Saddle Point Geometry Research Articles

An ab Initio Study of the Three-Channel Reaction between Methanol and Hydrogen Atoms: BAC-MP4 and Gaussian-2 Calculations

Rate coefficients for the three-channel reaction of methanol with H atoms were calculated from ab initio saddle point properties using conventional transition state theory. The saddle point geometries and energies were determined using the BAC-MP4 and the Gaussian-2 methods. The (classical) ab initio barrier heights for the formation of CH2OH, CH3O, and CH3 are 11.3, 16.3, and 30.5 kcal mol-1, respectively, as obtained using the BAC-MP4 method, and 10.6, 16.3, and 25.6 kcal mol-1, respectively, from Gaussian-2 calculations. The rate coefficients obtained from the G-2 calculations are 2.0 × 10-16, 1.9 × 10-20, and 1.9 × 10-28 cm3 molecule-1 s-1 at 298 K. The BAC-MP4 rate coefficient at 298 K is similar for channel 2 and lower than the G2 rate coefficient of the overall reaction agrees, within a factor of 2, with the recommendation of Tsang in a broad temperature range. Its temperature dependence is represented by k = (1.57 ± 0.56) × 10-15T1.70±0.05 exp(−2735 ± 23 K/T) cm3 molecule-1 s-1. Theory suggests that formation of CH2OH is the dominant channel, contributing to the overall reaction by over 95% below 1200 K and by about 90% at 2000 K. The formation of CH3 + H2O, which is the most exothermic channel, is unimportant in the whole temperature range studied.

Critical points when there is no saddle point geometry

We show how mountain pass methods can be used even when there is no mountain pass or saddle point geometry. The functional can grow on linking subsets. Applications are given.

The molecular structure of C6: A theoretical investigation

The question of the lowest energy structure of the C6 molecule has been addressed using high level of theory ab initio methods such as the coupled cluster and multiconfiguration perturbation theory approaches. The results show that the linear cumulenic chain and the monocyclic six-membered ring structure with D3h symmetry are very close in energy, indicating that both structures may be observed experimentally. The hexagonal six-membered ring structure of D6h symmetry was confirmed as a saddle point geometry. These results are in partial contradiction with two earlier ab initio studies that either find the distorted hexagon structure [Raghavachari, Whiteside, and Pople, J. Chem. Phys. 85, 6623 (1986)] or the linear cumulenic chain [V. Parasuk and J. Almlöf, J. Chem. Phys. 91, 1137 (1989)] to be the lowest energy structure.

A relation between critical values and eigenvalues in nonliner minimax problems

The paper establishes a relation between constrained minimax values of a functional g on a Hilbert space and related eigenvalues. If g is Frechet differentiable and weakly continuous, in presence of a saddle point geometry the minimax value σ(t) of g over corresponds to a set of eigenfunctions satisfying Moreover,γ has left and right hand derivatives and each of the is an eigenvalue. This abstract statement is written in mind of applications to existence of multiple nodal solutions for quasilinear elliptic equations.

Combining doubly charged cations and anions to form new species

In this study we predict, based on our ab initio electronic structure calculations, the existence and relative stabilities of several new species such as H3SMgF3, H2SMgF2, and HSMgF derived from combining the geometrically metastable and electronically stable parent doubly charged ions H4S+2 and MgF−24. Although this study focuses on compounds obtained from these particular double ions, we suggest that analogous observations will be obtained when other double ions are used. Stable structures of the HSMgF, and H2SMgF2 molecules, as well as a local energy minimum and two different second-order saddle point geometries for the H3SMgF3 molecule were found. The lowest-energy stable structure is that found for H3SMgF3, which is best described as a dative adduct of H2S, MgF2, and HF, and which lies ∼570 kcal/mol below the separated-ion starting materials and ∼140 kcal/mol below the (H4S+2)(MgF−24) contact ion pair.

Ab initio quantum chemistry study of the gas-phase reaction of CIO with HO2

The reaction of CIO with HO2 has been studied using ab initio molecular orbital theory with electron correlation being taken into account by Møller–Plesset (MP) perturbation theory. Saddle-point geometries, energies and harmonic vibrational wavenumbers have been calculated at the MP2/6-31G** level and barrier heights at the MP4/6-311G** level. The study shows that the products and mechanism depend on which potential-energy surface the reaction occurs. If the reaction proceeds along the triplet reaction surface, ground-state HOCl (1A′) and ground-state O2(3Σg–) are formed. If the reaction takes place on the singlet reaction surface the same products are formed, but in this case the molecular oxygen is formed in a singlet state. The CIO + HO2 reaction proceeds via a multi-step reaction mechanism on the singlet surface and via a direct hydrogen-abstraction mechanism on the triplet surface.

A theoretical study of the collinear reaction F+H 2→HF+H using multiconfigurational second-order perturbation theory (CASPT2)

The second-order perturbation method (CASPT2) with a single state multiconfigurational reference function generated in complete active self-consistent field (CASSCF) calculations has been used to compute the collinear barrier height, saddle point geometry, and exothermicity of the reaction F+H 2→HF+H. Comparison with full configuration (FCI) calculations with small basis sets shows that the CASPT2 method is capable of reproducing accurately the exact benchmark results correlating seven electrons. Large atomic natural orbital basis sets are used at the seven- and nine-electron level of correlation. With the largest ANO basis set used, F[7s6p5d4f2g]/H[6s5p4d2f], the computed nine-electron barrier height, 2.47 kcal/mol, is about 0.5 kcal/mol higher than results obtained using MRCI+Q and CCSD(T) methods employing basis sets of similar quality. The nine-electron exothermicity obtained with this basis set is 31.25 kcal/mol, about 0.5 kcal/mol below the experimental value.

Orientational dependence of the N(4S)+ NO(X2Π) and N(4S)+ O2(X3Σ–g) reactions: comparison of the angle-dependent line-of-centres model with quasiclassical trajectories

The study of orientational or steric effects in the field of reaction dynamics is a rapidly expanding field both experimentally and theoretically. In this theoretical work, we report the results of a comparison between simple angle-dependent line-of-centres model predictions for the dynamics of the N(4S)+ O2→ NO + O(3P) and N(4S)+ NO → N2+ O(3P) reactions and the results of extensive quasiclassical trajectory calculations on Sorbie–Murrell analytical potential-energy surfaces for both systems (lowest 2A′ and 3A″ surfaces, respectively). The use of a simple bending potential around the saddle-point geometry in the above-mentioned model furnishes in both cases results that compare very well with the quasiclassical trajectory results, although the comparison is not so good in the case of the N(4S)+ O2 reaction. By using a better choice for the angle-dependent barrier height functions only small improvements are achieved. Both surfaces exhibit marked anisotropic behaviours and seem to be capable of reorienting the systems even if they start with rather unfavourable geometrical arrangements for reaction, especially in the case of the N(4S)+ NO reaction. It is concluded that this model could be a good and computationally cheap way of providing an a priori estimate of orientational effects on the reaction cross-sections and opacity functions of reactions similar to the ones studied here, by using a simple angle-dependent barrier height function based on a few ab initio points, even for bent transition states.

Dynamics of the N(4S u) + NO(X 2Π) → N2(X 1Σg+) + O(3P g) atmospheric reaction on the 3A″ ground potential energy surface. I. Analytical potential energy surface and preliminary quasiclassical trajectory calculations

The N(4Su)+NO(X 2Π)→N2(X 1Σg+)+O(3Pg) reaction plays an important role in the upper atmosphere chemistry and as a calibration system for discharge flow systems. Surprisingly, very little theoretical and experimental work has been devoted to the characterization of the dynamical features of this system. In this work a Sorbie–Murrell expression for the lowest 3A″ potential energy surface (PES) connecting reactants in their ground electronic states based upon the fitting of an accurate ab initio CI grid of points has been derived. The PES fitted shows no barrier to reaction with respect to the reactants asymptote in accordance with experimental findings and becomes highly repulsive as the NNO angle is varied away from the saddle point geometry. The results of preliminary quasiclassical trajectory calculations on this surface reproduce very well the experimental energy disposal in products, even though the vibrational distribution derived from trajectories seems to be a bit cooler than the experimental data. Moreover, thermal rate constants derived from trajectories are in excellent accordance with experimental values.

Complex solutions for the scalar field model of the Universe.

The Hartle-Hawking proposal is implemented for Hawking's scalar field model of the Universe. For this model the complex saddle-point geometries required by the semiclassical approximation to the path integral cannot simply be deformed into real Euclidean and real Lorentzian sections. Approximate saddle points are constructed which are fully complex and have contours of real Lorentzian evolution. The semiclassical wave function is found to give rise to classical spacetimes at late times and extra terms in the Hamilton-Jacobi equation do not contribute significantly to the potential.

Theoretical analyses of hydrogen abstraction by aldehyde triplet excited states

The fully optimized transition states for hydrogen abstraction from methane by formaldehyde and acetaldehyde have been computed using UMP2/6-31G(d)//6-31G(d) calculations. The geometry of the formaldehyde/methane transition state matches well with the geometry obtained previously using the 3-21G basis set, but the energy is lowered somewhat (18.7 versus 22 kcal/mol, respectively). Approach of the methane trans-periplanar (i.e. anti) to the acetaldehyde methyl group leads to a transition state similar to that for formaldehyde (saddle point at 17.9 kcal/mol). Approach syn to the methyl group leads to a modest variation in both the saddle point geometry and energy (19.1 kcal/mol), both attributed to unfavorable steric interactions in this trajectory.

The effect of higher than double excitations on the F+H2→FH+H barrier

The classical barrier height and saddle point geometry are computed using the averaged coupled-pair functional (ACPF) method, correlating both seven and nine electrons. The size-consistent ACPF method indicates that 2s correlation substantially reduces the barrier. The excellent agreement between the ACPF and MRCI+Q results at both the seven and nine electron level provides additional support for the +Q correction. Thus the ACPF treatment supports a low (1.65 kcal/mol) barrier. The seven-electron CISDTQ results are shown to be consistent with the MRCI+Q and ACPF results.

Theoretical investigations of reactions of some radicals with hydroperoxo. 1. Hydrogen abstractions by direct mechanisms

Ab initio quantum mechanical methods are used to calculate saddle-point geometries and energies for hydrogen abstractions from HO{sub 2} by N, ClO, O, Cl, H, OH, and F assuming direct attack at the hydrogen atom. Results are consistent with bond energy-bond order principles and indicate that activation energies for these reactions should decrease with increasing exothermicity of reaction. In addition, the large rate constant for OH + HO{sub 2} {yields} H{sub 2}O + O{sub 2} is interpreted to be due to long-range dipole-dipole attraction, leading ultimately to formation of a hydrogen bond and to stabilization of an early transition state. Results for the ClO + HO{sub 2} {yields} HOCl + O{sub 2} reaction suggest a dual mechanism dominated by direct abstraction at high temperatures and by elimination from a stable intermediate at lower temperatures, perhaps the only reaction in this series which does so. These results are in good agreement with current experimental rate data.

Theoretical investigation involving electronic and vibrational calculations of the 2 2A1(3p)→1 2B2(3p) and the 3 2A1(4s)→1 2B2(3p) transitions in FH2 and FD2

Theoretical calculations have been carried out on the X 2A1, 1 2B2(3p), 2 2A1(3p), and 3 2A1(4s) electronic states of FH2. Equilibrium geometries and rotational constants as well as the first few vibrational levels of the excited states have been calculated, in order to obtain theoretical information on the 2 2A1(3p)→1 2B2(3p) and the 3 2A1(4s)→1 2B2(3p) transitions in FH2, which might be relevant to the observed spectra at about 7500 and 8000 Å. The results show that the equilibrium geometry of the first excited state of FH2, 1 2B2(3p), is quite different from those of the other excited states. The estimated transition energies (ΔE0) in FH2 are 1.68 and 1.97 eV for the transitions 2 2A1(3p)→1 2B2(3p) and 3 2A1(4s)→1 2B2(3p), respectively, while in FD2 the corresponding quantities are 1.65 and 1.95 eV, respectively. A search for a minimum on the ground state surface of FH2, which has been carried out near two saddle point geometries, has not found one. Thus the present calculations do not find a metastable ground state species.

Polyatomic surface fitting, vibrational-rotational analysis, expectation value and intensity program

A computer program, SURVIBTM, has been developed for fitting multi-dimensional potential energy and property surfaces and calculating vibrational-rotational spectra of symmetric and asymmetric top polyatomic molecules. Given surfaces in the form of internal coordinates and energy or property points, the program performs seven main types of calculations. These include determining equilibrium and saddle point geometries, internal coordinate force fields, normal mode eigensolutions, normal coordinate force fields, spectroscopic constants, expectation values of properties, and transition dipole moments and intensities. Numerous options are available for each type of calculation. High-degree expansions for several forms of analytical expressions are implemented for the representations of force fields. The vibrational analysis and transition dipole results are presented in the form of spectroscopic constants, which include anharmonicity through quartic terms according to second-order perturbation theory. Point-group symmetry is utilized for reducing the length of internal coordinate expansions and for the analysis of selection rules in calculations of vibrational absorption intensities.

ECE diagnostic for ATF

Electron cyclotron emission (ECE) from the Advanced Toroidal Facility (ATF) torsatron will allow measurement of plasma electron temperature. For low-field operation (0.95 T) the second harmonic is cut off at a relatively low density; therefore, third-harmonic emission from 67 to 83 GHz is used to yield central electron temperatures. At high-field operation (1.9 T) second-harmonic emission from 82 to 114 GHz is optically thick and can provide Te(r) information. A vertical view of the saddle-point geometry of the ATF mod B spatial contours provides a line of sight along which the mod B contours are symmetric with respect to flux surfaces. A single horn–lens viewing beam system with a vertical view is designed to cover the entire 67–114-GHz range, providing a spot size on the order of 6 cm. Radiation will be delivered to one of three waveguide mixers by C-band waveguide. Each of the three mixers covers a 16-GHz segment of the emission spectrum, downconverting it to the 2–18-GHz intermediate-frequency band, where it is processed by a 16-channel array of bandpass filters, providing 1-GHz frequency resolution.

Molecular dynamics studies of the equilibrium and saddle-point geometries of MXn molecules (n = 2-7)

Two nuclear potential functions that have the property of invariance to the operations of the permutation group of nuclei in molecules of the general formula MX/sub n/, n = 2-7, are described. Such potential functions allow equivalent isomers to have equal energies so that various statistical mechanical properties can be simply determined. The first contains two-center interactions between pairs of peripheral atoms, and the second function contains three-center interactions. Equations are given which define both the functions in terms of k and Q, force constants, /Delta/r/sub /alpha//mu//, the change in bond length between the x atom /alpha/ and the central atom /mu/, and /theta/, the angle subtended at the central atom X by atoms /sup /alpha//mu//beta///alpha/ and /beta/ for which the preferred value is /pi/. The force fields derived from these two potential functions have been used to determine the equilibrium and saddle-point geometries of the series of molecules MX/sub n/, n = 2-7. These fields predict equivalent equilibrium and saddle-point geometries for MX/sub 2/ through MX/sub 6/ but not for MX/sub 7/. In this case, the first function gives a D/sub 5h/ but equilibrium geometry with two close-lying saddle-point geometries (the first of symmetry C/sub 2v/, a trigonal prismmore » capped on a square face; the other C/sub 3v/, an octahedron capped on a face). The second potential function gives an equilibrium geometry with symmetry C/sub 1/ and the three geometries above as close-lying saddle-point ones. In addition, the dynamic behavior of MX/sub 5/ and MX/sub 7/ molecules follows as a natural consequence of these force fields in contrast to the relative rigidity of the others which belong to the crystallographic point groups. 41 refs., 2 figs., 3 tabs.« less

Ab initio study of the two competitive channels HO 2 + H → H 2 + O 2 and HO 2 + H → H 2O + O

Saddle point geometries and barrier heights have been calculated for the H abstraction reaction HO 2( 2A″)+H( 2S) → H 2( 1Σ + g)+O 2( 3Σ − g) and the concerted H approach-O removing reaction HO 2 ( 2A″)+H( 2S) → H 2O( 1A 1)+O( 3P) by using SDCI wavefunctions with a valence double-zeta plus polarization basis set. The saddle points are found to be of C s symmetry and the barrier heights are respectively 5.3 and 19.8 kcal by including size consistent correction. Moreoever kinetic parameters have been evaluated within the framework of the TST theory. So activation energies and the rate constants are estimated to be respectively 2.3 kcal and 0.4×10 9 ℓ mol −1 s −1 for the first reaction, 20.0 kcal and 5.4.10 −5 ℓ mol −1 s −1 for the second. Comparison of these results with experimental determinations shows that hydrogen abstraction on HO 2 is an efficient mechanism for the formation of H 2 + O 2, while the concerted mechanism envisaged for the formation of H 2O + O is highly unlikely.

An improved calculation of the transition state for the F + H 2 reaction

Using a large, balanced one-electron basis set, fully optimized reaction space (FORS) calculations to optimize the orbitals and to estimate the internal correlation energy, multi-reference configuration interaction calculations including all single and double excitations out of the FORS reference space to estimate a fraction of the external correlation energy, and the method of scaled external correlation (SEC), we calculate the interaction energy of F with H 2 in the vicinity of the saddle point for the reaction F + H 2 → HF + H. Our calculated barrier height, 1.6 kcal/mol, is considerably lower than values obtained in recent ab initio calculations, and the saddle point geometry is about 0.3 a 0 looser. This indicates that the part of the external correlation energy omitted from MR CISD calculations because of the incompleteness of the one-electron basis set and the truncation of the CI expansion, as estimated by the SEC method, has a significant effect on both the saddle point energy and its geometry.

Theoretical studies of the energetics of the abstraction and exchange reactions in H + HX, with X = F-I

Energy defects, barriers to reaction, and saddle point geometries have been calculated for the H + HX (X = F-I) abstraction and exchange reactions by using generalized valence bond and configuration interaction methods. For this prototypical series of homologous reactions nearly quantitative relationships could be established between (1) the barrier heights and the energy of the bond being broken and (2) the bond extensions at the saddle points. While a simple bond energy-bond order type relationship was found between the bond extensions at the saddle points for the abstraction reactions, such arguments applied to the energetics of the reactions do not provide a satisfactory explanation of the barrier heights.