Ab initio procedure for aqueous-phase pKa calculation: the acidity of nitrous acid

We present an ab initio procedure for accurately calculating aqueous-phase pKa values and apply it to study the acidity of nitrous acid (HNO2, or HONO). The aqueous-phase pK(a) of nitrous acid was obtained from calculated gas-phase acidities and solvation free energies via a thermodynamic cycle and the solvation model chemistry of Barone et al. (J. Chem. Phys. 1997, 107, 3210). Solvation free energies were calculated at the HF/6-31G(d) level using the dielectric-polarizable continuum and the integral equation formalism-polarizable continuum solvent models (D-PCM and IEF-PCM, respectively), with the D-PCM model yielding the most accurate pKa values. For HF free energies of solvation, significant improvements in accuracy could be made by moving to the larger 6-311++G(3df,3pd) and aug-cc-pVQZ basis sets. Solvation free energies were also calculated using the density functional theory (DFT) methods B3LYP, TPSS, PBE0, B1B95, VSXC, B98 and O3LYP, with the most accurate methods being TPSS and VSXC, which provided average errors of less than 0.11 pKa units. Solvation free energies calculated with the different DFT methods were relatively insensitive to the basis set used. Our theoretical calculations are compared with experimental results obtained using stopped flow spectrophotometry. The pKa of nitrous acid was measured as 3.16 at 25 degrees C, and the enthalpy and entropy of nitrous acid dissociation were calculated from measurements as 6.7 kJ mol(-1) and -38.4 J mol(-1) K(-1), respectively, between 25 and 45 degrees C. The UV/visible absorption spectra of the nitrite ion and nitrous acid were also examined, and molar extinction coefficients were obtained for each.     

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.     

First-principle predictions of absolute pKa's of organic acids in dimethyl sulfoxide solution

MP2/6-311++G(d,p) and B3LYP/6-311++G(2df,p) methods were found to be able to predict the gas-phase acidities of various organic acids with a precision of 2.2 and 2.3 kcal/mol. A PCM cluster-continuum solvation method was developed that could predict the solvation free energies of various neutral, cationic, and anionic organic species in DMSO with a precision of about 2.0 kcal/mol. Using these carefully tested methods, we successfully predicted the pKa's of 105 organic acids in DMSO with a precision of 1.7-1.8 pKa units. We also predicted the pKa's of a variety of organosilanes in DMSO for the first time using the newly developed methods. This study was one of the first that employed first-principle methods for calculating pKa's of unrelated compounds in organic solutions.     

Computation of pKa values of substituted aniline radical cations in dimethylsulfoxide solution

A newly developed computation strategy was used to calculate the absolute pKa values of 18 substituted aniline radical cations in dimethylsulfoxide (DMSO) solution with the error origin elucidated and deviation minimized. The B3LYP/6-311++G(2df,2p) method was applied and was found to be capable of reproducing the gas-phase proton-transfer free energies of substituted anilines with a precision of 0.83 kcal/mol. The IEF-PCM solvation model with gas-phase optimized structures was adopted in calculating the pKa values of the substituted neutral anilines in DMSO, regenerating the experimental results within a standard deviation of 0.4 pKa unit. When the IEF-PCM solvation model was applied to calculate the standard redox potentials of anilide anions, it showed that the computed values agreed well with experiment, but the redox potentials of substituted anilines were systematically overestimated by 0.304 eV. The cause of this deviation was found to be related to the inaccuracy of the calculated solvation free energies of aniline radical cations. By adjusting the size of the cavity in the IEF-PCM method, we derived a reliable procedure that can reproduce the experimental pKa values of aniline radical cations within 1.2 pKa units to those from experiment.     

One-electron reduction potential for oxygen- and sulfur-centered organic radicals in protic and aprotic solvents

We estimated one-electron reduction potentials of redox-active organic molecules for a spectrum of eight different functional groups (phenoxyl, p-benzoquinone, phenylthiyl, p-benzodithiyl, carboxyl, benzoyloxyl, carbthiyl, and benzoylthiyl) in protic (water) and aprotic (acetonitrile, N,N-dimethylacetamide) solvents. Electron affinities (EA) were evaluated in a vacuum with high level quantum chemical methods using Gaussian3-MP2 (G3MP2) and Becke 3 Lee, Yang, and Parr functional B3LYP with aug-cc-pVTZ basis set. To evaluate one-electron redox potentials, gas-phase free energies were combined with solvation energies obtained in a two-step computational approach. First, atomic partial charges were determined in a vacuum by the quantum chemical method B3LYP/6-31G(d,p). Second, solvation energies were determined, solving the Poisson equation with these atomic partial charges. Redox potentials computed this way, compared to experimental data for the 21 considered organic compounds in different solvents, yielded overall root-mean-square deviations of 0.058 and 0.131 V using G3MP2 or B3LYP to compute electronic energies, respectively, while B3LYP/6-31G(d,p) was used to compute solvation energies.     

Calculation of electron affinities of polycyclic aromatic hydrocarbons and solvation energies of their radical anion

Electron affinities (EAs) and free energies for electron attachment (DeltaGo(a,298K)) have been directly calculated for 45 polynuclear aromatic hydrocarbons (PAHs) and related molecules by a variety of theoretical methods, with standard regression errors of about 0.07 eV (mean unsigned error = 0.05 eV) at the B3LYP/6-31 + G(d,p) level and larger errors with HF or MP2 methods or using Koopmans' Theorem. Comparison of gas-phase free energies with solution-phase reduction potentials provides a measure of solvation energy differences between the radical anion and neutral PAH. A simple Born-charging model approximates the solvation effects on the radical anions, leading to a good correlation with experimental solvation energy differences. This is used to estimate unknown or questionable EAs from reduction potentials. Two independent methods are used to predict DeltaGo(a,298K) values: (1) based upon DFT methods, or (2) based upon reduction potentials and the Born model. They suggest reassignments or a resolution of conflicting experimental EAs for nearly one-half (17 of 38) of the PAH molecules for which experimental EAs have been reported. For the antiaromatic molecules, 1,3,5-tri-tert-butylpentalene and the dithia-substituted cyclobutadiene 1, the reduction potentials lead to estimated EAs close to those expected from DFT calculations and provide a basis for the prediction of the EAs and reduction potentials of pentalene and cyclobutadiene. The Born model has been used to relate the electrostatic solvation energies of PAH and hydrocarbon radical anions, and spherical halide anions, alkali metal cations, and ammonium ions to effective ionic radii from DFT electron-density envelopes. The Born model used for PAHs has been successfully extended here to quantitatively explain the solvation energy of the C60 radical anion.     

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     

Dissolution thermochemistry of alkali metal dianion salts (M2X1, M = Li+, Na+, and K+ with X = CO3(2-), SO4(2-), C8H8(2-), and B12H12(2-))

The dissolution Gibbs free energies (ΔG°(diss)) of salts (M(2)X(1)) have been calculated by density functional theory (DFT) with Conductor-like Polarizable Continuum Model (CPCM) solvation modeling. The absolute solvation free energies of the alkali metal cations (ΔG(solv)(M(+))) come from the literature, which coincide well with half reduction potential versus SHE data. For solvation free energies of dianions (ΔG(solv)(X(2-))), four different DFT functionals (B3LYP, PBE, BVP86, and M05-2X) were applied with three different sets of atomic radii (UFF, UAKS, and Pauling). Lattice free energies (ΔG(latt)) of salts were determined by three different approaches: (1) volumetric, (2) a cohesive Gibbs free energy (ΔG(coh)) plus gaseous dissociation free energy (ΔG(gas)), and (3) the Born-Haber cycle. The G4 level of theory, electron propagator theory, and stabilization by dielectric medium were used to calculate the second electron affinity to form the dianions CO(3)(2-) and SO(4)(2-). Only the M05-2X/Pauling combination with the three different methods for estimating ΔG(latt) yields the expected negative dissolution free energies (ΔG°(diss)) of M(2)SO(4). Salts with large dianions like M(2)C(8)H(8) and M(2)B(12)H(12) reveal the limitation of using static radii in the volumetric estimation of lattice energies. The value of ΔE(coh) was very dependent on the DFT functional used.     

Structure and stability of the (001) alpha-quartz surface

The structure and surface energies of the cleaved, reconstructed, and fully hydroxylated (001) alpha-quartz surface of various thicknesses are investigated with periodic density functional theory (DFT). The properties of the cleaved and hydroxylated surface are reproduced with a slab thickness of 18 atomic layers, while a thicker 27-layer slab is necessary for the reconstructed surface. The performance of the hybrid DFT functional B3LYP, using an atomic basis set, is compared with the generalised gradient approximation, PBE, employing plane waves. Both methodologies give similar structures and surface energies for the cleaved and reconstructed surfaces, which validates studying these surfaces with hybrid DFT. However, there is a slight difference between the PBE and B3LYP approach for the geometry of the hydrogen bonded network on the hydroxylated surface. The PBE adsorption energy of CO on a surface silanol site is in good agreement with experimental values, suggesting that this method is more accurate for hydrogen bonded structures than B3LYP. New hybrid functionals, however, yield improved weak interactions. Since these functionals also give superior activation energies, we recommend applying the new functionals to contemporary issues involving the silica surface and adsorbates on this surface.     

Ab initio description of photoabsorption and electron transfer in a doubly-linked porphyrin-fullerene dyad

Structure, photoabsorption and excited states of two representative conformations obtained from molecular dynamics (MD) simulations of a doubly-linked porphyrin-fullerene dyad DHD6ee are studied by using both DFT and wavefunction based methods. Charge transfer from the donor (porphyrin) to the acceptor (fullerene) and the relaxation of the excited state are of special interest. The results obtained with LDA, GGA, and hybrid functionals (SVWN, PBE, and B3LYP, respectively) are analyzed with emphasis on the performance of used functionals as well as from the point of view of their comparison with wavefunction based methods (CCS, CIS(D), and CC2). Characteristics of the MD structures are retained in DFT optimization. The relative orientation of porphyrin and fullerene is significantly influencing the MO energies, the charge transfer (CT) in the ground state of the dyad and the excitation of ground state CT complex (g-CTC). At the same time, the excitation to the locally excited state of porphyrin is only little influenced by the orientation or cc distance. TD-DFT underestimates the excitation energy of the CT state, however for some cases (with relatively short donor-acceptor separations), the use of a hybrid functional like B3LYP alleviates the problem. Wavefunction based methods and CC2 in particular appear to overestimate the CT excitation energies but the inclusion of proper solvation models can significantly improve the results.     

Theoretical study on infrared vibrational spectra of boric-acid in gas-phase using density functional methods

Density functional theory (DFT) methods with various exchange-correlation functionals such as SVWN, BVWN, BVWN5, BLYP, B1LYP, B3LYP, B3PW91, and BH and H are employed in a theoretical study of molecular boric-acid in gas-phase. In the calculations, the split valence 6-311++G** and 6-31G* basis sets were used. The geometry, zero-point vibrational energies (ZPVEs), and harmonic infrared vibrational (IR) frequencies are predicted. The calculated C_3h-symmetry geometrical parameters are compared with Hartree–Fock (HF) calculation results and experimental data. IR frequencies predicted by the BLYP, B3LYP, and B3PW91 calculations are in good agreement with experimental data. The frequency calculations presented here also suggest that the C_3h-symmetrical structure corresponds to a minimum in the potential energy surface, but neither is D_3h- or C₃-symmetrical structure.     

Solvation Free Energy Calculations: The Combination between the Implicitly Polarized Fixed-charge Model and the Reference Potential Strategy

The IPolQ-Mod charges, which are the average of two charge sets fitted in vacuum state and condensed phase, take account of polarization effect implicitly in the solvation free energy calculation. However, the performance of the IPolQ-Mod charges sensitively depends on the QM levels used to generate the electrostatic potential from which the charges are fitted. In addition, the forces on atoms are not accurate theoretically in the molecular dynamics (MD) simulation as the solvent only feels the electrostatic potential of a half-polarized density of the solute according to the derivation of the IPolQ-Mod charges. To study these issues in detail, the IPolQ-Mod charges are combined with the reference potential (RP) strategy to predict the solvation free energies in the present study. It is found that the thermodynamic perturbation (TP) corrections utilizing total energy difference and interaction energy difference are almost the same and free of bias. The solvation free energies estimated by the RP method match very well with those obtained by applying IPolQ-Mod charges into MD simulation directly. By means of the RP strategy, the performances of the IPolQ-Mod charges with the change of the strength of the exact HF exchange in several DFT functionals are determined effectively. Although the “optimal” strengths are found in B3LYP and LC-ωPBE, the improvements over the default strength are not too much. In addition to the IPolQ-Mod charges, other charge models like bond charge correction (BCC) charges could also be combined with the RP strategy to study the thermodynamic properties like solvation free energy. © 2019 Wiley Periodicals, Inc.     

Molecular structures and properties of the complete series of bromophenols: Density functional theory calculations

The complete series of 19 bromophenols have been studied by density functional theory (DFT) calculations at the B3LYP/6-311G++(d,p) level. The molecular structures and properties of bromophenols are strongly influenced by intramolecular hydrogen bonding of ortho-bromine, steric and inductive effects of substituted bromine, and other intramolecular electrostatic interactions. Systematic trends in several structural parameters and molecular properties of bromophenols have been found with the increasing number of bromine substitutions, including increase in O-H bond length, decrease in C-O bond length, red shift in O-H stretching frequency, and blue shift in O-H torsional frequency. Correlations among several key molecular parameters as well as those with available aqueous pKa values are examined. Comparisons with chlorophenols have indicated that the inductive effect of substituted bromine appears larger and bromophenols are slightly stronger acids than chlorophenols.     

Derivatives of azacalix[3](2,6)pyridine are strong neutral organic superbases: a DFT study

The gas phase basicities and pKa values in acetonitrile of azacalix[3](2,6)pyridine and its derivatives are determined by the B3LYP DFT method. It is found that all compounds of this series are neutral organic superbases. The proton attacks the inner pyridine N(sp2) atom, thus forming a bifurcated intramolecular hydrogen bond. The most powerful superbase is provided by the hexakis(dimethylamino) derivative of the title compound. Its gas phase proton affinity is 296.6 kcal mol-1, its basicity is 291.3 kcal mol-1, and its pKa(MeCN) is 30.9 units. [structure: see text]     

Absolute calculations of acidity of C-substituted tetrazoles in solution

The CBS-QB3 method was used to calculate the gas-phase free energy difference between nine tetrazole derivatives and their anions, and the DPCM and CPCM continuum solvation methods were applied to calculate the free energy differences of solvation. The calculations were performed on both gas-phase and solvent-phase optimized structures. Absolute pKa calculations using the CPCM method and the gas-phase optimized structures yielded mean unsigned error of 0.4 pKa unit. The calculations were made with the routine settings implemented in Gaussian 98. The study is as accurate as the best reported so far for six carboxylic acids and phenols and, to our knowledge, the best reported for the acidities of heterocyclic compounds in solution.     

Scaling dynamical correlation energy from density functional theory correlation functionals

The scaling of dynamical correlation energy in molecules obtained by the correlation functionals of density functional theory (DFT) is examined. The approach taken is very similar to the scaled external correlation method of Brown and Truhlar but is based on the observation that DFT correlation functionals, especially the LYP, appear to represent the dynamical portion of the correlation energy in molecules. We examine whether higher accuracy in atomization energies can be gained by scaling without significant deterioration of the structural and spectroscopic properties of the molecules using four DFT functionals (BLYP, OLYP, B3LYP, and O3LYP) on 19 molecules including the six molecule AE6 database, the latter being representative of a much larger, 109 molecule training set. We show that, with molecule specific scale factors, nearly perfect agreement with experiment can be achieved in atomization energies without increasing the average errors in other molecular properties relative to the DFT calculation. We further show that it is possible to find optimal scale factors which reduce the mean unsigned error per bond to levels comparable to those of some multilevel multicoefficient methods.     

Assessment of the OLYP and O3LYP density functionals for first-row transition metals

We have investigated the performance of the OLYP and O3LYP density functionals for predicting atomic excitation energies and ionization potentials, and bond dissociation energies, geometries, and vibrational frequencies for selected first-row transition metal compounds, including hydrides (MH) and singly charged methylene and methyl cations. The OLYP and O3LYP functionals are similar to the well-known BLYP and B3LYP functionals, respectively, but use a new optimized exchange functional (OPTX) developed by Handy and Cohen (Mol Phys 2001, 99, 403) in place of the standard B88 exchange. A previous study by us on organic reactions (J Chem Phys 2002, 117, 1331) indicated that both OLYP and O3LYP gave results for heats of reaction and barrier heights that were overall superior to those using the popular B3LYP functional. For transition metals, however, although OLYP is overall superior to BLYP for molecular calculations, it is inferior to B3LYP. O3LYP provides results for molecules of about the same quality as B3LYP. For atomic excitation and 4s ionization energies, unless relativistic effects are included, OLYP and O3LYP are clearly worse than both BLYP and B3LYP. There is thus no real incentive to use either OLYP or O3LYP in place of B3LYP for calculations involving first-row transition metals.     

A density functional theory formulation of the reaction field model of solvent effects

It is possible to reformulate the reaction field (RF ) model of continuum solvent effects, by considering an approximate expression describing the energy changes from one ground state to another, in the frame of density functional theory (DFT ). The energy functional for an arbitrary electronic system coupled to a spin-independent electrostatic external perturbation is used to derive the well-known Born expression giving the electrostatic component of the solvation energy of an atomic ion. The approximate RF –DFT model is illustrated for a series of representative singly positive and negatively charged atomic ions. A Kohn–Sham (KS )-like formalism is then proposed to compute solvation energies within a self-consistent field scheme. The extension of the RF -DFT model to molecular systems is also outlined. © 1995 John Wiley & Sons, Inc.     

咪唑醋酸离子液体热力学性质的理论研究

咪唑醋酸离子液体在催化、电化学、萃取等领域具有潜在的应用价值,对其热力学性质的深入研究将为其应用提供理论依据。本文采用密度泛函理论(DFT)方法和Born-Fajans-Haber (BFH)循环法对咪唑醋酸离子液体[C_nmim][OAc] (n=1-6)进行热力学性质的理论研究。计算其相变过程中的解离焓、汽化焓、熔化焓、晶格焓、溶解焓等,并与已有实验值进行比较。利用Gaussian 09程序在B3LYP/6-311+G(d, p)和M062X/TZVP两种水平下计算解离焓值,同时通过计算得到分子体积和总气相能的焓修正值,借助Matlab计算软件拟合得到汽化焓值,取得与已有实验值很好的一致性。使用Jenkins公式求得晶格能,计算得到晶格焓,最后利用BFH循环计算得到溶解焓。