Energies Of Stationary Points Research Articles

Theoretical study on the reaction mechanism of the reaction of FC(O)O with NO

Density functional theory was used to study the mechanism of the reaction of FC(O)O with NO. The geometric configurations of reactants, intermediates, transition states and products were optimized by B3LYP method at 6-311G(d,p) level. The energies of stationary points along the pathway were calculated at CCSD(T) level. Intermediates and transition states were confirmed by the results of vibrational analysis. From the results of the reaction mechanism of the reaction of FC(O)O with NO, one can see that the reaction of FC(O)O+NO has four pathways and several steps. Comparing the four pathways’activation energies, one can find that the pathway FC(O)O+NO→M3→TS6→M5→FNO+CO2 is the main reaction pathway and FNO radical and CO2 are the main products, which is in good agreement with the result reported in the literature.

Conformational Preferences and Internal Rotation in Alkyl- and Phenyl-Substituted Thiourea Derivatives

Potential energy surfaces (PES) for rotation about the N-C(sp(3)) or N-C(aryl) bond and energies of stationary points on PES for rotation about the C(sp(2))-N bond are reported for methylthiourea, ethylthiourea, isopropylthiourea, tert-butylthiourea, and phenylurea, using the MP2/aug-cc-pVDZ method. Analysis of alkylthioureas shows that conformations, with alkyl groups cis to the sulfur atom, are more stable (by 0.4-1.5 kcal/mol) than the trans forms. All minima adopt anti configurations with respect to nitrogen pyramidalization, whereas syn configurations are not stationary points on the MP2 potential surface. In contrast, analysis of phenylthiourea reveals that a trans isomer in a syn geometry is the global minimum, whereas a cis isomer in an anti geometry is a local minimum with a relative energy of 2.7 kcal/mol. Rotation about the C(sp(2))-N bond in alkyl and phenyl thioureas is slightly more hindered (9.1-10.2 kcal/mol) than the analogous motion in the unsubstituted molecule (8.6 kcal/mol). The maximum barriers to rotation for the methyl, ethyl, isopropyl, tert-butyl, and phenyl substituents are predicted to be 1.2, 8.9, 8.6, 5.3, and 0.9 kcal/mol, respectively. Corresponding PESs are consistent with the experimental dihedral angle distribution observed in crystal structures. The results of the electronic structure calculations are used to benchmark the performance of the MMFF94 force field. Systematic discrepancies between MMFF94 and MP2 results were improved by modification of selected torsion parameters and one of the van der Waals parameters for sulfur.

Theoretical study on the mechanism of cycloaddition between dimethyl methylene carbene and acetone

The mechanism of the cycloaddition reaction of singlet dimethyl methylene carbene and acetone has been studied by using second-order Moller-Plesset perturbation and density functional theory. The geometrical parameters, harmonic vibrational frequencies and energy of stationary points on the potential energy surface are calculated by MP2/6-31G* and B3LYP/6-31G* methods. The results show that path b of the cycloaddition reaction (1) would be the major reactive channel of the cycloaddition reaction between singlet dimethyl methylene carbene and acetone, which proceeds in two steps: i) The two reactants form an energy-rich intermediate (INT1b), which is an exothermic reaction of 23.3 kJ/mol with no energy barrier. ii) The intermediate INT1b isomerizes to a three-membered ring product (P1) via transition state TS1b with energy barrier of 22.2 kJ/mol. The reaction rate of this reaction and its competitive reactions do greatly differ, with excellent selectivity. In view of dynamics and thermodynamics, this reaction is suitable for occurring at 1 atm and temperature range of 300–800 K, in which the reaction will have not only the larger spontaneous tendency and equilibrium constant but also the faster reaction rate.

Ab initio and DFT benchmark study for nucleophilic substitution at carbon (SN2@C) and silicon (SN2@Si)

To obtain a set of consistent benchmark potential energy surfaces (PES) for the two archetypal nucleophilic substitution reactions of the chloride anion at carbon in chloromethane (S(N)2@C) and at silicon in chlorosilane (S(N)2@Si), we have explored these PESes using a hierarchical series of ab initio methods [HF, MP2, MP4SDQ, CCSD, CCSD(T)] in combination with a hierarchical series of six Gaussian-type basis sets, up to g polarization. Relative energies of stationary points are converged to within 0.01 to 0.56 kcal/mol as a function of the basis-set size. Our best estimate, at CCSD(T)/aug-cc-pVQZ, for the relative energies of the [Cl(-), CH(3)Cl] reactant complex, the [Cl-CH(3)-Cl](-) transition state and the stable [Cl-SiH(3)-Cl](-) transition complex is -10.42, +2.52, and -27.10 kcal/mol, respectively. Furthermore, we have investigated the performance for these reactions of four popular density functionals, namely, BP86, BLYP, B3LYP, and OLYP, in combination with a large doubly polarized Slater-type basis set of triple-zeta quality (TZ2P). Best overall agreement with our CCSD(T)/aug-cc-pVQZ benchmark is obtained with OLYP and B3LYP. However, OLYP performs better for the S(N)2@C overall and central barriers, which it underestimates by 2.65 and 4.05 kcal/mol, respectively. The other DFT approaches underestimate these barriers by some 4.8 (B3LYP) to 9.0 kcal/mol (BLYP).

Theoretical Studies of Dissociative Phosphoryl Transfer in Interconversion of Phosphoenolpyruvate to Phosphonopyruvate: Solvent Effects, Thio Effects, and Implications for Enzymatic Reactions

The conversion of phosphoenolpyruvate (PEP) to phosphonopyruvate (P-pyr) is catalyzed by PEP mutase via a dissociative mechanism. In this work, we investigate the uncatalyzed reaction using ab initio methods, density functional theory, and the semiempirical MNDO/d method. Comparisons of geometries and relative energies of stationary points (minima and transition states) with density functional results indicate that the semiempirical method is reasonably accurate. Solvent effects are examined using implicit solvent models, including the recently extended smooth conductor-like screening model. Due to the large negative charge carried by the system, solvation is found to drastically alter the location and energy of stationary points along the dissociative reaction pathways. The influence of substituting a nonbridging phosphoryl oxygen by sulfur (thio effects) was also investigated. Implications of these results for the enzymatic reaction are discussed.

DFT benchmark study for the oxidative addition of CH 4 to Pd. Performance of various density functionals

We have evaluated the performance of 24 popular density functionals for describing the potential energy surface (PES) of the archetypal oxidative addition reaction of the methane C–H bond to the palladium atom by comparing the results with our recent ab initio [CCSD(T)] benchmark study of this reaction. The density functionals examined cover the local density approximation (LDA), the generalized gradient approximation (GGA), meta-GGAs as well as hybrid density functional theory. Relativistic effects are accounted for through the zeroth-order regular approximation (ZORA). The basis-set dependence of the density-functional-theory (DFT) results is assessed for the Becke–Lee–Yang–Parr (BLYP) functional using a hierarchical series of Slater-type orbital (STO) basis sets ranging from unpolarized double-ζ (DZ) to quadruply polarized quadruple-ζ quality (QZ4P). Stationary points on the reaction surface have been optimized using various GGA functionals, all of which yield geometries that differ only marginally. Counterpoise-corrected relative energies of stationary points are converged to within a few tenths of a kcal/mol if one uses the doubly polarized triple-ζ (TZ2P) basis set and the basis-set superposition error (BSSE) drops to 0.0 kcal/mol for our largest basis set (QZ4P). Best overall agreement with the ab initio benchmark PES is achieved by functionals of the GGA, meta-GGA, and hybrid-DFT type, with mean absolute errors of 1.3–1.4 kcal/mol and errors in activation energies ranging from +0.8 to −1.4 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with an only slightly larger mean absolute error of 2.5 kcal/mol and an underestimation by −1.9 kcal/mol of the overall barrier (i.e., the difference in energy between the TS and the separate reactants). For comparison, with B3LYP we arrive at a mean absolute error of 3.8 kcal/mol and an overestimation of the overall barrier by 4.5 kcal/mol.

Conformational Analysis and Rotational Barriers of Alkyl- and Phenyl-Substituted Urea Derivatives

Potential energy surfaces (PES) for rotation about the N-C(sp(3)) or N-C(aryl) bond and energies of stationary points on PES for rotation about the C(sp(2))-N bond are reported for methylurea, ethylurea, isopropylurea, tert-butylurea, and phenylurea, using the B3LYP/DZVP2 and MP2/aug-cc-pVDZ methods. The analysis of alkylureas reveals cis and (less stable) trans isomers that adopt anti geometries, whereas syn geometries do not correspond to stationary points. In contrast, the analysis of phenylurea reveals that the lowest energy form at the MP2 level is a trans isomer in a syn geometry. The fully optimized geometries are in good agreement with crystal structure data, and PESs are consistent with the experimental dihedral angle distribution. Rotation about the C(sp(2))-N bond in alkylureas and phenylurea is slightly more hindered (8.6-9.4 kcal/mol) than the analogous motion in the unsubstituted molecule (8.2 kcal/mol). At the MP2 level of theory, the maximum barriers to rotation for the methyl, ethyl, isopropyl, tert-butyl, and phenyl groups are predicted to be 0.9, 6.2, 6.0, 4.6, and 2.4 kcal/mol, respectively. The results are used to benchmark the performance of the MMFF94 force field. Systematic discrepancies between MMFF94 and MP2 results were improved by modification of several torsional parameters.

CH4 Loss from (CH3)4N+ Revisited: How Does This High Energy Elimination Compete with •CH3 Loss?

The rate of CH4 elimination from the tetramethylammonium ion increases faster than simple •CH3 loss with increasing internal energy at both high and low energies. Improved understanding of this highly unusual competition is sought by ab initio theory and RRKM calculations. Geometries and energies of stationary points and pathways as traced by intrinsic reaction coordinate calculations are given. A transition state at an energy much higher than those of both the reactant (414 kJ mol−1 above) and the products (361 kJ mol−1 above) was found for methane elimination from (CH3)4N+. More importantly, this transition state was also 14 kJ mol−1 above one found for methyl loss. However, according to results obtained and presented by RRKM theory, methane elimination through this transition state would be too slow to compete with methyl loss. This transition state may be for a concerted or a complex-mediated process. It is unlikely that CH4 is actually lost by a concerted elimination because only a small fraction of the reverse activation energy becomes translational energy, whereas concerted eliminations usually convert substantial fractions of their reverse activation energies into translational energy. Also, complex-mediated CH4 loss is unlikely because such eliminations are usually very quickly overwhelmed by simple dissociation of the partners just above threshold with increasing energy, opposite to the behavior of the system studied. Thus it is concluded that CH4 elimination from (CH3)4N+ occurs by loss of •CH3 followed by loss of H• at all energies, even though that is a higher energy process than methane elimination. Kinetic shifts and a reverse activation energy for •CH3 loss appear to raise the energy in the ions dissociating in the field free regions high enough to dissociate (CH3)4N+• + to (CH3)2N=CH2+• + •CH3 + H•.

Ab initio benchmark study for the oxidative addition of CH4 to Pd: Importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order Møller-Plesset perturbation theory, fourth-order Møller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values.

Direct ab Initio Dynamics Study of the Unimolecular Reaction of CH2FO

A direct ab initio dynamics study is carried out for three channels of the unimolecular reaction of fluoromethoxy, CH2FO. The minimum energy paths (MEPs) of the three channels are computed with the MPW1K/6-31+G(d,p) method. The geometries, harmonic vibrational frequencies, energies, and enthalpies of all stationary points are calculated at the MPW1K and QCISD levels of theory in conjunction with the 6-31+G(d,p) basis set. The energies of stationary points and the points along MEP for each channel are further refined by using single-point multilevel energy calculations. The rate constants are evaluated by means of the conventional transition state theory (TST), the canonical varitional transition state theory (CVT), and the canonical varitional transition state theory with small-curvature tunneling correction (CVT/SCT) in the temperature range of 200−2500 K. The fitted Arrhenius expressions of the calculated CVT/SCT rate constants are k1CVT/SCT(T) = (1.26 × 106)T2.19e-7150.6/T s-1, k2CVT/SCT(T) = (3.68 × 102)T3.23e-12327.7/T s-1, k3CVT/SCT(T) = (9.97 × 10-26)T10.90e-3873.3/T s-1 for the H elimination, HF elimination, and isomerization channels, respectively.

New results for the OH (nu = 0,j = 0) + CO (nu = 0,j = 0) --> H + CO2 reaction: Five- and full-dimensional quantum dynamical study on several potential energy surfaces.

Full- [six-dimensional (6-D)] and reduced-dimensional [five-dimensional (5-D)] quantum wave packet calculations have been performed for the title reaction to obtain reaction probabilities deriving from the ground rovibrational states of OH and CO with total angular momentum J = 0. Three potential energy surfaces (PES) are studied, namely, those of Bradley and Schatz (BS), Yu, Muckerman, and Sears (YMS), and Lakin, Troya, Schatz, and Harding (LTSH). 6-D calculations are performed only for the BS PES, while 5-D results are reported for all three PES'. The 6-D results obtained in the present work improve on those previously reported, since a larger vibrational basis and a better representation of the OH and CO bonds has been introduced. In particular, we now employ a generalized Lanczos-Morse discrete variable representation for both the OH and CO vibrations. In a further improvement, the generalized discrete variable representation of the CO vibration is based on different CO intramolecular potentials for the asymptotic and product grids employed in our projection formalism. This new treatment of the vibrational bases allows for a large reduction in computation time with respect to our previous implementation of the wave packet method, for a given level of accuracy. As a result, we have been able to extend the range of collision energies for which we can obtain converged 6-D results to a higher energy (0.8 eV) than was possible before (0.5 eV). The comparison of the new 6-D and previous 5-D results for the BS PES shows good agreement of the general trend in the reaction probabilities over all collision energies considered (0.1-0.8 eV), while our previous 6-D calculation showed reaction probabilities that differed from the 5-D results by up to 10% between 0.5 and 0.8 eV. The 5-D reaction probabilities reveal interesting trends for the different PES'. In particular, at low energies (< 0.2 eV) the LTSH PES gives rise to much larger reactivity than the other PES', while at high energies (> 0.3 eV) its reaction probability decreases with respect to the BS and YMS PES', being more than a factor of 2 smaller at 0.8 eV. A 5-D calculation on a modified version of the LTSH surface shows that the van der Waals interaction in the entrance channel, which is not correctly described in the other PES' is largely responsible for its larger reactivity at low energies. The large difference between the 5-D reaction probabilities for the YMS and LTSH PES' serves to emphasize the importance of the van der Waals interaction for the reactivity at low energies, because most of the stationary point energies on the YMS and LTSH PES are rather similar, being in line with high-level ab initio information.

Direct ab Initio Dynamics Study of the Reaction of the Hydrogen Atom with Formyl Chloride

A direct ab initio dynamics study is presented on two channels of the gas-phase reaction of the hydrogen atom with formyl chloride, HCOCl. The geometries, harmonic vibrational frequencies, energies, and enthalpies of all of the stationary points are calculated at the BHandHLYP, MP2, and QCISD levels of theory with the cc-pVDZ basis set. The minimum energy paths (MEPs) of both channels of the title reaction are also computed with the same methods and basis set. The energies of stationary points and the points along the MEP for each channel are refined by means of some single-point multilevel energy calculations (HL). The rate constants are evaluated with the conventional transition state theory (TST), the improved canonical varitional transition state theory (ICVT), and the improved canonical varitional transition state theory with small-curvature tunneling correction (ICVT/SCT) in the temperature range of 300−2500 K. The fitted Arrhenius expressions of the calculated ICVT/SCT rate constants at the HL//BHa...

A Theoretical Study on the Kinetics of Disproportionation versus Association Reaction of CH3 + C2H5

Two possible reaction paths for the CH3 + C2H5 system are direct hydrogen abstraction or association reaction. In the present study, the kinetics of the two possible reactions are investigated from a theoretical point of view. Unimolecular dissociation of propane is also studied. As one expects, association or dissociation reactions are pressure dependent processes, while hydrogen abstraction reaction is not sensitive to the pressure. Potential energy surfaces for both reaction paths are explored by UMP2, CAS, QCISD, and DFT methods. Energies of stationary points were calculated by CASMP2, B3LYP, MP4SDTQ, and QCISD methods. Canonical variational transition-state theory and microcanonical variational RRKM calculations were used to locate the position of bottleneck for the association reaction of methyl and ethyl radicals. The RRKM method was used to calculate the pressure dependency of the rate constants for dissociation of propane and association of methyl and ethyl radicals. Conventional transition-state theory was used to calculate the rate constant for hydrogen abstraction reaction of the two radicals in the title in a temperature range of 200−2500 K. According to our RRKM calculations, the high-pressure Arrhenius parameters for dissociation reaction of propane and association reaction of the two radicals were found as k-1 = 1.1 × 1017 exp(−369.1 kJ mol-1/RT) s-1 and k1 = 5.5 × 1011 T-0.56 exp(0.53 kJ mol-1/RT) L mol-1s-1. According to generalized transition-state theory, the rate constant for hydrogen abstraction reaction were found as k2 = 9.8 × 108 L mol-1s-1 over the temperature range of 200−2500 K.

High level theoretical study of the structure and rotational barriers of trans-stilbene

The relative energies of stationary points on the potential energy surface of trans-stilbene have been accurately determined using Hartree–Fock, second and third-order Møller–Plesset (MP2, MP3), as well as Coupled Clusters theories with single and double excitations (CCSD), together with a perturbative estimate of connected triple excitations [CCSD(T)], in conjunction with basis sets of increasing size, containing up to 1130 basis functions. A focal point analysis has been carried out in order to determine how the energy differences and rotational barriers approach convergence, enabling extrapolation of the CCSD(T) results to a near-complete basis set. The investigated saddle points pertain to independent rotations of the phenyl rings about the single C–C bond, and to pedalling motions described by a twofold rotation of the central ethylene bond about the longitudinal axis of the molecule. The benchmark calculations presented in this study lead to the conclusion that, in the nonrelativistic limit and within the frozen core approximation, trans-stilbene in vacuum is a strictly planar molecule in its absolute energy minimum form, in sharp contrast with many previous theoretical studies. This point has been ultimately confirmed by an MP2 geometry optimization using the aug-cc-pVDZ basis set. At last, the energy of cis-stilbene relative to the trans-isomer is accurately evaluated.

Quantum dynamics of the photoinitiated unimolecular dissociation of HOCO

The photodissociation dynamics of HOCO in the overtone νOH=3 are studied using a time-dependent wave packet dynamics approach. The dynamics calculations are carried out using a four-dimensional planar model in which the terminal C=O bond (spectator) is fixed at its equilibrium bond distance in the trans-HOCO conformer based on an empirical potential energy surface for HOCO fit to accurate ab initio calculations of the stationary point energies. The branching fraction into the H+CO2 products, and the resonance states associated with νOH=3 are investigated in detail.

Potential-energy landscapes of simple liquids.

Changes in the potential-energy surface as a function of the range and curvature of the pair potential are studied using isothermal-isobaric ensemble Monte Carlo simulations of Morse liquids. The configurational energies of stationary points are found to be linear functions of the fraction of imaginary modes, with slopes that are proportional to the range of the potential. The relative energies of saddles, minima, and instantaneous configurations show qualitatively different behavior for short, long, and intermediate range potentials, which imply corresponding variations in liquid state relaxation dynamics.

A Kohn–Sham study of the oxirene–ketene potential energy surface

Stationary points on the oxirene–ketene potential energy surface (PES) are determined using Kohn–Sham density functional theory (DFT) with the B3LYP, B97-1, and B97-2 hybrid exchange-correlation energy functionals. B3LYP and B97-1 predict oxirene to be a transition state, which is at variance with large basis set CCSD(T) calculations, which predict a minimum. The B97-2 functional, which was recently shown to provide improved reaction barriers over B3LYP and B97-1 for a series of simple reactions, predicts oxirene to be a minimum. B97-2 relative stationary point energies are closest to the best CCSD(T) values.

Theoretical study on the mechanism of the cycloaddition reaction between stannylene and ethylene or formaldehyde

AbstractThe mechanism of the cycloaddition reaction of singlet stannylene and ethylene or formaldehyde has been studied by using density functional theory. The geometrical parameters, harmonic vibrational frequencies and energies of stationary points for potential energy surface are calculated by RB3LYP/3–21G* method. The results show that the two reaction processes are both two steps: (1) stannylene and ethylene or formaldehyde form an energy‐rich intermediate complex respectively, which is an exothermal reaction with no barrier; (2) two intermediate complexes isomerize to the product, respectively, with the barriers of these two reactions being 52.97 and 45.15 kJ/mol at RB3LYP/3–21G* level.

On the structure of the monohydrated superoxide molecular anion, O2-·(H2O). An ab initio molecular orbital study

The ground-state potential energy surface of the monohydrated superoxide ion–dipole complex O2-·(H2O) was investigated viaabinitio molecular orbital theory in order to establish firmly the relative energies of stationary points on this surface. Using the configuration interaction (CI) theoretical approach to accommodate the effects of electron correlation, the global minimum on the potential energy surface corresponds to a structure adopting Cs molecular symmetry with one end of the water molecule forming a hydrogen bond with one end of the superoxide. A more symmetric structure adopting C2v molecular symmetry is shown to be a transition state linking two equivalent forms of the Cs geometry via a water rocking motion. Using a highly flexible triple-zeta basis set with quadratic configuration interaction theory incorporating all single and double electron substitutions [QCISD/6–311++G**], the scaled zero point energies for the C2v and Cs geometries are 64.6 and 64.1 kJ mol-1, respectively. The energy barrier to the water rocking motion along the reaction coordinate is 3.9 kJ mol-1. The frequencies of the symmetric and asymmetric water O–H stretches in the C2v structure are 3731 and 3765 cm-1, respectively. The water O–H stretching frequencies in the Cs structure are 3178 cm-1 for the “hydrogen bonded’' OH and 3937 cm-1 for the “free’' OH. The geometry of the global minimum of O2-·(H2O) on the equivalent of the first electronically excited potential energy surface of the bare superoxide was also determined using the complete active space self-consistent field (CASSCF) theoretical approach. A vibrational frequency analysis confirms that the excited-state stationary point is a local minimum geometry. The excited-state geometry differs significantly from that in the ground electronic state. The overall molecular symmetry in the excited state remains as Cs, but the water molecule adopts an orientation approximately midway between the ground-state Cs and C2v configurations.

Ab Initio Study of the Transition State and Forward and Reverse Rate Constants for C2H5 ⇌ H + C2H4

Different levels of ab initio theory are used to calculate geometries, vibrational frequencies, and energies for stationary points on the H + C2H4 ⇌ C2H5 potential energy surface. Frequencies and geometries calculated for C2H4 at the QCISD/6-311G** and MRCI/cc-pVDZ levels of theory are in very good agreement with experiment. The ab initio normal modes for the H- - -C2H4 transition state are similar to those for C2H4, and ratios between the C2H4 experimental anharmonic frequencies and ab initio harmonic frequencies are used to estimate anharmonic frequencies for the transition state. Nine of the 10 frequencies assigned for C2H5 from experiment are consistent with the ab initio calculations. The CC stretch was apparently misassigned and reassigned here. The ab initio calculations do not give definitive values for the H + C2H4 → C2H5 barrier height and heat of reaction. Using these two energy terms as adjustable parameters in concert with the above stationary point geometries and frequencies, transition stat...