几种过渡态结构的有效优化方法

通过双桥反应机理、电环合反应和催化反应三个不同类型的过渡态优化，说明当标准方法难以给出结果时，对物理问题本身的分析有助于给出过渡态优化的线索．第一个例子根据化学问题给出限制条件，通过平衡几何构型优化方法优化得到过渡态；第二个例子是在使用标准过渡态优化方法失败后，根据物理问题从反应途径上用平衡几何构型优化方法选择过渡态优化的初始结构；第三个例子通过Gaussian 98程序中的标准方法QST2直接得到过渡态．     

Systematic characterization of transition states for radical decompositions

A one-parameter analytical potential energy function for β-bonds in free radicals is described, which accounts quantitatively for their observed stretching frequencies and the position and size of the activation barriers for their fission. It is shown that such a function can be used to characterize a priori the corresponding transition states by assuming that the structural and spectroscopic changes taking place along the minimum energy path track the development of pi bonding rather than following a simple exponential dependence on the reaction coordinate. This procedure, tested by comparing predicted A-factors and isotope effects with experimental data for alkyl radicals and ab-initio calculations on C₂H₅, fully encodes the basic features of radical decomposition reactions and provides a simple, realistic, and self-consistent technique for the estimation of their kinetic parameters.     

Near ab-initio methods for the calculations of large molecules: Comparison of pseudopotential and ab-initio results

Results from pseudopotential calculations on 5-hydroxyindole, tryptamine, 5-hydroxytryptamine, 6-hydroxytryptamine and the imidazolium cation are compared to full ab-initio calculations. The localization of all molecular orbitals is found to be identical with the two methods. Orbital energies from the two methods are found to be linearly correlated for all molecules: the slope is close to unity and the orbital energies from the pseudopotential calculation show a very slight and virtually constant shift to lower values. Electron density maps and molecular electrostatic potential maps calculated from the wavefunctions show that the charge distributions and molecular reactivity characteristics predicted by the two methods are nearly identical.     

Finding transition states using reduced potential-energy surfaces

 We propose a method to locate saddle points that is based on the interplay between the driving coordinate and the restricted quasi-Newton algorithm. The method locates the transition state using a reduced potential-energy surface. The reduced potential-energy surface is characterized by the set of driving coordinates. The proposed algorithm starts at a point on the surface that is slightly perturbed from either reactant or product and, in principle, converges to the transition state. Finally we give a special type of update Hessian matrix formula that should be applied in optimizations carried out on reduced potential-energy surfaces. Received: 29 September 2000 / Accepted: 3 January 2001 / Published online: 3 April 2001     

Efficient methods for finding transition states in chemical reactions: comparison of improved dimer method and partitioned rational function optimization method

A combination of interpolation methods and local saddle-point search algorithms is probably the most efficient way of finding transition states in chemical reactions. Interpolation methods such as the growing-string method and the nudged-elastic band are able to find an approximation to the minimum-energy pathway and thereby provide a good initial guess for a transition state and imaginary mode connecting both reactant and product states. Since interpolation methods employ usually just a small number of configurations and converge slowly close to the minimum-energy pathway, local methods such as partitioned rational function optimization methods using either exact or approximate Hessians or minimum-mode-following methods such as the dimer or the Lanczos method have to be used to converge to the transition state. A modification to the original dimer method proposed by [Henkelman and Jonnson J. Chem. Phys. 111, 7010 (1999)] is presented, reducing the number of gradient calculations per cycle from six to four gradients or three gradients and one energy, and significantly improves the overall performance of the algorithm on quantum-chemical potential-energy surfaces, where forces are subject to numerical noise. A comparison is made between the dimer methods and the well-established partitioned rational function optimization methods for finding transition states after the use of interpolation methods. Results for 24 different small- to medium-sized chemical reactions covering a wide range of structural types demonstrate that the improved dimer method is an efficient alternative saddle-point search algorithm on medium-sized to large systems and is often even able to find transition states when partitioned rational function optimization methods fail to converge.     

Theoretical studies of transition states by the multioverlap molecular dynamics methods

The multioverlap molecular dynamics method gives a flat probability distribution in the multidimensional dihedral-angle-distance space, where the dihedral-angle distance of a configuration with respect to a reference state gives a measure for structural similarity. Hence, this method realizes a random walk among specific configurations in the multidimensional dihedral-angle-distance space at a constant temperature and explores widely in the configurational space. We applied the multioverlap molecular dynamics method to a pentapeptide, Met-enkephalin, in gas phase as a test system. Comparing the results of this method with those of the conventional canonical and multicanonical algorithms, we demonstrate its effectiveness. Furthermore, from the detailed free-energy landscape obtained from the results of the multioverlap molecular dynamics simulation, we obtain the transition state between two specific reference configurations of Met-enkephalin. We also deduce the transition pathway between the two specific reference configurations.     

Bifurcations and transition states

Bifurcations of reaction channels are related to valley-ridge inflection points and it is examined what happens when these do not coincide with transition states. Under such conditions there result bifurcating regions. There exist a number of different prototypes for such regions which are discussed explicitly on the basis of the pertinent Taylor expansions. When bifurcations occur close enough to transition states then there result bifurcating transition regions. An example for a bifurcating transition region is exhibited which is obtained from a quantum mechanical ab initio calculation for the ring opening of cyclopropylidene to aliene. In general there exist no orthogonal trajectory patterns which could serve as simplified models for channel bifurcations.Operated for the U.S. Department of Energy by Iowa State University under Contract No. W-7405-ENG-82. This work was supported by the Office of Basic Energy Sciences     

Efficient algorithm for asymptotics-based configuration-interaction methods and electronic structure of transition metal atoms

Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schro?dinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wave functions, and use of Slater-type orbitals (STOs). The required Coulomb integrals for STOs are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to 3d transition metal atoms are in good agreement with experimental data. In particular, we reproduce the anomalous magnetic moment and orbital filling of chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.     

Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations

An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical errors. This combination allows to achieve fast convergence to the correct values of density of states. We propose that the violation of TTT identities may serve as a qualitative criterion to check the convergence of density of states. The simulation process can be parallelized by cutting the entire interval of simulation into subintervals. The violation of ergodicity in this case is discussed. We test the algorithm on a set of peptides of different lengths and observe good statistical convergent properties for the density of states. We believe that the method is of general nature and can be used for simulations of other systems with either discrete or continuous energy spectrum.     

A semiclassical trace formula using coherent states methods

We present a simple and rigorous proof of a ‘Gutzwiller type’ trace formula, using semiclassical formulas for the propagation of coherent states.     

On ab-initio calculations of singly excited states of atoms with augmented fuess-type basis functions

It is suggested that by simply augmenting a given optimized basis set for the ground state wavefunction of an atom by Fuess-type functions, quality wavefunctions of the singly excited states of the atom could be obtained. The non-linear parameters of the Fuess-type functions are determined from the known quantum defect data. As an illustrative example we present the results for the singly excited ¹S and ¹P states of He. The calculated energies are within 0.2% of the experimental values. The dipole oscillator strengths are also calculated from both the length and the velocity formulas. The results compare well with the experimental values; the velocity form giving generally slightly closer agreement with observations.     

Microstructure characterization of polyethylene using thermo-rheological methods

In the present work, we use the viscoelastic moduli of a large number of industrially available polyethylenes in order to evaluate/test some of the previously proposed correlations between levels of long chain branching and polydispersity with the rheological properties. These correlations together with some new ones can be used to correct for the effects of polydispersity or long chain branching in order to assess the effect of these two molecular features on the rheological properties independently. The effects of short and long chain branching are studied providing a methodology to detect rheologically levels of short and long chain branching.     

Efficient simulation of binary adsorption isotherms using transition matrix Monte Carlo

Molecular simulations of binary adsorption in porous materials are a useful complement to experimental studies of mixture adsorption. Most molecular simulations of binary adsorption are performed using grand canonical Monte Carlo (GCMC) to independently examine a range of state points of interest. A disadvantage of this approach is that it only yields information at a discrete set of state points; therefore, if a complete isotherm is required for arbitrary conditions, some type of data fitting or interpolation must be used in combination with the GCMC data. We show that the transition matrix Monte Carlo (TMMC) method of Shen and Errington (Shen, V. K.; Errington, J. R. J. Chem.Phys. 2005, 122, 064508) is well-suited to simulation of binary adsorption in porous materials. At the completion of a TMMC simulation, the adsorption isotherm for all possible bulk phase compositions and pressures is available without data fitting or interpolation. It is also straightforward to use results from TMMC to compute derivatives of the isotherm such as the mixture thermodynamic correction factors, partial differential ln f(i)/partial differential ln c(j), again without data fitting or interpolation. This approach should be useful in contexts where information on the full adsorption isotherm is needed, such as the design of adsorption- or membrane-based separations.     

Dynamical dimer method for the determination of transition states with ab initio molecular dynamics

A dynamical formulation of the dimer method for the determination of transition states is presented. The method is suited for ab initio molecular dynamics using the fictitious Lagrangian formulation. The method has been applied to the conrotatory ring opening of chlorocyclobutadiene, an example, where the application of the drag method is problematic.     

From transition paths to transition states and rate coefficients

Transition states are defined as points in configuration space with the highest probability that trajectories passing through them are reactive (i.e., form transition paths between reactants and products). In the high-friction (diffusive) limit of Langevin dynamics, the resulting ensemble of transition states is shown to coincide with the separatrix formed by points of equal commitment (or splitting) probabilities for reaching the product and reactant regions. Transition states according to the new criterion can be identified directly from equilibrium trajectories, or indirectly by calculating probability densities in the equilibrium and transition-path ensembles using umbrella and transition-path sampling, respectively. An algorithm is proposed to calculate rate coefficients from the transition-path and equilibrium ensembles by estimating the frequency of transitions between reactants and products.     

An automated method to find transition states using chemical dynamics simulations

A procedure to automatically find the transition states (TSs) of a molecular system (MS) is proposed. It has two components: high‐energy chemical dynamics simulations (CDS), and an algorithm that analyzes the geometries along the trajectories to find reactive pathways. Two levels of electronic structure calculations are involved: a low level (LL) is used to integrate the trajectories and also to optimize the TSs, and a higher level (HL) is used to reoptimize the structures. The method has been tested in three MSs: formaldehyde, formic acid (FA), and vinyl cyanide (VC), using MOPAC2012 and Gaussian09 to run the LL and HL calculations, respectively. Both the efficacy and efficiency of the method are very good, with around 15 TS structures optimized every 10 trajectories, which gives a total of 7, 12, and 83 TSs for formaldehyde, FA, and VC, respectively. The use of CDS makes it a powerful tool to unveil possible nonstatistical behavior of the system under study. © 2014 Wiley Periodicals, Inc.     

Lycopene: The need for better methods for characterization and determination

The healthy properties of lycopene – a red pigment present in tomato and other vegetables and fruits – make it a key carotenoid in the human diet. The present demand of high-purity lycopene for use in food, pharmaceutical, cosmetic and dye industries makes it essential to revisit its chemical characteristics, human absorption, transport and distribution in tissues, metabolism and, particularly, the analytical methods available for its extraction, separation, detection and preparative isolation. The aim of this state-of-the-art review of lycopene is to establish a starting point for the new research needed on this topic.     

A determination of antioxidant efficiencies using ESR and computational methods

Using Transition-State Theory, experimental rate constants, determined over a range of temperatures, for reactions of Vitamin E type antioxidants are analysed in terms of their enthalpies and entropies of activation. It is further shown that computational methods may be employed to calculate enthalpies and entropies, and hence Gibbs free energies, for the overall reactions. Within the linear free energy relationship (LFER) assumption, that the Gibbs free energy of activation is proportional to the overall Gibbs free energy change for the reaction, it is possible to rationalise, and even to predict, the relative contributions of enthalpy and entropy for reactions of interest, involving potential antioxidants. A method is devised, involving a competitive reaction between *CH3 radicals and both the spin-trap PBN and the antioxidant, which enables the relatively rapid determination of a relative ordering of activities for a series of potential antioxidant compounds, and also of their rate constants for scavenging *CH3 radicals (relative to the rate constant for addition of *CH3 to PBN).     

Hydrolysis of phosphotriesters: determination of transition states in parallel reactions by heavy-atom isotope effects

The remote label method was used to measure primary and secondary (18)O isotope effects in the alkaline hydrolysis of O,O-diethylphosphorylcholine iodide (DEPC) and the primary (18)O effect in the alkaline hydrolysis of O,O-diethyl-m-nitrobenzyl phosphate (DEmNBP). Both the leaving group of interest (choline or m-nitrobenzyl alcohol) and ethanol can be ejected during hydrolysis due to the similarity of their pK values. The heavy-atom isotope effects were measured by isotope ratio mass spectrometry. Parallel reaction and incomplete labeling corrections were made for both systems. DEPC has a primary (18)O isotope effect of 1.041 +/- 0.003 and a secondary (18)O isotope effect of 1.033 +/- 0.002. The primary (18)O isotope effect for DEmNBP was 1.052 +/- 0.003. These large effects suggest a highly associative transition state in which the nucleophile approaches very close to the phosphorus atom to eject the leaving group. The large values are also indicative of a large compression, or general movement, on the reaction coordinate.