Molecular orientations at interfaces by extended polarizable continuum model

This study presents an investigation into orientation of molecular solutes at the interface of liquid water and other media. The calculation of electrostatic free energy of molecular solute is based on an extension of the polarizable continuum model (PCM) to interfacial system. The extended PCM computational scheme is incorporated with the self‐consistent field procedure which is necessary to obtain more accurate electrostatic free energy and charge density distribution. The computation of non‐electrostatic energy for interfacial system is also realized. Applying the numerical procedure to molecular systems, N,N′‐diethyl‐p‐nitroaniline (DEPNA) at air/water interface and p‐nitrophenol (PNP) at cyclohexane/water interface, the average orientational angles are in reasonable agreement with the experimental results. Taking both the electrostatic and the non‐electrostatic energies into account, the analysis on the energy profiles shows that the electrostatic solvation energy is the dominant factor in determining the orientation angle for PNP, whereas for DEPNA, the orientation angle mainly depends on the cavitation energy. This suggests that, in addition to the electrostatic energy, taking the cavitation energy into account may provide a more complete view when we survey the molecular orientation at interface. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Quantum chemical model of solvation for calculation of electrode potentials of redox processes involving ferrocene,cobaltocene, and their ions

Quantum chemical calculations of solvation energy for ferrocene and cobaltocene molecules and their ionic forms in water, acetonitrile, methanol, and acetone are performed in terms of the B3LYP density functional method by taking into account solvation effects and using the polarized continuum model (PCM). Standard electrode potentials of the corresponding redox pairs, the effect of solvent on them, and the overall energy of the transfer of cobaltocene cation and anion between two solvents are calculated. The calculation results well agree with the available experimental data. The present study provides sufficiently reliable grounds for the application of an ion—metallocene molecule redox pair as a pilot system for the comparison of electrode potentials and solvation energies in different solvents.     

丙酮分子n→π%*跃迁光谱的平均溶剂静电势/分子动力学方法研究

采用量子力学/分子动力学方法研究了具体溶剂分子结构对溶质光谱行为的静电影响. 通过拟合溶质所处外电场和引入溶剂分子极化率, 考虑了溶质溶剂分子之间的相互极化效应, 得到合理的溶质和溶剂分子的电荷分布. 经过严格推导发现, 在传统的显溶剂模型中, 平衡和非平衡溶剂化能表达式均未考虑溶剂分子永久偶极弹簧能的贡献. 因此, 在正确计算永久偶极弹簧能的基础上, 重新建立了溶剂化能的表达式和新的吸收/发射光谱移动公式. 采用修改后的ASEP/MD程序, 计算得到了与实验值比较吻合的丙酮在水溶液中n→π*跃迁的光谱移动值, 验证了新公式的合理性.     

Exploiting graphical processing units to enable quantum chemistry calculation of large solvated molecules with conductor-like polarizable continuum models

The conductor-like polarizable continuum model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in quantum chemistry. We have previously implemented C-PCM solvation for Hartree-Fock (HF) and density functional theory (DFT) on graphical processing units (GPUs), enabling the quantum mechanical treatment of large solvated biomolecules. Here, we first propose a GPU-based algorithm for the PCM conjugate gradient linear solver that greatly improves the performance for very large molecules. The overhead for PCM-related evaluations now consumes less than 15% of the total runtime for DFT calculations on large molecules. Second, we demonstrate that our algorithms tailored for ground state C-PCM are transferable to excited state properties. Using a single GPU, our method evaluates the analytic gradient of the linear response PCM time-dependent density functional theory energy up to 80× faster than a conventional central processing unit (CPU)-based implementation. In addition, our C-PCM algorithms are transferable to other methods that require electrostatic potential (ESP) evaluations. For example, we achieve speed-ups of up to 130× for restricted ESP-based atomic charge evaluations, when compared to CPU-based codes. We also summarize and compare the different PCM cavity discretization schemes used in some popular quantum chemistry packages as a reference for both users and developers.     

Quantum chemical study of solvent and substituent effects on the 1,5-hydride shift in 2,6-dimethyl-2-heptyl cations

The mechanism of the degenerate 1,5-hydride shift in 2,6-dimethyl-2-heptyl cations has been investigated using ab initio MP2 and density functional theory (DFT) hybrid (B3LYP) calculations. The potential-energy profile for the 1,5-hydride shift consists of three minima corresponding to two equivalent acyclic carbocations and one symmetrically mu-hydrido-bridged carbocation, while two equivalent unsymmetrically hydrido-bridged carbocations were located as transition-state structures. The calculated relative energy differences between acyclic carbocations and symmetrically mu-hydrido-bridged structure are significantly affected by introduction of alkyl and (CH2)n-substituents at the C4 position of the 2,6-dimethyl-2-heptyl cation structure. DFT self-consistent isodensity polarizable continuum method (SCI-PCM) and MP2 PCM continuum methods have been used to calculate the effect of solvation on geometries and relative energies of the species involved in the 1,5-hydride shift. It is found that relative energies of acyclic and mu-hydrido-bridged carbocation structures as well as the energy barriers for 1,5-hydride shifts are in accord with experimental data if solvation effects are taken into account.     

Vibrational study of fluorobenzene and its solvation with methanol via polarized Raman measurements and quantum chemical calculations

Raman spectra of neat fluorobenzene (C₆H₅F, FB) and its binary mixtures with methanol (CH₃OH, M) at varying mole fractions of FB from 0.1 to 0.9 were recorded in order to understand the influence of intermolecular interaction on spectral features corresponding to some selected vibrational bands of FB in the region 1200-450 cm⁻¹. Only few vibrational bands of fluorobenzene show a significant change in their peak position in going from neat liquid to the complexes. The 803, 829 and 994 cm⁻¹ bands show blue shift upon complexation which indicates significant amount of charge transfer between the reference molecule and the solvent. However, the linewidths do not show any appreciable change. Density functional theory (DFT) calculations were performed employing B3LYP method and high level basis set 6-311++G(d,p) to obtain the ground state geometry of neat FB and its hydrogen bonded complexes with methanol in gas phase. In order to account for the solvent effect and also to realize a condition quite close to the experiment, polarizable continuum model (PCM) calculations considering bulk solvation as well as explicit (specific plus bulk) solvation approaches were also performed. A detailed vibrational assignment of the various normal modes has been performed on the basis of potential energy distribution (PED) calculations. Depolarization ratios for the different vibrational bands were calculated and the values match nicely with the depolarization ratio determined from the experimental data.     

Solvation of ferrocene,cobaltocene, and their ions by the data of quantum-chemical calculations

Quantum-chemical calculations of solvation energy for ferrocene and cobaltocene molecules and their ionic forms in water, acetonitrile, methanol, acetone, and dimethylsulfoxide are performed in terms of the density functional method of the B3LYP type, taking into account the effect of solvent and using the Polarized Continuum Model (PCM). It is shown that the optimization of metallocene structure in liquid introduces only slight quantitative changes as compared with the data calculated for the structures optimized in the gas phase. It is shown that earlier observed deviation of experimental redox potentials of cobaltocene system in dimethylsulfoxide from the regularities of continuum electrostatics is caused by a stronger effect of this solvent on the distribution of electron density over the molecule of dissolved substance.     

Theoretical studies of 31P NMR spectral properties of phosphanes and related compounds in solution

Selected theoretical methods, basis sets and solvation models have been tested in their ability to predict (31)P NMR chemical shifts of large phosphorous-containing molecular systems in solution. The most efficient strategy was found to involve NMR shift calculations at the GIAO-MPW1K/6-311++G(2d,2p)//MPW1K/6-31G(d) level in combination with a dual solvation model including the explicit consideration of single solvent molecules and a continuum (PCM) solvation model. For larger systems it has also been established that reliable (31)P shift predictions require Boltzmann averaging over all accessible conformations in solution.     

Electronic g-tensors of solvated molecules using the polarizable continuum model

We present the implementation of density functional response theory combined with the polarizable continuum model (PCM), enabling first principles calculations of molecular g-tensors of solvated molecules. The calculated g-tensor shifts are compared with experimental g-tensor shifts obtained from electron paramagnetic resonance spectra for a few solvated species. The results indicate qualitative agreement between the calculations and the experimental data for aprotic solvents, whereas PCM fails to reproduce the electronic g-tensor behavior for protic solvents. This failure of PCM for protic solvents can be resolved by including into the model those solvent molecules which are involved in hydrogen bonding with the solute. The results for the protic solvents show that the explicit inclusion of the solvent molecules of the first solvation sphere is not sufficient in order to reproduce the behavior of the electronic g-tensor in protic solvents, and that better agreement with experimental data can be obtained by including the long-range electrostatic effects accounted for by the PCM approach on top of the explicit hydrogen-bonded complexes.     

Spectral shift of the n → π* transition for acetone and formic acid with an explicit solvent model

In our recent work, a new form of the electrostatic solvation energy for the nonequilibrium polarization has been derived by introducing the method of constrained equilibrium state in the framework of continuous medium theory. Up until now, the idea of the constrained equilibrium state method has not been introduced into the explicit solvent model by others; therefore this nonequilibrium energy form was further equivalently extended to the explicit solvent model in this work based on the discrete representation of the solvent permanent charges and induced dipoles. Making use of this expression in explicit solvent model, we modified the nonequilibrium module in the averaged solvent electrostatic potential/molecular dynamics program to implement numerical calculations. Subsequently, the new codes were applied to study the solvatochromic shifts of the n → π* absorption spectra for acetone and trans-formic acid in aqueous solution. The calculation results show a good agreement with the experimental observations. When our results of spectral shift are compared with those achieved directly from the continuum model, it can be seen that both the explicit solvent model and continuum model derived based on the constrained equilibrium approach can give reasonable predictions. The hydrogen bond effect was also discussed and deemed to be a dominant contribution to the spectral shift by calculating the n → π* absorption spectra of acetone-water complexes.     

Quantum-Chemical Study of the Electronic Structure of the Complex Ions [Ru(NH3)5pyz]2 + and [Ru(CN)5pyz]3 - in Solution

The hydration shell of the complex ions [Ru(NH₃)₅pyz]^{2 +} and [Ru(CN)₅pyz]^{3 -} was simulated on the basis of ab initio Hartree-Fock calculations in the supermolecular approximation, within the framework of the multicavity polarizable continuum model. In calculations of the spectral characteristics of complexes with a pronounced nonuniformity of electron density distribution, it is primarily necessary to take into account the shift of energy levels of particular fragments under the action of the electrostatic potential produced by the solvation surrounding. Consideration of the charge transfer between the complex and the outer-sphere water molecules has no significant effect on the calculated electronic spectrum; the transferred electron density is below 1e.     

Efficient and accurate solvation energy calculation from polarizable continuum models

A new approach is proposed to enhance the efficiency and accuracy for calculation of the long-range electrostatic interaction from implicit solvation models, i.e., the polarizable continuum model (PCM) and its variants, conductorlike PCM/conductorlike screening model and integral equation formalism PCM. In these methods the solvent electrostatics effects are represented by a set of discrete apparent charges distributed on tesserae of the molecular cavity surface embedding the solute. In principle, the accuracy of these methods is improved if the cavity surface is tessellated to finer tesserae; however, the computational time is increased rapidly. We show that such undesired dependency between accuracy and efficiency is a result of the inaccurate treatment of the apparent charge self-contribution to the potential and/or electric field. By taking into account the full effects due to the size and curvature of the segment occupied by each apparent charge, the error in calculated electrostatic solvation free energy is essentially zero for ions (point charge at the center of a sphere) regardless of the degree of tessellation used. For molecules where gradient of apparent charge density is nonzero at the cavity surface, we propose a multiple-sampling technique which significantly lowers the calculated error compared to the original PCM methods, especially when very few numbers of tesserae are used.     

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.     

Theoretical studies on the effects of methods and parameterization on the calculated free energy of hydration for small molecules

Free energies of hydration (FEH) have been computed for 13 neutral and nine ionic species as a difference of theoretically calculated Gibbs free energies in solution and in the gas phase. In‐solution calculations have been performed using both SCIPCM and PCM polarizable continuum models at the density functional theory (DFT)/B3LYP and ab initio Hartree–Fock levels with two basis sets (6‐31G* and 6‐311++G**). Good linear correlation has been obtained for calculated and experimental gas‐phase dipole moments, with an increase by ～30% upon solvation due to solute polarization. The geometry distortion in solution turns out to be small, whereas solute polarization energies are up to 3 kcal/mol for neutral molecules. Calculation of free energies of hydration with PCM provides a balanced set of values with 6‐31G* and 6‐311++G** basis sets for neutral molecules and ionic species, respectively. Explicit solvent calculations within Monte Carlo simulations applying free energy perturbation methods have been considered for 12 neutral molecules. Four different partial atomic charge sets have been studied, obtained by a fit to the gas‐phase and in‐solution molecular electrostatic potentials at in‐solution optimized geometries. Calculated FEH values depend on the charge set and the atom model used. Results indicate a preference for the all‐atom model and partial charges obtained by a fit to the molecular electrostatic potential of the solute computed at the SCIPCM/B3LYP/6‐31G* level. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Coupled cluster theory with the polarizable continuum model of solvation

The environment may significantly affect molecular properties. Thus, it is desirable to account explicitly for these effects on the wave function and its derivatives, especially when the latter are evaluated with accurate methods, such as those belonging to coupled cluster (CC) theory. In this tutorial review, we discuss how to combine CC methods with the polarizable continuum model of solvation (PCM). We describe useful approximations that include the solvent response to the correlation and excited state equations while maintaining the computational cost comparable to in vacuo calculations. Although applied to PCM, the theoretical framework presented in this review is general and can be used with any polarizable embedding model. Representative applications of the CC-PCM method to ground and excited state properties of solvated molecules are presented, and comparisons with experiment, and between the full and approximate schemes are discussed.     

Peculiarities of the environmental influence on the optical properties of push-pull nonlinear optical molecules: a theoretical study

Gas-phase geometry optimization of NLO-active molecules is one of the standard approaches in the first principle computational methodology, whereas the important role of the environment is usually not considered during the evaluation of structural parameters. With a wide variety of environmentally influenced models in most cases only the high quality single point calculations are prepared. Among different approaches, the most used polarizable continuum model (PCM) seems to be promising. In this study, we have compared the electronic properties of gas-phase optimized geometries of imidazole-derived push-pull compounds with those optimized using PCM solvation approach including CH(2)Cl(2) and PMMA as media. We have focused particularly on the linear optical properties of investigated molecules, namely on the UV-vis absorption spectra. The analysis of presented results shows the applicability of the different quantum chemical (QC) methods for the UV-vis spectra calculations of linear NLO molecules. Herein we also present the need of molecule geometry optimization affected by the environment. Following the performed calculations, the electronic properties of gas-phase optimized molecules give conformable results with respect to those obtained by more time-consuming continuum optimizations. All computational data are supported by experimental investigations.     

Building cavities in a fluid of spherical or rod-like particles: a contribution to the solvation free energy in isotropic and anisotropic polarizable continuum model

A general formalism for the calculation of cavitation energies in the framework of the scaled particle theory has been implemented in the Polarizable Continuum Model (PCM), contributing to the nonelectrostatic part of the molecular free energy in solution. The solute cavity and the solvent molecules are described as hard spherocylinders, whose radius and length are related to the actual molecular shape, while the solvent density is estimated from experimental data, or from the solvent molecular volume, suitably scaled. The present model can describe isotropic solutions of spherical and rod-like molecules in spherical or rod-like solvents, and also anisotropic solutions in which the solvent molecules are oriented in space: in this case, the cavitation energy also depends on the relative orientation of solute and solvent molecules. Test calculations have been performed on simple systems to evaluate the accuracy of the present approach, in comparison with other methods and with the available experimental estimates of the cavitation energy, giving encouraging results.     

First-principles calculation of pKa for cocaine, nicotine, neurotransmitters, and anilines in aqueous solution

The absolute pKa values of 24 representative amine compounds, including cocaine, nicotine, 10 neurotransmitters, and 12 anilines, in aqueous solution were calculated by performing first-principles electronic structure calculations that account for the solvent effects using four different solvation models, i.e., the surface and volume polarization for electrostatic interaction (SVPE) model, the standard polarizable continuum model (PCM), the integral equation formalism for the polarizable continuum model (IEFPCM), and the conductor-like screening solvation model (COSMO). Within the examined computational methods, the calculations using the SVPE model lead to the absolute pKa values with the smallest root-mean-square-deviation (rmsd) value (1.18). When the SVPE model was replaced by the PCM, IEFPCM, and COSMO, the rmsd value of the calculated absolute pKa values became 3.21, 2.72, and 3.08, respectively. All types of calculated pKa values linearly correlate with the experimental pKa values very well. With the empirical corrections using the linear correlation relationships, the theoretical pKa values are much closer to the corresponding experimental data and the rmsd values become 0.51-0.83. The smallest rmsd value (0.51) is also associated with the SVPE model. All of the results suggest that the first-principles electronic structure calculations using the SVPE model are a reliable approach to the pKa prediction for the amine compounds.