scholarly journals Erratum: “A finite difference Davidson procedure to sidestep full ab initio hessian calculation: Application to characterization of stationary points and transition state searches” [J. Chem. Phys. 140, 164115 (2014)]

2014 ◽  
Vol 140 (22) ◽  
pp. 229902 ◽  
Author(s):  
Shaama Mallikarjun Sharada ◽  
Alexis T. Bell ◽  
Martin Head-Gordon
Keyword(s):  
Finite Difference ◽  
Transition State ◽  
Ab Initio ◽  
Chem Phys ◽  
Stationary Points

scholarly journals Benchmark ab initio and dynamical characterization of the stationary points of reactive atom + alkane and SN2 potential energy surfaces

2020 ◽  
Vol 22 (8) ◽  
pp. 4298-4312 ◽  
Author(s):  
Gábor Czakó ◽  
Tibor Győri ◽  
Balázs Olasz ◽  
Dóra Papp ◽  
István Szabó ◽  
...  
Keyword(s):  
Potential Energy ◽  
Ab Initio ◽  
Potential Energy Surfaces ◽  
Stationary Points ◽  
Ion Molecule Reactions ◽  
Energy Surfaces ◽  
Reactive Atom

We review composite ab initio and dynamical methods and their applications to characterize stationary points of atom/ion + molecule reactions.

Active Learning Accelerates Ab Initio Molecular Dynamics on Pericyclic Reactive Energy Surfaces

2020 ◽  
Author(s):  
Shi Jun Ang ◽  
Wujie Wang ◽  
Daniel Schwalbe-Koda ◽  
Simon Axelrod ◽  
Rafael Gomez-Bombarelli
Keyword(s):  
Molecular Dynamics ◽  
Potential Energy ◽  
Transition State ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Energy Surface ◽  
Computational Cost ◽  
Reactive Trajectories ◽  
Dynamics Simulations ◽  
Energy Surfaces

<div>Modeling dynamical effects in chemical reactions, such as post-transition state bifurcation, requires <i>ab initio</i> molecular dynamics simulations due to the breakdown of simpler static models like transition state theory. However, these simulations tend to be restricted to lower-accuracy electronic structure methods and scarce sampling because of their high computational cost. Here, we report the use of statistical learning to accelerate reactive molecular dynamics simulations by combining high-throughput ab initio calculations, graph-convolution interatomic potentials and active learning. This pipeline was demonstrated on an ambimodal trispericyclic reaction involving 8,8-dicyanoheptafulvene and 6,6-dimethylfulvene. With a dataset size of approximately</div><div>31,000 M062X/def2-SVP quantum mechanical calculations, the computational cost of exploring the reactive potential energy surface was reduced by an order of magnitude. Thousands of virtually costless picosecond-long reactive trajectories suggest that post-transition state bifurcation plays a minor role for the reaction in vacuum. Furthermore, a transfer-learning strategy effectively upgraded the potential energy surface to higher</div><div>levels of theory ((SMD-)M06-2X/def2-TZVPD in vacuum and three other solvents, as well as the more accurate DLPNO-DSD-PBEP86 D3BJ/def2-TZVPD) using about 10% additional calculations for each surface. Since the larger basis set and the dynamic correlation capture intramolecular non-covalent interactions more accurately, they uncover longer lifetimes for the charge-separated intermediate on the more accurate potential energy surfaces. The character of the intermediate switches from entropic to thermodynamic upon including implicit solvation effects, with lifetimes increasing with solvent polarity. Analysis of 2,000 reactive trajectories on the chloroform PES shows a qualitative agreement with the experimentally-reported periselectivity for this reaction. This overall approach is broadly applicable and opens a door to the study of dynamical effects in larger, previously-intractable reactive systems.</div>

scholarly journals Topological Approach to Mathematical Programs with Switching Constraints

2021 ◽  
Author(s):  
Vladimir Shikhman
Keyword(s):  
Stationary Point ◽  
Mountain Pass Theorem ◽  
Strong Stability ◽  
Complete Characterization ◽  
Stationary Points ◽  
Mathematical Programs ◽  
Linear Independence Constraint Qualification ◽  
Point Set ◽  
Stationary Level

AbstractWe study mathematical programs with switching constraints (for short, MPSC) from the topological perspective. Two basic theorems from Morse theory are proved. Outside the W-stationary point set, continuous deformation of lower level sets can be performed. However, when passing a W-stationary level, the topology of the lower level set changes via the attachment of a w-dimensional cell. The dimension w equals the W-index of the nondegenerate W-stationary point. The W-index depends on both the number of negative eigenvalues of the restricted Lagrangian’s Hessian and the number of bi-active switching constraints. As a consequence, we show the mountain pass theorem for MPSC. Additionally, we address the question if the assumption on the nondegeneracy of W-stationary points is too restrictive in the context of MPSC. It turns out that all W-stationary points are generically nondegenerate. Besides, we examine the gap between nondegeneracy and strong stability of W-stationary points. A complete characterization of strong stability for W-stationary points by means of first and second order information of the MPSC defining functions under linear independence constraint qualification is provided. In particular, no bi-active Lagrange multipliers of a strongly stable W-stationary point can vanish.

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