Rigid Rotor Harmonic Oscillator Approximation Research Articles

On Analytical Corrections for Restraints in Absolute Binding Free Energy Calculations.

Double decoupling absolute binding free energy simulations require an intermediate state at which the ligand is held solely by restraints in a position and orientation resembling the bound state. One possible choice consists of one distance, two angle, and three dihedral angle restraints. Here, I demonstrate that in practically all cases the analytical correction derived under the rigid rotator harmonic oscillator approximation is sufficient to account for the free energy of the restraints.

Monohalogenated methyl- and methoxy-benzoic acids: A combined experimental and quantum chemical theoretical study on their structure, vibrational analysis and molecular parameters

In this paper, the molecules 3-fluoro-2-methylbenzoic acid; 3-chloro-2-methoxybenzoic acid; and 3-bromo-2-methylbenzoic were investigated using experimental and quantum chemical theoretical approach for vibrational and electronic properties from the optimized structure. Becke three parameter Lee–Yang–Parr density functionals along with 6-311++G(d,p) basis set were employed to compute their geometric optimization, fundamental frequencies and molecular parameters. The detected FT-IR and FT-Raman spectra were compared with their simulated spectra and the rms error between the detected and simulated vibrational frequencies was found at 6.17, 7.22 and 6.76 cm−1 for FMA, CMA and BMA, respectively. All the vibrational fundamentals were assigned unequivocally using potential energy distribution (PED) obtained in the computations. 1H and 13C NMR chemical shifts were evaluated by integrating the gauge-independent atomic orbital (GIAO) method with DFT and compared with corresponding experimental values. TD-DFT approach was followed to compare the simulated absorption maxima (λmax) in DMSO-d6 solvent with observed values and interpreted in terms of HOMO and LUMO. The global reactive descriptors were estimated from the associated energies of HOMO and LUMO which describe the reactivity and stability of the molecules. Molecular electrostatic potential (MEP) surface has been determined using the charge density distributions to demonstrate electrophilic and nucleophilic nature of the molecules. DFT computations also ascertained the applicability of the titled molecules as NLO materials from the computed values of dipole moment and hyperpolarizability. Thermodynamic parameters and rotational constants were also evaluated employing rigid rotor harmonic oscillator approximation. Natural bond orbital (NBO) analysis confirmed the charge delocalization due to intra-molecular interactions.

Heat Capacity and Bond Dissociation Energy Calculations of Some Fluorinated Ethanol’s and its Radicals: CH<sub>3-x</sub>CH<sub>2</sub>F<sub>x</sub>OH, CH<sub>3</sub>CH<sub>2-x</sub>F<sub>x</sub>OH

Structures and thermochemical properties of these species were determined by the gaussian M-062x/6-31 + g (d, p) calculation enthalpies of formation for 19 fluorinated ethanol and some radicals were calculated with a popular Ab initio and density functional theory methods: The gaussian M-062x/6-31 + g (d, p) via several series of isodesmic reactions. Entropies (S298°K in Cal·Mol-1 K-1) were estimated using the M-062x/6-31 + g (d, p) computed frequencies and geometries. Contributions of entropy, S298°K, and heat capacities, Cp(T) due to vibration, translation, and external rotation of the molecules were calculated based on the vibration frequencies and structures obtained from the M-062x/6-31 + g (d, p) Density Functional Method. Potential barriers are calculated using M-062x/6-31 + g (d, p) density functional method and are used to calculate rotor contributions to entropy and heat capacity using integration over energy levels of rotational potential. Rotational barriers were determined and hindered internal rotational contributions for S298° - 1500°K, and Cp (T) were calculated using the rigid rotor harmonic oscillator approximation, with direct integration over energy levels of the intramolecular rotation potential energy curves. Thermochemical properties of fluorinated alcohols are needed for understanding their stability and reactions in the environment and in thermal process

Thermodynamic Functions of 1, 2, 3- tri-meth-oxy-benzene and m-methyl-meth-oxy benzene

The statistical computation of an ideal gas state thermodynamic functions namely enthalpy, entropy, free energy, heat capacity of 1,2,3 – Trimethoxy benzene, m-methyl methoxybenzene have been performed. These calculations have been made at a pressure of 1 atmosphere in the temperature range 100°K to 1500°K under rigid rotor harmonic oscillator approximation for 1 mole of perfect gas and on the basis of vibrational frequencies obtained from FTIR and Raman spectra and also with the help of moment of inertia.

Gaussian M-062x/6-31+g (d,p) Calculation of Standard Enthalpy, Entropy and Heat Capacity of Some Fluorinated Alcohol’s and Its Radicals at Different Temperatures

Thermochemical properties of fluorinated alcohols are needed for understanding their stability and reactions in the environment and in thermal process. Structures and thermochemical properties of these species were determined by the Gaussian M-062x/6-31+g (d,p) calculation. Contributions of entropy, S°298, and heat capacities, Cp(T) due to vibration, translation, and external rotation of the molecules were calculated based on the vibration frequencies and structures obtained from the M-062x/6-31+g (d,p) density functional method. Potential barriers are calculated using M-062x/6-31+g (d,p) density functional method and are used to calculate rotor contributions to entropy and heat capacity using integration over energy levels of rotational potential. Enthalpies of formation for 19 fluorinated ethanol and some radicals were calculated with a popular ab initio and density functional theory methods: the Gaussian M-062x/6-31+g (d,p) via several series of isodesmic reactions. The recommended ideal gas phase ΔHf298 ° (kcal mol−1) values calculated in this study are the following: -101.74 ± 0.72 for CH2FCH2OH; -113.51 ±1.39 for CH3CHFOH; -50.66 ± 0.75 for C•HFCH2OH; -56.05±0.62 for CH2FCH•OH; -45.00±1.31 for CH2FCH2O•; -59.61±1.20 for CH2•CHFOH; -67.99± 1.29 for CH3CF•OH; -58.76±1.20 for CH3CHFO•; -154.12±1.72 for CH2FCHFOH; -155.26±1.67 for CF2HCH2OH; -174.53±1.54 for CH3CF2OH; -104.07 ± 1.45 for CH2FC•FOH; -105.63±1.74 for C•HFCFHOH; -99.08±1.57 for CH2FCHFO•; -102.34±1.74 for CHF2C•HOH; -102.23±1.57 for C•F2CH2OH; -98.86±1.57 for CHF2CH2O•; -119.41±1.74 for CH2•CF2OH; -110.56±1.62 for CH3CF2O•. Entropies (S298° in cal mol−1 K−1) were estimated using the M-062x/6-31+g (d,p) computed frequencies and geometries. Rotational barriers were determined and hindered internal rotational contributions for S298°- 1500°, and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation, with direct integration over energy levels of the intramolecular rotation potential energy curves.

First-principles calculation of ideal-gas thermodynamic properties of long-chain molecules by R1SM approach-Application to n-alkanes.

First-principles calculations, coupled with statistical thermodynamics, can provide ideal-gas thermodynamic properties but get complicated and less reliable with an increasing number of conformers. An approach designed for calculation of ideal-gas thermodynamic properties of long-chain molecules, R1SM, and its simplified version, sR1SM, is tested in this work by calculation of ideal-gas heat capacities and entropies for a homologous series of n-alkanes up to n-tetradecane. The R1SM approach incorporates the rigid rotor-harmonic oscillator approximation in combination with a correction for internal rotations of methyl tops using the one-dimensional hindered rotor scheme and the mixing model accounting for the population of conformers based on the Boltzmann distribution. The R1SM approach is applicable for compounds with up to hundreds of conformers, while the simplified sR1SM approach can be used for molecules with up to 105 conformers when coupled with rules for enumeration of stable conformers and estimation scheme for their energies. The obtained results for n-alkanes are compared with experimental values and previously employed computational schemes. As the conformational behavior and conformer energies are inherent parts of the proposed approaches, a thorough conformational study of n-alkanes is performed and compared with experiments and the Tasi rules for enumeration of n-alkane conformers. Finally, the standard uncertainty of the R1SM-calculated ideal-gas thermodynamic properties is estimated based on the error propagation from the used input quantities and approximations as well as on comparison to experimental values and amounts to less than 1% for both ideal-gas heat capacity and standard ideal-gas entropy.

Structural and thermochemical properties of methyl ethyl sulfide alcohols: HOCH2SCH2CH3, CH3SCH(OH)CH3, CH3SCH2CH2OH, and radicals corresponding to loss of H atom

AbstractSulfide alkoxy radicals are important intermediates during the partial oxidation of alkyl sulfides in atmospheric chemistry and in combustion. The atmospheric reaction sequence to formation of the alkoxy radicals includes (1) initial reaction with OH to create a radical on a carbon site, (2) the carbon radical then associates with 3O2 to form a peroxy radical, and (3) an NO radical reacts with the peroxy radical to form an alkoxy radical (RO•) plus NO2. This study determines structural parameters, internal rotor potentials, bond dissociation energies, and thermochemical properties (ΔfH°, S°, and Cp(T)) of 3 corresponding alcohols HOCH2SCH2CH3, CH3SCH(OH)CH3, and CH3SCH2CH2OH of methyl ethyl sulfides studied in order to characterize the thermochemistry of the respective alkoxy radicals. The lowest energy molecular structures were calculated using the B3LYP density functional level of theory with the 6‐311G(2d,d,p) basis set. Standard enthalpies of formation (ΔfH°298) for the radicals and their parent molecules were calculated using B3LYP/6‐31 + G(2d,p), CBS‐QB3, M062x/6‐311 + g(2d,p), and G3MP2B3 methods. Isodesmic reactions were used to determine ∆fH° values. Internal rotation potential energy diagrams and rotation barriers were investigated using the B3LYP/6‐31 + G(d,p) level theory. The contributions for S°298 and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation based on the structures and vibrational frequencies obtained by CBS‐QB3 calculations, with contributions from torsion frequencies replaced by internal rotor contributions. Group additivity and hydrogen bond increment values were developed for estimating properties of structurally similar and larger sulfur‐containing peroxide molecules and their radicals.

A theoretical explanation of RbBH4’s fractionally occupied ground-state phase and the reorientational motion of the [BH4]− group

In this work, a pseudo-structure model is adopted to describe the fractionally occupied phase of RbBH4 at low temperatures. The fractionally occupied cubic ground state with Fm3m symmetry can be explained as a superposition and average of three well-defined pseudo-structures with P43m, F43m and P42/nmc symmetries. First, both mechanical and dynamical stability of these pseudo-structures are supported by the calculated elastic constants and phonon spectra, respectively. By comparing the electronic structure, elastic properties and thermodynamic properties of these well-defined pseudo-structures, it can be found that all pseudo-structures exhibit a certain degree of similarity. Second, the system is stabilized by charge transfer. Bader charge analysis of the pseudo-structures shows that charge transfer in RbBH4 contributes a constant shift in formation energy. Coulomb interaction energy and total electronic energy variations with the unit cell volume have been obtained. The results show that the larger the volume of the unit cell, the lower the difference of Coulomb interaction energy between the pseudo-structures P43m, F43m and P42/nmc. Third, the barrier energies calculated for paths of transitions between these pseudo-structures vary significantly with the volume. As the cell volume decreases from 512 to 216 Å3, the B–H covalent bonds are compressed from 1.242 to 1.208 Å. Meanwhile, the rotational barrier of [BH4]− anion increases rapidly, from 0.04 to 0.97 eV. Last, considering the temperature effect, the free energy and entropy contributions are calculated based on the rigid rotor harmonic oscillator approximation. The Gibbs free energy shows that at low temperature the P42/nmc structure is the preferred structure, and with increasing temperature, the P43m structure becomes the preferred structure. We found that the fractionally occupied phase of RbBH4 can be explained by the size of the Rb+ cation and a subtle balance between the Coulomb interaction energy, electronic total energy and thermal vibration energy.

Structures and thermochemistry of methyl ethyl sulfide and its hydroperoxides: HOOCH2SCH2CH3, CH3SCH(OOH)CH3, CH3SCH2CH2OOH, and radicals

AbstractHydroperoxides and the corresponding peroxy radicals are important intermediates during the partial oxidation of methyl ethyl sulfide (CH3SCH2CH3) in both atmospheric chemistry and in combustion. Structural parameters, internal rotor potentials, bond dissociation energies, and thermochemical properties (ΔHfo, So and Cp(T)) of 3 corresponding hydroperoxides CH2(OOH)SCH2CH3, CH3SCH(OOH)CH3, CH3SCH2CH2OOH of methyl ethyl sulfides, and the radicals formed via loss of a hydrogen atom are important to understanding the oxidation reactions of MES. The lowest energy molecular structures were identified using the density functional B3LYP/6‐311G(2d,d,p) level of theory. Standard enthalpies of formation (ΔHfo298) for the radicals and their parent molecules were calculated using the density functional B3LYP/6‐31G(d,p), B3LYP/6‐31 + G(2d,p), and the composite CBS‐QB3 ab initio methods. Isodesmic reactions were used to determine ∆Hfo values. Internal rotation potential energy diagrams and rotation barriers were investigated using the B3LYP/6‐31G(d,p) level theory. Contributions for So298 and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation based on the structures and vibrational frequencies obtained by the density functional calculations, with contributions from torsion frequencies replaced by internal rotor contributions. The recommended values for enthalpies of formation of the most stable conformers of CH3SCH2CH2, CH2(OOH)SCH2CH3, CH3SCH(OOH)CH3, and CH3SCH2CH2OOH are −14.0, −33.0, −37.2, and −32.7 kcal/mol, respectively. Group additivity values were developed for estimating properties of structurally similar and larger sulfur‐containing peroxides. Groups for use in group additivity estimation of sulfur peroxide thermochemical properties were developed.

Anharmonicity of Coupled Torsions: The Extended Two-Dimensional Torsion Method and Its Use To Assess More Approximate Methods.

In this work we present the extended two-dimensional torsion (E2DT) method and use it to analyze the performance of several methods that incorporate torsional anharmonicity more approximately for calculating rotational-vibrational partition functions. Twenty molecules having two hindered rotors were studied for temperatures between 100 and 2500 K. These molecules present several kinds of situations; they include molecules with nearly separable rotors, molecules in which the reduced moments of inertia change substantially with the internal rotation, and molecules presenting compound rotation. Partition functions obtained by the rigid-rotor harmonic oscillator approximation, a method involving global separability of torsions and the multistructural methods without explicit potential coupling [MS-T(U)] and with explicit potential coupling [MS-T(C)] of torsions, are compared to those obtained with a quantized version - called the extended two-dimensional torsion (E2DT) method - of the extended hindered rotor approximation of Vansteenkiste et al. ( Vansteenkiste et al. J. Chem. Phys. 2006 , 124 , 044314 ). In the E2DT method, quantum effects due to the torsional modes were incorporated by the two-dimensional nonseparable method, which is a method that is based on the solution of the torsional Schrödinger equation and that includes full coupling in both the kinetic and potential energy. By comparing other methods to the E2DT method and to experimental thermochemical data, this study concludes that the harmonic approximation yields very poor results at high temperatures; the global separation of torsions from the rest of the degrees of freedom is not justified even when an accurate method to treat the torsions is employed; it is confirmed that methods based on less complete potential energy coupling of torsions, such as MS-T(U), are not accurate when dealing with rotors with different barrier heights, and more complete inclusion of torsional coupling to the method in MS-T(C) improves substantially the results in such a way that it could be used in cases where the E2DT method is unaffordable.

Thermodynamic functions of germanium oxide molecules in the gaseous phase: GeO2(g), Ge2O2(g), and Ge3O3(g)

Critical analysis of experimental and theoretical data on the structure and vibrational frequencies of GeO2, Ge2O2, and Ge3O3 molecules is performed. The values of molecular constants are chosen, and thermodynamic functions in the rigid rotator–harmonic oscillator approximation are calculated in temperature interval Т = 298.15–3000 K. The values obtained are introduced into the data base of the IVTANTERMO program complex.

Structural and thermochemical studies on CH3SCH2CHO, CH3CH2SCHO, CH3SC(═O)CH3, and radicals corresponding to loss of H atom

AbstractCH3SCH2CHO, CH3CH2SCHO, and CH3SC(═O)CH3 are intermediates during the partial oxidation of CH3SCH2CH3 in the atmosphere and in combustion processes. Thermochemical properties (ΔHfo, So and Cp(T)), structures, internal rotor potentials, and C─H bond dissociation energies of the parent molecules and their radicals formed after loss of a hydrogen atom are of value in understanding the oxidation processes of methyl ethyl sulfide. The lowest energy molecular structures were initially determined using the density functional B3LYP/6‐311G/(2d,d,p) level of theory. Standard enthalpies of formation (ΔHfo298) for the radicals and their parent molecules were calculated using the density functional B3LYP/6‐31G(d,p), B3LYP/6‐31 + G(2d,p), and the composite CBS‐QB3 ab initio methods using isodesmic reactions. Internal rotation potential energy diagrams and internal rotation barriers were investigated using B3LYP/6‐31 + G(d,p) level calculations. The contributions for So298 and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation on the basis of the structures and vibrational frequencies obtained by the density functional calculations, with contributions from torsion frequencies replaced by internal rotor contributions from the method of Pitzer‐Gwinn. The recommended values for enthalpies of formation of the most stable conformers of CH3SCH2CHO, CH3CH2SCHO, and CH3SC(═O)CH3 are −34.6 ± 0.8, −42.4 ± 1.2, and ‐49.7 ± 0.8 kcal/mol, respectively. The structural and thermochemical data presented for CH3SCH2CHO, CH3CH2SCHO, and CH3SC(═O)CH3 and their radicals are of value in understanding the mechanism and kinetics of methyl ethyl sulfide oxidation under varied temperatures and pressures. Group additivity values are developed for estimating properties of structurally similar, larger sulfur‐containing compounds.

Formation of the H2SO4 ·HSO−4 dimer in the atmosphere as a function of conditions: a simulation study

ABSTRACTThe detailed structure and clustering free energy of aerosol particles are important for understanding of new particle formation from molecules and ions in the atmosphere. In this paper, configurations of the H2SO4 ·HSO−4 dimer were sampled with meta-dynamics aided ab initio molecular dynamics (MTD-AIMD) simulations. Based on the rigid rotor harmonic oscillator (RRHO) approximation and the law of mass action, the binding free energies (ΔG) of the dimer in the most stable configuration were calculated for three atmospheric circumstances, i.e. at the ground level and in the middle and upper troposphere. The results show that, the most stable H2SO4 ·HSO−4 dimer is combined via triple O–H⋅⋅⋅O hydrogen bonds. It can be generated efficiently in both the middle and upper troposphere, but not at the ground level. All our simulations were carried out at the level of hybrid density functional theory (PBE0, hybrid-DFT), which is more accurate than DFT only.

Elucidation of Mechanisms and Selectivities of Metal-Catalyzed Reactions using Quantum Chemical Methodology.

Quantum chemical techniques today are indispensable for the detailed mechanistic understanding of catalytic reactions. The development of modern density functional theory approaches combined with the enormous growth in computer power have made it possible to treat quite large systems at a reasonable level of accuracy. Accordingly, quantum chemistry has been applied extensively to a wide variety of catalytic systems. A huge number of problems have been solved successfully, and vast amounts of chemical insights have been gained. In this Account, we summarize some of our recent work in this field. A number of examples concerned with transition metal-catalyzed reactions are selected, with emphasis on reactions with various kinds of selectivities. The discussed cases are (1) copper-catalyzed C-H bond amidation of indoles, (2) iridium-catalyzed C(sp(3))-H borylation of chlorosilanes, (3) vanadium-catalyzed Meyer-Schuster rearrangement and its combination with aldol- and Mannich-type additions, (4) palladium-catalyzed propargylic substitution with phosphorus nucleophiles, (5) rhodium-catalyzed 1:2 coupling of aldehydes and allenes, and finally (6) copper-catalyzed coupling of nitrones and alkynes to produce β-lactams (Kinugasa reaction). First, the methodology adopted in these studies is presented briefly. The electronic structure method in the great majority of these kinds of mechanistic investigations has for the last two decades been based on density functional theory. In the cases discussed here, mainly the B3LYP functional has been employed in conjunction with Grimme's empirical dispersion correction, which has been shown to improve the calculated energies significantly. The effect of the surrounding solvent is described by implicit solvation techniques, and the thermochemical corrections are included using the rigid-rotor harmonic oscillator approximation. The reviewed examples are chosen to illustrate the usefulness and versatility of the adopted methodology in solving complex problems and proposing new detailed reaction mechanisms that rationalize the experimental findings. For each of the considered reactions, a consistent mechanism is presented, the experimentally observed selectivities are reproduced, and their sources are identified. Reproducing selectivities requires high accuracy in computing relative transition state energies. As demonstrated by the results summarized in this Account, this accuracy is possible with the use of the presented methodology, benefiting of course from a large extent of cancellation of systematic errors. It is argued that as the employed models become larger, the number of rotamers and isomers that have to be considered for every stationary point increases and a careful assessment of their energies is therefore necessary in order to ensure that the lowest energy conformation is located. This issue constitutes a bottleneck of the investigation in some cases and is particularly important when analyzing selectivities, since small energy differences need to be reproduced.

Thermodynamic properties of indan: Experimental and computational results

Measurements leading to the calculation of thermodynamic properties in the ideal-gas state for indan (Chemical Abstracts registry number [496-11-7], 2,3-dihydro-1H-indene) are reported. Experimental methods were adiabatic heat-capacity calorimetry, differential scanning calorimetry, comparative ebulliometry, and vibrating-tube densitometry. Molar thermodynamic functions (enthalpies, entropies, and Gibbs energies) for the condensed and ideal-gas states were derived from the experimental studies at selected temperatures. Statistical calculations were performed based on molecular geometry optimization and vibrational frequencies calculated at the B3LYP/6-31+G(d,p) level of theory. Computed ideal-gas properties derived with the rigid-rotor harmonic-oscillator approximation are shown to be in excellent accord with ideal-gas entropies derived from thermophysical property measurements of this research, as well as with experimental heat capacities for the ideal-gas state reported in the literature. Literature spectroscopic studies and ab initio calculations report a range of values for the barrier to ring puckering. Results of the present work are consistent with a large barrier that allows use of the rigid-rotor harmonic-oscillator approximation for ideal-gas entropy and heat-capacity calculations, even with the stringent uncertainty requirements imposed by the calorimetric and physical property measurements reported here. All experimental results are compared with property values reported in the literature.

Thermochemical Properties Enthalpy, Entropy, and Heat Capacity of C1-C4 Fluorinated Hydrocarbons: Fluorocarbon Group Additivity.

Enthalpies of formation for 14 C2–C4 fluorinated hydrocarbons were calculated with nine popular ab initio and density functional theory methods: B3LYP, CBS-QB3, CBS-APNO, M06, M06-2X, ωB97X, G4, G4(MP2)-6X, and W1U via several series of isodesmic reactions. The recommended ideal gas phase ΔHf298° (kcal mol(–1)) values calculated in this study are the following: −65.4 for CH3CH2F; −70.2 for CH3CH2CH2F; −75.3 for CH3CHFCH3; −75.2 for CH3CH2CH2CH2F; −80.3 for CH3CHFCH2CH3; −108.1 for CH2F2; −120.9 for CH3CHF2; −125.8 for CH3CH2CHF2; −133.3 for CH3CF2CH3; −166.7 for CHF3; −180.5 for CH3CF3; −185.5 for CH3CH2CF3; −223.2 for CF4; and −85.8 for (CH3)3CF. Entropies (S298° in cal mol(–1) K(–1)) were estimated using B3LYP/6-31+G(d,p) computed frequencies and geometries. Rotational barriers were determined and hindered internal rotational contributions for S298°, and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation, with direct integration over energy levels of the intramolecular rotation potential energy curve. Thermochemical properties for the fluorinated carbon groups C/C/F/H2, C/C2/F/H, C/C/F2/H, C/C2/F2, and C/C/F3 were derived from the above target fluorocarbons. Previously published enthalpies and groups for 1,2-difluoroethane, 1,1,2-trifluoroethane, 1,1,2,2-tetrafluoroethane, 1,1,1,2-tetrafluoroethane, 1,1,1,2,2-pentafluoroethane, 2-fluoro-2-methylpropane that were previously determined via work reaction schemes are revised using updated reference species values. Standard deviations are compared for the calculation methods.

Theoretical Study of Intermolecular Chain Transfer to Polymer Reactions of Alkyl Acrylates

Mechanisms of intermolecular chain transfer to polymer (CTP) reactions in monomer self-initiated polymerization of alkyl acrylates, such as methyl acrylate, ethyl acrylate, and n-butyl acrylate, are studied using density functional theory calculations. Dead polymer chains with three different structures are considered, and three types of hybrid density functionals and four basis sets are used. The energy barrier and rate constant of each reaction are calculated using the transition state theory and the rigid rotor harmonic oscillator approximation. The study indicates that tertiary hydrogens of dead polymers formed by disproportionation reactions are most likely to be transferred to live polymer chains in CTP reactions. The length of the polymer chain has little effect on the calculated activation energies and transition-state geometries in all CTP mechanisms explored in this study. Moreover, CTP reactions of methyl, ethyl, and butyl acrylates have similar energy barriers and rate constants. The application of the integral equation formalism-polarizable continuum model results in higher CTP energy barriers. This increase in the predicted CTP energy barriers is larger in n-butanol than in p-xylene. However, the application of the conductor-like screening model does not affect the predicted CTP kinetic parameters.

Improved Force-Field Parameters for QM/MM Simulations of the Energies of Adsorption for Molecules in Zeolites and a Free Rotor Correction to the Rigid Rotor Harmonic Oscillator Model for Adsorption Enthalpies

Quantum mechanics/molecular mechanics (QM/MM) simulations provide an efficient avenue for studying reactions catalyzed in zeolite systems; however, the accuracy of such calculations is highly dependent on the zeolite MM parameters used. Previously reported parameters (P1), which were chosen to minimize the root mean square (RMS) deviations of adsorption energies compared with full QM ωB97X-D/6-31+G** adsorption energies, are shown to overestimate binding energies compared with experimental values, particularly for larger substrates. To address this issue, a new parameter set (P2) is derived by rescaling the previously reported characteristic energies of the Lennard-Jones potential in P1. The accuracy of the thermal correction for adsorption enthalpies determined by the rigid rotor-harmonic oscillator approximation (RRHO) is examined and shown to be improved by treating low-lying vibrational modes as free translational and rotational modes via a quasi-RRHO model. With P2 and quasi-RRHO, adsorption energies...

From orientation disordered to ordered--an ab initio simulation on ammonia borane phase transition within van der Waals corrections.

In this work, we report a detailed theoretical investigation of the phase transition of ammonia borane (NH(3) BH(3); AB), from a tetragonal I4mm (C(4v)(9)) phase with disordered orientation of hydrogen to an orthorhombic phase with Pmn2(1) (C(2v)(7)) symmetry, as a function of temperature based on Density Functional Theory calculations with semiempirical dispersion potential correction. We define a series of substructures with the NH(3) BH(3) moiety always in C(3v) symmetry and the partially occupied high temperature state can be described as a continuous transformation between these substructures. To understand the role of the van der Waals corrections to the physical properties, we use the empirical Grimme's dispersion potential correction (PBE-D2). Both Perdew-Burke-Emzerhof (PBE) and PBE-D2 functional yield almost the same energy sequence along the transition path. However, PBE-D2 functional shows obvious advantage in describing the lattice parameters of AB. The rigid rotor harmonic oscillator approximation is used to compute the free energy and the entropies contribution along the transition pathway. With knowledge of free energy surfaces along rotations of the --[NH(3)] and --[BH(3)] groups, complete transformation paths are mapped out. The phase transition is found to follow the sequence of partially occupied tetragonal system (I4mm) of a mixture of states with monoclinic (Cc), (CM) and orthorhombic (Pmn2(1)) symmetries to fully occupied quasitetragonal system (the intermediate phase, Pmn2(1)) to fully occupied orthorhombic system (Pmn2(1)).

Significance of Group Frequency Distributions for Group Additivity

The following hypothesis is proposed: When additivity is valid, the molecular frequency distribution (MFD) is a weighted sum of group frequency distributions (GFDs). On the basis of the transformation rules for distribution functions from statistical theory and the rigid-rotator harmonic oscillator approximation, it is shown analytically that the hypothesis leads to group additivity of vibrationally dependent thermochemical parameters. Graph theory has been used to find the structure of the matrices used to determine group additivity values, and the results show that, within the rigid-rotator harmonic oscillator approximation, additivity of the vibrational contributions leads to the experimentally observed group additivity of the total group contributions. Support for the hypothesis is obtained from ab initio and DFT frequency calculations of a total 182 different compounds from seven polymeric series. In agreement with the hypothesis, remarkable similarities of the MFDs are observed throughout each series. Molecular frequencies can be satisfactorily calculated from model calculations based on the hypothesis, and temperature dependent heat capacities for the monomeric units can be derived that are in agreement with experimental values.