Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase

 A replica path method has been developed and extended for use in complex systems involving hybrid quantum/classical (quantum mechanical/molecular mechanical) coupled potentials. This method involves the definition of a reaction path via replication of a set of macromolecular atoms. An “important” subset of these replicated atoms is restrained with a penalty function based on weighted root-mean-square rotation/translation best-fit distances between adjacent (i±1) and next adjacent (i±2) pathway steps. An independent subset of the replicated atoms may be treated quantum mechanically using the computational engine Gamess-UK. This treatment can be performed in a highly parallel manner in which many dozens of processors can be efficiently employed. Computed forces may be projected onto a reference pathway and integrated to yield a potential of mean force (PMF). This PMF, which does not suffer from large errors associated with calculated potential-energy differences, is extremely advantageous. As an example, the QM/MM replica path method is applied to the study of the Claisen rearrangement of chorismate to prephenate which is catalyzed by the Bacillus subtilis isolated, chorismate mutase. Results of the QM/MM pathway minimizations yielded an activation enthalpy ΔH ^†† of 14.9 kcal/mol and a reaction enthalpy of −19.5 kcal/mol at the B3LYP/6-31G(d) level of theory. The resultant pathway was compared and contrasted with one obtained using a forced transition approach based on a reaction coordinate constrained repeated walk procedure (ΔH ^†† =20.1 kcal/mol, ΔH _rxn = −20.1 kcal/mol, RHF/4-31G). The optimized replica path results compare favorably to the experimental activation enthalpy of 12.7±0.4 kcal/mol. Received: 16 December 2001 / Accepted: 6 September 2002 / Published online: 8 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 22nd National Meeting of the American Chemical Society, 2001. Correspondence to: H.L. Woodcock e-mail: hlwood@ccqc.uga.edu Acknowledgements. The authors thank Eric Billings, Xiongwu Wu, and Stephen Bogusz for helpful discussions and related work. The authors also show grateful appreciation to The National Institutes of Health and The National Science Foundation for support of the current research.     

Microhydration of protonated nucleic acid bases and protonated nucleosides in the gas phase

Thermochemical data, ΔH _n ^o , ΔS _n ^o , and ΔG _n ^o , for the hydration of protonated nucleic acid bases and protonated nucleosides have been experimentally studied by equilibrium measurements using an electrospray high-pressure mass spectrometer equipped with a pulsed ion-beam reaction chamber. For protonated nucleobases the hydration enthalpies were found to be similar for all studied systems and varied between 12.4–13.1 kcal/mol for the first and 11.2–11.5 kcal/mol for the second water molecule. While for protonated nucleosides the water binding enthalpies (11.7–13.3 kcal/mol) are very close to those for protonated nucleobases, the entropy values are “more negative.” The structural and energetic aspects of hydrated ions are discussed in conjunction with the available theoretical data.     

Theoretical predictions of the structure, gas-phase acidity and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid

Results of ab initio self-consistent-field (SCF) and density functional theory (DFT) calculations of the gas-phase structure, acidity (free energy of deprotonation, ΔG^o), and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid (3,4-dithiohydroxy-3-cyclobutene-1,2-diselenone, H₂C₄Se₂S₂) are reported. The global minimum found on the potential energy surface of 1,2-diseleno-3,4-dithiosquaric acid presents a planar conformation. The ZZ isomer was found to have the lowest energy among the three planar conformers and the ZZ and ZE isomers are very close in energy. The optimized geometric parameters exhibit a bond length equalization relative to reference compounds, cyclobutanediselenone, and cyclobutenedithiol. The computed aromatic stabilization energy (ASE) by homodesmotic reaction (Eq 1) is −20.1 kcal/mol (MP2(fu)/6-311+G** //RHF/6-311+G**) and −14.9 kcal/mol (B3LYP//6-311+G**//B3LYP/6-311+G**). The aromaticity of 1,2-diseleno-3,4-dithiosquaric acid is indicated by the calculated diamagnetic susceptibility exaltation (Λ) −17.91 (CSGT(IGAIM)-RHF/6-311+G**//RHF/6-311+G**) and −31.01 (CSGT(IGAIM)-B3LYP/6-311+G**//B3LYP/6-311+G**). Thus, 1,2-diseleno-3,4-dithiosquaric acid fulfils the geometric, energetic and magnetic criteria of aromaticity. The calculated theoretical gas-phase acidity is ΔG^o _1(298K)=302.7 kcal/mol and ΔG^o _2(298K)=388.4 kcal/mol. Hence, 1,2-diseleno-3,4-dithiosquaric acid is a stronger acid than squaric acid(3,4-dihydroxy-3-cyclobutene-1,2-dione, H₂C₄O₄). Received: 11 April 2000 / Accepted: 7 July 2000 / Published online: 27 September 2000     

Extension of the platform of applicability of the SM5.42R universal solvation model

We present eight new parameterizations of the SM5.42R solvation model: in particular we present parameterizations for HF/MIDI!, HF/6-31G^*, HF/6-31+G^*, HF/cc-pVDZ, AM1, PM3, BPW91/MIDI!, and B3LYP/MIDI!. Two of the new cases are parameterized using the reaction-field operator presented previously, and six of the new cases are parameterized with a simplified reaction-field operator; results obtained by the two methods are compared for selected examples. For a training set of 2135 data for 275 neutral solutes containing H, C, N, O, F, S, P, Cl, Br, and I in 91 solvents (water and 90 nonaqueous solvents), seven of the eight new parameterizations give mean unsigned errors in the range 0.43–0.46 kcal/mol, and the eighth – for a basis set containing diffuse functions – gives a mean unsigned error of 0.53 kcal/mol. The mean unsigned error for 49 ionic solutes (containing the same elements) in water is 3.5–3.9 kcal/mol for the Hartree–Fock, Becke–Perdew–Wang-1991 and Becke three-parameter Lee–Yang–Parr cases and 4.1 and 4.0 kcal/mol for parameterized model 3 and Austin model 1, respectively. The methods are tested for sensitivity of solvation free energies to geometry and for predicting partition coefficients of carbonates, which were not included in the training set. Received: 24 November 1998 / Accepted: 31 December 1998 / Published online: 7 June 1999     

Calorimetric determination enthalpy of the formation of natural pyromorphite

A calorimetric study of natural pyromorphite Pb₅[PO₄]₃Cl was performed. Its enthalpy of formation was determined by melt solution calorimetry from elements Δ_f H _el^∘(298.15 K) = −4124 ± 20 kJ/mol. Value Δ_f G _el^o(298.15 K) = −3765 ± 20 kJ/mol was calculated.     

Ab initio calculations find 2,2-disilylcyclopentane-1,3-diyl is a singlet diradical with a high barrier to ring closure

Ab initio calculations on the lowest singlet and triplet states of 2,2-disilylcyclopentane-1,3-diyl find that the singlet lies well below the triplet. The C ₂ singlet diradical is calculated to be a minimum on the potential energy surface with an enthalpic barrier to ring closure of ΔH ^‡ ₂₉₈ = 13.5 kcal/mol at the CASPT2/6-31G* level of theory. The energy of the 1,3-divinyl-substituted singlet diradical is calculated to be only 0.8 kcal/mol higher than that of 5,5-disilyl-1,3-divinylbicyclo[2.1.0]pentane at this level of theory, but the transition state for their equilibration is computed to be 12.8 kcal/mol above the diradical in energy. Received: 2 July 1998 / Accepted: 4 August 1998 / Published online: 16 November 1998     

Conformational analysis of caprolactam,cycloheptene and caprolactone

The conformations of ε-caprolactam, cis-cycloheptene and ε-caprolactone have been investigated at the B3LYP and CCSD(T) levels of theory using the 6-311+G(d,p) basis set. Inversion of the most stable chair conformation was calculated to require a free energy of ΔG ^‡ = 10.5 kcal/mol for caprolactam, ΔG ^‡ = 5.0 kcal/mol for cycloheptene and ΔG ^‡ = 8.4 kcal/mol for caprolactone. These results are in good agreement with the available experimental data of 10.3 and 5.0 kcal/mol for caprolactam and cycloheptene, respectively. Analysis of a classical force field expression fitted to the quantum mechanical energy surface suggests that the caprolactam ring is more strained than cycloheptene owing to unfavourable bending interactions.     

Determination of the gas-phase acidity of methylthioacetic acid using the Cooks’ kinetic method

We determined the gas-phase acidity of methylthioacetic acid (MTA) in a triple-quadrupole mass spectrometer using the Cooks’ kinetic method with the consideration of entropy effects. The negatively charged proton-bound dimers were generated by electrospray ionization. Collision-induced dissociation was applied to the dimer ions and the product ion ratios were measured at four different collision energies. The gas-phase acidity (ΔH _acid) of MTA was determined to be 340.0±1.7 kcal/mol using the extended kinetic method and 339.8±1.7 kcal/mol using the standard kinetic method. The entropy term is insignificant in this case and can be ignored. The standard kinetic method yielded a free energy of deprotonation of MTA (ΔG _acid) of 333.0±1.7 kcal/mol. The entropy of the acid dissociation, ΔS _acid, was estimated to be 22.8 cal/mol K. Theoretical prediction at the B3LYP/6-31+G* level of theory gives a similar value for ΔH _acid of 338. 9 kcal/mol. In the gas-phase, MTA is a stronger acid than methoxyacetic acid, although in solution, MTA is a weaker one.     

Theoretical study of the neutral hydrolysis of methyl formate via a concerted and stepwise water-assisted mechanism using free-energy curves and molecular dynamics simulation

A procedure previously described by us is used for the theoretical study of chemical reactions in solution by means of molecular dynamics simulation, with solute–solvent interaction potentials LJ (12-6-1) derived from ab initio quantum calculations. We apply the procedure to the case of the neutral hydrolysis of methyl formate, HCOOCH₃ + 3H₂O → HCOOH + CH₃OH + 2H₂O in aqueous solution, via concerted and stepwise water-assisted mechanisms. We use the solvent as reaction coordinate, and the free-energy curves for the calculation of the activation energies. The theoretical calculation for the thermodynamics of this hydrolysis reaction in aqueous solution, assisted by three water molecules, is in agreement with the available experimental information. In particular our study gives values of ΔG ^≠ = 28.88 and 28.17 kcal/mol for the concerted and stepwise mechanisms, close to the experimental activation barrier of 28.8 kcal/mol, and a significant improvement over the values of 48.05 and 45.66 kcal/mol found in another similar study using the PCM model.     

Hybrid density functional theory with a specific reaction parameter: hydrogen abstraction reaction of trifluoromethane by the hydroxyl radical

Potential energy surfaces are developed and tested for the OH + CHF₃ → H₂O + CF₃ reaction. The objective is to obtain surfaces that give calculated rate constants comparable to the experimental ones. The potential energy surfaces are constructed using hybrid and hybrid meta density functional theory methods (mPW1PW91, B1B95, and mPW1B95) with specific reaction parameters in conjunction with the 6–31+ G(d,p) basis set. The rate constants are calculated over the temperature range 200–1,500 K using variational transition state theory with multidimensional tunneling contributions. The hybrid density functional theory methods with specific-reaction-parameter Hartree-Fock exchange contributions (32.8–34.8% for mPW1PW91, 34.2–36.0% for B1B95, and 37.8–39.7% for mPW1B95, respectively) provide accurate rate constants over an extended temperature range. The classical barrier height for the hydrogen abstraction reaction is determined to be 6.5–6.9 kcal/mol on these potential energy surfaces, and the best estimate value is 6.77 kcal/mol. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users.     

Rational design,synthesis and biological evaluations of amino-noscapine: a high affinity tubulin-binding noscapinoid

Noscapine and its derivatives are important microtubule-interfering agents shown to have potent anti-tumor activity. The binding free energies (ΔG _bind) of noscapinoids computed using linear interaction energy (LIE) method with a surface generalized Born (SGB) continuum solvation model were in agreement with the experimental ΔG _bind with average root mean square error of 0.082 kcal/mol. This LIE–SGB model guided us in designing a novel derivative of noscapine, amino-noscapine [(S)-3-((R)-9-amino-4-methoxy-6-methyl-5,6,7,8-tetrahydro [1, 3] dioxolo[4,5-g]isoquinolin-5-yl)-6,7-dimethoxy isobenzo-furan-1(3H)-one] that has higher tubulin binding activity (predicted ΔG _bind = −6.438 kcal/mol and experimental ΔG _bind = −6.628 kcal/mol) than noscapine, but does not significantly change the total extent of the tubulin subunit/polymer ratio. The modes of interaction of amino-noscapine with the binding pocket of tubulin involved three hydrogen bonds and are distinct compared to noscapine which involved only one hydrogen bond. Also the patterns of non-bonded interactions are albeit different between both the lignads. The ‘blind docking’ approach (docking of ligand with different binding sites of a protein and their evaluations) as well as the reasonable accuracy of calculating ΔG _bind using LIE–SGB model constitutes the first evidence that this class of compounds binds to tubulin at a site overlapping with colchicine-binding site or close to it. Our results revealed that amino-noscapine has better anti-tumor activity than noscapine.     

Microcalorimetric determination of displacement adsorption enthalpies of protein refolding on a moderately hydrophobic surface at 308 K

Both microcalorimetric determination of displacement adsorption enthalpies ΔH and measurement of adsorbed amounts of guanidine – denatured lysozyme (Lys) refolding on the surface of hydrophobic interaction chromatography (HIC) packings at 308 K were carried out and compared with that at 298 K. Study shows that both temperature and concentration of guanidine hydrochloride (GuHCl) affect the molecular mechanism of hydrophobic interaction of protein with adsorbent based on the analysis of dividing ΔH values into three kinds of enthalpy fractions. The adsorption in higher concentrations of GuHCl (>1.3 mol L^–1) at 308 K is an enthalpy-driving process, and the adsorption under other GuHCl concentrations is an entropy-driving process. The fact that the Lys denatured by 1.8 mol L^–1 GuHCl forms a relatively stable intermediate state under the studied conditions will not be changed by temperature.     

Oxidation of 1,3,7-trimethylxanthine by hypochlorite ion

The kinetics of the oxidative conversion of 1,3,7-trimethylxanthine upon treatment with hypochlorite ions (OCl⁻) in aqueous medium at 283–298 K and pH 8.2 was studied. The reaction order with respect to each component was determined and proved to be 1. It was established that the temperature dependence of the reaction rate follows the Arrhenius equation. The activation parameters of the reaction were measured: E _a = 33.58 kJ/mol, ΔH ^≠ = 31.12 kJ/mol, ΔS ^≠ = −170.02 J/(K mol), ΔG ^≠ = 81.45 kJ/mol. The stoichiometry of the reaction was studied, and the chemistry of the oxidative conversion of caffeine treated with OCl⁻ is discussed.     

3,3-Sigmatropic Shifts of Allyl Group Along Cyclopentadiene Ring Perimeter

Reversible non-degenerate 3,3-sigmatropic shifts of the allyl group along the perimeter of the five-membered ring occurring with energy barriers ΔG°≠ = 28.5–30.2 kcal/mol (o-dichlorobenzene-d4) have been detected in the allyl derivatives of 5-methyl-1,2,3,4-tetramethoxycarbonylcyclopentadiene by NMR method. Using DFT B3LYP/6-311++G(d,p) method, it has been shown that degenerate migrations of the allyl group in the related 5-allyl-1,2,3,4,5-pentamethoxycarbonylcyclopentadiene should occur via 3,3-sigmatropic shift through transition states with conformation of a six-membered ring (chair or boat, with close barriers ΔG°≠ = 27.4 or 27.7 kcal/mol, respectively). The simulated higher barrier of alternative 1,5-sigmatropic shifts of the allyl group (ΔG°≠ = 30.8 kcal/mol) indicates the energy preference of the migrations via 3,3-shifts.     

Theoretical study of the structure and stability of the Na2Cl+, NaCl 2? , Na3Cl 2+ , and Na2Cl 3? ions

The geometrical parameters, normal vibration frequencies, and thermochemical characteristics of the Na₂Cl⁺, NaCl ₂ ⁻ , Na₃Cl ₂ ⁺ , and Na₂Cl ₃ ⁻ ions in saturated vapors over sodium chloride were calculated by the ab initio methods including electron correlation. According to calculations, the Na₂Cl⁺ and NaCl ₂ ⁻ triatomic ions have a linear equilibrium D _∞h configuration. The pentaatomic ions can exist in the form of the D _∞h linear isomer, C _2v planar cyclic isomer, or D _3h bipyramidal isomer. At ∼1000 K the Na₃Cl ₂ ⁺ and Na₂Cl ₃ ⁻ ions exist predominantly in the form of the linear isomers. The energies and enthalpies of the ion-molecule reactions involving the above ions were calculated. The formation enthalpy of the ions Δ_f H ⁰(0 K) was determined: 230 ± 2 kJ/mol (Na₂Cl⁺), −96 ± 4 kJ/mol (Na₂Cl ₃ ⁻ ), −616 ± 2 kJ/mol (NaCl ₂ ⁻ ), and −935 ± 4 kJ/mol (Na₂Cl ₃ ⁻ ). Original Russian Text Copyright ? 2007 by T. P. Pogrebnaya, A. M. Pogrebnoi, and L. S. Kudin __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 48, No. 6, pp. 1053–1061, November–December, 2007.     

Thermodynamic characteristics of the acid dissociation of dopamine hydrochloride in water-ethanol solutions

Enthalpies of the interaction of protonated dopamine with a hydroxide ion in water-ethanol mixtures in the concentration range of 0–0.8 EtOH mole fractions are measured calorimetrically. The neutralization process of dopamine hydrochloride is shown to occur endothermally in solvents with an ethanol concentration of ≥0.5 mole fractions. Standard thermodynamic characteristics (Δ_r H ^○, Δ_r G ^○, and Δ_r S ^○) of the first-step acid dissociation of dopamine hydrochloride in solutions are calculated with regard to the autoprotolysis enthalpy of binary solvents. It is found that dissociation enthalpies vary within 9.1–64.8 kJ/mol, depending on the water-ethanol solvent composition.     

Thermophysical Investigations of the Polymorphous Phases of Calcium Carbonate

1. Results of thermodynamic and kinetic investigations for the different crystalline calcium carbonate phases and their phase transition data are reported and summarized (vaterite: V; aragonite: A; calcite: C). A→C: T _tr=455±10°C, Δ_tr H=403±8 J mol^–1 at T _tr, V→C: T _tr=320–460°C, depending on the way of preparation,Δ_tr H=–3.2±0.1 kJ mol^–1 at T _tr,Δ_tr H=–3.4±0.9 kJ mol^–1 at 40°C, S _V ^Θ= 93.6±0.5 J (K mol)^–1, A→C: E _A=370±10 kJ mol^–1; XRD only, V→C: E _A=250±10 kJ mol^–1; thermally activated, iso- and non-isothermal, XRD 2. Preliminary results on the preparation and investigation of inhibitor-free non-crystalline calcium carbonate (NCC) are presented. NCC→C: T _tr=276±10°C,Δ_tr H=–15.0±3 kJ mol^–1 at T _tr, T _tr – transition temperature, Δ_tr H – transition enthalpy, S ^Θ – standard entropy, E _A – activation energy. 3. Biologically formed internal shell of Sepia officinalis seems to be composed of ca 96% aragonite and 4% non-crystalline calcium carbonate. This revised version was published online in July 2006 with corrections to the Cover Date.     

The thermodynamic properties of S-lactic acid

The enthalpies of combustion and formation of S-lactic acid at 298.15 K, Δ_c H _m^o(cr.) = −1337.9 ± 0.8 and Δ_f H _m^o(cr.) = −700.1 ± 0.9 kJ/mol, were determined by calorimetry. The temperature dependence of acid vapor pressure was studied by the transpiration method, and the enthalpy of its vaporization was obtained, Δ_vap H ^o(298.15 K) = 69.1 ± 1.0 kJ/mol. The temperature and enthalpy of fusion, T _m (330.4 K) and Δ_m H ^o(298.15 K) = 14.7 ± 0.2 kJ/mol, were determined by differential scanning calorimetry. The enthalpy of formation of the acid in the gas phase was obtained. Ab initio methods were used to perform a conformational analysis of the acid, calculate fundamental vibration frequencies, moments of inertia, and total and relative energies of the stablest conformers. Thermodynamic properties were calculated in the ideal gas state over the temperature range 0–1500 K. A thermodynamic analysis of mutual transformation processes (the formation of SS- and RS(meso)-lactides from S-lactic acid and the racemization of these lactides) and the formation of poly-(RS)-lactide from S-lactic acid and SS- and RS(meso)-lactides was performed.     

Etude par Spectrophotometrie d'absorption de l'Equilibre Pu4++Cl−⇋Pu3++1/2 Cl2 dans le melange LiCl−KCl (70–30% mol) fondu

The quantitative study of the equilibrium Pu⁴⁺+Cl⁻⇋Pu³⁺+1/2 Cl₂ in LiCl−KCl (70–30% mol) at 455, 500, 550 and 600°C by visible and near I.R. absorption spectrophotometry allows the calculation of the reaction's equilibrium constant, the mean thermodynamic data ΔH=27±14 kJ·mol⁻¹ and ΔS=37±17 J·mol⁻¹·K⁻¹ and the standard potential of the couple .      

Gas-phase acidities of cysteine-polyglycine peptides: The effect of the cysteine position

The sequence and conformational effects on the gas-phase acidities of peptides have been studied by using two pairs of isomeric cysteine-polyglycine peptides, CysGly_3,4NH₂ and Gly_3,4CysNH₂. The extended Cooks kinetic method was employed to determine the gas-phase acidities using a triple quadrupole mass spectrometer with an electrospray ionization source. The ion activation was achieved via collision-induced dissociation experiments. The deprotonation enthalpies (Δ_acid H) were determined to be 323.9 ± 2.5 kcal/mol (CysGly₃NH₂), 319.2 ± 2.3 kcal/mol (CysGly₄NH₂), 333.8 ± 2.1 kcal/mol (Gly₃CysNH₂), and 321.9 ± 2.8 kcal/mol (Gly₄CysNH₂), respectively. The corresponding deprotonation entropies (Δ_acid S) of the peptides were estimated. The gas-phase acidities (Δ_acid G) were derived to be 318.4 ± 2.5 kcal/mol (CysGly₃NH₂), 314.9 ± 2.3 kcal/mol (CysGly₄NH₂), 327.5 ± 2.1 kcal/mol (Gly₃CysNH₂), and 317.4 ± 2.8 kcal/mol (Gly₄CysNH₂), respectively. Conformations and energetic information of the neutral and anionic peptides were calculated through simulated annealing (Tripos), geometry optimization (AM1), and single point energy calculations (B3LYP/6-31+G(d)), respectively. Both neutral and deprotonated peptides adopt many possible conformations of similar energies. All neutral peptides are mainly random coils. The two C-cysteine anionic peptides, Gly_3,4(Cys-H)⁻NH₂, are also random coils. The two N-cysteine anionic peptides, (Cys-H)⁻Gly_3,4NH₂, may exist in both random coils and stretched helices. The two N-cysteine peptides, CysGly₃NH₂ and CysGly₄NH₂, are significantly more acidic than the corresponding C-terminal cysteine ones, Gly₃CysNH₂ and Gly₄CysNH₂. The stronger acidities of the former may come from the greater stability of the thiolate anion resulting from the interaction with the helix-macrodipole, in addition to the hydrogen bonding interactions.