Locating all transition states and studying the reaction pathways of potential energy surfaces

Westerberg, Karl M.; Floudas, Christodoulos A.

doi:10.1063/1.478850

Cited by 58 publications

(56 citation statements)

References 34 publications

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“…Interestingly, the S1/P conformation was 1.8 kcal/mol lower in energy than the starting S1/R conformation. Accidentally, the S1/P conformation corresponds to the global minimum of alanine in the gas phase that was the subject of earlier theoretical [50][51][52] and experimental 53,54 studies.…”

Section: The C α -Nh 2 Pathmentioning

confidence: 99%

Exploring chemical reaction mechanisms through harmonic Fourier beads path optimization

Khavrutskii

Smith

Wallqvist

2013

The Journal of Chemical Physics

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Here, we apply the harmonic Fourier beads (HFB) path optimization method to study chemical reactions involving covalent bond breaking and forming on quantum mechanical (QM) and hybrid QM/molecular mechanical (QM/MM) potential energy surfaces. To improve efficiency of the path optimization on such computationally demanding potentials, we combined HFB with conjugate gradient (CG) optimization. The combined CG-HFB method was used to study two biologically relevant reactions, namely, L- to D-alanine amino acid inversion and alcohol acylation by amides. The optimized paths revealed several unexpected reaction steps in the gas phase. For example, on the B3LYP/6-31G(d,p) potential, we found that alanine inversion proceeded via previously unknown intermediates, 2-iminopropane-1,1-diol and 3-amino-3-methyloxiran-2-ol. The CG-HFB method accurately located transition states, aiding in the interpretation of complex reaction mechanisms. Thus, on the B3LYP/6-31G(d,p) potential, the gas phase activation barriers for the inversion and acylation reactions were 50.5 and 39.9 kcal/mol, respectively. These barriers determine the spontaneous loss of amino acid chirality and cleavage of peptide bonds in proteins. We conclude that the combined CG-HFB method further advances QM and QM/MM studies of reaction mechanisms.

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Section: The C α -Nh 2 Pathmentioning

confidence: 99%

Exploring chemical reaction mechanisms through harmonic Fourier beads path optimization

Khavrutskii

Smith

Wallqvist

2013

The Journal of Chemical Physics

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“…The point x * is called a transition state or index-1 saddle point. One emerging approach to this problem is based on the use of deterministic global search methods in which one aims first to locate all critical points and then to identify within those the physically relevant ones, namely index-1 saddle points (and possibly minima that are also of interest) [16,17,26]. However, in such an approach, it is necessary to obtain full convergence for all critical points, including those that are not of practical relevance.…”

Section: Examples 7-9: Identification Of Non Index-1 Areasmentioning

confidence: 99%

“…(24) end if (25) [2] being the second entry of the first sublist in L. (26) iter++. (27) if L is empty or BUB − BLB < then (28) Return BLB and BUB.…”

Section: The Interval-matrix Branch-and-bound Algorithmmentioning

confidence: 99%

An interval-matrix branch-and-bound algorithm for bounding eigenvalues

Nerantzis

Adjiman

2016

Optimization Methods and Software

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We present and explore the behaviour of a branch-and-bound algorithm for calculating valid bounds on the kth largest eigenvalue of a symmetric interval matrix. Branching on the interval elements of the matrix takes place in conjunction with the application of Rohn's method (an interval extension of Weyl's theorem) in order to obtain valid outer bounds on the eigenvalues. Inner bounds are obtained with the use of two local search methods. The algorithm has the theoretical property that it provides bounds to any arbitrary precision > 0 (assuming infinite precision arithmetic) within finite time. In contrast with existing methods, bounds for each individual eigenvalue can be obtained even if its range overlaps with the ranges of other eigenvalues. Performance analysis is carried out through nine examples. In the first example, a comparison of the efficiency of the two local search methods is reported using 4000 randomly generated matrices. The eigenvalue bounding algorithm is then applied to five randomly generated matrices with overlapping eigenvalue ranges. Valid and sharp bounds are indeed identified given a sufficient number of iterations. Furthermore, most of the range reduction takes place in the first few steps of the algorithm so that significant benefits can be derived without full convergence. Finally, in the last three examples, the potential of the algorithm for use in algorithms to identify index-1 saddle points of nonlinear functions is demonstrated.

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“…One approach to resolving this difficulty is given by Westerberg and Floudas [87], who transform the equation-solving problem ∇V = 0 into an equivalent optimization problem that has global minimizers corresponding to the solutions of the equation system (i.e., the stationary points of V). A deterministic global optimization algorithm, based on a branch-and-bound strategy with convex underestimators, then is used to find these global minimizers.…”

Section: Transition State Analysismentioning

confidence: 99%