Evaluation of DFT Methods and Implicit Solvation Models for Anion‐Binding Host‐Guest Systems

Although supramolecular chemistry is traditionally an experimental discipline, computations have emerged as important tools for the understanding of supramolecules. We have explored how well commonly used density functional theory quantum mechanics and polarizable continuum solvation models can calculate binding affinities of host‐guest systems. We report the calculation of binding affinities for eight host–guest complexes and compare our results to experimentally measured binding free energies that span the range from ?2.3 to ?6.1 kcal mol^?1. These systems consist of four hosts (biotin[6]uril, triphenoxymethane, cryptand, and bis‐thiourea) with different halide ions (F^?, Cl^?, Br^?) in various media including organic and aqueous. The mean average deviation (MAD) of calculated from measured ΔG_a is 2.5 kcal mol^?1 when using B3LYP‐D3 with either CPCM or PCM. This MAD value lowers even more by eliminating two outliers: 1.1 kcal mol^?1 for CPCM and 1.2 kcal mol^?1 for PCM. The best DFT and implicit solvation model combination that we have studied is B3LYP?D3 with either CPCM or PCM.     

Mechanism of the Thermal Z⇌E Isomerization of a Stable Silene; Experiment and Theory

The E and Z geometric isomers of a stable silene (tBu₂MeSi)(tBuMe₂Si)Si=CH(1‐Ad) ( 1 ) were synthesized and characterized spectroscopically. The thermal Z to E isomerization of 1 was studied both experimentally and computationally using DFT methods. The measured activation parameters for the 1Z ? 1E isomerization are: E_a=24.4 kcal mol^?1, ΔH^≠=23.7 kcal mol^?1, ΔS^≠=?13.2 e.u. Based on comparison of the experimental and DFT calculated (at BP86‐D3BJ/def2‐TZVP(‐f)//BP86‐D3BJ/def2‐TZVP(‐f)) activation parameters, the Z?E isomerization of 1 proceeds through an unusual (unprecedented for alkenes) migration–rotation–migration mechanism (via a silylene intermediate), rather than through the classic rotation mechanism common for alkenes.     

Data on the thermochemistry of azoalkanes

The rate constant of the primary decomposition step was determined for four symmetrical and four unsymmetrical azoalkanes. From the experimental activation energies and some literature enthalpy data, the following enthalpies of formation of radicals and group contributions were calculated: ΔH_? (CH₃N₂) = 51.5 ± 1.8 kcal mol^?1, ΔH_? (C₂H₅N₂) = 44.8 ± 2.5 kcal mol^?1, ΔH_? (2?C₃H₇N₂) = 37.9 ± 2.2 kcal mol^?1, [N_A-(C)] = 27.6 ± 3.7 kcal mol^?1, [N_A-(?_A) (C)] = 61.2 ± 3.1 kcal mol^?1.     

Heterolysis of H2 Across a Classical Lewis Pair, 2,6‐Lutidine⋅BCl3: Synthesis,Characterization, and Mechanism

We report that 2,6‐lutidine?trichloroborane (Lut?BCl₃) reacts with H₂ in toluene, bromobenzene, dichloromethane, and Lut solvents producing the neutral hydride, Lut?BHCl₂. The mechanism was modeled with density functional theory, and energies of stationary states were calculated at the G3(MP2)B3 level of theory. Lut?BCl₃ was calculated to react with H₂ and form the ion pair, [LutH⁺][HBCl₃^?], with a barrier of ΔH^≠=24.7 kcal mol^?1 (ΔG^≠=29.8 kcal mol^?1). Metathesis with a second molecule of Lut?BCl₃ produced Lut?BHCl₂ and [LutH⁺][BCl₄^?]. The overall reaction is exothermic by 6.0 kcal mol^?1 (Δ_rG°=?1.1). Alternate pathways were explored involving the borenium cation (LutBCl₂⁺) and the four‐membered boracycle [(CH₂{NC₅H₃Me})BCl₂]. Barriers for addition of H₂ across the Lut/LutBCl₂⁺ pair and the boracycle B?C bond are substantially higher (ΔG^≠=42.1 and 49.4 kcal mol^?1, respectively), such that these pathways are excluded. The barrier for addition of H₂ to the boracycle B?N bond is comparable (ΔH^≠=28.5 and ΔG^≠=32 kcal mol^?1). Conversion of the intermediate 2‐(BHCl₂CH₂)‐6‐Me(C₅H₃NH) to Lut?BHCl₂ may occur by intermolecular steps involving proton/hydride transfers to Lut/BCl₃. Intramolecular protodeboronation, which could form Lut?BHCl₂ directly, is prohibited by a high barrier (ΔH^≠=52, ΔG^≠=51 kcal mol^?1).     

Kinetics and mechanism study of aniline addition to ethyl propiolate

The kinetics of the addition reaction of aniline to ethyl propiolate in dimethylsulfoxide (DMSO) as solvent was studied. Initial rate method was used to determine the order of the reaction with respect to the reactants, and pseudo‐first‐order method was used to calculate the rate constant. This reaction was monitored by UV–Vis spectrophotometer at 399 nm by the variable time method. On the basis of the experimental results, the Arrhenius equation for this reaction was obtained as log k = 6.07 ‐ (12.96/2.303 RT). The activation parameters, E_a, ΔH^#, ΔG^#, and ΔS^# at 300 K were 12.96, 13.55, 23.31 kcal mol^?1 and ?32.76 cal mol^?1 K^?1, respectively. The results revealed a first‐order reaction with respect to both aniline and ethyl propiolate. In addition, based on the experimental results and using also density functional theory (DFT) at B3LYP/6‐31G* level, a mechanism for this reaction was proposed. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 38: 144–151, 2006     

Solvent effects on the activation parameters of the reaction between an α‐tocopherol analogue and dpph•: The role of H‐bonded complexes

The analysis of the activation parameters for the formal H‐atom transfer reaction between 2,2,5,7,8‐pentamethyl‐6‐chromanol (ChrOH) and 2,2‐diphenyl‐1‐picrylhydrazyl (dpph^?) reveals that these parameters are effective probes of the actual reaction mechanism. Indeed, the A factors measured in various polar and apolar solvents are localized in three distinct domains according to whether the reaction occurs via outer‐sphere electron transfer (ET) from the anion ChrO^? or hydrogen atom transfer (HAT). For instance, A = 5.9 × 10⁵ M^?1 s^?1 and E_a = 2.5 kcal mol^?1 in cyclohexane where the reaction proceeds by HAT, whereas in methanol, ethanol, and their mixtures with water where there is a substantial ET contribution A > 10⁹ M^?1s^?1 and E_a > 7 kcal mol^?1. Interestingly, in nonhydroxylic polar solvents, A～ 10⁷ M^?1s^?1 and the E_a values reflect the H‐bond accepting ability of the solvent in agreement with the “standard” kinetic solvent effects on HAT reactions. Addition of small quantities of pyridine accelerates the reaction rates in these solvents. This suggests that the H‐bonded complex (ChrOH···Py) is able to react via intermolecular ET with dpph^?. It is known, in fact, that pyridine lowers the oxidation potential of phenols by ～0.5 V and the ΔG_ET of ChrOH + dpph^? consequently decreases by about 10 kcal mol^?1. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 524–531, 2012     

Investigation of kinetic and mechanism of triphenylphosphine addition to para‐naphthoquinone

This work reports the results of a kinetic and mechanistic investigations of the addition reaction of triphenylphosphine to para‐naphtoquinone in 1,2‐dichloromethane as solvent. The order of reaction with respect to the reactants was determined using initial rate method, and the rate constant was obtained on the basis of pseudo‐first‐order method. Variable time method using Uv–Vis spectrophotometry (at 400 nm) was utilized for monitoring this addition reaction, for which the following Arrhenius equation was obtained: The resulting activation parameters E_a, ΔH^#, ΔG^#, and ΔS^# at 300 K were 13.63, 14.42, 18.75 kcal mol^?1, and ?14.54 cal mol^?1K^?1, respectively. The results suggest that the reaction is first order with respect to both triphenylphosphine and para‐naphthoquinone. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 427–433, 2005     

Thermochemical properties for n‐propyl,iso‐propyl,and tert‐butyl nitroalkanes,alkyl nitrites,and their carbon‐centered radicals

Density functional theory (DFT) based calculations are performed on a series of alkyl nitrites and nitroalkanes representing large‐scale primary, secondary, and tertiary nitro compounds and their radicals resulting from the loss of their skeletal hydrogen atoms. Geometries, vibration frequencies, and thermochemical properties [S°(T) and C°_p(T) (10 K ? T ? 5000 K)] are calculated at the B3LYP/6‐31G(d,p) DFT level. Δ_fH°₂₉₈ values are from B3LYP/6‐31G(d,p), B3LYP/6‐31+G(2d,2p), and the composite CBS‐QB3 levels. Potential energy barriers for the internal rotations have been computed at the B3LYP/6‐31G(d,p) level of theory, and the lower barrier contributions are incorporated into entropy and heat capacity data. The standard enthalpies of formation at 298 K are evaluated using isodesmic reaction schemes with several work reactions for each species. Recommended values derived from the most stable conformers of respective nitro‐ and nitrite isomers include ?30.57 and ?28.44 kcal mol^?1 for n‐propane‐, ?33.89 and ?32.32 kcal mol^?1 for iso‐propane‐, ?42.78 and ?41.36 kcal mol^?1 for tert‐butane‐nitro compounds and nitrites, respectively. Entropy and heat capacity values are also reported for the lower homologues: nitromethane, nitroethane, and corresponding nitrites. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 181–199, 2010     

Kinetic study of triphenylphosphine addition to para‐benzoquinone

Kinetics of the addition reaction of triphenylphosphine to para‐benzoquinone in 1,2‐dichloroethane as solvent was studied. Initial rate method was used to determine the order of the reaction with respect to the reactants. Pseudo‐first‐order method was also used to calculate the rate constant. This reaction was monitored by UV‐vis spectrophotometry at 520 nm by variable time method. On the basis of the obtained results, the Arrhenius equation of this reaction was obtained: The activation parameters, E_a, ΔH^#, ΔG^#, and ΔS^# at 300 K were 5.701, 6.294, 19.958 kcal mol^?1 and ?45.853 cal mol^?1 K^?1, respectively. This reaction is first and second order with respect to triphenylphosphine and para‐benzoquinone, respectively. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36:472–479, 2004     

Activation of Strong Boron–Fluorine and Silicon–Fluorine σ‐Bonds: Theoretical Understanding and Prediction

The oxidative addition of BF₃ to a platinum(0) bis(phosphine) complex [Pt(PMe₃)₂] ( 1 ) was investigated by density functional calculations. Both the cis and trans pathways for the oxidative addition of BF₃ to 1 are endergonic (ΔG°=26.8 and 35.7 kcal mol^?1, respectively) and require large Gibbs activation energies (ΔG°^≠=56.3 and 38.9 kcal mol^?1, respectively). A second borane plays crucial roles in accelerating the activation; the trans oxidative addition of BF₃ to 1 in the presence of a second BF₃ molecule occurs with ΔG°^≠ and ΔG° values of 10.1 and ?4.7 kcal mol^?1, respectively. ΔG°^≠ becomes very small and ΔG° becomes negative. A charge transfer (CT), F→BF₃, occurs from the dissociating fluoride to the second non‐coordinated BF₃. This CT interaction stabilizes both the transition state and the product. The B?F σ‐bond cleavage of BF₂Ar^F (Ar^F=3,5‐bis(trifluoromethyl)phenyl) and the B?Cl σ‐bond cleavage of BCl₃ by 1 are accelerated by the participation of the second borane. The calculations predict that trans oxidative addition of SiF₄ to 1 easily occurs in the presence of a second SiF₄ molecule via the formation of a hypervalent Si species.     

An ab initio molecular orbital study of the potential energy surface of the N2H → N2 + H system

The N₂H potential energy surface has been examined by ab initio molecular orbital theory using the 6-31G^** basis set with correlation energy evaluated by Møller—Plesset perturbation theory to fourth order. The ΔE for N₂H → N₂ + H is ?14.4 kcal mol^?1 and the barrier to dissociation is 10.5 kcal mol^?1. Inclusion of zero-point vibrational energies reduces the barrier to 5.8 kcal mol^?1.     

Evidence for a Rapid Degenerate Hetero‐Cope‐Type Rearrangement in [Cp*W(S)2S‐CH2‐CHCH2]

Treatment of the salt [PPh₄]⁺[Cp*W(S)₃]^? ( 6 ) with allyl bromide gave the neutral complex [Cp*W(S)₂S‐CH₂‐CH?CH₂] ( 7 ). The product 7 was characterized by an X‐ray crystal structure analysis. Complex 7 features dynamic NMR spectra that indicate a rapid allyl automerization process. From the analysis of the temperature‐dependent NMR spectra a Gibbs activation energy of ΔG^≠ (278 K)≈13.7±0.1 kcal mol^?1 was obtained [ΔH^≠≈10.4±0.1 kcal mol^?1; ΔS^≠≈?11.4 cal mol^?1 K^?1]. The DFT calculation identified an energetically unfavorable four‐membered transition state of the “forbidden” reaction and a favorable six‐membered transition state of the “Cope‐type” allyl rearrangement process at this transition‐metal complex core.     

Thermal Behavior of N,N＇Bis[N-（2,2,2-trinitroethyl）-N-nitro]ethylenediamine

The thermal behavior and kinetic parameters of the exothermic decomposition reaction of N‐N‐bis[N‐(2,2,2‐tri‐nitroethyl)‐N‐nitro]ethylenediamine in a temperature‐programmed mode have been investigated by means of differential scanning calorimetry (DSC). The results show that kinetic model function in differential form, apparent activation energy E_a and pre‐exponential factor A of this reaction are 3(1 ‐α)^2/3, 203.67 kJ·mol^?1 and 10^20.61s^?1, respectively. The critical temperature of thermal explosion of the compound is 182.2 °C. The values of ΔS^≠ ΔH^≠ and ΔG^≠ of this reaction are 143.3 J·mol^?1·K^?1, 199.5 kJ·mol^?1 and 135.5 kJ·mol^?1, respectively.     

Stabilization of HHeF by Complexation: Is it a Really Viable Strategy?

Ab initio calculations at the MP2 and CCSD(T) levels of theory have disclosed the conceivable existence of fluorine‐coordinated complexes of HHeF with alkali‐metal ions and molecules M⁺ (M⁺=Li⁺–Cs⁺), M⁺–OH₂, M⁺–NH₃ (M⁺=Li⁺, Na⁺), and MX (M=Li, Na; X=F, Cl, Br). All these ligands L induce a shortening of the H? He distance and a lengthening of the He? F distance accompanied by consistent blue‐ and redshifts, respectively, of the H? He and He? F stretching modes. These structural effects are qualitatively similar to those predicted for other investigated complexes of the noble gas hydrides HNgY, but are quantitatively more pronounced. For example, the blueshifts of the H? He stretching mode are exceptionally large, ranging between around 750 and 1000 cm^?1. The interactions of HHeF with the ligands investigated herein also enhance the (HHe)⁺F^? dipole character and produce large complexation energies of around 20–60 kcal mol^?1. Most of the HHeF–L complexes are indeed so stable that the three‐body dissociation of HHeF into H+He+F, exothermic by around 25–30 kcal mol^?1, becomes endothermic. This effect is, however, accompanied by a strong decrease in the H? He? F bending barrier. The complexation energies, ΔE, and the bending barriers, E*, are, in particular, related by the inverse relationship E*(kcal mol^?1)=6.9exp[?0.041ΔE(kcal mol^?1)]. Therefore the HHeF? L complexes, which are definitely stable with respect to H+He+F+L (ΔE≈25–30 kcal mol^?1), are predicted to have bending barriers of only 0.5–2 kcal mol^?1. Overall, our calculations cast doubt on the conceivable stabilization of HHeF by complexation.     

Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using complete basis set and Gaussian‐n models combined with CPCM continuum solvation methods

Complete basis set and Gaussian‐n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pK_a values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of ?264.61 kcal/mol for the free energy of solvation of H⁺, ΔG_s(H⁺), was combined with a value for G_gas(H⁺) of ?6.28 kcal/mol, to calculate pK_a values with cycle 1. The complete basis set gas‐phase methods used to calculate gas‐phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed‐phase free energies are slightly less accurate than the gas‐phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle 1 and the complete basis set models combined with the CPCM solvation methods yielded pK_a values accurate to less than half a pK_a unit. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Etude des melanges d'antipodes optiques—XII: Mesure de la stabilite des racemiques vrais

The stability of true racemates is defined by the free energy change ΔG^φ of the process D-crystal + L-crystal → DL-crystal. ΔG^φ, varying in the range 0 to ?2 kcal mol^?1, is roughly proportional to the difference in melting points between racemate and antipodes, T_R^f ? T_A^f. In most of the examples studied, the formation of racemates is exothermic. The study of the variation of ΔG^φ with temperature explains the occurrence of crystalline transitions between racemate and conglomerate. Few racemates can give rise to such transitions, particularly when their enthalpies and entropies of formation, ΔH^φ and ΔS^φ, are both positive.     

Thermal [1,5] sigmatropic rearrangements in (σ-7-cycloheptatrienyl)triphenyltin and (σ-5-cyclohepta-1,3-dienyl)triphenyltin: A 1H and 13C NMR reinvestigation

It has been confirmed by ¹H and ¹³C NMR spectroscopies that Sn(σ-C₇H₇)Ph₃ undergoes either 1,4- or 1,5-shifts of the SnPh₃ moiety around the cycloheptatrienyl ring with ΔH³ = 13.8 ± 0.4 kcal mol^?1, ΔS3 = ?5.6 ± 1.2 cal mol^?1 deg^?1, and ΔG³₃₀₀ = 15.44 ± 0.14 kcal mol^?1. Similarly, (σ-5-cyclohepta-1,3-dienyl)triphenyltin undergoes 1,5-shifts with ΔH³ = 12.4 ± 0.6 kcal mol^?1, ΔS³ = ?11.2 ± 1.8 cal mol^?1 deg^?1, and ΔG³₃₀₀ = 15.76 ± 0.13 kcal mol^?1. It is therefore probable that Sn(σ-5-C₅H₅)R₃ and Sn(σ-3-indenyl)R₃ do not undergo 1,2-shifts as previously suggested but really undergo 1,5-shifts.     

Structures and Dynamic Solution Behavior of Cationic,Two‐Coordinate Gold(I)–π‐Allene Complexes

A family of seven cationic gold complexes that contain both an alkyl substituted π‐allene ligand and an electron‐rich, sterically hindered supporting ligand was isolated in >90 % yield and characterized by spectroscopy and, in three cases, by X‐ray crystallography. Solution‐phase and solid‐state analysis of these complexes established preferential binding of gold to the less substituted C?C bond of the allene and to the allene π face trans to the substituent on the uncomplexed allenyl C?C bond. Kinetic analysis of intermolecular allene exchange established two‐term rate laws of the form rate=k₁[complex]+k₂[complex][allene] consistent with allene‐independent and allene‐dependent exchange pathways with energy barriers of ΔG^≠₁=17.4–18.8 and ΔG^≠₂=15.2–17.6 kcal mol^?1, respectively. Variable temperature (VT) NMR analysis revealed fluxional behavior consistent with facile (ΔG^≠=8.9–11.4 kcal mol^?1) intramolecular exchange of the allene π faces through η¹‐allene transition states and/or intermediates that retain a staggered arrangement of the allene substituents. VT NMR/spin saturation transfer analysis of [{P(tBu)₂o‐binaphthyl}Au(η²‐4,5‐nonadiene) ]⁺SbF₆^? ( 5 ), which contains elements of chirality in both the phosphine and allene ligands, revealed no epimerization of the allene ligand below the threshold for intermolecular allene exchange (ΔG^≠_298K=17.4 kcal mol^?1), which ruled out the participation of a η¹‐allylic cation species in the low‐energy π‐face exchange process for this complex.     

Kinetische untersuchung der reversiblen dimerisierung von o-phenylendioxidimethylsilan

The reversible dimerisation of o-phenylenedioxydimethylsilane (2,2-dimethyl-1,3,2-benzodioxasilole) has been studied by ¹H NMR spectroscopy. The kinetics of this reaction can be described quantitatively by a bimolecular 10-ring formulation reaction and a monomolecular backreaction. The thermodynamic and kinetic parameters are: ΔH⁰ = ?43 kJ mol^?1; ΔS⁰ = ?112 J mol^?1 K^?1; ΔG⁰₂₉₈ = ?9.6 kJ mol^?1; ΔH³₂₉₈ = 57 kJ mol^?1; ΔS³₂₉₈ = ?129 J mol^?1 K^?1; ΔG³₂₉₈ = 96 kJ mol^?1; E_a = 60 kJ mol^?1; A = 3.17 × 10⁶ l mol^?1 s^?1. Remarkable is the low activation energy of formation of the ten-membered ring, considering that two SiO bonds have to be cleaved during the reaction. Transition states and possible structures of the ten-membered heterocycle are discussed.     

Cross‐Aldol Reaction of Isatin with Acetone Catalyzed by Leucinol: A Mechanistic Investigation

Comprehensive mechanistic studies on the enantioselective aldol reaction between isatin ( 1 a ) and acetone, catalyzed by L ‐leucinol ( 3 a ), unraveled that isatin, apart from being a substrate, also plays an active catalytic role. Conversion of the intermediate oxazolidine 4 into the reactive syn‐enamine 6 , catalyzed by isatin, was identified as the rate‐determining step by both the calculations (ΔG^≠=26.1 kcal mol^?1 for the analogous L ‐alaninol, 3 b ) and the kinetic isotope effect (k_H/k_D=2.7 observed for the reaction using [D₆]acetone). The subsequent reaction of the syn‐enamine 6 with isatin produces (S)‐ 2 a (calculated ΔG^≠=11.6 kcal mol^?1). The calculations suggest that the overall stereochemistry is controlled by two key events: 1) the isatin‐catalyzed formation of the syn‐enamine 6 , which is thermodynamically favored over its anti‐rotamer 7 by 2.3 kcal mol^?1; and 2) the high preference of the syn‐enamine 6 to produce (S)‐ 2 a on reaction with isatin ( 1 a ) rather than its enantiomer (ΔΔG^≠=2.6 kcal mol^?1).