Torsional anharmonicity in the conformational thermodynamics of flexible molecules

Nuclear quantum effects in gas-phase 2-fluoroethanol

Torsional motions along the FCCO and HOCC dihedrals lead to the five unique conformations of 2-fluoroethanol, of which the conformer that is gauche along both dihedrals has the lowest energy. In this work, we explore how nuclear quantum effects (NQEs) manifest in the structural parameters of the lowest energy conformer, in the intramolecular free energy landscape along the FCCO and HOCC dihedrals, and also in the infrared spectrum of the title molecule, through the use of path integral simulations. We have first developed a full dimensional potential energy surface using the reaction surface Hamiltonian framework. On this potential, we have carried out path integral molecular dynamics simulations at several temperatures starting from the minimum energy well to explore structural influences of NQEs including geometrical markers of the interaction between the OH and F groups. From the computed free energy landscapes, significant reduction of the torsional barrier is found at low temperature near the cis region of the dihedrals, which can be understood through the trends in the radii of gyration of the atomic ring polymers. We find that the inclusion of NQEs in the computation of infrared spectrum is important to obtain good agreement with the experimental band positions.

Global Master Equation Analysis of Rate Data for the Reaction C2H4 + H ⇄ C2H5: ΔfH0⊖C2H5

While forward and reverse rate constants are frequently used to determine enthalpies of reaction and formation, this process is more difficult for pressure-dependent association/dissociation reactions, especially since the forward and reverse reactions are usually studied at very different temperatures. The problems can be overcome by using a data-fitting procedure based on a master equation model. This approach has been applied to existing experimental pressure-dependent forward and reverse rate coefficients for the reaction C₂H₄ + H ⇄ C₂H₅ (k₁, k_-1) using the MESMER code to determine Δ_fH₀^⊖C₂H₅ from the enthalpy of the reaction. New measurements of k₁, k_-1 were included in analysis. They are based on laser flash photolysis with direct observation of H atom time profiles by vacuum ultraviolet laser-induced fluorescence under conditions where the approach to equilibrium could be observed. Measurements were made over the temperature range 798-828 K and with [He] from 2.33 to 7.21 × 10¹⁸ molecule cm^-3. These data were then combined with a wide range of existing experimental data with helium as the bath gas (112 measurements of k₁ and k_-1, covering the temperature range 285-1094 K, and [He] = 7.1 × 10¹⁵-1.9 × 10¹⁹ molecule cm^-3) and fitted using the master equation solver MESMER. The required vibrational frequencies and rotational constants of the system were obtained from ab initio calculations, and the activation threshold for association (ΔE_thresh), enthalpy of reaction (Δ_rH₀^⊖), imaginary frequency (υ_imag), and helium energy-transfer parameters (⟨ΔE⟩_d,298(T/298)ⁿ) were optimized. The resulting parameters (errors are 2σ) are ΔE_thresh = 11.43 ± 0.34 kJ mol^-1, Δ_rH₀^⊖ = -145.34 ± 0.60 kJ mol^-1, υ_imag = 730 ± 130 cm^-1, ⟨ΔE⟩_d,298 = 54.2 ± 7.6 cm^-1, and n = 1.17 ± 0.12. A value of Δ_fH_298.15^⊖(C₂H₅) = 120.49 ± 0.57 kJ mol^-1 is obtained by combining Δ_rH₀^⊖ with standard enthalpies of formation for H and C₂H₄ and making the appropriate temperature corrections. The dependence of these parameters on how the internal rotor and CH₂ inversion modes are treated has been explored. The experimental data for other bath gases have been analyzed, and data sets compatible with the potential energy surface parameters determined above have been identified. The parameters are virtually identical but with slightly smaller error limits. Parameterization of k₁, k_-1 using the Troe formalization has been used to investigate competition between ethyl decomposition and reaction with oxygen under combustion conditions.

Accounting for conformational flexibility and torsional anharmonicity in the H + CH3CH2OH hydrogen abstraction reactions: a multi-path variational transition state theory study

This work reports a detailed theoretical study of the hydrogen abstraction reactions from ethanol by atomic hydrogen. The calculated thermal rate constants take into account torsional anharmonicity and conformational flexibility, in addition to the variational and tunneling effects. Specifically, the kinetics calculations were performed by using multi-path canonical variational transition state theory with least-action path tunneling corrections, to which we have added the two-dimensional non-separable method to take into account torsional anharmonicity. The multi-path thermal rate constant is expressed as a sum over conformational reaction channels. Each of these channels includes all the transition states that can be reached by internal rotations. The results show that, in the interval of temperatures between 250 and 2500 K, the account for multiple paths leads to higher thermal rate constants with respect to the single path approach, mainly at low and at high temperatures. In addition, torsional anharmonicity enhances the slope of the Arrhenius plot in this range of temperatures. Finally, we show that the incorporation of tunneling into the hydrogen abstraction reactions substantially changes the contribution of each of the transition states to the conformational reaction channel.

Large entropic effects on the thermochemistry of silicon nanodusty plasma constituents

Determination of the thermodynamic properties of reactor constituents is the first step in designing control strategies for plasma-mediated deposition processes and is also a key fundamental issue in physical chemistry. In this work, a recently proposed multistructural statistical thermodynamic method is used to show the importance of multiple structures and torsional anharmonicity in determining the thermodynamic properties of silicon hydride clusters, which are important both in plasmas and in thermally driven systems. It includes five different categories of silicon hydride clusters and radicals, including silanes, silyl radicals, and silenes. We employed a statistical mechanical approach, namely the recently developed multistructural (MS) anharmonicity method, in combination with density functional theory to calculate the partition functions, which in turn are used to estimate thermodynamic quantities, namely Gibbs free energy, enthalpy, entropy, and heat capacity, for all of the systems considered. The calculations are performed using all of the conformational structures of each molecule or radical by employing the multistructural quasiharmonic approximation (MS-QH) and also by including torsional potential anharmonicity (MS-T). For those cases where group additivity (GA) results are available, the thermodynamic quantities obtained from our MS-T calculations differ considerably due to the fact that the GA method is based on single-structure data for isomers of each stoichiometry, and hence lack multistructural effects; whereas we find that multistructural effects are very important in silicon hydride systems. Our results also indicate that the entropic effect on the thermochemistry is huge and is dominated by multistructural effects. The entropic effect of multiple structures is also expected to be important for other kinds of chain molecules, and its effect on nucleation kinetics is expected to be large.

Torsional anharmonicity in transition state theory calculations

We present a new application for the Torsional Path Integral Monte Carlo (TPIMC) method in which the TPI partition functions are introduced into the calculation of Transition State Theory (TST) rate constants. In this way, an explicit treatment of torsional anharmonicity is included in the TST calculations and the magnitude of these effects can be assessed. The new method is tested on the C(2)H(6) + H hydrogen abstraction reaction and concerted hydrogen transfer in the carbonic acid dimer, for which we have developed torsional potential energy surfaces. For the C(2)H(6) + H reaction the rate constants are halved at room temperature on including a treatment of torsional anharmonicity, while the effects are found to be much smaller for the hydrogen transfer reaction in the carbonic acid dimer.

Torsional anharmonicity in the conformational analysis of tryptamine

In this paper we calculate the relative conformer populations of the tryptamine molecule. Our approach combines high level electronic structure conformer energies with harmonic frequencies and an anharmonic treatment of the torsional motions using the torsional path integral Monte Carlo method. We have developed a 3-D potential energy surface as a function of the torsional coordinates at the B3LYP/6-31+G(d) level using 2535 grid points. Eight conformers of tryptamine were found to be significantly populated at 430 K as opposed to the experimental observation of seven. This, along with further comparisons with various experimental data, leads us to suppose that conformer interconversion occurs during the cooling phases of many of the experiments. The ordering of the calculated populations fits well with available experimental data. Torsional anharmonicity is found to affect conformer populations more significantly at 430 K than at 100 K (although overall the effects are small), while quantum mechanical effects are not important at either temperature.

Quantum Simulation of a Hydrated Noradrenaline Analog with the Torsional Path Integral Method

An extended version of the torsional path integral Monte Carlo (TPIMC) method is presented and shown to be useful for studying the conformation of flexible molecules in solvated clusters. The new technique is applied to the hydrated clusters of the 2-amino-1-phenyl-ethanol (APE) molecule. APE + nH2O clusters with n = 0-4 are studied at 100 and 300 K using both classical and quantum simulations. Only at the lower temperature is the hydration number n found to impact the conformational distribution of the APE molecule. This is shown to be a result of the temperature-dependent balance between the internal energy and entropy contributions to the relative conformer free energies. Furthermore, at 100 K, large quantum effects are observed in the calculated conformer populations. A particularly large quantum shift of 30% of the total population is calculated for the APE + 2H2O cluster, which is explained in terms of the relative zero point energy of the lowest-energy hydrated structures for this cluster. Finally, qualitative agreement is found between the reported calculations and recent spectroscopy experiments on the hydrated clusters of APE, including an entropically driven preference for the formation of AG-type hydrated structures and the formation of a water "droplet" in the APE + 4H2O cluster.

Torsional Anharmonicity in the Conformational Analysis of β-d-Galactose

Schemes to include a treatment of torsional anharmonicity in the conformational analysis of biological molecules are introduced. The approaches combine ab initio electronic energies and harmonic frequencies with anharmonic torsional partition functions calculated using the torsional path integral Monte Carlo method on affordable potential energy surfaces. The schemes are applied to the conformational study of the monosaccharide beta-d-galactose in the gas phase. The global minimum structure is almost exclusively populated at 100 K, but a large number of conformers are present at ambient and higher temperatures. Both quantum mechanical and anharmonic effects in the torsional modes have little effect on the populations at all temperatures considered, and it is, therefore, expected that standard harmonic treatments are satisfactory for the conformational study of monosaccharides.

Calculation of rotational partition functions by an efficient Monte Carlo importance sampling technique

The evaluation of the classical rotational partition function represented by a configuration integral over all external and internal rotational degrees of freedom of nonrigid chain polyatomic molecules is described. The method of Pitzer and Gwinn is used to correct the classical partition function for quantum mechanical effects at low temperatures. The internal rotor hindrance and all coupling arising from the external and internal rotational degrees of freedom are explicitly taken into account. Importance sampling Monte Carlo based on the adaptive VEGAS algorithm to perform multidimensional integration is implemented within the TINKER program package. A multidimensional potential energy hypersurface is calculated with the MM3(2000) molecular mechanics force field. Numerical tests are performed on a number of small n-alkanes (from ethane to octane), for which the absolute entropies calculated at three different temperatures are compared both with the experimental values and with the previous theoretical results. The application of a more efficient importance sampling technique developed here results in a substantial reduction of statistical errors in the evaluation of the configuration integral for a given number of Monte Carlo steps. Error estimates for the calculated entropies are given, and possible sources of systematic errors, and their importance for a reliable prediction of the absolute entropy, are discussed.