水溶液中铵离子pKa值的理论计算

在HF/6-31+G*和B3LYP/6-31+G*水平上, 采用导体极化连续模型(CPCM)及UAKS孔穴计算了11种铵离子在水溶剂中的溶剂化自由能, 与实验值相比较, 平均误差和标准偏差分别为0.17, 12.04和0.96, 10.96 kJ/mol. 结合B3LYP/6-31+G*水平上的11种铵离子气相质子转移反应自由能, 得到了水溶剂中的绝对pKa值, 计算结果与实验数据吻合得很好, 相应的平均误差和标准偏差分别为0.05, 1.50和0.45, 1.40 pKa单位. 可见, 采用CPCM-UAKS模型能够较为精确地计算铵离子型化合物的绝对pKa值.     

Theoretical calculation of the pKa values of some drugs in aqueous solution

In this work, calculations of pK_a values have been performed on benzoic acid and its para‐substituted derivatives and some drugs by using Gaussian 98 software package. Gas‐phase energies were calculated with HF/6‐31 G** and B3LYP/6‐31 G** levels of theory. Free energies of solvation have been computed using the polarizable continuum model (PCM), conductor‐like PCM (CPCM), and the integral equation formalism‐PCM at the same levels which have been used for geometry determination in the gas‐phase. The results that show the calculated pK_a values using the B3LYP are better than those using the corresponding HF. In comparison to the other models, the results obtained indicate that the PCM model is a suitable solvation model for calculating pK_a values. For the investigated compounds, a good agreement between the experimental and the calculated pK_a values was also observed. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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.     

Water solvent effects using continuum and discrete models: The nitromethane molecule,CH3NO2

The first three valence transitions of the two nitromethane conformers (CH₃NO₂) are two dark n → π* transitions and a very intense π → π* transition. In this work, these transitions in gas‐phase and solvated in water of both conformers were investigated theoretically. The polarizable continuum model (PCM), two conductor‐like screening (COSMO) models, and the discrete sequential quantum mechanics/molecular mechanics (S‐QM/MM) method were used to describe the solvation effect on the electronic spectra. Time dependent density functional theory (TDDFT), configuration interaction including all single substitutions and perturbed double excitations (CIS(D)), the symmetry‐adapted‐cluster CI (SAC‐CI), the multistate complete active space second order perturbation theory (CASPT2), and the algebraic‐diagrammatic construction (ADC(2)) electronic structure methods were used. Gas‐phase CASPT2, SAC‐CI, and ADC(2) results are in very good agreement with published experimental and theoretical spectra. Among the continuum models, PCM combined either with CASPT2, SAC‐CI, or B3LYP provided good agreement with available experimental data. COSMO combined with ADC(2) described the overall trends of the transition energy shifts. The effect of increasing the number of explicit water molecules in the S‐QM/MM approach was discussed and the formation of hydrogen bonds was clearly established. By including explicitly 24 water molecules corresponding to the complete first solvation shell in the S‐QM/MM approach, the ADC(2) method gives more accurate results as compared to the TDDFT approach and with similar computational demands. The ADC(2) with S‐QM/MM model is, therefore, the best compromise for accurate solvent calculations in a polar environment. © 2015 Wiley Periodicals, Inc.     

Structure, energetics, and electronic coupling in the (TCNE2)-* encounter complex in solution: a polarizable continuum study

For the prototypical dyad (TCNE2)-*, previous in vacuo calculations indicate that sizable distortion of the equilibrium gas-phase structure may be required to reduce the donor/acceptor electronic coupling element (HDA) to the solution-phase experimental estimates. We employ the polarizable continuum model (PCM) to simulate the solvation environment for several polar solvents, finding noticeable structure change associated with the promotion of charge localization due to solvation. We have extended the counterpoise (CP) correction procedure so as to include fragment relaxation energies within the PCM model, and it would be of interest to incorporate this approach into schemes for optimizing coordinates on CP-corrected energy surfaces. The calculations include face-to-face encounter geometries as well as several lateral and twist distortions of the face-to-face structures. In proceeding from vacuum to solution, the calculated stabilization energy is reduced from -18 to -3 kcal/mol, and the calculated energy surface becomes flatter, with a somewhat larger minimum-energy separation of the monomer units (rDA). The corresponding minimum-energy structures are, respectively, delocalized and charge-localized. Using TD-DFT, spin-projected MP2 (PUMP2), and state-averaged two-configuration SCF (SA-TCSCF) calculations to evaluate HDA for symmetric encounter complex geometries (models for transition-state structures) indicates that HDA has comparable magnitude in the gas phase and in solution for a given dimer structure. SA-TCSCF calculations comparing HDA based on symmetric charge-delocalized structures and their asymmetric (minimum-energy) charge-localized counterparts (at a given rDA) yield very similar values. Even with account taken of the energetically accessible configurations probed by the PCM calculations, the HDA values remain significantly higher than the experimental estimates inferred from solution spectra and assumption of rDA based on crystal data. Clearly, additional calculations based on molecular-level solvent models would be of value in helping to characterize the intermolecular structures accessible to the encounter complex in polar solution.     

基于全极化连续介质模型计算溶液分子的第一原理电子结构理论方法的发展和应用

This is a brief review of some recent progress in the development and application of first-principles electronic structure approaches for molecules in solution.In particular,it accounts for the background,theoretical features,and representative applications of a recently developed,truly accurate continuum solvation model which is known as Surface and Volume Polarization for Electrostatics(SVPE) or Fully Polarizable Continuum Model(FPCM) in literature.The FPCM-based first-principles electronic structure approaches have been widely employed to study a variety of chemical and biochemical problems and serve as an integrated part of various computational protocols for rational drug design.Some perspective of the future of the FPCM-based first-principles electronic structure approaches is also given.     

Electronic confinement effects on the reaction field type calculations of solvent effects

We analyze some procedures to introduce the effect of confining the electrons of the hydrogen atoms in cavitation spheres like those used in the self‐consistent reaction field models for studying the solvent influence on molecular properties [as polarizable continuum model (PCM), or conductor screening model (COSMO)]. We have found that the boundary conditions to be applied have an important effect on the system energy that by no means should be neglected in this type of calculations. We have found as well that “‐nG” expansion technique could be applicable in this kind of calculations (even at the very simple “‐3G” level) and lead us to a relatively simple form of applying the theory. Moreover, we have found a way to define the cavitation radius of PCM calculations, by minimizing the system energy with respect to this parameter, which could be a more satisfactory procedure—at least from a theoretical point of view—than the use of empirical values characteristic of most of the PCM or COSMO standard calculations. © 2013 Wiley Periodicals, Inc.     

Complexation reactions,electronic properties,and reactivity descriptors of cysteamine-based ligands in aqueous solution: a PCM/DFT study

Computational approaches based on density functional theory (DFT) combined with polarizable continuum model (PCM) of solvation have been used to probe the likelihood of complexation in water between oxo-vanadium(IV) and various medicinal cysteamine-based ligands. The experimental electronic spectra of a complex formed by oxo-vanadium(IV) and penicillamine in water agree well with the theoretical spectra based on the time-dependent density functional theory (TD-DFT) calculations. Among all density functionals adopted, CAM-B3LYP outperforms the others in predicting both structural and spectroscopic properties of oxo-transition metal complexes of cysteamine-based ligands. A variety of chelation behaviors have been found for the ligands tested, depending on the choice of substituent added to the cysteamine backbone. Solvation has a great impact on the thermodynamic driving force for cysteine and its derivatives to undergo complexation. In all cases, the thiolate sulfur atom forms stronger coordination bond than either the amine nitrogen or carboxylate oxygen atoms. Based on the thermodynamic and nucleophilicity index calculations, penicillamine has the highest potential to form complex with oxo-vanadium(IV).     

pKa calculations of aliphatic amines, diamines, and aminoamides via density functional theory with a Poisson-Boltzmann continuum solvent model

In order to make reliable predictions of the acid-base properties of macroligands with a large number of ionizable sites such as dendrimers, one needs to develop and validate computational methods that accurately estimate the acidity constants (pKa) of their chemical building blocks. In this article, we couple density functional theory (B3LYP) with a Poisson-Boltzmann continuum solvent model to calculate the aqueous pKa of aliphatic amines, diamines, and aminoamides, which are building blocks for several classes of dendrimers. No empirical correction terms were employed in the calculations except for the free energy of solvation of the proton (H+) adjusted to give the best match with experimental data. The use of solution-phase optimized geometries gives calculated pKa values in excellent agreement with experimental measurements. The mean absolute error is <0.5 pKa unit in all cases. Conversely, calculations for diamines and aminoamides based on gas-phase geometries lead to a mean absolute error >0.5 pKa unit compared to experimental measurements. We find that geometry optimization in solution is essential for making accurate pKa predictions for systems possessing intramolecular hydrogen bonds.     

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.     

Modeling ultrafast solvated electronic dynamics using time-dependent density functional theory and polarizable continuum model

A first-principles solvated electronic dynamics method is introduced. Solvent electronic degrees of freedom are coupled to the time-dependent electronic density of a solute molecule by means of the implicit reaction field method, and the entire electronic system is propagated in time. This real-time time-dependent approach, incorporating the polarizable continuum solvation model, is shown to be very effective in describing the dynamical solvation effect in the charge transfer process and yields a consistent absorption spectrum in comparison to the conventional linear response results in solution.     

Energies,structures, and electronic properties of molecules in solution with the C-PCM solvation model

The conductor-like solvation model, as developed in the framework of the polarizable continuum model (PCM), has been reformulated and newly implemented in order to compute energies, geometric structures, harmonic frequencies, and electronic properties in solution for any chemical system that can be studied in vacuo. Particular attention is devoted to large systems requiring suitable iterative algorithms to compute the solvation charges: the fast multipole method (FMM) has been extensively used to ensure a linear scaling of the computational times with the size of the solute. A number of test applications are presented to evaluate the performances of the method.     

Calculation of solvent shifts on electronic g-tensors with the conductor-like screening model (COSMO) and its self-consistent generalization to real solvents (direct COSMO-RS)

The conductor-like screening model (COSMO) was used to investigate the solvent influence on electronic g-values of organic radicals. The previously studied diphenyl nitric oxide and di-tert-butyl nitric oxide radicals were taken as test cases. The calculations employed spin-unrestricted density functional theory and the BP and B3LYP density functionals. The g-tensors were calculated as mixed second derivative properties with respect to the external magnetic field and the electron magnetic moment. The first-order response of the Kohn-Sham orbitals with respect to the external magnetic field was determined through the coupled-perturbed DFT approach. The spin-orbit coupling operator was treated using an accurate multicenter spin-orbit mean-field (SOMF) approach. Provided that important hydrogen bonds are explicitly modeled by a supermolecule approach and that the basis set is sufficiently saturated, the COSMO calculations lead to accurate predictions of isotropic g-shifts with deviations of not more than 100 ppm relative to experiment. Very accurate results were obtained by employing a recently developed self-consistent modification of the COSMO method to real solvents (COSMO-RS), which we briefly introduce in this paper as direct COSMO-RS (D-COSMO-RS). This model gives isotropic g-shifts of similar high accuracy for water without using the supermolecule approach. This is an important result because it solves many of the problems associated with the supermolecule approach such as local minima and the choice of a suitable model system. Thus, the self-consistent D-COSMO-RS incorporates some specific solvation effects into continuum models, in particular it appears to successfully model the effects of hydrogen bonding. Although not yet widely validated, this opens a novel approach for the calculation of properties which so far only could be calculated by the inclusion of explicit solvent molecules in continuum solvation methods.     

Charge-dependent cavity radii for an accurate dielectric continuum model of solvation with emphasis on ions: aqueous solutes with oxo, hydroxo, amino, methyl, chloro, bromo, and fluoro functionalities

Dielectric continuum solvation models are widely used because they are a computationally efficacious way to simulate equilibrium properties of solutes. With advances that allow for molecular-shaped cavities, they have reached a high level of accuracy, in particular for neutral solutes. However, benchmark tests show that existing schemes for defining cavities are unable to consistently predict accurately the effects of solvation on ions, especially anions. This work involves the further development of a protocol put forth earlier for defining the cavities of aqueous solutes, with resulting advances that are most striking for anions. Molecular cavities are defined as interlocked spheres around atoms or groups of atoms in the solute, but the sphere radii are determined by simple empirically based expressions involving the effective atomic charges of the solute atoms (derived from molecular electrostatic potential) and base radii. Both of these terms are optimized for the different types of atoms or functional groups in a training set of neutral and charged solutes. Parameters in these expressions for radii were fitted by minimizing residuals between calculated and measured standard free energies of solvation (DeltaG(s)*), weighted by the uncertainty in the measured value. The calculations were performed using density functional theory with the B3LYP functional and the 6-311+G** basis set and the COnductor-like Screening MOdel (COSMO). The optimized radii definitions reproduce DeltaG(s)* of neutral solutes and singly charged ions in the training set to within experimental uncertainty and, more importantly, accurately predict DeltaG(s)* of compounds outside the training set, in particular anions (J. Phys. Chem. A 2003, 107, 5778). Inherent to this approach, the cavity definitions reflect the strength of specific solute-water interactions. We surmise that this feature underlies the success of the model, referred to as the CD-COSMO model for Charge-Dependent (also Camaioni-Dupuis) COSMO model. These findings offer encouragement that we can keep extending this scheme to other functional groups and obtain better accuracy in using continuum solvation models to predict equilibrium properties of aqueous ionic solutes. The approach is illustrated for a number of test cases, including the determination of acidities of an amine base, a study of the tautomerization equilibrium of a zwitterionic molecule (glycine), and calculating solvation energies of transition states toward a full characterization of reaction pathways in aqueous phase, here in S(N)2 exchange reactions. The calculated reaction barriers in aqueous solution are in excellent agreement with experimental values.     

Hybrid supermolecule-polarizable continuum approach to solvation: Application to the mechanism of the Stevens rearrangement

Semiempirical molecular orbital theory has been used to study the effects of solvation by acetonitrile on the Stevens rearrangement of methylammonium formylmethylide to 2-aminopropanal. Three methods of solvation have been used to investigate both the electrostatic and specific solvent–solute effects of solvation: a supermolecule calculation involving the complete geometry optimization of up to six solvent molecules about the solute, the conductor-like screening model (COSMO) polarizable continuum method which allows for geometry optimization of the solute in a solvent defined by its dielectric constant, and a hybrid method in which up to five solvent molecules are incorporated inside the solute cavity and complete geometry optimization of the complex is carried out within the polarizable continuum. A comparison of the calculated geometries, rearrangement activation energies, and enthalpies of solvation from these approaches is presented, and the explicit versus bulk solvation effects are discussed. The overall effect of all methods for incorporating solvation effects is that the radical pair pathway is perferred over the concerted mechanism. © 1996 by John Wiley & Sons, Inc.     

Rare tautomer hypothesis supported by theoretical studies: ab initio investigations of prototropic tautomerism in the N-methyl-p base

Density functional theory calculations were applied to the prediction of the tautomeric properties of N-methyl-P (6-methyl-3,4-dihydro-8H-pyrimido[4,5-c][1,2]oxazin-7-one), a base of the nucleoside analogue dP (6-(2-deoxy-beta-D-ribofuranosyl)-3,4-dihydro-8H-pyrimido[4,5-c][1,2]oxazin-7-one), for which water-solution experimental data have become available recently. The calculations have been performed for three tautomers in the gas phase, with various numbers of water molecules, and within the polarizable continuum model (PCM) of solvation. The obtained results correctly predict the presence of two tautomers and reproduce accurately the experimentally obtained ratio of the two most stable tautomeric forms when using a combination of explicit water molecules and the PCM of solvation. This lends additional support to the rare tautomer hypothesis of substitution mutagenesis in DNA replication.     

A new method of accurate pKb determinations for some organic amines

The accurate pK_b determinations for some amines have been investigated using the combination of the extended clusters‐continuum model with the polarizable continuum solvation model. The formation of molecular clusters by means of the amines wrapped up with water molecules leads to the weakness of the mutual function between the polar solvents and the amines, and, hence, the accuracy of pK_b has been enhanced by using a coherent and well‐defined approach without external approximations or experimental data. The calculations are performed at the HF/6‐311++G(d, p) level and agreed well with experimental data because electron correlation effect cancels mutually in the calculated value of ΔG which is not an absolute value, but a relative value. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Prediction of Henry's law constant of benzene derivatives using quantum chemical continuum‐solvation models

Semiempirical (SM2, SM5.4A, MST‐AM1, COSMO‐AM1) and ab inito (HF/PCM‐vdW, MP2//PCM‐vdW, COSMO‐DFT) dielectric continuum‐solvation models as well as the surface‐tension model SM5.0R are analyzed with respect to predicting Henry's law constant at 25°C using a compound set of benzene and 39 benzene derivatives. Both hydrophilic and hydrophobic compounds are covered with a total variation in Henry's law constant of almost eight orders of magnitude corresponding to 44 kJ/mol, and the data set is selected such that there are cases where subtle changes in the molecular structure result in substantial changes of the free energy of solvation. The calculations with SM2, COSMO‐AM1, and COSMO‐DFT include solution‐phase geometry optimization, and the ab initio results refer to polarized basis sets of double‐zeta quality, with two gradient‐corrected functionals (BPW and BLYP) being used for the DFT‐based models. The results show considerable differences in performance between the different continuum‐solvation models, and among the methods yielding solvation free energies the systematic error ranges from −0.9 kJ/mol (SM5.0R) to 12.1 kJ/mol (MP2//PCM‐vdW). In particular, the nonelectrostatic solvation energy contributions of SM2, SM5.4A, MST‐AM1, and PCM‐vdW do not correlate with each other, and with PCM‐vdW omission of the nonelectrostatic component significantly improves the relative trend. The best statistics after scaling through linear regression are achieved with the electrostatic component of MP2//PCM‐vdW (r=0.94) and with COSMO‐DFT (r=0.93). The discussion includes detailed analyses of pecularities associated with certain functional groups, deviations from the expected relationship between dipole moment and solvation energy, and a simple approach to model dispersion interaction and cavitation energy by surface area terms that differentiate between individual atom types. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 17–34, 2000