Parallel variable selection of molecular dynamics clusters as a tool for calculation of spectroscopic properties

Clusters of a solute and a few solvent molecules obtained from molecular dynamics (MD) are a powerful tool to study solvation effects by advanced quantum chemical (QC) methods. For spectroscopic properties strongly dependent on the solvation, however, a large number of clusters are needed for a good convergence. In this work, a parallel variable selection (PVS) method is proposed that in some cases efficiently reduces the number of clusters needed for the averaging. The mass, charge, or atomic density MD distributions are used as a secondary variable to preselect the most probable cluster geometries used for averaging of solute spectral properties. When applied to nuclear magnetic resonance chemical shift of a model alcohol, the method allowed one to significantly reduce the total computational time, by a factor of 10. Even larger savings were achieved for the modeling of Raman and Raman optical activity spectra of (S)‐lactamide molecule dissolved in water. The results thus suggest that the PVS method can be generally used for simulations of spectroscopic properties of solvated molecules and makes multiscale MD/QC computations more affordable. © 2012 Wiley Periodicals, Inc.     

Solution reaction space Hamiltonian based on an electrostatic potential representation of solvent dynamics

Quantum chemical solvation models usually rely on the equilibrium solvation condition and is thus not immediately applicable to the study of nonequilibrium solvation dynamics, particularly those associated with chemical reactions. Here we address this problem by considering an effective Hamiltonian for solution-phase reactions based on an electrostatic potential (ESP) representation of solvent dynamics. In this approach a general ESP field of solvent is employed as collective solvent coordinate, and an effective Hamiltonian is constructed by treating both solute geometry and solvent ESP as dynamical variables. A harmonic bath is then attached onto the ESP variables in order to account for the stochastic nature of solvent dynamics. As an illustration we apply the above method to the proton transfer of a substituted phenol-amine complex in a polar solvent. The effective Hamiltonian is constructed by means of the reference interaction site model self-consistent field method (i.e., a type of quantum chemical solvation model), and a mixed quantum/classical simulation is performed in the space of solute geometry and solvent ESP. The results suggest that important dynamical features of proton transfer in solution can be captured by the present approach, including spontaneous fluctuations of solvent ESP that drives the proton from reactant to product potential wells.     

Stability of ion triplets in ionic liquid/lithium salt solutions: Insights from implicit and explicit solvent models and molecular dynamics simulations

Binding energies of ion triplets formed in ionic liquids by Li⁺ with two anions have been studied using quantum‐chemical calculations with implicit and explicit solvent supplemented by molecular dynamics (MD) simulations. Explicit solvent approach confirms variation of solute‐ionic liquid interactions at distances up to 2 nm, resulting from structure of solvation shells induced by electric field of the solute. Binding energies computed in explicit solvent and from the polarizable continuum model approach differ largely, even in sign, but relative values generally agree between these two models. Stabilities of ion triplets obtained in quantum‐chemical calculations for some systems disagree with MD results; the discrepancy is attributed to the difference between static optimized geometries used in quantum chemical modeling and dynamic structures of triplets in MD simulations. © 2015 Wiley Periodicals, Inc.     

Simulating the formation of sodium:electron tight-contact pairs: watching the solvation of atoms in liquids one molecule at a time

The motions of solvent molecules during a chemical transformation often dictate both the dynamics and the outcome of solution-phase reactions. However, a microscopic picture of solvation dynamics is often obscured by the concerted motions of numerous solvent molecules that make up a condensed-phase environment. In this study, we use mixed quantum/classical molecular dynamics simulations to furnish the molecular details of the solvation dynamics that leads to the formation of a sodium cation-solvated electron contact pair, (Na(+), e(-)), in liquid tetrahydrofuran following electron photodetachment from sodide (Na(-)). Our simulations reveal that the dominant solvent response is comprised of a series of discrete solvent molecular events that work sequentially to build up a shell of coordinating THF oxygen sites around the sodium cation end of the contact pair. With the solvent response described in terms of the sequential motion of single molecules, we are then able to compare the calculated transient absorption spectroscopy of the sodium species to experiment, providing a clear microscopic interpretation of ultrafast pump-probe experiments on this system. Our findings suggest that for solute-solvent interactions similar to the ones present in our study, the solvation dynamics is best understood as a series of kinetic events consisting of reactions between chemically distinct local structures in which key solvent molecules must be considered to be part of the identity of the reacting species.     

Computational Analysis of Solute–Solvent Coupling Magnitude in the Z/E Isomerization Reaction of Nitroazobenzene and Benzylideneanilines

The dynamic solvent effect often arises in solution reactions, where coupling between chemical reaction and solvent fluctuation plays a decisive role in the reaction kinetics. In this study, the Z/E isomerization reaction of nitoroazobenzene and benzylideneanilines in the ground state was computationally studied by molecular dynamics simulations. The non-equilibrium solvation effect was analyzed using two approaches: (1) metadynamics Gibbs energy surface exploration and (2) solvation Gibbs energy evaluation using a frozen solvation droplet model. The solute–solvent coupling parameter (C_coupled) was estimated by the ratio of the solvent fluctuation Gibbs energy over the corresponding isomerization activation Gibbs energy. The results were discussed in comparison with the ones estimated by means of the analytical models based on a reaction–diffusion equation with a sink term. The second approach using a frozen solvation droplet reached qualitative agreement with the analytical models, while the first metadynamics approach failed. This is because the second approach explicitly considers the non-equilibrium solvation in the droplet, which consists of a solute at the reactant geometry immersed in the pre-organized solvents fitted with the solute at the transition state geometry.     

Shells theory of solvation and the long-range Born correction

A new solvation model, named shells theory of solvation, is proposed. In this approach, the solvent is divided in two regions, the S₁ shell, close to the solute and describing specific solute–solvent interactions, and the S₂ shell, representing the remain solvent and accounting for the long-range interaction contribution. A simple theoretical equation can be derived which allows the computation of the solvation free energy using two-point thermodynamic integration and configurations generated from molecular dynamics simulation. The discrete/continuum version of this theory provides rigorous theoretical foundations for the popular long-range Born correction and presents a new reliable expression for including this contribution. Further, it converges to the full discrete representation of the solvent when the number of solvent molecules goes to infinity. The method can be easily applied when the solute–solvent interaction (S₁ shell) is treated by full quantum mechanics, while the S₂ shell is described by a dielectric continuum solvation method. A simple test of the theory was done for solvation of fluoride ion in benzene solution. The S₁ shell was composed of the fluoride ion plus 32 benzene molecules, and the interaction with the S₂ shell was calculated at Hartree–Fock level with the MINI basis set and using the polarizable continuum model.     

Solvent effects on NMR isotropic shielding constants. a comparison between explicit polarizable discrete and continuum approaches

The gas-to-aqueous solution shifts of the 17O and 13C NMR isotropic shielding constants for the carbonyl chromophore in formaldehyde and acetone are investigated. For the condensed-phase problem, we use the hybrid density functional theory/molecular mechanics approach in combination with a statistical averaging over an appropriate number of solute-solvent configurations extracted from classical molecular dynamics simulations. The PBE0 exchange-correlation functional and the 6-311++G(2d,2p) basis set are used for the calculation of the shielding constants. London atomic orbitals are employed to ensure gauge-origin independent results. The effects of the bulk solvent molecules are found to be crucial in order to calculate accurate solvation shifts of the shielding constants. Very good agreement between the computed and experimental solvation shifts is obtained for the shielding constants of acetone when a polarizable water potential is used. Supermolecular results based on geometry-optimized molecular structures are presented. We also compare the results obtained with the polarizable continuum model to the results obtained using explicit MM molecules to model the bulk solvent effect.     

Be2+在水、甲醇和乙醇中结构性质的从头算分子动力学模拟

采用Car-Parrinello分子动力学(CPMD)方法分别研究了Be²⁺在水、甲醇和乙醇中的溶剂结构性质, 并对Be²⁺的第一溶剂壳结构的实验及理论结果进行了比较. 所得第一溶剂壳结构与已报道的实验和理论结果较为一致. 对径向分布函数、配位数以及角度分布等进行了详细的分析. 结果表明: 在水、甲醇和乙醇中, Be²⁺第一溶剂壳为稳定理想的四面体结构. 在本文的模拟时间尺度内,没有观察到第一溶剂壳中的分子与第二溶剂壳中的分子进行交换, 进一步证明Be²⁺第一溶剂壳为稳定的四配位结构. 根据计算得到的空间分布函数, Be²⁺在溶剂分子的等高面上主要集中分布在溶剂分子接受氢键的方向. 根据氧原子在Be²⁺周围的分布, 壳层分子主要集中分布在Be²⁺周围的四个区域, 进一步证实溶剂壳为四面体对称.     

Molecular dynamics study of the tautomeric equilibrium in the 4-nitro- and 2,4,6-trichloro derivatives of 2-(N,N-dialkyloaminomethyl)phenol

 Molecular dynamics thermodynamic integration (MDTI) method and quantum chemical calculations at the density functional theory B3LYP 6-31+(d,p) level, which included the Tomasi model of the solvent reaction field, were applied to study the tautomeric equilibrium of Mannich base in methanol solution. The values obtained for the free-energy difference are in good agreement with experimental data. However, the results from quantum mechanical calculations were not as good as the results of MDTI simulations owing to inappropriate treatment of intermolecular hydrogen bonds between the solute molecule and the first shell of solvent molecules in the Tomasi model of the solvent reaction field. The radial distribution functions between solute atoms and solvent atoms confirmed the formation of hydrogen bonds between the solute molecule and surrounding methanol molecules and indicated that the zwitterionic form is associated more with an organized solvent structure at the level of the first solvation shell than is the molecular form. Received: 26 April 2002 / Accepted: 9 September 2002 / Published online: 31 March 2003     

A noniterative mean-field QM/MM-type approach with a linear response approximation toward an efficient free-energy evaluation

Mean-field treatment of solvent provides an efficient technique to investigate chemical processes in solution in quantum mechanics/molecular mechanics (QM/MM) framework. In the algorithm, an iterative calculation is required to obtain the self-consistency between QM and MM regions, which is a time-consuming step. In the present study, we have proposed a noniterative approach by introducing a linear response approximation (LRA) into the solvation term in the one-electron part of Fock matrix in a hybrid approach between molecular-orbital calculations and a three-dimensional (3D) integral equation theory for molecular liquids (multicenter molecular Ornstein–Zernike self-consistent field [MC-MOZ-SCF]; Kido et al., J. Chem. Phys. 2015, 143, 014103). To save the computational time, we have also developed a fast method to generate electrostatic potential map near solute and the solvation term in Fock matrix, using Fourier transformation (FT) and real spherical harmonics expansion (RSHE). To numerically validate the LRA and FT-RSHE method, we applied the present approach to water, carbonic acid, and their ionic species in aqueous solution. Molecular properties of the solutes were evaluated by the present approach with four different types of initial wave functions and compared with those by the original (MC-MOZ-SCF). We found that an initial wave function considering solvation effects is needed to appropriately reproduce the properties by MC-MOZ-SCF. Furthermore, a benchmark test for 32 solute molecules was performed to evaluate the accuracy of the present approach for solvation free energy (SFE) and measure the speedup ratio for MC-MOZ-SCF. The error of SFE for MC-MOZ-SCF does not correlate with the SFE but increases in proportion to the electronic reorganization energy. Similar to water and carbonic acid, an initial wave function with solvation effects is also important to make the error small. From the averaged speed up ratio, the present approach is 13.5 times faster than MC-MOZ-SCF. © 2019 Wiley Periodicals, Inc.     

Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies

Our previously developed approaches for integrating quantum mechanical molecular orbital methods with microscopic solvent models are refined and examined. These approaches consider the nonlinear solute–solvent coupling in a self-consistent way by incorporating the potential from the solvent dipoles in the solute Hamiltonian, while considering the polarization of the solvent by the potential from the solute charges. The solvent models used include the simplified Langevin Dipoles (LD) model and the much more expensive surface constrained All Atom Solvent (SCAAS) model, which is combined with a free energy pertubation (FEP) approach. Both methods are effectively integrated with the quantum mechanical AMPAC package and can be easily combined with other quantum mechanical programs. The advantages of the present approaches and their earlier versions over macroscopic reaction field models and supermolecular approaches are considered. A LD/MNDO study of solvated organic ions demonstrates that this model can yield reliable solvation energies, provided the quantum mechanical charges are scaled to have similar magnitudes to those obtained by high level ab initio methods. The incorporation of a field-dependent hydrophobic term in the LD free energy makes the present approach capable of evaluating the free energy of transfer of polar molecules from non polar solvents to aqueous solutions. The reliability of the LD approach is examined not only by evaluating a rather standard set of solvation energies of organic ions and polar molecules, but also by considering the stringent test case of sterically hindered hydrophobic ions. In this case, we compare the LD/MNDO solvation energies to the more rigorous FEP/SCAAS/MNDO solvation energies. Both methods are found to give similar results even in this challenging test case. The FEP/SCAAS/AMPAC method is incorporated into the current version of the program ENZYMIX. This option allows one to study chemical reactions in enzymes and in solutions using the MNDO and AM1 approximations. A special procedure that uses the EVB method as a reference potential for SCF MO calculations should help in improving the reliability of such studies.     

Elucidating Solvent Effects on Strong Intramolecular Hydrogen Bond: DFT-MD Study of Dibenzoylmethane in Methanol Solution

The dynamic aspect of solvation plays a crucial role in determining properties of strong intramolecular hydrogen bonds since solvent fluctuations modify instantaneous hydrogen-bonded proton transfer barriers. Previous studies pointed out that solvent-solute interactions in the first solvation shell govern the position of the proton but the ability of the electric field due to other solvent molecules to localize the proton remains an important issue. In this work, we examine the structure of the O−H⋅⋅⋅O intramolecular hydrogen bond of dibenzoylmethane in methanol solution by employing density functional theory-based molecular dynamics and quantum chemical calculations. Our computations showed that homogeneous electric fields with intensities corresponding to those found in polar solvents are able to considerably alter the proton transfer barrier height in the gas phase. In methanol solution, the proton position is correlated with the difference in electrostatic potentials on the oxygen atoms of dibenzoylmethane even when dibenzoylmethane-methanol hydrogen bonding is lacking. On a timescale of our simulation, the hydrogen bonding and solvent electrostatics tend to localize the proton on different oxygen atoms. These findings provide an insight into the importance of the solvent electric field on the structure of a strong intramolecular hydrogen bond.     

99Tc NMR as a promising technique for structural investigation of biomolecules: theoretical studies on the solvent and thermal effects of phenylbenzothiazole complex

The phenylbenzothiazole compounds show antitumor properties and are highly selective. In this paper, the ⁹⁹Tc chemical shifts based on the (^99mTc)(CO)₃(NNO) complex conjugated to the antitumor agent 2‐(4′‐aminophenyl)benzothiazole are reported. Thermal and solvent effects were studied computationally by quantum‐chemical methods, using the density functional theory (DFT) (DFT level BPW91/aug‐cc‐pVTZ for the Tc and BPW91/IGLO‐II for the other atoms) to compute the NMR parameters for the complex. We have calculated the ⁹⁹Tc NMR chemical shifts of the complex in gas phase and solution using different solvation models (polarizable continuum model and explicit solvation). To evaluate the thermal effect, molecular dynamics simulations were carried, using the atom‐centered density matrix propagation method at the DFT level (BP86/LanL2dz). The results highlight that the ⁹⁹Tc NMR spectroscopy can be a promising technique for structural investigation of biomolecules, at the molecular level, in different environments. Copyright © 2014 John Wiley & Sons, Ltd.     

New approach to free energy of solvation applying continuum models to molecular dynamics simulation

A new approach to the calculation of the free energy of solvation from trajectories obtained by molecular dynamics simulation is presented. The free energy of solvation is computed as the sum of three contributions originated at the cavitation of the solute by the solvent, the solute-solvent nonpolar (repulsion and dispersion) interactions, and the electrostatic solvation of the solute. The electrostatic term is calculated based on ideas developed for the broadly used continuum models, the cavitational contribution from the excluded volume by the Claverie-Pierotti model, and the Van der Waals term directly from the molecular dynamics simulation. The proposed model is tested for diluted aqueous solutions of simple molecules containing a variety of chemically important functions: methanol, methylamine, water, methanethiol, and dichloromethane. These solutions were treated by molecular dynamics simulations using SPC/E water and the OPLS force field for the organic molecules. Obtained free energies of solvation are in very good agreement with experimental data.     

An explicit quantum chemical method for modeling large solvation shells applied to aminocoumarin C151

The absorption spectra of aminocoumarin C151 in water and n-hexane solution are investigated by an explicit quantum chemical solvent model. We improved the efficiency of the frozen-density embedding scheme, as used in a former study on solvatochromism (J. Chem. Phys. 2005, 122, 094115) to describe very large solvent shells. The computer time used in this new implementation scales approximately linearly (with a low prefactor) with the number of solvent molecules. We test the ability of the frozen-density embedding to describe specific solvent effects due to hydrogen bonding for a small example system, as well as the convergence of the excitation energy with the number of solvent molecules considered in the solvation shell. Calculations with up to 500 water molecules (1500 atoms) in the solvent system are carried out. The absorption spectra are studied for C151 in aqueous or n-hexane solution for direct comparison with experimental data. To obtain snapshots of the dye molecule in solution, for which subsequent excitation energies are calculated, we use a classical molecular dynamics (MD) simulation with a force field adapted to first-principles calculations. In the calculation of solvatochromic shifts between solvents of different polarity, the vertical excitation energy obtained at the equilibrium structure of the isolated chromophore is sometimes taken as a guess for the excitation energy in a nonpolar solvent. Our results show that this is, in general, not an appropriate assumption. This is mainly due to the fact that the solute dynamics is neglected. The experimental shift between n-hexane and water as solvents is qualitatively reproduced, even by the simplest embedding approximation, and the results can be improved by a partial polarization of the frozen density. It is shown that the shift is mainly due to the electronic effect of the water molecules, and the structural effects are similar in n-hexane and water. By including water molecules, which might be directly involved in the excitation, in the embedded region, an agreement with experimental values within 0.05 eV is achieved.     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

Density functional theory for efficient ab initio molecular dynamics simulations in solution

We present a density functional for first-principles molecular dynamics simulations that includes the electrostatic effects of a continuous dielectric medium. It allows for numerical simulations of molecules in solution in a model polar solvent. We propose a smooth dielectric model function to model solvation into water and demonstrate its good numerical properties for total energy calculations and constant energy molecular dynamics.     

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3 kcal/mol, the hybrid approach yields an improved RMSD of 1.6 kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1 kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.