/6‐31G* level) is used to optimize the solution structure of the 304‐atom Trp‐cage miniprotein and the result is in agreement with NMR experiments. The key factors determining the relative stability of the α‐helix, β‐turn and the extended form in solution are elucidated for polyalanine. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Quantum mechanics and mixed quantum mechanics/molecular mechanics simulations of model nerve agents with acetylcholinesterase

 The accurate modeling of biological processes presents major computational difficulties owing to the inherent complexity of the macromolecular systems of interest. Simulations of biochemical reactivity tend to require highly computationally intensive quantum mechanical methods, but localized chemical effects tend to depend significantly on properties of the extended biological environment – a regime far more readily examined with lower-level classical empirical models. Mixed quantum/classical techniques are gaining in popularity as a means of bridging these competing requirements. Here we present results comparing two quantum mechanics/molecular mechanics implementations (the SIMOMM technique of Gordon et al. as implemented in GAMESS, and the ONIOM technique of Morokuma et al. found in Gaussian 98) as performed on the enzyme acetylcholinesterase and model nerve agents. This work represents part of the initial phase of a DoD HPCMP Challenge project in which we are attempting to reliably characterize the biochemical processes responsible for nerve agent activity and inhibition, thereby allowing predictions on compounds unrelated to those already studied. Received: 10 October 2001 / Accepted: 13 November 2002 / Published online: 1 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: M. M. Hurley e-mail: hurley@arl.army.mil