Application of potential constants: Electronic chemical potentials of polyatomic molecules—VIII

A new approach for the calculation of electronic chemical potentials of polyatomic systems is developed by applying the quadratic potential (force) constants which are available from normal coordinate analyses using spectroscopic data. The approach is constructed within the framework of density-functional theory into which the simple bond-charge model is incorporated. To evaluate the utility of such an approach, we have calculated electronic chemical potentials for various kinds of polyatomic molecules, and the calculated results have been compared favorably with experimental values as well as those obtained from ab initio SCF calculations. It seems that this approach offers the possibility of chemical potential calculations for polyatomic molecules whose quadratic stretching force constants are obtained by normal coordinate analyses.     

Heteronuclear diatomic force constants clarified through perturbation theory II

A simple relationship between the heteronuclear diatomic force constant (K(AB)) and the homonuclear diatomic force constants (K(AA), K(BB)), which was proposed in a previous report, has been improved through the second-order perturbation theory as K(AB) = zeta3(K(AA) x K(BB))(1/2); zeta = (R(AA) x R(BB))(1/2)/R(AB) where zeta denotes the correction factor in which R(AB), R(AA), and R(BB) are the equilibrium internuclear distances of diatomic molecules AB, AA, and BB, respectively. To test the above expression, a large number of heteronuclear diatomic force constants have been calculated and compared with those obtained from normal coordinate analyses as well as ab initio quantum mechanical methods (Gaussian 98W). We have found that the above modified expression better reproduces the force constants of most heteronuclear diatomic molecules than the previous expression. It is therefore expected that the expression may also be applied to the prediction of stretching force constants between heteronuclear diatomics in various polyatomic molecules.     

Investigation of solvent effects for the Claisen rearrangement of chorismate to prephenate: mechanistic interpretation via near attack conformations

Solvent effects on the rate of the Claisen rearrangement of chorismate to prephenate have been examined in water and methanol. The preequilibrium free-energy differences between diaxial and diequatorial conformers of chorismate, which had previously been implicated as the sole basis for the observed 100-fold rate increase in water over methanol, have been reframed using the near attack conformation (NAC) concept of Bruice and co-workers. Using a combined QM/MM Monte Carlo/free-energy perturbation (MC/FEP) method, 82%, 57%, and 1% of chorismate conformers were found to be NAC structures (NACs) in water, methanol, and the gas phase, respectively. As a consequence, the conversion of non-NACs to NACs provides no free-energy contributions to the overall relative reaction rates in water versus methanol. Free-energy perturbation calculations yielded differences in free energies of activation for the two polar protic solvents and the gas phase. The rate enhancement in water over the gas phase arises from preferential hydration of the transition state (TS) relative to the reactants via increased hydrogen bonding and long-range electrostatic interactions, which accompany bringing the two negatively charged carboxylates into closer proximity. More specifically, there is an increase of 1.3 and 0.6 hydrogen bonds to the carboxylate groups and the ether oxygen, respectively, in going from the reactant to the TS in water. In methanol, the corresponding changes in hydrogen bonding with first shell solvent molecules are small; the rate enhancement arises primarily from the enhanced long-range interactions with solvent molecules. Thus, the reaction occurs faster in water than in methanol due to greater stabilization of the TS in water by specific interactions with first shell solvent molecules.     

Single-molecule force spectroscopy measurements of bond elongation during a bimolecular reaction

It is experimentally challenging to directly obtain structural information of the transition state (TS), the high-energy bottleneck en route from reactants to products, for solution-phase reactions. Here, we use single-molecule experiments as well as high-level quantum chemical calculations to probe the TS of disulfide bond reduction, a bimolecular nucleophilic substitution (S N2) reaction. We use an atomic force microscope in force-clamp mode to apply mechanical forces to a protein disulfide bond and obtain force-dependent rate constants of the disulfide bond reduction initiated by a variety of nucleophiles. We measure distances to the TS or bond elongation (Delta x), along a 1-D reaction coordinate imposed by mechanical force, of 0.31 +/- 0.05 and 0.44 +/- 0.03 A for thiol-initiated and phosphine-initiated disulfide bond reductions, respectively. These results are in agreement with quantum chemical calculations, which show that the disulfide bond at the TS is longer in phosphine-initiated reduction than in thiol-initiated reduction. We also investigate the effect of solvent environment on the TS geometry by incorporating glycerol into the aqueous solution. In this case, the Delta x value for the phosphine-initiated reduction is decreased to 0.28 +/- 0.04 A whereas it remains unchanged for thiol-initiated reduction, providing a direct test of theoretical calculations of the role of solvent molecules in the reduction TS of an S N2 reaction. These results demonstrate that single-molecule force spectroscopy represents a novel experimental tool to study mechanochemistry and directly probe the sub-?ngstr?m changes in TS structure of solution-phase reactions. Furthermore, this single-molecule method opens new doors to gain molecular level understanding of chemical reactivity when combined with quantum chemical calculations.     

Anharmonic Force Fields and Perturbation Theory in the Interpretation of Vibrational Spectra of Polyatomic Molecules

The problem of describing real vibrational spectra of large molecules in terms of perturbation theory is considered. Equations necessary for presenting theoretical anharmonic force fields in various coordinate systems (Cartesian, normal, and internal curvilinear) are discussed. A review of second-order perturbation theory equations necessary for calculating certain spectroscopic values (anharmonicity constants, rotational-vibrational interaction, etc.) is given. A scheme for including resonances based on the construction of the interaction matrix between vibrational transitions of various types is described. This scheme can be used as a basis for anharmonic calculations of vibrations of medium-sized molecules.     

Chiral force constants: Recommendations for the presentation of internal coordinate force constants

Some force constants associated with the internal coordinates that sense handedness or chirality can have opposite signs in the enantiomers of chiral molecules. Examples of such force constants include interaction force constants between a torsional and stretching or bending internal coordinates. The sign reversal for these force constants in the enantiomers of chiral molecules or in opposite-handed molecular segments is best recognized by labeling them as chiral force constants. Recognition of chiral force constants suggests that certain guidelines are to be followed in the presentation of internal coordinate force constants. © 1993 by John Wiley & Sons, Inc. © John Wiley & Sons, Inc.     

Tracing the minimum-energy path on the free-energy surface

The free-energy profile of a reaction can be estimated in a molecular-dynamics approach by imposing a mechanical constraint along a reaction coordinate (RC). Many recent studies have shown that the temperature can greatly influence the path followed by the reactants. Here, we propose a practical way to construct the minimum-energy path directly on the free-energy surface at a given temperature. First, we follow the blue-moon ensemble method to derive the expression of the free-energy gradient for a given RC. These derivatives are then used to find the actual minimum-energy reaction path at finite temperature, in a way similar to the intrinsic reaction path of Fukui on the potential-energy surface. [K. Fukui, J. Phys. Chem. 74, 4161 (1970)]. Once the path is known, one can calculate the free-energy profile using thermodynamic integration. We also show that the mass-metric correction cancels for many types of constraints, making the procedure easy to use. Finally, the minimum-free-energy path at 300 K for the addition of CCl2 to ethylene is compared with a path based on a simple one-dimensional reaction coordinate. A comparison is also given with the reaction path at 0 K.     

Cope elimination: elucidation of solvent effects from QM/MM simulations

The Cope elimination reactions for threo- and erythro-N,N-dimethyl-3-phenyl-2-butylamine oxide have been investigated using QM/MM calculations in water, THF, and DMSO. The aprotic solvents provide up to million-fold rate accelerations. The effects of solvation on the reactants, transition structures, and rates of reaction are elucidated here using two-dimensional potentials of mean force (PMF) derived from free-energy perturbation calculations in Monte Carlo simulations (MC/FEP). The resultant free energies of activation in solution are in close agreement with experiment. Ab initio calculations at the MP2/6-311+G-(2d,p) level using the PCM continuum solvent model were also carried out; however, only the QM/MM methodology was able to reproduce the large rate increases in proceeding from water to the dipolar aprotic solvents. Solute-solvent interaction energies and radial distribution functions are also analyzed and show that poorer solvation of the reactant in the aprotic solvents is primarily responsible for the observed rate enhancements. It is found that the amine oxide oxygen is the acceptor of three hydrogen bonds from water molecules for the reactant but only one to two weaker ones at the transition state. The overall quantitative success of the computations supports the present QM/MM/MC approach, featuring PDDG/PM3 as the QM method.     

Polyatomic,anharmonic, vibrational–rotational analysis. Application to accurate ab initio results for formaldehyde

A computer program SURVIB is described for calculating vibrational anharmonicity constants for polyatomic molecules. The program requires as input a grid of calculated energies in the vicinity of a stationary point. This grid is fit, in a least squares sense, to a polynomial function of the internal coordinates. This analytic representation of the energy surface is employed in a normal mode analysis, and the energy is reexpanded as a polynominal function of the normal mode coordinates (expressed as vectors in the mass-weighted atomic Cartesian coordinate space). The resulting coefficients are used in a second-order perturbation theory analysis to obtain the vibrational anharmonicity constants. Also reported is an application of this program to formaldehyde employing ab initio, RHF , MP 2, MP 3, and RHF -CI calculations. The spectroscopic constants obtained for H₂CO are in good agreement with experimentally derived values recently reported by Reisner.     

Potential-Barrier Profile for an Adiabatic Electron Transfer Reaction in a Condon Approximation with Allowance for Nonsphericity of Electron Wavefunctions

The free-energy surface profile for an adiabatic electron transfer reaction in a polar solvent is calculated. The calculation allows for the dependence of electron wavefunctions of reactants on the environment polarization and for nonsphericity of electron wavefunctions. Allowance for the nonsphericity reduces significantly the activation barrier and increases the reaction rate.     

On the mechanism of surfactant adsorption on solid surfaces: free-energy investigations

The adsorption free-energy of surfactant on solid surfaces has been calculated by molecular dynamics (MD) simulation for a model surfactant/solvent system. The umbrella-sampling with the weight histogram analysis method (WHAM) was applied. The entropic and enthalpic contributions to the full potential of mean force (PMF) were obtained to evaluate the detailed thermodynamics of surfactant adsorption in solid/liquid interfaces. Although we observed that this surfactant adsorption process is driven mainly by a favorable enthalpy change, a highly unfavorable entropic contribution still existed. By decomposing the free energy (including its entropic and enthalpic components) into the solvent-induced contribution and the surfactant-wall term, the effect of surface and solvent on the adsorption free-energy has been distinguished. The contribution to the PMF from the surface effect is thermodynamically favorable, whereas the solvent term displays an obviously unfavorable component with a monotonic increase as the surfactant approaches to the surface. The impact of various interactions from the surfaces (both solvent-philic and solvent-phobic) and the solvent on the adsorption PMF of surfactant has been compared and discussed. Compared to the solvent-philic surface, the solvent-phobic surface generates more stable site for the surfactant adsorption. However, the full PMF profile for the solvent-phobic system shows a clear positive maximum value at the bulk-interface transition region, which leads to a considerable long-range free-energy barrier to the surfactant adsorption. These results have been analyzed in terms of the local interfacial structures. In summary, this comprehensive study is expected to reveal the microscopic interaction mechanisms determining the surfactant adsorption on solid surfaces.     

OUH体系的结构和分析势能函数

采用密度泛涵B3LYP方法优化出了OUH分子的各种结构，确定了最稳定构型和离解能，以及它们的谐性力常数，并导出双原子分子UH,UO的Murrell-Sorbie势能函数及其光谱数据。采用多体项展式方法，导出OUH(X^4A')基态分子的分析势能函数，获得OUH(X^4A')体系的势能面，考察了这个势能函数的基本性质，正确地复现出OUH分子的平衡结构特征，结果表明：U+OH,O+UH,H+UO的反应均为无阈能的放热能反应。为进一步探讨OUH体系的反应动力学过程打下了基础。     

Application of potential constants: Molecular chemical potential changes on formation of heteronuclear diatomic molecules—VI

The harmonic and anharmonic potential (force) constants of heteronuclear diatomic molecules, which are usually available from normal coordinate analyses, are applied to problems of determining the molecular chemical potential changes on formation of such molecules. The approach developed here is mainly based on density—functional theory, that is, the respective atomic energies in a molecule are expanded with the numbers of electrons and the nuclear potentials. These expansions are allowable because the ground-state energy for a system of N electrons and given nuclear potential ν(r) is a functional of N and ν(r). To test the reliability of the approach, we have calculated the molecular chemical potentials of alkali halides and other heteronuclear diatomic molecules, and their results have been compared favorably with the data obtained from Sanderson's Principle and the ab initio SCF calculation. We have also estimated apparent chemical hardnesses as well as integral terms including Fukui functions that provide good measures for electron transfers between atoms on molecule formation. Brief discussions on the molecular chemical potential changes are given.     

Equilibrium structure and spectroscopic constants of maleic anhydride

The quadratic, cubic, and semi-diagonal quartic force fields of maleic anhydride have been calculated at the MP2 level of theory employing the cc-pVTZ basis set. The spectroscopic constants derived from the force field are in excellent agreement with the corresponding experimental values. The semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational corrections calculated from the cubic force field. This semi-experimental equilibrium structure is in excellent agreement with the ab initio structures computed at the CCSD(T) level of theory and it is closer to the ab initio structure than the purely experimental (or empirical) structures r ₀, r _m⁽¹⁾, and r _m⁽²⁾ obtained by microwave spectroscopy as well as the equilibrium structure derived from gas-phase electron diffraction data.     

Rotational spectroscopy and equilibrium structures of S3 and S4

The sulfur molecules thiozone S3 and tetrasulfur S4 have been observed in a supersonic molecular beam in the centimeter-wave band by Fourier transform microwave spectroscopy, and in the millimeter- and submillimeter-wave bands in a low-pressure glow discharge. For S3 over 150 rotational transitions between 10 and 458 GHz were measured, and for S4 a comparable number between 6 and 271 GHz. The spectrum of S3 is reproduced to within the measurement uncertainties by an asymmetric top Hamiltonian with three rotational and 12 centrifugal distortion constants; ten distortion constants, but an additional term to account for very small level shifts caused by interchange tunneling, are required to reproduce to comparable accuracy the spectrum of S4. Empirical equilibrium (r(e)(emp)) structures of S3 and S4 were derived from experimental rotational constants of the normal and sulfur-34 species and vibrational corrections from coupled-cluster theory calculations. Quantum chemical calculations show that interchange tunneling occurs because S4 automerizes through a transition state with D2h symmetry which lies about 500 cm(-1) above the two equivalent C2upsilon minima on the potential energy surface.     

Using a family of dividing surfaces normal to the minimum energy path for quantum instanton rate constants

One of the outstanding issues in the quantum instanton (QI) theory (or any transition-state-type theory) for thermal rate constants of chemical reactions is the choice of an appropriate "dividing surface" (DS) that separates reactants and products. (In the general version of the QI theory, there are actually two dividing surfaces involved.) This paper shows one simple and general way for choosing DSs for use in QI theory, namely, using the family of (hyper) planes normal to the minimum energy path on the potential energy surface at various distances s along it. Here the reaction coordinate is not one of the dynamical coordinates of the system (which will in general be the Cartesian coordinates of the atoms), but rather simply a parameter which specifies the DS. It is also shown how this idea can be implemented for an N atom system in three-dimensional space in a way that preserves overall translational and rotational invariance. Numerical application to a simple system (the collinear H+H(2) reaction) is presented to illustrate the procedure.     

On the role of dissipation on the Casimir-Polder potential between molecules in dielectric media

An expression for the Casimir-Polder potential between molecules in a homogeneous dispersive and absorptive dielectric medium is derived. The effect of retardation on the interaction energy is discussed by examining the wave-zone and nonretarded limits of the potential. Unlike Lifshitz theory, the interaction energy is not derived from the potential between macroscopic bodies. In this work, a Green function that explicitly accounts for absorption in the medium is obtained. This function leads to possible dissipation effects and presents a near-zone form that vanishes in the limit of nonabsorptive medium. Employing a two-level model, it is shown that the retarded van der Waals dispersion potential in a medium may become repulsive as a consequence of absorption by the medium. It is suggested that the repulsive dispersion force may delay precipitation of nonpolar molecules from a dielectric solvent or even inhibit chemical reaction between them.     

Characterization of ester hydrolysis in terms of microscopic rate constants

Hydroxide-catalyzed ester hydrolysis for molecules of coexisting species is quantitated in terms of microscopic rate constants, a new, species-specific physicochemical parameter. Relationships between the overall and component reactions, as well as the macroscopic and microscopic rate constants are deduced. Experimental techniques, evaluation methods, and feasibility are discussed. Species-specific, pH-independent rate constants of four coexisting, differently hydrolyzing microspecies are determined for the first time. Protonation of an alpha-amino and beta-imidazolyl site in amino acid esters has been found to accelerate the hydroxide-catalyzed hydrolysis by factors of 120 and 7.5, respectively, whereas they jointly exert a nearly 3000-fold acceleration. A total of 20 microscopic protonation equilibrium constants, as component parameters in the rate equations, have also been determined. The species-specific rate constants have been found to correlate with the site- and species-specific basicity of the leaving group and the NMR chemical shift of an adjacent proton. Individual contributions of the various microforms to the overall hydrolysis rate are depicted in microscopic reaction fraction diagrams.     

Analysis of vibrational spectra of 3-halo-1-propanols CH(2)XCH(2)CH(2)OH (X is Cl and Br)

The conformational stability and the three rotor internal rotations in 3-chloro- and 3-bromo-1-propanols were investigated by DFT-B3LYP/6-311+G and ab initio MP2/6-311+G, MP3/6-311+G and MP4(SDTQ)//MP3/6-311+G levels of theory. On the calculated potential energy surface twelve distinct minima were located all of which were not predicted to have imaginary frequencies at the B3LYP level of theory. The calculated lowest energy minimum in the potential curves of both molecules was predicted to correspond to the Gauche-gauche-trans (Ggt) conformer in excellent agreement with earlier microwave and electron diffraction results. The equilibrium constants for the conformational interconversion of the two 3-halo-1-propanols were calculated at the B3LYP/6-311+G level of calculation and found to correspond to an equilibrium mixture of about 32% Ggt, 18% Ggg1, 13% Tgt, 8% Tgg and 8% Gtt conformations for 3-chloro-1-propanol and 34% Ggt, 15% Tgt, 13% Ggg1, 9% Tgg and 7% Gtt conformations for 3-bromo-1-propanol at 298.15K. The nature of the high energy conformations was verified by carrying out solvent experiments using formamide ( epsilon=109.5) and MP3 and MP4//MP3 calculations. The vibrational frequencies of each molecule in its three most stable forms were computed at the B3LYP level and complete vibrational assignments were made based on normal coordinate calculations and comparison with experimental data of the molecules.     

Steady-state nucleation rate and flux of composite nucleus at saddle point

The steady-state nucleation rate and flux of composite nucleus at the saddle point is studied by extending the theory of binary nucleation. The Fokker-Planck equation that describes the nucleation flux is derived using the Master equation for the growth of the composite nucleus, which consists of the core of the final stable phase surrounded by a wetting layer of the intermediate metastable phase nucleated from a metastable parent phase recently evaluated by Iwamatsu [J. Chem. Phys. 134, 164508 (2011)]. The Fokker-Planck equation is similar to that used in the theory of binary nucleation, but the non-diagonal elements exist in the reaction rate matrix. First, the general solution for the steady-state nucleation rate and the direction of nucleation flux is derived. Next, this information is then used to study the nucleation of composite nucleus at the saddle point. The dependence of steady-state nucleation rate as well as the direction of nucleation flux on the reaction rate in addition to the free-energy surface is studied using a model free-energy surface. The direction of nucleation current deviates from the steepest-descent direction of the free-energy surface. The results show the importance of two reaction rate constants: one from the metastable environment to the intermediate metastable phase and the other from the metastable intermediate phase to the stable new phase. On the other hand, the gradient of the potential Φ or the Kramers crossover function (the commitment or splitting probability) is relatively insensitive to reaction rates or free-energy surface.