Internal Rotational Modes Research Articles

Automated reaction kinetics and network exploration (Arkane): A statistical mechanics, thermodynamics, transition state theory, and master equation software

AbstractThe open‐source statistical mechanics software described here, Arkane–Automated Reaction Kinetics and Network Exploration–facilitates computations of thermodynamic properties of chemical species, high‐pressure limit reaction rate coefficients, and pressure‐dependent rate coefficient over multi‐well molecular potential energy surfaces (PES) including the effects of collisional energy transfer on phenomenological kinetics. Arkane can use estimates to fill in information for molecules or reactions where quantum chemistry information is missing. The software solves the internal energy master equation for complex unimolecular reaction systems. Inputs to the software include converged electronic structure computations performed by the user using a variety of supported software packages (Gaussian, Molpro, Orca, TeraChem, Q‐Chem, Psi4). The software outputs high‐pressure limit rate coefficients and pressure‐dependent phenomenological rate coefficients, as well as computed thermodynamic properties (enthalpy, entropy, and constant pressure heat capacity) with added energy corrections. Some of the key features of Arkane include treatment of 1D, 2D or ND hindered internal rotation modes, treatment of free internal rotation modes, quantum tunneling effect consideration, transition state theory (TST) and Rice‐Ramsperger‐Kassel‐Marcus (RRKM) rate coefficient computations, master equation solution with four implemented methods, inverse‐Laplace transform of high‐pressure limit rate coefficients into the energy domain, energy corrections based on bond‐additivity or isodesmic reactions, automated and efficient PES exploration, and PES sensitivity analysis. The present work describes the design of Arkane, how it should be used, and refers to the theory that it employs. Arkane is distributed via the RMG‐Py software suite (https://github.com/ReactionMechanismGenerator/RMG‐Py).

Raman and Structural Characterization of Spinel Compound Zn8/5Al4/15TiO4

Microwave dielectric materials have been attracted enormous attention for their application in microwave communication. A new microwave dielectric material with composition Zn8/5Al4/15TiO4 was synthesized by conventional solid-state reaction method. The structure of Zn8/5Al4/15TiO4 was refined with the cubic P4332 space group (number of formula unit per unit cell, Z = 4). The Rietveld refinement study revealed the theoretical density ρ = 4.80 g/cm3 and lattice parameter a = 8.405 Å. This compound was crystallized in cubic spinel structure and 1:3 ordering was observed on the octahedral sites. Raman spectrum of the compound was collected at room temperature. Theoretical Factor group analysis for this compound predicts 40 Raman modes and 22 IR modes. However, experimentally 13 vibrational modes have been observed in the Raman spectrum which can be separated into internal TiO6 vibration and external rotation and translation TiO6 modes. Raman modes in the range of 500-800 cm-1 are assigned to internal vibrational modes.

Large Amplitude Motions of Pyruvic Acid (CH3-CO-COOH).

Torsional and rotational spectroscopic properties of pyruvic acid are determined using highly correlated ab initio methods and combining two different theoretical approaches: Second order perturbation theory and a variational procedure in three-dimensions. Four equilibrium geometries of pyruvic acid, Tc, Tt, Ct, and CC, outcome from a search with CCSD(T)-F12. All of them can be classified in the Cs point group. The variational calculations are performed considering the three internal rotation modes responsible for the non-rigidity as independent coordinates. More than 50 torsional energy levels (including torsional subcomponents) are localized in the 406–986 cm−1 region and represent excitations of the ν24 (skeletal torsion) and the ν23 (methyl torsion) modes. The third independent variable, the OH torsion, interacts strongly with ν23. The A1/E splitting of the ground vibrational state has been evaluated to be 0.024 cm−1 as it was expected given the high of the methyl torsional barrier (338 cm−1). A very good agreement with respect to previous experimental data concerning fundamental frequencies (νCAL − νEXP ~ 1 cm−1), and rotational parameters (B0CAL − B0EXP < 5 MHz), is obtained.

Vibrational Energy Redistribution between CH Stretching Modes in Alkyl Chain Monolayers Revealed by Time-Resolved Two-Color Pump-Probe Sum Frequency Spectroscopy.

The vibrational dynamics of the various CH stretching modes in a fatty acid Langmuir-Blodgett film was studied using a resonant narrowband infrared (IR) laser pulse for pumping and a broadband femtosecond IR visible pulse pair for detection in a sum frequency spectroscopy setup. The resulting two-dimensional spectra indicate that pumping either the antisymmetric methyl or methylene stretch results in the transfer of energy to the other modes on a time scale faster than 2 ps. This rapid process is followed by energy redistribution to other modes, presumably the bending and internal rotational modes, with a time constant of approximately 85 ps. The formation of gauche defects is not observed within the first 250 ps. The whole spectrum recovers on a time scale of several nanoseconds, indicating dissipation of the excitation energy into the substrate.

Identification of hindered internal rotational mode for complex chemical species: A data mining approach with multivariate logistic regression model

Thermodynamic properties are essential to understand and describe many chemical/biological processes in the real environment. To obtain correct thermodynamic data of chemical species for a wide range of temperatures, a rigorous Hindered Internal Rotation (HIR) treatment must be considered. Such a treatment requires detailed information about the internal rotation (i.e., rotational axis, group, frequency, symmetry and hindrance potential). However, it is very tedious, even prone-to-error, for chemists to prepare the input parameters for such a treatment. Among the HIR parameters, the rotational frequency (or mode) is the most difficult element due to the complex molecular structure and mixing vibrational modes of chemical species. Recently, a rule-based framework has been proposed to help chemists with this tedious process (Le et al., Comput. Theor. Chem., 2017, 61). This approach has been demonstrated to work well for simple species; however, it still lacked the ability to handle more complex cases. Therefore, in this study, a data mining approach is proposed to overcome the challenges of the previous algorithm. Within this framework, the HIR pattern was found using the features extracted from existing data provided by chemists. More specifically, multivariate logistic regression was implemented to analyze the chemical data to better predict the rotational frequency (mode) of chemical species as well as to highlight the effect of each attribute of the rotation. The experimental results were demonstrated to be more accurate than the previous study in terms of both accuracy and completeness. It also gives meaningful insights into the HIR itself. The proposed approach of this research will be integrated into MSMC-GUI (https://sites.google.com/site/msmccode/manual/gui-1) to provide chemists with both an interactive and robust tool to prepare the data for their thermodynamic calculations on-the-fly.

Weak intramolecular interaction effects on the torsional spectra of ethylene glycol, an astrophysical species.

An elaborate variational procedure of reduced dimensionality based on explicitly correlated coupled clusters calculations is applied to understand the far infrared spectrum of ethylene-glycol, an astrophysical species. This molecule can be classified in the double molecular symmetry group G8 and displays nine stable conformers, gauche and trans. In the gauche region, the effect of the potential energy surface anisotropy due to the formation of intramolecular hydrogen bonds is relevant. For the primary conformer, stabilized by a hydrogen bond, the ground vibrational state rotational constants are computed to be A0 = 15 369.57 MHz, B0 = 5579.87 MHz, and C0 = 4610.02 MHz corresponding to differences of 6.3 MHz, 7.2 MHz, and 3.5 MHz from the experimental parameters. Ethylene glycol displays very low torsional energy levels whose classification is not straightforward and requires a detailed analysis of the torsional wavefunctions. Tunneling splittings are significant and unpredictable due to the anisotropy of the potential energy surface PES. The ground vibrational state splits into 16 sublevels separated ∼142 cm(-1). The splitting of the "G1 sublevels" was calculated to be ∼0.26 cm(-1) in very good agreement with the experimental data (0.2 cm(-1) = 6.95 MHz). Transitions corresponding to the three internal rotation modes allow assignment of previously observed Q branches. Band patterns, calculated between 362.3 cm(-1) and 375.2 cm(-1), 504 cm(-1) and 517 cm(-1), and 223.3 cm(-1) and 224.1 cm(-1), that correspond to the tunnelling components of the v21 fundamental (v21 = OH-torsional mode), are assigned to the prominent experimental Q branches.

Influence of solvent chemistry on 1H NMR spectral and relaxation properties of a long-chain ionic surfactant in chloroform-d

1H NMR chemical shift, line width, indirect nuclear splitting value, peak area integration value, and spin–lattice and spin–spin relaxation times at 298 K are compared for low-concentration isotropic solutions of n-octylammonium n-octadecanoate prepared via different techniques and conditions using dried, distilled, and degassed deuterochloroform and the nontreated solvent containing tetramethylsilane. The nature of the variation of observed spectral parameters and relaxation/rotational behavior with chemical composition (presence of oxygen and other paramagnetic species, stabilizer, impurities, and degradation products) of the solvent, history of the solution, and sample containment are analyzed. Relaxation times are interpreted in terms of monomer structure and reorientation and internal rotation modes as a function of atomic position along the n-alkyl chains. Collectively, the relaxation behavior of the surfactant complies with the two-step model of fast picosecond internal rotations of different size segments containing methylene groups separated in timescale from slower large segment and overall molecular tumbling modes of the monomer. Fast motional phenomena do not appear to be appreciably influenced by the chemistry of the solvent in contrast to spectral parameters such as chemical shift and line width of the labile ammonium protons. A model is also presented to explain anomalous variation of the peak area integration value with chemical shift of the ammonium resonance peak.

Soft elasticity in solids composed of ellipse-shaped particles

We present a method for studying the influence of internal rotational degrees of freedom on the elastic properties of crystals composed of ellipsoidal particles. We derive the conditions under which a stretched-triangular lattice of ellipsoidal particles can exhibit a vanishing shear modulus. Analytical predictions are confirmed with numerical calculations. Numerical results also show that internal rotational modes can delay the proliferation of dislocations in the plastic regime.

On the applicability of the molecular dynamics SCC-DFTB treatment on optical spectra simulations for thiophene and phenyl containing oligomers

The applicability of the semiempirical Self-Consistent Charge Density-Functional Based Tight Binding approach (SCC-DFTB) is tested and compared with the reference ab initio Møller–Plesset perturbation theory up to the second-order (MP2) and density functional theory (DFT). In this context, the calculations of 2-phenylthiophene and 2,2′-bithiophene molecules are presented with respect to the optimal geometries and torsional potentials. The vibrational broadenings of absorption spectra based on the combined on-the-fly molecular dynamics (MD) simulations were analyzed for the studied model molecules as well as for selected representative oligomeres or star-shaped molecules built from the thiophene and phenyl units. Our calculations showed that the SCC-DFTB method has the tendency to planarize the mutual distortion between the thiophene–thiophene or thiophene–phenyl units and to overestimate the energy barriers for perpendicular structures with respect to the benchmark MP2 and DFT results. The semiempirical TD-B3LYP//MD(SCC-DFTB) or ZINDO//MD(SCC-DFTB) simulations at a temperature of 300K produce narrower absorption spectroscopic bands comparing to the reference TD-B3LYP//MD(B3LYP) results. The temperature increase to 600K ensures the higher population of distorted MD(SCC-DFTB) geometries and consequently a more realistic shape of the absorption bands with respect to the internal vibrational and rotational modes.

Quantum computing using molecular vibrational and rotational modes of the open-shell 14N16O molecule

In this paper, we investigate the possibility of using internal molecular vibrational and rotational modes of an open-shell molecule for one of the most important quantum algorithms: the Deutsch-Jozsa algorithm. The molecular system of interest is one of the representative open-shell molecules: 14 N 16 O. The gate pulses are constructed by utilizing multi-target optimal control theory (MTOCT). The gate fidelities of each quantum gate are more than 95.23%. Upon implementing the Deutsch-Jozsa algorithm combining these elementary gates, we obtained fidelity of at least 94.76%. This indicates that vibrational and rotational qubits of the open-shell 14 N 16 O molecule are about as promising for processing quantum algorithms as those of the closed-shell molecule 12 C 16 O that we studied earlier.

Effects of entropy on the gas‐phase pyrolysis of ethyl N,N‐dimethylcarbamate

In this study, we examined the gas-phase pyrolysis of ethyl N,N-dimethylcarbamate theoretically at various theoretical levels. The reaction consists of a two-step mechanism, with N,N-dimethylcarbamic acid and ethylene as reaction intermediates. In the first step, the reaction proceeds via a six-membered cyclic transition state (TS), which is more favorable than that via a four-membered cyclic TS. Here, the contribution of entropy to the overall potential energy surface was found to play an important role in determining the rate-limiting step, which was found to be the second step when viewed in terms of the enthalpy of activation (DeltaH(not equal)), but the first step when entropy changes (-TDeltaS(not equal)) were considered. These results are consistent with experimental findings. Moreover, the experimental activation entropy can be reproduced by using the hindered rotor approximation, which converts some low vibration frequencies that correspond to internal rotational modes into hindered rotors.

Quantum Chemical and Theoretical Kinetics Study of the O(3P) + C2H2 Reaction: A Multistate Process

The potential energy surfaces of the two lowest-lying triplet electronic surfaces 3A'' and 3A' for the O(3P) + C2H2 reaction were theoretically reinvestigated, using various quantum chemical methods including CCSD(T), QCISD, CBS-QCI/APNO, CBS-QB3, G2M(CC,MP2), DFT-B3LYP and CASSCF. An efficient reaction pathway on the electronically excited 3A' surface resulting in H(2S) + HCCO(A2A') was newly identified and is predicted to play an important role at higher temperatures. The primary product distribution for the multistate multiwell reaction was then determined by RRKM statistical rate theory and weak-collision master equation analysis using the exact stochastic simulation method. Allowing for nonstatistical behavior of the internal rotation mode of the initial 3A'' adducts, our computed primary-product distributions agree well with the available experimental results, i.e., ca. 80% H(2S) + HCCO(X2A'' + A2A') and 20% CH2(X3B1) + CO(X1sigma+) independent of temperature and pressure over the wide 300-2000 K and 0-10 atm ranges. The thermal rate coefficient k(O + C2H2) at 200-2000 K was computed using multistate transition state theory: k(T) = 6.14 x 10(-15)T (1.28) exp(-1244 K/T) cm3 molecule(-1) s(-1); this expression, obtained after reducing the CBS-QCI/APNO ab initio entrance barriers by 0.5 kcal/mol, quasi-perfectly matches the experimental k(T) data over the entire 200-2000 K range, spanning 3 orders of magnitude.

Theoretical study of deuterium kinetic isotope effect in peroxidation of phenol and toluene

Reaction mechanisms of hydrogen abstraction from phenol and toluene by the hydroperoxyl radical are probed by theoretical calculations of deuterium kinetic isotope effect (KIE). In experiment the given free-radical reactions have nearly equal reaction heats and rates differing by 6 orders of magnitudes, yet demonstrate high H/D KIEs. The mechanism of phenol–peroxyl reaction is described by the proton-coupled electron transfer (PCET), while the toluene–peroxyl reaction follows the non-polar H-atom transfer (HAT). In present work, the H/D KIEs are assessed for several isotopomers of phenol and toluene using the DFT B3LYP/6-311+G(2d,2p) calculations and the post-processing Bigeleisen treatment with one-dimensional tunnel corrections. Differing patterns of bending vibrations are noted for the PCET and HAT TSs considered. The computed KIEs are 10.7 and 17.0 (at 65 °C) for the phenol and toluene reactions, respectively, that agrees with the available experimental results. The corresponding semi-classical contributions are 4.5 and 5.1, whereas the tunnel correction computed for unsymmetrical Eckart function yields the factors of 2.4 and 3.3 for phenol and toluene, respectively. The advantage of using Bigeleisen formula for reaction intermediates with low-frequency internal rotation modes is discussed.

Internal Rotational Motion of the Chloromethyl Group of the Jet-Cooled Benzyl Chloride Molecule

The mass-resolved resonance enhanced two-photon ionization spectra of jet-cooled benzyl chloride were measured. Some low-frequency vibronic bands around the S1-S0 origin band were assigned to transitions of the internal rotational mode of the chloromethyl group. The internal rotational motion was analyzed by using the one-dimensional free rotor approximation. The conformation in the S1 state was found to be that in which the C-Cl bond lies in orthogonal to the benzene plane. For the species with m/e 126, the transition energy of the internal rotational bands corresponded well to the potential energy values of V2 = 1900 cm(-1) and V4 = 30 cm(-1) in the S1 state and the reduced rotational constant B values 0.50 and 0.47 cm(-1) in the S0 and S1 states, respectively. The B values obtained for the chlorine isotopomer (m/e 128) were slightly different. The S1 potential barrier height was found to be about 3 times larger than that for the S0 state. Molecular orbital calculations suggest that the difference between energies of the HOMO and LUMO with respect to the rotation of the chloromethyl group correspond approximately to the potential energy curve obtained for the S1 state.

Fourier transform millimeter-wave spectroscopy of the ethyl radical in the electronic ground state.

The pure rotational spectrum of the ethyl radical (C2H5) has been detected for the first time with the Fourier transform millimeter-wave spectrometer. The ethyl radical is produced by discharging the C2H5I gas diluted in Ar. The 1(01)-0(00) rotational transition of the ethyl radical is observed in the frequency range from 43,680 to 43,780 MHz. The observed spectrum shows a very complicated pattern of the fine and hyperfine structures of a doublet radical with the nuclear spins of five protons. The fine and hyperfine components are assigned with the aid of measurements of the Zeeman splittings. As a result, the 22 lines are ascribed to the transitions in the ground vibronic state (A2"). The rotational constant, the spin-rotation interaction constant, and hyperfine interaction constants are determined by the least-squares fit. The Fermi contact term of the alpha-proton is determined to be -64.1654 MHz in the gas phase, indicating that the structure of the -CH2 is essentially planar. The present rotational spectroscopic study further supports that the methyl group of the ethyl radical can be regarded as a nearly free internal rotor with a low energy barrier. A few unassigned lines still remain, which may be vibrational satellites of the internal rotation mode.

Time resolved solvent rearrangement dynamics.

Ultrafast pump-probe studies of I2- recombination in size-selected I2- (CO2)n cluster ions demonstrate long time coherent motions in size-selected clusters and the resulting non-statistical energy flow in the cluster. For I2- photodissociated to produce either I- + I or I- + I*, we identify a solvent-driven energy transfer process without a condensed phase counterpart. The mechanism involved is a Marcus-like solvent-driven curve crossing, with the driving force arising from asymmetric solvation, not just from solvent orientation. By substituting another halogen for one I atom, we "break" the I2- symmetry, and thus obtain direct information on the electron transfer process. New experiments on IBr- (CO2)n photodissociation products confirm the behavior suspected in the I2- studies. Time-resolved experiments on IBr- and theoretical modeling of the dynamics provide quantitative information on the multiple curve crossings encountered in the recombination process. In related investigations, femtosecond negative ion-neutral-positive ion charge reversal apparatus is employed to investigate transient neutral species evolving along a reaction coordinate. We report studies of the rearrangement dynamics of Cu(OH2) produced by photodetachment of the corresponding anion. Following a controlled delay period, a second ultrafast tunable laser pulse initiates resonant multiphoton photoionization of the time-evolving Cu...OH2 complex. The time-resolved Cu+ and Cu+(OH2) signals provide information both on the prompt dissociation of the complex and on energy redistribution between internal rotational and radial modes of the evolving complex. Calculations of the time evolution of the anion geometric configuration on the neutral potential energy surface yield deeper insight into the nature of the rearrangement process and the energy flow within the complex.

Dependence of the rate constants on the treatment of internal rotation modes: the reaction OH + CH3SH --> CH3S + H2O as an example.

The title reaction has been used as an example to test the importance of using a hindered rotor treatment instead of a harmonic oscillator model for calculating vibrational partition functions corresponding to low-frequency internal rotation modes. First, a normal-mode analysis according to the Ayala and Schlegel's algorithm has been used to identify the internal rotation modes of methanethiol and the transition state structure. Then, after calculation of the energy barrier for each internal rotation, the corresponding hindered rotor partition functions have been calculated following the CW scheme of Chuang and Truhlar. The results show that the anharmonic treatment produces a rather modest improvement of the rate constants at room temperature or below.

On the evaluation of thermal corrections to gas phase ab initio relative energies: implications to the conformational analysis study of cyclooctane

In this paper we present an investigation of the influence of the thermal correction on the conformational population for the boat–chair (BC) and CROWN forms of the cyclooctane molecule, calculated using quantum mechanical ab initio Hartree–Fock (HF), MP2, MP4SDQ, CCSD and density functional methods (B3LYP, BLYP, BP86) in conjunction with various basis sets. A previous experimental gas phase electron diffraction study pointed out that the BC is either the exclusive or at least the strongly predominant form in gas phase at room temperature. We therefore analyzed the performance of various levels of calculation for the evaluation of the relative conformational population and also the role played by the thermal correction to gas phase calculated relative energies. It turns out that the thermal correction is very sensitive to the presence of low frequency modes that are indeed internal rotations and need to be treated separately, in what the cyclooctane molecule is concerned. Once internal rotations were considered, it can be seen that the HF level of calculation produces very satisfactory values for thermal correction, compared to MP2. Therefore, it can be used in single-point energy calculations employing a high correlated level of theory (MP4SDQ, CCSD), leading to a quite trustable Gibbs free energy difference data. When thermal energies are not corrected for low frequency internal rotation modes, a range of contrasting results is obtained by varying both the quantum mechanical approach and the basis set.

On the dissociation dynamics of the benzyl chloride radical anion. An ab initio dynamic reaction coordinate analysis study

The dynamics of the dissociation of the benzyl chloride radical anion to a benzyl radical and chloride anion was studied theoretically. To this end two different conformations of benzyl chloride were examined: one featuring a 90° angle between the Cl–C bond and the aromatic ring (conformation S), the other with the Cl–C bond and the aromatic moiety lying coplanar (conformation E). The potential-energy (PE) surface shows the existence of a conical intersection when studied as a function of the C–Cl bond length and of the rotation angle around the C(sp 2)–C(sp 3) bond. Information on the dynamics of this process was obtained using the dynamic reaction coordinate (DRC) algorithm for tracing reaction paths. The DRC method shows a qualitative difference in the dissociation mechanism of the two conformers. The lifetime of conformation E depends on the amount of kinetic energy assigned to the internal rotational mode motion, whereas that of conformation S does not.

Theoretical investigation of the torsional spectra of 2,2,2-trifluoroethanol

The structure and the torsional spectra of various isotopic varieties of 2,2,2-trifluoroethanol (TFE) are investigated with MP4(SDQ)/cc-pVTZ ab initio calculations. The energy levels corresponding to the CF 3 and the OH internal rotation modes, are calculated variationally. With the predicted frequencies and intensities, previous assignments are reviewed. The position of several combination bands are predicted. The most stable conformation of TFE has a gauche geometry which is stabilized by the formation of intramolecular F–H hydrogen bonds. A second trans conformer lies 681.5 cm −1 over the gauche form. The torsional barriers have been calculated to be V 3 (gauche)=1534.0 cm −1 , V 3 (trans)=1490.9 cm −1 , V OH (α=34°)=707.5 cm −1 and V OH (α=180°)=804.9 cm −1 . The fundamental bands of the gauche-TFE have been evaluated at 286.7 and 283.3 cm −1 (OH torsion) and 115.0 and 114.9 cm −1 (CF 3 torsion) and their corresponding intensities to be 21.73×10 −4 and 23.16×10 −4, and 0.009×10 −4 and 0.002×10 −4, respectively.