Unraveling the Catalytic Mechanism of ß-Cyclodextrin in the Vitamin D Formation.

Previous experimental studies have shown that the isomerization reaction of previtamin D3 (PreD3) to vitamin D3 (VitD3) is accelerated 40-fold when it takes place within a ß-cyclodextrin dimer, in comparison to the reaction occurring in conventional isotropic solutions. In this study, we employ quantum mechanics-based molecular dynamics (MD) simulations and statistical multistructural variational transition state theory to unveil the origin of this acceleration. We find that the conformational landscape in the PreD3 isomerization is highly dependent on whether the system is encapsulated. In isotropic media, the triene moiety of the PreD3 exhibits a rich torsional flexibility. However, when encapsulated, such a flexibility is limited to a more confined conformational space. In both scenarios, our calculated rate constants are in close agreement with experimental results and allow us to identify the PreD3 flexibility restriction as the primary catalytic factor. These findings enhance our understanding of VitD3 isomerization and underscore the significance of MD and environmental factors in biochemical modeling.

Effect of temperature on the gas-phase reaction of CH3CN with OH radicals: experimental (T = 11.7-177.5 K) and computational (T = 10-400 K) kinetic study.

Acetonitrile (CH3CN) is present in the interstellar medium (ISM) in a variety of environments. However, at the ultracold temperatures of the ISM, radical-molecule reactions are not widely investigated because of the experimental handicap of getting organic molecules in the gas phase by conventional techniques. The CRESU (French acronym for Reaction Kinetics in a Uniform Supersonic Flow) technique solves this problem. For this reason, we present in this work the kinetic study of the gas-phase reaction of CH3CN with one of the most ubiquitous radicals, the hydroxyl (OH) radical, as a function of temperature (11.7-177.5 K). The kinetic technique employed to investigate the CH3CN + OH reaction was the pulsed laser photolysis-laser induced fluorescence. The rate coefficient for this reaction k(T) has been observed to drastically increase from 177.5 K to 107.0 K (about 2 orders of magnitude), while the increase in k(T) from 107.0 K to 11.7 K was milder (around 4 times). The temperature dependent expressions for k(T) are provided in the two distinct T-ranges, excluding the upper limit obtained for k(177.5 K): In addition, the rate coefficients estimated by the canonical competitive unified statistical (CCUS) theory show a similar behaviour to the experimental results, when evaluated within the high-pressure limit. This is consistent with the experimentally observed independence of k(T) with total gas density at selected temperatures. Astrochemical networks, such as the KIDA database or UMIST, do not include the CH3CN + OH reaction as a potential depletion process for acetonitrile in the ISM because the current studies predict very low rate coefficients at IS temperatures. According to the model (T = 10 K), the impact of the titled reaction on the abundances of CH3CN appears to be negligible in dark molecular clouds of the ISM (∼1% of the total depletion reactions included in UMIST network). With respect to the potential formation of the CH2CN radical in those environments, even in the most favourable scenario, where this radical could be formed in a 100% yield from the CH3CN + OH reaction, this route would only contribute around 2% to the current assumed formation routes by the UMIST network.

Gas-phase formation of glycolonitrile in the interstellar medium.

Our automated reaction discovery program, AutoMeKin, has been utilized to investigate the formation of glycolonitrile (HOCH2CN) in the gas phase under the low temperatures of the interstellar medium (ISM). The feasibility of a proposed pathway depends on the absence of barriers above the energy of reactants and the availability of the suggested precursors in the ISM. Based on these criteria, several radical-radical reactions and a radical-molecule reaction have been identified as viable formation routes in the ISM. Among the radical-radical reactions, OH + CH2CN appears to be the most relevant, considering the energy of the radicals and its ability to produce glycolonitrile in a single step. However, our analysis reveals that this reaction produces hydrogen isocyanide (HNC) and formaldehyde (CH2O), with rate coefficients ranging from (7.3-11.5) × 10-10 cm3 molecule-1 s-1 across the temperature range of 10-150 K. Furthermore, the identification of this remarkably efficient pathway for HNC elimination from glycolonitrile significantly broadens the possibilities for any radical-radical mechanism proposed in our research to be considered as a feasible pathway for the formation of HNC in the ISM. This finding is particularly interesing given the persistently unexplained overabundance of hydrogen isocyanide in the ISM. Among the radical-molecule reactions investigated, the most promising one is OH + CH2CHNH, which forms glycolonitrile and atomic hydrogen with rate coefficients in the range (0.3-6.6) × 10-10 cm3 molecule-1 s-1 within the 10-150 K temperature range. Our calculations indicate that the formation of both hydrogen isocyanide and glycolonitrile is efficient under the harsh conditions of the ISM.

Equilibrium structures of selenium compounds: The torsionally flexible molecule of selenophenol.

The equilibrium structure of selenophenol has been investigated using rotational spectroscopy and high-level quantum mechanical calculations, offering electronic and structural insight into the scarcely studied selenium compounds. The jet-cooled broadband microwave spectrum was measured in the 2-8 GHz cm-wave region using broadband (chirped-pulse) fast-passage techniques. Additional measurements up to 18 GHz used narrow-band impulse excitation. Spectral signatures were obtained for six isotopic species of selenium (80Se, 78Se, 76Se, 82Se, 77Se, and 74Se), together with different monosubstituted 13C species. The (unsplit) rotational transitions associated with the non-inverting µa-dipole selection rules could be partially reproduced with a semirigid rotor model. However, the internal rotation barrier of the selenol group splits the vibrational ground state into two subtorsional levels, doubling the dipole-inverting µb transitions. The simulation of the double-minimum internal rotation gives a very low barrier height (B3PW91: 42 cm-1), much smaller than for thiophenol (277 cm-1). A monodimensional Hamiltonian then predicts a huge vibrational separation of 72.2 GHz, justifying the non-observation of µb transitions in our frequency range. The experimental rotational parameters were compared with different MP2 and density functional theory calculations. The equilibrium structure was determined using several high-level ab initio calculations. A final Born-Oppenheimer (reBO) structure was obtained at the coupled-cluster CCSD(T)_ae/cc-wCVTZ level of theory, including small corrections for the wCVTZ → wCVQZ basis set enlargement calculated at the MP2 level. The mass-dependent method with predicates was used to produce an alternative rm(2) structure. The comparison between the two methods confirms the high accuracy of the reBO structure and offers information on other chalcogen-containing molecules.

Revealing Internal Rotation and 14N Nuclear Quadrupole Coupling in the Atmospheric Pollutant 4-Methyl-2-nitrophenol: Interplay of Microwave Spectroscopy and Quantum Chemical Calculations.

The structure and interactions of oxygenated aromatic molecules are of atmospheric interest due to their toxicity and as precursors of aerosols. Here, we present the analysis of 4-methyl-2-nitrophenol (4MNP) using chirped pulse and Fabry-Pérot Fourier transform microwave spectroscopy in combination with quantum chemical calculations. The rotational, centrifugal distortion, and 14N nuclear quadrupole coupling constants of the lowest-energy conformer of 4MNP were determined as well as the barrier to methyl internal rotation. The latter has a value of 106.4456(8) cm-1, significantly larger than those from related molecules with only one hydroxyl or nitro substituent in the same para or meta positions, respectively, as 4MNP. Our results serve as a basis to understand the interactions of 4MNP with atmospheric molecules and the influence of the electronic environment on methyl internal rotation barrier heights.

An integrated protocol to study hydrogen abstraction reactions by atomic hydrogen in flexible molecules: application to butanol isomers.

This work presents a protocol designed to study hydrogen abstraction reactions by atomic hydrogen in molecules with multiple conformations. The protocol starts with the search and location of the conformers of the equilibrium structures using the TorsiFlex program. By a simple modification of the starting geometry of reactants, a Python script generates the input for the hydrogen abstraction transition states. Initially, the search of the stationary points (reactants and transition states) is carried out at a low-level employing firstly a preconditioned search and secondly a random search. The low-level conformers were reoptimized using a higher level electronic structure method. This information allows the evaluation of the multistructural harmonic-oscillator partition functions, which are corrected for zero-point energy anharmonicity by the hybrid degeneracy-corrected second-order vibrational perturbation theory and for torsional anharmonicity by the multistructural torsional method, as implemented in the MsTor program. The structural information of the stationary points is used by Pilgrim to evaluate the multipath canonical variational transition state theory thermal rate constants with multidimensional small-curvature corrections for tunneling. Therefore, the thermal rate constants include variational (recrossing) and tunneling effects in addition to the effect of multiple conformations on the thermal rate constants. These features grant the applicability of the method to a wide range of temperatures. The method was applied to each of the hydrogen abstraction sites of the four isomers of butanol. The methodology employed allowed us to calculate the thermal rate constants in the temperature range of 250-2500 K and to accurately fit them to analytical expressions. The variety of abstraction sites shows that the protocol is robust and that it can be employed to study hydrogen abstraction reactions in molecules containing carbon and oxygen as heavy atoms.

Correction: An integrated protocol to study hydrogen abstraction reactions by atomic hydrogen in flexible molecules: application to butanol isomers.

Correction for 'An integrated protocol to study hydrogen abstraction reactions by atomic hydrogen in flexible molecules: application to butanol isomers' by David Ferro-Costas et al., Phys. Chem. Chem. Phys., 2022, DOI: 10.1039/d1cp03928h.

Reaction of OH radicals with CH3NH2 in the gas phase: experimental (11.7-177.5 K) and computed rate coefficients (10-1000 K).

Nitrogen-bearing molecules, like methylamine (CH3NH2), can be the building blocks of amino acids in the interstellar medium (ISM). At the ultralow temperatures of the ISM, it is important to know its gas-phase reactivity towards interstellar radicals and the products formed. In this work, the kinetics of the OH + CH3NH2 reaction was experimentally and theoretically investigated at low- and high-pressure limits (LPL and HPL) between 10 and 1000 K. Moreover, the CH2NH2 and CH3NH yields were computed in the same temperature range for both pressure regimes. A pulsed CRESU (French acronym for Reaction Kinetics in a Uniform Supersonic Flow) apparatus was employed to determine the rate coefficient, k(T), in the 11.7-177.5 K range. A drastic increase of k(T) when the temperature is lowered was observed in agreement with theoretical calculations, evaluated by the competitive canonical unified statistical (CCUS) theory, below 300 K in the LPL regime. The same trend was observed in the HPL regime below 350 K, but the theoretical k(T) values were higher than the experimental ones. Above 200 K, the calculated rate coefficients are improved with respect to previous computational studies and are in excellent agreement with the experimental literature data. In the LPL, the formation of CH3NH becomes largely dominant below ca. 100 K. Conversely, in the HPL regime, CH2NH2 is the only product below 100 K, whereas CH3NH becomes dominant at 298 K with a branching ratio similar to the one found in the LPL regime (≈70%). At T > 300 K, both reaction channels are competitive independently of the pressure regime.

Chemical reactivity from the vibrational ground-state level. The role of the tunneling path in the tautomerization of urea and derivatives.

Recent developments of low-temperature techniques are providing valuable knowledge about chemical processes that manifest in the quantum regimen. The tunneling effect from the vibrational ground-state is the main mechanism of these reactions, which usually involves the motion or transfer of hydrogen atoms. Theoretical methods can enrich the information supplied by these experimental methods through an insightful analysis of the tunneling process. In this context, canonical variational transition state theory with multidimensional tunneling corrections (CVT/MT) can handle this type of reaction, and it has been applied to several systems within the small-curvature approximation for tunneling (SCT). This method is of proven reliability for polyatomic reactions occurring at room temperature and above, but no tests have been performed to check its performance when only the lowest energy level is populated. In this work, we compare SCT against the least-action tunneling (LAT) method to study the tautomerization and cis-trans interconversion reactions in the enol forms of urea, thiourea, and selenourea. To the best of our knowledge, this is the first time that the LAT method is applied to a polyatomic reaction occurring in the deep-tunneling region. The theoretical results indicate that the reaction mechanisms are controlled by tunneling. The SCT and LAT tautomerization reaction times are in good agreement with the experimental values; however, LAT seems superior to SCT for reactions (tautomerizations) that involve moderate reaction path curvature, whereas the opposite is true for reactions with small curvature (interconversions). These results led us to introduce and recommend the microcanonically optimized tunneling path that selects the tunneling probability as the maximum between the SCT and LAT tunneling probabilities.

Kinetics of the Methanol Reaction with OH at Interstellar, Atmospheric, and Combustion Temperatures.

The OH radical is the most important radical in combustion and in the atmosphere, and methanol is a fuel and antifreeze additive, model biofuel, and trace atmospheric constituent. These reagents are also present in interstellar space. Here we calculate the rate constants, branching ratios, and kinetic isotope effects (KIEs) of the hydrogen abstraction reaction of methanol by OH radical in a broad temperature range of 30-2000 K, covering interstellar space, the atmosphere, and combustion by using the competitive canonical unified statistical (CCUS) model in both the low-pressure and high-pressure limits and, for comparison, the pre-equilibrium model. Coupled cluster CCSD(T)-F12a theory and multi-reference CASPT2 theory were used to carry out benchmark calculations of the stationary points on the potential energy surface to select the most appropriate density functional method for direct dynamics calculations of rate constants. We find a significant effect of the anharmonicity of high-frequency modes of transition states on the low-temperature rate constant, and we show how tunneling leads to an unusual negative temperature dependence of the rate constants in the range 200 K > T > 100 K. The calculations also demonstrate the importance of the extent of stabilization of the pre-reactive complex. The capture rate for the formation of the complex is the dominant dynamical bottleneck for T < 100 K, and it leads to weak temperature dependence of the rate below 100 K in the high-pressure-limit of the CCUS model. We also report the pressure dependence of branching ratios (which are hard to measure so theory is essential) and the KIEs, and we report an unusual nonmonotonic variation of the KIE in the high-pressure limit at low temperatures.

Influence of Multiple Conformations and Paths on Rate Constants and Product Branching Ratios. Thermal Decomposition of 1-Propanol Radicals.

The potential energy surface involved in the thermal decomposition of 1-propanol radicals was investigated in detail using automated codes (tsscds2018 and Q2DTor). From the predicted elementary reactions, a relevant reaction network was constructed to study the decomposition at temperatures in the range 1000-2000 K. Specifically, this relevant network comprises 18 conformational reaction channels (CRCs), which in general exhibit a large wealth of conformers of reactants and transition states. Rate constants for all the CRCs were calculated using two approaches within the formulation of variational transition-state theory (VTST), as incorporated in the TheRa program. The simplest, one-well (1W) approach considers only the most stable conformer of the reactant and that of the transition state. In the second, more accurate approach, contributions from all the reactant and transition-state conformers are taken into account using the multipath (MP) formulation of VTST. In addition, kinetic Monte Carlo (KMC) simulations were performed to compute product branching ratios. The results show significant differences between the values of the rate constants calculated with the two VTST approaches. In addition, the KMC simulations carried out with the two sets of rate constants indicate that, depending on the radical considered as reactant, the 1W and the MP approaches may display different qualitative pictures of the whole decomposition process.

Entanglement and co-tunneling of two equivalent protons in hydrogen bond pairs.

A theoretical study is reported of a system of two identical symmetric hydrogen bonds, weakly coupled such that the two mobile protons can move either separately (stepwise) or together (concerted). It is modeled by two equivalent quartic potentials interacting through dipolar and quadrupolar coupling terms. The tunneling Hamiltonian has two imaginary modes (reaction coordinates) and a potential with a single maximum that may turn into a saddle-point of second order and two sets of (inequivalent) minima. Diagonalization is achieved via a modified Jacobi-Davidson algorithm. From this Hamiltonian the mechanism of proton transfer is derived. To find out whether the two protons move stepwise or concerted, a new tool is introduced, based on the distribution of the probability flux in the dividing plane of the transfer mode. While stepwise transfer dominates for very weak coupling, it is found that concerted transfer (co-tunneling) always occurs, even when the coupling vanishes since the symmetry of the Hamiltonian imposes permanent entanglement on the motions of the two protons. We quantify this entanglement and show that, for a wide range of parameters of interest, the lowest pair of states of the Hamiltonian represents a perfect example of highly entangled quantum states in continuous variables. The method is applied to the molecule porphycene for which the observed tunneling splitting is calculated in satisfactory agreement with experiment, and the mechanism of double-proton tunneling is found to be predominantly concerted. We show that, under normal conditions, when they are in the ground state, the two porphycene protons are highly entangled, which may have interesting applications. The treatment also identifies the conditions under which such a system can be handled by conventional one-instanton techniques.

Methanol dimer formation drastically enhances hydrogen abstraction from methanol by OH at low temperature.

The kinetics of the reaction of methanol with hydroxyl radicals is revisited in light of the reported new kinetic data, measured in cold expansion beams. The rate constants exhibit an approximately 10(2)-fold increase when the temperature decreases from 200 to 50 K, a result that cannot be fully explained by tunneling, as we confirm by new calculations. These calculations also show that methanol dimers are much more reactive to hydroxyl than monomers and imply that a dimer concentration of about 30% of the equilibrium concentration can account quantitatively for the observed rates. The assumed presence of dimers is supported by the observation of cluster formation in these and other cold beams of molecules subject to hydrogen bonding. The calculations imply an important caveat with respect to the use of cold expansion beams for the study of interstellar chemistry.

Hindered rotor tunneling splittings: an application of the two-dimensional non-separable method to benzyl alcohol and two of its fluorine derivatives.

In this work we present a novel application of the two-dimensional non-separable (2D-NS) method to the calculation of torsional tunneling splittings in systems with two hindered internal rotors. This method could be considered an extension of one-dimensional methods for the case of compounds with two tops. The 2D-NS method includes coupling between torsions in the kinetic and potential energy. Specifically, it has been applied to benzyl alcohol (BA) and two of its fluorine derivatives: 3-fluorobenzyl alcohol (3FBA) and 4-fluorobenzyl alcohol (4FBA). These molecules present two torsions, i.e., about the -CH2OH (ϕ1) and -OH (ϕ2) groups. The electronic structure calculations to build the two-dimensional torsional potential energy surface were performed at the DF-LMP2-F12//DF-LMP2/cc-pVQZ level of theory. For BA and 4FBA the calculated ground-state vibrational level splittings are 429 and 453 MHz, respectively, in good agreement with the experimental values of 337.10 and 492.82 MHz, respectively. In these two cases there are four equivalent wells and the tunneling splitting is the result of transitions between the two closer minima along ϕ1. The analysis of the wavefunctions, as well as the previous experimental work on the system, supports this conclusion. For 3FBA the observed ground-state splitting is 0.82 MHz, whereas in this case the calculated value amounts only to 0.02 MHz. The 2D-NS method, through the analysis of the wavefunctions, shows that this tiny tunneling splitting occurs between the two most stable minima of the potential energy surface. Additionally, we predict that the first vibrationally excited tunneling splitting will also be small and exclusively due to the interconversion between the second lowest minima.

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.

Tunneling splitting in double-proton transfer: direct diagonalization results for porphycene.

Zero-point and excited level splittings due to double-proton tunneling are calculated for porphycene and the results are compared with experiment. The calculation makes use of a multidimensional imaginary-mode Hamiltonian, diagonalized directly by an effective reduction of its dimensionality. Porphycene has a complex potential energy surface with nine stationary configurations that allow a variety of tunneling paths, many of which include classically accessible regions. A symmetry-based approach is used to show that the zero-point level, although located above the cis minimum, corresponds to concerted tunneling along a direct trans - trans path; a corresponding cis - cis path is predicted at higher energy. This supports the conclusion of a previous paper [Z. Smedarchina, W. Siebrand, and A. Fernández-Ramos, J. Chem. Phys. 127, 174513 (2007)] based on the instanton approach to a model Hamiltonian of correlated double-proton transfer. A multidimensional tunneling Hamiltonian is then generated, based on a double-minimum potential along the coordinate of concerted proton motion, which is newly evaluated at the RI-CC2/cc-pVTZ level of theory. To make it suitable for diagonalization, its dimensionality is reduced by treating fast weakly coupled modes in the adiabatic approximation. This results in a coordinate-dependent mass of tunneling, which is included in a unique Hermitian form into the kinetic energy operator. The reduced Hamiltonian contains three symmetric and one antisymmetric mode coupled to the tunneling mode and is diagonalized by a modified Jacobi-Davidson algorithm implemented in the Jadamilu software for sparse matrices. The results are in satisfactory agreement with the observed splitting of the zero-point level and several vibrational fundamentals after a partial reassignment, imposed by recently derived selection rules. They also agree well with instanton calculations based on the same Hamiltonian.

Combined DFT and Kinetic Monte Carlo Study of UiO-66 Catalysts for γ-Valerolactone Production.

Zr-based metal-organic frameworks (MOFs) are excellent heterogeneous porous catalysts due to their thermal stability. Their tunability via node and linker modifications makes them amenable for theoretical studies on catalyst design. However, detailed benchmarks on MOF-based reaction mechanisms combined with kinetics analysis are still scarce. Thus, we here evaluate different computational models and density functional theory (DFT) methods followed by kinetic Monte Carlo studies for a case reaction relevant in biomass upgrading, i.e., the conversion of methyl levulinate to γ-valerolactone catalyzed by UiO-66. We show the impact of cluster versus periodic models, the importance of the DF of choice, and the direct comparison to experimental data via simulated kinetics data. Overall, we found that Perdew-Burke-Ernzerhof (PBE), a widely employed method in plane-wave periodic calculations, greatly overestimates reaction rates, while M06 with cluster models better fits the available experimental data and is recommended whenever possible.

Comprehensive computational automated search of barrierless reactions leading to the formation of benzene and other C6-membered rings.

We present the systematic exploration of various potential energy surfaces for systems with C6H6-x (x = 0, 1, 2, or 3) empirical formula using an automatic search approach. The primary objective of this study is to identify reaction pathways that lead to the creation of benzene, o-benzyne, and other rings. These pathways initiate with a barrierless recombination reaction and involve subsequent isomerization reactions with submerged transition states until the final product is reached. The reported reaction profiles are consistent with the existing conditions in the interstellar medium if the hot complex formed can cool down through radiative relaxation. Recent studies on the deactivation of polyaromatic hydrocarbons (PAHs) support the possibility of these reactions taking place. The C6-membered rings are considered precursors of PAHs, and our focus is on identifying pathways originating from the barrierless recombination of reactive molecules known to exist in the interstellar medium, with potential implications in other environments.

Zero-point tunneling splittings in compounds with multiple hydrogen bonds calculated by the rainbow instanton method.

Zero-point tunneling splittings are calculated, and the values are compared with the experimentally observed values for four compounds in which the splittings are due to multiple-proton transfer along hydrogen bonds. These compounds are three binary complexes, namely, the formic acid and benzoic acid dimer and the 2-pyridone-2-hydroxypyridine complex, in which the protons move in pairs, and the calix[4]arene molecule, in which they move as a quartet. The calculations make use of and provide a test for the newly developed rainbow approximation for the zero-temperature instanton action which governs the tunneling splitting (as well as the transfer rate). This approximation proved to be much less drastic than the conventional adiabatic and sudden approximations, leading to a new general approach to approximate the instanton action directly. As input parameters the method requires standard electronic-structure data and the Hessians of the molecule or complex at the stationary configurations only; the same parameters also yield isotope effects. Compared to our earlier approximate instanton method, the rainbow approximation offers an improved treatment of the coupling of the tunneling mode to the other vibrations. Contrary to the conventional instanton approach based on explicit evaluation of the instanton trajectory, both methods bypass this laborious procedure, which renders them very efficient and capable of handling systems that thus far have not been handled by other theoretical methods. Past results for model systems have shown that the method should be valid for a wide range of couplings. The present results for real compounds show that it gives a satisfactory account of tunneling splittings and isotope effects in systems with strong coupling that enhances tunneling, thus demonstrating its applicability to low-temperature proton dynamics in systems with multiple hydrogen bonds.

Accurate treatment of two-dimensional non-separable hindered internal rotors.

This work presents an accurate way for calculating partition functions of strongly coupled hindered rotors in two dimensions. The two-dimensional torsional potential is generated from electronic structure calculations and fitted to Fourier series. The kinetic energy includes off-diagonal terms which are allowed to vary with the torsional angles, and these terms were also fitted to Fourier series. The resulting Hamiltonian leads to a coupled Schrödinger equation which was solved by the variational method. Therefore, the final two-dimensional non-separable (2D-NS) partition function incorporates coupling terms in both the kinetic and the potential energy. The methodology has been tested for propane, methyl formate, and a hydrogen abstraction transition state from propanone by the OH radical. How to incorporate the 2D-NS partition function in the total vibrational-rotational partition function is also discussed.