Showing papers on "Potential energy surface published in 2002"

A SN2 Reaction That Avoids Its Deep Potential Energy Minimum

Abstract: Chemical dynamics trajectory simulations were used to study the atomic-level mechanisms of the OH- + CH3F --> CH3OH + F- SN2 nucleophilic substitution reaction. The reaction dynamics, from the [OH...CH3...F]- central barrier to the reaction products, are simulated by ab initio direct dynamics. The reaction's potential energy surface has a deep minimum in the product exit channel arising from the CH3OH...F- hydrogen-bonded complex. Statistical theories of unimolecular reaction rates assume that the reactive system becomes trapped in this minimum and forms an intermediate, with random redistribution of its vibrational energy, but the majority of the trajectories (90%) avoided this potential energy minimum and instead dissociated directly to products. This finding is discussed in terms of intramolecular vibrational energy redistribution (IVR) and the relation between IVR and molecular structure. The finding of this study may be applicable to other reactive systems where there is a hierarchy of time scales for intramolecular motions and thus inefficient IVR.

A first-principles study of methanol decomposition on Pt(111).

Abstract: A periodic, self-consistent, Density Functional Theory study of methanol decomposition on Pt(111) is presented. The thermochemistry and activation energy barriers for all the elementary steps, starting with O[bond]H scission and proceeding via sequential hydrogen abstraction from the resulting methoxy intermediate, are presented here. The minimum energy path is represented by a one-dimensional potential energy surface connecting methanol with its final decomposition products, CO and hydrogen gas. It is found that the rate-limiting step for this decomposition pathway is the abstraction of hydroxyl hydrogen from methanol. CO is clearly identified as a strong thermodynamic sink in the reaction pathway while the methoxy, formaldehyde, and formyl intermediates are found to have low barriers to decomposition, leading to very short lifetimes for these intermediates. Stable intermediates and transition states are found to obey gas-phase coordination and bond order rules on the Pt(111) surface.

Anchoring the water dimer potential energy surface with explicitly correlated computations and focal point analyses

Abstract: Ten stationary points on the water dimer potential energy surface have been characterized with the coupled-cluster technique which includes all single and double excitations as well as a perturbative approximation of triple excitations [CCSD(T)] Using a triple-ζ basis set with two sets of polarization functions augmented with higher angular momentum and diffuse functions [TZ2P(f,d)+dif], the fully optimized geometries and harmonic vibrational frequencies of these ten stationary points were determined at the CCSD(T) theoretical level In agreement with other ab initio investigations, only one of these ten stationary points is a true minimum Of the other nine structures, three are transition structures, and the remaining are higher order saddle points These high-level ab initio results indicate that the lowest lying transition state involved in hydrogen interchange is chiral, of C1 symmetry rather than Cs as suggested by recently developed 6D potential energy surfaces The one- and n-particle limits of t

Efficient characterization of stationary points on potential energy surfaces

Abstract: Traditional methods for characterizing an optimized molecular structure as a minimum or as a saddle point on the nuclear potential energy surface require the full Hessian. However, if f denotes the number of nuclear degrees of freedom, a full Hessian calculation is more expensive than a single point geometry optimization step by the order of magnitude of f. Here we present a method which allows to determine the lowest vibrational frequencies of a molecule at significantly lower cost. Our approach takes advantage of the fact that only a few perturbed first-order wave functions need to be computed in an iterative diagonalization scheme instead of f ones in a full Hessian calculation. We outline an implementation for Hartree–Fock and density functional methods. Applications indicate a scaling similar to that of a single point energy or gradient calculation, but with a larger prefactor. Depending on the number of soft vibrational modes, the iterative method becomes effective for systems with more than 30–50 atoms.

The incorporation of quantum effects in enzyme kinetics modeling.

Abstract: We present an overview of new procedures for including quantum mechanical effects in enzyme kinetics. Quantum effects are included in three ways: (1) The electronic structure of the atoms in the catalytic center is treated quantum mechanically in order to calculate a realistic potential energy surface for the bond rearrangement process. (2) The discrete nature of quantum mechanical vibrational energies is incorporated in the treatment of nuclear motion for computing the potential of mean force. (3) Multidimensional tunneling contributions are included. These procedures are illustrated by applications to proton abstractions catalyzed by enolase and methylamine dehydrogenase and hydride-transfer reactions by alcohol dehydrogenase and xylose isomerase.

Spectroscopic Calibration of Modern Density Functional Methods Using [CuCl4]2-

Abstract: Density functional theory has become a popular method for studying the electronic structure and potential energy surface properties of large molecules. Its accuracy has been extensively validated for organic and organometallic systems. However, this is not yet the case for classical inorganic compounds with biological importance. This study presents a systematic evaluation of modern DFT calculations using the spectroscopically well understood molecule [CuCl4]2-. The BP86 and B3LYP functionals with saturated basis sets give a ground-state bonding description that is too covalent, and the calculated ligand-field and ligand-to-metal charge transitions are shifted to higher and lower energies, respectively, relative to experiment. A spectroscopically adjusted hybrid DFT functional (B(38HF)P86) was optimized to match the ground-state experimental Cu spin density (0.62 ± 0.02e). This adjusted hybrid functional also gives an improved excited-state description with a rms error in transition energies of 1000 cm-1....

Ab initio potential energy surface and vibrational-rotational energy levels of X2Σ+ CaOH

Abstract: The equilibrium structure and potential energy surface of calcium monohydroxide in its ground doublet state, X2Σ+ CaOH, have been determined from large-scale ab initio calculations using the spin-r...

Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids

Abstract: The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of |∇E|2, which has been used in previous work to support these theories. The examples we consider are a two-dimensional model energy surface and binary Lennard-Jones liquids and solids. A shortcoming of the mapping is its failure to divide the potential energy surface into basins of attraction surrounding saddle points, because there are many minima of |∇E|2 that do not correspond to stationary points of the potential energy. In fact, most liquid configurations are mapped to such points for the system we consider. We therefore develop an alternative route to investigate higher-index saddle points and obtain near complete distributions of saddles for small Lennard-Jones clusters. The distribution of the number of stationary points as a function of the index is found to be Gaussian, and the average energy increases linearly with saddle point index in agreement with previous results for bulk systems.

The vibrational energies of ozone up to the dissociation threshold: Dynamics calculations on an accurate potential energy surface

Abstract: We present an ab initio potential energy surface for the ground electronic state of ozone. It is global, i.e., it covers the three identical C2v (open) minima, the D3h (ring) minimum, as well as the O(3P)+O2(3Σg−) dissociation threshold. The electronic structure calculations are performed at the multireference configuration interaction level with complete active space self-consistent-field reference functions and correlation consistent polarized quadruple zeta atomic basis functions. Two of the O–O bond distances, R1 and R2, and the O–O–O bending angle are varied on a regular grid (ca. 5000 points with R1⩾R2). An analytical representation is obtained by a three-dimensional cubic spline. The calculated potential energy surface has a tiny dissociation barrier and a shallow van der Waals minimum in the exit channel. The ring minimum is separated from the three open minima by a high potential barrier and therefore presumably does not influence the low-temperature kinetics. The dissociation energy is reproduce...

Quantum studies of Eley–Rideal reactions between H atoms on a graphite surface

Abstract: Results from electronic structure studies and quantum scattering calculations are presented for the reaction of gas-phase H atoms with H atoms adsorbed onto a graphite surface to form H2(g). H can chemisorb on graphite directly over a carbon atom, with the carbon puckering out of the surface plane by several tenths of an A. Using an ab initio approach based on the density functional theory, and treating the graphite substrate as a slab, we compute the potential energy surface for this reaction, for three cases. In the first case the adsorbed H is initially in the chemisorbed state and the lattice is held fixed in the puckered position during the reaction. In the second case the adsorbed H is initially in the chemisorbed state, but the lattice is allowed to fully relax for each configuration of the two H atoms. In the third case the H initially on the surface is in the physisorbed state. We use a fully quantum mechanical scattering approach to compute reaction cross sections and product H2 translational, r...

Degenerate perturbation theory corrections for the vibrational self-consistent field approximation: Method and applications

Abstract: A new algorithm for computing anharmonic vibrational states for polyatomic molecules is proposed. The algorithm starts with the vibrational self-consistent field (VSCF) method and uses degenerate perturbation theory to correct for effects of correlation between different vibrational modes. The algorithm is developed in a version that computes the anharmonic vibrational spectroscopy directly from potential energy surface points calculated by using ab initio codes. The method is applied to several molecules where near degeneracies occur for excited vibrational states, including HOOH, HSSH, and HOOOH. The method yields results in very good accordance with experiments and generally provides improvements over nondegenerate perturbation corrections for VSCF.

Development of transferable interaction models for water. I. Prominent features of the water dimer potential energy surface

Abstract: We present an analysis of the morphology of the water dimer potential energy surface (PES) obtained from ab initio electronic structure calculations and perform a quantitative comparison with the results from various water potentials. In order to characterize the morphology of the PES we have obtained minimum energy paths (MEPs) as a function of the intermolecular O–O separation by performing constrained optimizations under various symmetries (Cs, Ci, C2, and C2v). These constitute a primitive map of the dimer PES and aid in providing an account for some of its salient features such as the energetic stabilization of “doubly hydrogen-bonded” configurations for R(O–O)<2.66 A. Among the various interaction potentials that are examined, it is found that the family of anisotropic site potential (ASP) models agrees better with the ab initio results in reproducing the geometries along the symmetry-constrained MEPs. It is demonstrated that the models that produce closest agreement with the morphology of the ab initio PES, tend to better reproduce the experimental data for the second virial coefficients. We finally comment on the functional forms of simple water models and discuss how effects such as charge overlap can be incorporated into such models.

Quantum mechanics/molecular mechanics studies of triosephosphate isomerase-catalyzed reactions: effect of geometry and tunneling on proton-transfer rate constants.

Abstract: The role of tunneling for two proton-transfer steps in the reactions catalyzed by triosephosphate isomerase (TIM) has been studied. One step is the rate-limiting proton transfer from Cα in the substrate to Glu 165, and the other is an intrasubstrate proton transfer proposed for the isomerization of the enediolate intermediate. The latter, which is not important in the wild-type enzyme but is a useful model system because of its simplicity, has also been examined in the gas phase and in solution. Variational transition-state theory with semiclassical ground-state tunneling was used for the calculation with potential energy surface determined by an AM1 method specifically parametrized for the TIM system. The effect of tunneling on the reaction rate was found to be less than a factor of 10 at room temperature; the tunneling becomes more important at lower temperature, as expected. The imaginary frequency (barrier) mode and modes that have large contributions to the reaction path curvature are localized on th...

Energetics and vibrational states for hydrogen on Pt(111).

Abstract: We present a combination of theoretical calculations and experiments for the low-lying vibrational excitations of H and D atoms adsorbed on the Pt(111) surface. The vibrational band states are calculated based on the full three-dimensional adiabatic potential energy surface obtained from first-principles calculations. For coverages less than three quarters of a monolayer, the observed experimental high-resolution electron peaks at 31 and 68 meV are in excellent agreement with the theoretical transitions between selected bands. Our results convincingly demonstrate the need to go beyond the local harmonic oscillator picture to understand the dynamics of this system.

Reactive and diffractive scattering of H-2 from Pt(111) studied using a six-dimensional wave packet method

Abstract: We present results of calculations on dissociative and rotationally (in)elastic diffractive scattering of H2 from Pt(111), treating all six molecular degrees of freedom quantum mechanically. The six-dimensional (6D) potential energy surface was taken from density functional theory calculations using the generalized gradient approximation and a slab representation of the metal surface. The 6D calculations show that out-of-plane diffraction is very efficient, at the cost of in-plane diffraction, as was the case in previous four-dimensional (4D) calculations. This could explain why so little in-plane diffraction was found in scattering experiments, suggesting the surface to be flat, whereas experiments on reaction suggested a corrugated surface. Results of calculations for off-normal incidence of (v=0,j=0) H2 show that initial parallel momentum inhibits dissociation at low normal translational energies, in agreement with experiment, but has little effect for higher energies. Reaction of initial (v=1,j=0) H2 ...

Quantum effects in the differential cross Ssctions for the insertion reaction N(2D) + H2.

Abstract: The quantum (QM) scattering theory has been difficult to apply to the family of insertion reactions and the approximate quasiclassical trajectory (QCT) method or statistical calculations were mostly applied. In this Letter, we compare the experimental differential cross sections for the title insertion reaction with the results of QM and QCT calculations on an ab initio potential energy surface. The QM results reproduce well the crossed beam experiment, while a small, but significant, difference in the QCT ones points to quantum effects, possibly the occurrence of tunneling through the combined potential and centrifugal barrier.

First-Principles Kinetics of CO Desorption from Oxygen Species on Carbonaceous Surface

Abstract: We present an ab initio direct dynamics study on the desorption of CO from semiquinone carbon−oxygen species in carbonaceous surfaces. Density functional theory, in particular B3LYP/6-31G(d) level, was used to calculate the potential energy surface information. We found that in the initial stage of the desorption process, the six-member ring of the carbonaceous model opens slightly to let the CO break away, and then closes up to form the five-member ring. Because of low-lying excited estates in the carbon−oxygen complexes, electronic crossing occurs from reactants to products. Transition-state structures were found for the ground-state path, and the activation desorption energy is in excellent agreement with existing experimental data. Transition-state theory was used to calculate the thermal rate constant for desorption of CO in the range of 600−1700 °C. The fitted Arrhenius expression for the calculated rate constants is k(T) = 1.81 × 1017 exp[−47682/T(K)](s-1), which is within the experimental uncertai...

F+D2 reaction at ultracold temperatures

Abstract: We present a quantum mechanical study of the reaction F+D2 at ultracold temperatures based on the potential energy surface of Stark and Werner. The reaction cross section at low energies is controlled by the tunneling through the activation barrier, a mechanism that is favored by the long duration of the collision at those energies. Differences are found in the behavior of the reactive cross section compared to that for F+H2, due to the changed mass and zero point energy. A new feature is detected in the reaction probabilities and is attributed to a Feshbach resonance corresponding to a metastable state in the exit channel.

Ab Initio and Improved Empirical Potentials for the Calculation of the Anharmonic Vibrational States and Intramolecular Mode Coupling of N-Methylacetamide

Abstract: The second-order Moller-Plesset ab initio electronic structure method is used to compute points for the anharmonic mode-coupled potential energy surface of N-methylacetamide (NMA) in the trans(sub ct) configuration, including all degrees of freedom. The vibrational states and the spectroscopy are directly computed from this potential surface using the Correlation Corrected Vibrational Self-Consistent Field (CC-VSCF) method. The results are compared with CC-VSCF calculations using both the standard and improved empirical Amber-like force fields and available low temperature experimental matrix data. Analysis of our calculated spectroscopic results show that: (1) The excellent agreement between the ab initio CC-VSCF calculated frequencies and the experimental data suggest that the computed anharmonic potentials for N-methylacetamide are of a very high quality; (2) For most transitions, the vibrational frequencies obtained from the ab initio CC-VSCF method are superior to those obtained using the empirical CC-VSCF methods, when compared with experimental data. However, the improved empirical force field yields better agreement with the experimental frequencies as compared with a standard AMBER-type force field; (3) The empirical force field in particular overestimates anharmonic couplings for the amide-2 mode, the methyl asymmetric bending modes, the out-of-plane methyl bending modes, and the methyl distortions; (4) Disagreement between the ab initio and empirical anharmonic couplings is greater than the disagreement between the frequencies, and thus the anharmonic part of the empirical potential seems to be less accurate than the harmonic contribution;and (5) Both the empirical and ab initio CC-VSCF calculations predict a negligible anharmonic coupling between the amide-1 and other internal modes. The implication of this is that the intramolecular energy flow between the amide-1 and the other internal modes may be smaller than anticipated. These results may have important implications for the anharmonic force fields of peptides, for which N-methylacetamide is a model.

An accurate analytic H4 potential energy surface

Abstract: The interaction potential energy surface (PES) of H4 is of great importance for quantum chemistry as a test case for molecule–molecule interactions. It is also required for a detailed understanding of certain astrophysical processes, namely collisional excitation and dissociation of H2 in molecular clouds, at densities too low to be accessible experimentally. The 6101 ab initio H4 energies reported in 1991 by Boothroyd et al. demonstrated large inaccuracies in analytic H4 surfaces available at that time. Some undesirable features remained in the more accurate H4 surfaces fitted to these energies by Keogh and by Aguado et al., due in part to the relatively sparse coverage of the six-dimensional H4 conformation space afforded by the 6101 ab initio energies. To improve the coverage, 42 079 new ab initio H4 energies were calculated, using Buenker’s multiple reference (single and) double excitation configuration interaction program. Here the lowest excited states were computed as well as the ground state, and energies for the original 6101 conformations were recomputed. The ab initio energies have an estimated rms “random” error of ∼0.5 millihartree and a systematic error of ∼1 millihartree (0.6 kcal/mol). A new analytical H4 PES was fitted to these 48 180 ab initio energies (and to an additional 13 367 points generated at large separations), yielding a significant improvement over previous H4 surfaces. This new PES has an rms error of 1.43 millihartree relative to these 48 180 ab initio energies (the fitting procedure used a reduced weight for high energies, yielding a weighted rms error of 1.15 millihartree for these 48 180 ab initio energies). For the 39 064 ab initio energies that lie below twice the H2 dissociation energy, the new PES has an rms error of 0.95 millihartree. These rms errors are comparable to the estimated error in the ab initio energies themselves. The new PES also fits the van der Waals well to an accuracy of about 5%. For relatively compact conformations (energies higher than the H2 dissociation energy), the conical intersection between the ground state and the first excited state is the largest source of error in the analytic surface. The position of this conical intersection forms a somewhat complicated three-dimensional hypersurface in the six-dimensional conformation space of H4. A large portion of the position of the conical intersection has been mapped out, but trying to include the conical intersection explicitly in an analytic surface is beyond the scope of the present paper.

The N2–N2 system: An experimental potential energy surface and calculated rotovibrational levels of the molecular nitrogen dimer

Abstract: An accurate new representation for the potential energy surface for the N2–N2 dimer has been obtained from the analysis of scattering experiments from our laboratory, and of available second virial coefficient data. A harmonic expansion functional form describes the salient geometries of the dimer and accounts for the relative contributions to the intermolecular interaction from components of different nature. The equilibrium geometry is a T conformation with well depth 13.3 meV (107.14 cm−1) and at a distance of 4.03 A. In order to assist in the analysis of spectra, we calculated the bound rotovibrational states for the (N2)2 system for J⩽6 by solving a secular problem over the exact Hamiltonian, considering the N2 monomers as rigid rotors, and where the Coriolis coupling is included.

Energy profile of the interconversion path between T-shape and slipped-parallel benzene dimers

Abstract: The energy profile of the interconversion path between the T-shape and slipped-parallel dimers has been studied by high level ab initio calculations. The CCSD(T) (coupled cluster calculation with single and double substitutions with noniterative triple excitations) interaction energy at the basis set limit has been estimated from the MP2 (the second-order Moller–Plesset calculation) interaction energy near the basis set limit and the CCSD(T) correction term using the 6-311G* basis set. The calculated CCSD(T) level energy profile has shown that the potential is very flat and the interconversion barrier height is very small (around 0.2 kcal/mol). The MP2 calculations using large basis sets near the basis set limit considerably overestimate the attraction of the slipped-parallel dimer, which indicates the importance of higher level electron correlation correction for studying the potential energy surface of the benzene dimer.

Classical dynamics of dissociative adsorption for a nonactivated system: The role of zero point energy

Abstract: We present dissociative adsorption probabilities of H2 on Pd(111) computed with the classical trajectory method. We perform both classical (C) and quasiclassical (QC) calculations, the latter including, by contrast with the former, the initial zero point energy (ZPE) of H2. We analyze in detail the role played by the ZPE and demonstrate the strong and weak points of both C and QC calculations. We show that ZPE is crucial in accelerating the molecules toward the surface through vibrational softening. However, at low energies, dynamic trapping is quenched in QC calculations by processes of vibration to rotation energy transfer that would be associated with closed channels in a quantum approach. In this study we use a new representation of the H2/Pd(111) potential energy surface (obtained by interpolation of ab initio data) with a significantly better accuracy in the entrance channel region which plays a decisive role in the dissociation dynamics.

A globally smooth ab initio potential surface of the 1 A′ state for the reaction S(1D)+H2

Abstract: A procedure based on the reproducing kernel Hilbert space (RKHS) interpolation method has been implemented to produce a globally smooth potential energy surface (PES) for the 1 A′ state of the S(1D)+H2 reaction from a set of accurate ab initio data, calculated at the multireference configuration interaction level with augmented polarized quadruple-zeta basis sets and arranged on a three-dimensional regular full grid in the Jacobi coordinates. The procedure includes removing a small number of questionable ab initio data points, implementing a recently developed technique for efficiently handling a partially filled grid, and adopting a sequence of regularizations for attaining additional smoothness. The resulting RKHS PES is analytic, first-order differentiable, and fast to evaluate. Quasiclassical trajectory calculations have been performed and compared with the results based on a recent hybrid PES obtained from a combination of the RKHS interpolation in the entrance channel and Murrell–Carter (MC)-type fi...

Sampling along reaction coordinates with the Wang-Landau method

Abstract: The multiple range random walk algorithm recently proposed by Wang and Landau [2001, Phys. Rev. Lett., 86, 2050] is adapted to the computation of free energy profiles for molecular systems along reaction coordinates. More generally, we show how to extract partial averages in various statistical ensembles without invoking simulations with constraints, biasing potentials or unknown parameters. The method is illustrated on a model 10-dimensional potential energy surface, for which analytical results are obtained. It is then applied to the potential of mean force associated with the dihedral angle of the butane molecule in the gas phase and in carbon tetrachloride solvent. Finally, isomerization in a small rocksalt cluster, (NaF)4, is investigated in the microcanonical ensemble, and the results are compared to those of parallel tempering Monte Carlo.

Time-dependent density-functional theory investigation of the formation of the charge transfer excited state for a series of aromatic donor-acceptor systems. Part I

Abstract: Singlet excitation energies for a series of acceptor para-substituted N,N-dimethyl-anilines that are dual (4DMAB-CN, 3M4MAB-CN, MHD) and nondual (4AB-CN, 3M4AB-CN, 4MAB-CN, 3M4DMAB-CN, HHD, and MMD) fluorescent have been performed using the TDDFT method. The aim of this study is to investigate the influence of changing donor groups as well as the addition of methyl groups to the benzene moiety, on the fluorescence behavior of these molecules. Calculations of excitation energies have been performed with both B3LYP and MPW1PW91 functionals using a 6-311*(2p,d) (Bg) basis set. For all systems, ground-state geometries were optimized using density-functional theory with the Becke three parameter Lee–Yang–Parr functional combined with a 6-31G(d) (Sm) basis set. In addition, 4AB-CN, 4DMAB-CN, and MMD ground-state geometry has also been optimized using the MPW1PW91 functional with the Sm basis set. For all molecules, the potential energy surface (PES) has been investigated following the twisting intramolecular ch...

Kinetics of Reductive N−O Bond Fragmentation: The Role of a Conical Intersection

Abstract: N-alkoxyheterocycles can act as powerful one-electron acceptors in photochemical electron-transfer reactions. One-electron reduction of these species results in formation of a radical that undergoes N-O bond fragmentation to form an alkoxy radical and a neutral heterocycle. The kinetics of this N-O bond fragmentation reaction have been determined for a series of radicals with varying substituents and extents of delocalization. Rate constants varying over 7 orders of magnitude are obtained. A reaction potential energy surface is described that involves avoidance of a conical intersection. A molecular basis for the variation of the reaction rate constant with radical structure is given in terms of the relationship between the energies of the important molecular orbitals and the reaction potential energy surface. Ab initio and density functional electronic structure calculations provide support for the proposed reaction energy surface.

What are the best affordable multi-coefficient strategies for calculating transition state geometries and barrier heights?

Abstract: We compare hybrid density functional theory and multi-coefficient correlation methods for locating saddle point geometries and calculating barrier heights on a Born−Oppenhiemer potential energy surface. We located reactant, product, and saddle point stationary points by the multi-coefficient Gaussian-3 (MCG3) method for 15 reactions, and by the multi-coefficient quadratic configuration interaction with single and double excitations (MC-QCISD) method for 22 reactions; and the resulting structures and energies are compared to those obtained by the Moller−Plesset second order perturbation theory (MP2), QCISD, and modified Perdew−Wang 1-parameter-for-kinetics (MPW1K) methods. We examined three single-level methods with two basis sets, 6-31+G(d,p) and MG3. By comparison to calculations on five systems where the saddle point has been optimized at a high level of theory, we conclude that the best saddle point geometries for the methods tested are those found at the MC-QCISD, MCG3, and MPW1K levels. MP2 was shown...