Saddle Point Geometry Research Articles

Thermally activated transport of a dislocation loop within an elastic model

We report thermally activated transport of a dislocation loop in terms of a line tension model, where the dislocation line is assumed to be a flexible string. According to conventional rate theory, the features of thermal activation are determined by the saddle-point geometry in high dimensional configuration space. If the circumference of a dislocation loop L is longer than a critical length L c, the selected saddle-point configuration is the well known double-kink type solution. On the other hand, the manner of the thermal activation of a dislocation loop shorter than L c is rather point-defect-like. In the present work, we pay attention to the temperature dependence of transition rate which is represented such as ν 0 ∗ exp ( - E / k B T ) . The pre-exponential factor depends on temperature like ν 0 ∗ ∼ T - 1 / 2 for sufficiently long dislocation loops on the basis of the analysis.

Redistributed Charge and Dipole Schemes for Combined Quantum Mechanical and Molecular Mechanical Calculations

Special care is needed in carrying out combined quantum mechanical and molecular mechanical (QM/MM) calculations if the QM/MM boundary passes through a covalent bond. The present paper discusses the importance of correctly handling the MM partial point charges at the QM/MM boundary, and in particular, it contributes in two aspects: (1) Two schemes, namely, the redistributed charge (RC) scheme and the redistributed charge and dipole (RCD) scheme, are introduced to handle link atoms in QM/MM calculations. In both schemes, the point charge at the MM boundary atom that is replaced by the link atom is redistributed to the midpoint of the bonds that connect the MM boundary atom and its neighboring MM atoms. These redistributed charges serve as classical mimics for the auxiliary orbitals associated with the MM host atom in the generalized hybrid orbital (GHO) method. In the RCD scheme, the dipoles of these bonds are preserved by further adjustment of the values of the redistributed charges. The treatments are justified as classical analogues of the QM description given by the GHO method. (2) The new methods are compared quantitatively to similar methods that were suggested by previous work, namely, a shifted-charge scheme and three eliminated-charge schemes. The comparisons were carried out for a series of molecules in terms of proton affinities and geometries. Point charges derived from various charge models were tested. The results demonstrate that it is critical to preserve charge and bond dipole and that it is important to use accurate MM point charges in QM/MM boundary treatments. The RCD scheme was further applied to study the H atom transfer reaction CH3 + CH3CH2CH2OH --> CH4 + CH2CH2CH2OH. Various QM levels of theory were tested to demonstrate the generality of the methodology. It is encouraging to find that the QM/MM calculations obtained a reaction energy, barrier height, saddle-point geometry, and imaginary frequency at the saddle point in quite good agreement with full QM calculations at the same level. Furthermore, analysis based on energy decomposition revealed the quantitatively similar interaction energies between the QM and the MM subsystems for the reactant, for the saddle point, and for the product. These interaction energies almost cancel each other energetically, resulting in negligibly small net effects on the reaction energy and barrier height. However, the charge distribution of the QM atoms is greatly affected by the polarization effect of the MM point charges. The QM/MM charge distribution agrees much better with full QM results than does the unpolarized charge distribution of the capped primary subsystem.

Ab initio studies on the reagent Ph 3PCl 2

We report ab initio calculations at the B3LYP/6-311G** level of theory for the title reagent. Four stationary points on the molecular potential energy surface have been located and characterized. Three of these stationary points are energy minima, one a saddle point. The minima correspond to the conventional Ph 3PCl 2 (three-fold Cl–P–Cl axis with twisted phenyl rings), the ion-pair [Ph 3PCl] +Cl − and a four-coordinated Ph 3PCl 2 spoke structure that can best be described as charge transfer on account of the substantial charge transfer from the Ph 3P fragment to Cl 2 (as measured by conventional Mulliken population analysis). The saddle point geometry is similar to the conventional three-fold Cl–P–Cl structure, but the phenyl groups are coplanar.

Ab initio study of the structures and dynamic stereochemistry of biaryls

The static and dynamic stereochemistry of biphenyl ( 1), 1-phenylnaphthalene ( 2), 1-phenylanthracene ( 3), 9-phenylanthracene ( 4), 1,1′-binaphthyl ( 5), 1,1′-naphthylanthracene ( 6), 1,9′-naphtylantracene ( 7), 1,1′-bianthryl ( 8), 9,9′-bianthryl ( 9) and 1,9′-bianthryl ( 10) were examined using ab initio molecular orbital (MO) and the Becke, Lee, Yong and Parr density functional (B3LYP) methods. The structure of the ground states, the activation energies for rotation about the σ-bonds of compounds 1– 10 and the nature of deformation of aromatic rings in the equilibrium structures and saddle point geometries were also investigated. Studies on the HF/6-31G*//Hf/3-21G, MP2/6-31G*//HF/3-21G and B3LYP/6-31G*//HF/3-21G levels of theory confirm that compounds 5, 6 and 8 should racemize preferably the anti path, (with about 9 kcal mol −1 lower energy than the syn path). However, the resulted racemization energy for compound 5 through the syn path is found to contradict the previously reported semi-empirical calculations.

High excitations in coupled-cluster series: vibrational energy levels of ammonia

The ammonia molecule containing large amplitude inversion motion is a revealing system in examining high-order correlation effects on potential energy surfaces. Correlation contributions to the equilibrium and saddle point geometries, inversion barrier height and vibrational energy levels, including inversion splittings, have been investigated. A six-dimensional Taylor-type series expansion of the Born–Oppenheimer potential energy surface, which is scaled to different levels of theory, is used to determine vibrational energy levels and inversion splittings variationally. The electronic energies are calculated by coupled-cluster methods, combining explicitly correlated R12 theory (which includes the interelectronic coordinate in the electronic wave function) with a conventional approach including excitations up to the pentuple level. Finally, the electronic correlation contribution is scaled to the full configuration interaction limit. Corrections due to relativistic and non-Born–Oppenheimer effects are also included. Special emphasis is put on the convergence of the high-order contributions with respect to the size of the atomic basis set. To achieve an accuracy of 1 cm−1, it is essential to be at the basis set limit, include all the subtle effects and also include highly excited configurations—even up to the pentuple level in the coupled-cluster expansion.

Hybrid Meta Density Functional Theory Methods for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions: The MPW1B95 and MPWB1K Models and Comparative Assessments for Hydrogen Bonding and van der Waals Interactions

Based on the modified Perdew and Wang exchange functional (MPW) and Becke's 1995 correlation functional (B95), we developed two hybrid meta density functional theory (HMDFT) methods, namely MPW1B95 and MPWB1K. In addition, based on the new X functional of Xin and Goddard, again combined with B95 correlation functional, we developed two other new HMDFT methods, X1B95 and XB1K. MPW1B95 and X1B95 were optimized against a representative database of six atomization energies (AE6). MPWB1K and XB1K were optimized against a kinetics database of three forward barrier heights, three reverse barrier heights, and three energies of reaction for the reactions in the BH6 representative barrier height database. We compared the newly developed methods to other HMDFT and hybrid DFT methods for atomization energies, ionization potentials, electron affinities, barrier heights, saddle point geometries, hydrogen bonding, and weak van der Waals weak interactions. In addition, we optimized scaling factors for calculating zero-point energies from vibrational frequencies. The results show that the MPWB1K and XB1K methods give good results for thermochemistry, thermochemical kinetics, hydrogen bonding, and weak interactions, and they give excellent saddle point geometries. MPW1B95 and X1B95 are suitable for general applications in thermochemistry, and they give good performance for hydrogen bonding and weak interaction calculations.

Doubly Hybrid Meta DFT: New Multi-Coefficient Correlation and Density Functional Methods for Thermochemistry and Thermochemical Kinetics

This paper presents two new multi-coefficient correlation and density functional methods based on mixing scaling-all-correlation (SAC) theory and hybrid meta density functional theory with empirical parameters. Both methods were optimized against a database of 109 atomization energies and 42 barrier heights. The resulting methods, called MC3BB and MC3MPW, were tested against a database of saddle point geometries, and scaling factors were optimized for calculating vibrational frequencies. The two new methods were compared to the methods that we have previously determined to be most efficient for thermochemistry and thermochemical kinetics, where the criterion is the average of the mean unsigned errors for bond energies and barrier heights. These comparisons show that MC3BB is more accurate than any other method that has comparable cost. Both new methods are well suited for direct dynamics calculations that require Hessians. The new approach is called doubly hybrid density functional theory if kinetic energy density is not included in the functional and doubly hybrid meta density functional theory if it is.

Development and Assessment of a New Hybrid Density Functional Model for Thermochemical Kinetics

A new hybrid Hartree−Fock-density functional model called the Becke88−Becke95 1-parameter model for kinetics (BB1K) was optimized against a database of three forward barrier heights, three reverse barrier heights, and three energies of reaction for the reactions in the BH6 representative barrier height database. We then assessed the newly developed BB1K method against a saddle point geometries database, a database of 42 barrier heights, the AE6 representative atomization energy database, a molecular geometries data set, and a set of 13 zero point energies. The results show that BB1K can give excellent saddle point geometries and barrier heights, and its performance for calculating atomization energies is 40% better than MPW1K. Using a mean mean unsigned error criterion that equally weights the errors in barrier heights and in bond energies, the new BB1K method outperforms all other DFT and hybrid DFT methods by a large margin, and we therefore conclude that it is the best density functional-type method for thermochemical kinetics.

Does ozone have a barrier to dissociation and recombination?

The barrier associated with the dissociation and recombination of ozone has been calculated using highly correlated ab initio methods. Our calculations show that, for fixed equilibrium values of the bending angle and one bond distance, there is a very small barrier, 100 cm −1 , as opposed to much larger values previously reported. When the saddle point geometry is optimized, the reaction path still contains a barrier but the top of the barrier lies below the dissociation limit.

What Are the Best Affordable Multi-Coefficient Strategies for Calculating Transition State Geometries and Barrier Heights?

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 Møller−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 to have systematic deficiencies in predicting saddle point geometries. Our recommended most affordable methods are the MPW1K/6-31+G(d,p) and MC-QCISD methods for fully optimized calculations and the MCG3//MPW1K/6-31+G(d,p) method for single-point calculations with mean unsigned errors in calculating reaction energies and barrier heights of 1.6, 1.6, and 1.1 kcal/mol respectively.

Capability of LEP-Type Surfaces To Describe Noncollinear Reactions. 2. Polyatomic Systems

In this second article of the series, the popular LEP-type surface for collinear reaction paths and a “bent” surface, which involves a saddle point geometry with a nonlinear central angle, were used to examine the capacity of LEP-type surfaces to describe the kinetics and dynamics of noncollinear reaction paths in polyatomic systems. Analyzing the geometries, vibrational frequencies, curvature along the reaction path (to estimate the tunneling effect and the reaction coordinate-bound modes coupling), and the variational transition-state theory thermal rate constants for the NH3 + O(3P) reaction, we found that the “collinear” LEP-type and the “bent” surfaces for this polyatomic system show similar behavior, thus allowing a considerable saving in time and computational effort. This agreement is especially encouraging for this polyatomic system because in the Cs symmetry the reaction proceeds via two electronic states of symmetries 3A‘ and 3A‘ ‘, which had to be independently calibrated. Finally, this work o...

A converged calculation of the energy barrier to internal rotation in the ethylene–sulfur dioxide dimer

Geometrical parameters for the equilibrium (MIN) and lowest saddle-point (TS) geometries of the C2H4⋯SO2 dimer, and the corresponding binding energies, were calculated using the Hartree–Fock and correlated levels of ab initio theory, in basis sets ranging from the D95(d,p) double-zeta basis set to the aug-cc-pVQZ correlation consistent basis set. An assessment of the effect of the basis set superposition error (BSSE) on these results was made. The dissociation energy from the lowest vibrational state was estimated to be 705±100 cm−1 at the basis set limit, which is well within the range expected from experiment. The barrier to internal rotation was found to be 53±5 cm−1, slightly higher than the (revised) experimental result of 43 cm−1, probably due to zero-point vibrational effects. Our results clearly show that, in direct contrast with recent ideas, the BSSE correction affects differentially the MIN and TS binding energies and so has to be included in the calculation of small energy barriers such as that in the C2H4⋯SO2 dimer. Previous reports of positive MP2 frozen-core binding energies for this complex in basis D95(d,p) are confirmed. The anomalies are shown to be an artifact arising from an incorrect removal of virtual orbitals by the default frozen-core option in the GAUSSIAN program.

How Well Can Hybrid Density Functional Methods Predict Transition State Geometries and Barrier Heights?

We compare hybrid Hartree−Fock density-functional theory to ab initio approaches 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 for 22 reactions by the MP2 and QCISD ab initio methods and the B3LYP, BH&HLYP, mPW1PW91, and MPW1K hybrid Hartree−Fock DFT methods. We examined all of these 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 determined that the best saddle point geometries were obtained using the MPW1K and QCISD levels of theory. Of the methods tested, mPW1PW91 and B3LYP are the least effective for determining saddle point geometries and have mean unsigned error in barrier heights of 3.4−4.2 kcal/mol, depending on the basis set. In contrast, the MPW1K level of theory predicts the most accurate saddle point geometries and has a mean unsigned error of only 1.5 kcal/mol for either basis set. For even better accuracy, the combination of MPW1K/6-31+G(d,p) geometry calculations with QCISD(T)/MG3 or CCSD(T)/MG3 single-point energy calculations is shown to have an excellent performance-to-cost ratio. As a side product of this work, we report optimized scale factors for computing zero point energies by MPW1K.

Capability of LEPS Surfaces to Describe the Kinetics and Dynamics of Non-Collinear Reactions

The popular LEPS surface for collinear reaction paths and a simple bent surface yielding a nonlinear saddle point geometry were used to examine the capability of the LEPS surfaces in describing the kinetics and dynamics of systems with noncollinear reaction paths. The parameters calculated for the atom−diatom Cl + ClH reaction include geometries, vibrational frequencies, and curvatures (to estimate the tunneling effect) along the reaction path, as well as variational transition-state theory rate constants and kinetic isotope effects. The collinear LEPS and the bent surfaces for this triatomic system show similar behavior, so similar behavior in noncollinear polyatomic reactions may be expected, with the consequence of saving time and computational effort.

Trajectory Investigations of the Dissociation Dynamics of Vinyl Bromide on an ab Initio Potential-Energy Surface

The reaction dynamics of vibrationally excited vinyl bromide have been investigated using classical trajectory methods on a global, analytic potential-energy hypersurface that is developed primarily by least-squares fitting of appropriately chosen functional forms to the results of ab initio electronic structure calculations. These calculations are carried out at the MP4 level of theory with all single, double, and triple excitations included. A 6-31G(d,p) basis set is employed for the carbon and hydrogen atoms. Huzinaga's (4333/433/4) basis set augmented with split outer s and p orbitals (43321/4321/4) and a polarization f orbital with an exponent of 0.5 is used for the bromine atom. The present calculations focus upon the determination of the dependence of the potential upon the stretching coordinates for the bonded atoms in vinyl bromide, the C−C−H and C−C−Br bending coordinates and the dihedral angles. The couplings between these coordinates are also investigated. The total ab initio database is obtained by combining these results with previously reported studies of the vinylidene−acetylene system and our previous calculations of saddle-point geometries and energies for the various decomposition channels, reactant and product equilibrium structures, and vibrational frequencies. The analytic surface fitted to this data base (PES1) is then modified by adjustment of the potential curvatures at equilibrium to provide a better fit to the measured IR and Raman vibrational frequencies of vinyl bromide while simultaneously holding all other topographical features of the surface constant to the maximum extent possible. The surface so developed is labeled PES2. Finally, we have arbitrarily altered the reaction coordinate curvatures for three-center HBr and H2 elimination to produce a third potential surface (PES3). The dissociation dynamics of vinyl bromide on each of these potential surfaces are investigated at several excitation energies in the range 4.5 to 6.44 eV. Total decomposition rate coefficients and product branching ratios are computed as a function of excitation energy. The HBr vibrational-state distribution is computed and found to be Boltzmann with an effective vibrational temperature of 7084 K on PES1. These results are in virtually exact agreement with recently reported measurements of this distribution. Finally, we have investigated the dissociation mechanisms for three-center H2 and HBr elimination reactions. The results show that the dynamics are very similar on PES1, PES2, and PES3. Consequently, small variations in potential-energy curvatures at equilibrium and along the reaction coordinates do not exert significant influence upon the dissociation dynamics. However, some large qualitative variations between the dynamics on the ab initio surface and the more empirical surface previously employed are found to exist. We conclude that great care must be exercised when such surfaces are used to study reaction dynamics in polyatomic systems.

An ab initio path integral molecular dynamics study of double proton transfer in the formic acid dimer

Double proton transfer in the formic acid dimer has been investigated with Car–Parrinello ab initio molecular dynamics calculations. The electronic structure of the dimer has been obtained using gradient-corrected density functional theory based on the B-LYP (Becke exchange [Phys. Rev. A 38, 3098 (1988)] and Lee–Yang–Parr correlation [Phys. Rev. B 37, 785 (1988)] functional. The optimized equilibrium and saddle-point geometries, obtained by simulated annealing, are in good agreement with previous ab initio quantum chemical predictions and experiment. Thermal and quantum fluctuations of nuclei along the double proton transfer reaction path have also been investigated at T=300 K. Thermal fluctuations give a broad distribution of nuclei around the minimum energy path on the potential energy surface. Quantum fluctuations, investigated using ab initio path integral molecular dynamics, make the distribution even broader around the equilibrium structure, and cause the distribution to deviate appreciably from the minimum energy path on approaching the reaction barrier. In particular, the system passes through higher energy regions than the geometrical saddle point by tunneling; an observation which is consistent with the conventional understanding of heavy–light–heavy mass combination reactions. While there is asynchronous movement of the two protons around the equilibrium structure, synchronous movement becomes relevant on approaching the reaction barrier.

Characterization of proton transfer in HO2−and HF2+: An atoms in molecules study

AbstractProton transfer is examined in HO2−and HF2+. These species are isoelectronic and a direct comparison of their electron densities is possible. Electron densities are calculated at the QCISD/6‐311++G(2d,2p) level for the nonlinear equilibrium geometry and the C2vsaddle point and linear saddle point geometries. Bader's theory of atoms in molecules is applied to partition the electron density into its atomic components and atomic and molecular properties are calculated. These quantities are used to characterize the proton dynamics as being like internal rotation.

Understanding the activation energy trends for the C2H4+OH→C2H4OH reaction by using canonical variational transition state theory

The potential-energy hypersurface of the addition reaction OH+C2H4 was partially explored following two different approaches. First, the stationary points were located at the MP2(FULL)/6-31G(d,p) level and then the minimum energy path (MEP) was built starting from the MP2 saddle-point geometry. In order to improve the energetics along the MEP, single-point calculations were carried out at several higher levels, in particular, PMP2, MP4sdtq, PMP4sdtq, and QCIsd(t). In a different approach, the C–O bond length was assumed to provide an accurate parametrization of the reaction path in the vicinity of the transition state. The minimum energy structures at the MP4sdq/6-311+G(d,p) level for 16 points along the RC–O coordinate have been calculated, followed by a generalized normal-mode analysis at the MP2(FULL)/6-311+G(d,p) level for each point. The initial potential information from both approaches was used to calculate canonical variational transition state (CVT) association rate constants for the temperature range 200–1000 K. Our calculations at the PMP4sdtq/6-311+G(d,p)//MP4sdq/6-311+G(d,p)[MP2(FULL)/6-311 +G(d,p)] level reproduce the inverse dependence of the rate constant with temperature at T<565 K, in agreement with the experimental evidence that this reaction has a negative activation energy at room temperature. The analysis of the enthalpic and entropic contributions to the Gibbs free-energy profile has allowed us to understand those negative values of the activation energy.

Benchmark Calculations with Correlated Molecular Wave Functions. 11. Energetics of the Elementary Reactions F + H2, O + H2, and H‘ + HCl

An explicit treatment of electron correlation is required to predict accurate energetics, barrier heights, and saddle point geometries for chemical reactions. Several theoretical methods for treating electron correlation (multireference configuration interaction, perturbation theory, and coupled cluster methods) have been thoroughly evaluated for the F(2P) + H2(X1Σg+) and O(3P) + H2(X1Σg+) abstraction reactions as well as for the H‘(2S) + HCl(X1Σ+) exchange reaction using correlation consistent basis sets. The basis set dependence of the reaction energy defects, barrier heights, and saddle point geometries have been determined for each theoretical method. Addition of diffuse functions to the basis set (aug-cc-pVnZ) was found to substantially increase the convergence rate. Calculations with the largest basis set (aug-cc-pV5Z) allowed an unambiguous comparison of the relative performance of each correlation method. For each reaction, the R-UCCSD(T) results closely parallel the most accurate MRCI results and are in good agreement with experiment. In contrast, unrestricted perturbation theory methods predict barriers that are too large by 2.7−4.4 kcal/mol (MP2), 3.5−4.2 kcal/mol (MP3), and 1.3−1.7 kcal/mol (MP4).

Theoretical study of barrier height to linearity of bent triatomic molecules

A systematic ab initio investigation has been carried out to examine the effects of a basis set and correlation method on barrier height to linearity of bent triatomic CH2 and H2O in their ground electronic states. The theoretical models employed varied from Hartree–Fock with minimal STO-3G to highly correlated quadratic configuration interaction method QCISD(T) with Dunning’s correlation-consistent aug-cc-pVQZ basis set. It is shown that the barrier height to linearity is very sensitive to the choice of the model and it is necessary to employ a proper theoretical model with large enough basis set to be assured of the convergence of the calculated barrier height. We found that calculated barrier height to linearity tends to be higher than experimentally determined barrier height in most cases, which is caused by the slower convergence of energy at linear saddle point geometry than at bent equilibrium geometry. The effect of frozen core approximation in correlated calculations is shown to always increase the barrier height to linearity slightly (less than 3% of total amount) from the value with the full activation of orbitals, regardless of the basis set or correlation method used in the study.