title: Extensions to the likelihood maximization approach for finding reaction coordinates.
abstract: This paper extends our previous work on obtaining reaction coordinates from aimless shooting and likelihood maximization. We introduce a simplified version of aimless shooting and a half-trajectory likelihood score based on the committor probability. Additionally, we analyze and compare the absolute log-likelihood score for perfect and approximate reaction coordinates. We also compare the aimless shooting and likelihood maximization approach to the earlier genetic neural network (GNN) approach of Ma and Dinner [J. Phys. Chem. B 109, 6769 (2005)]. For a fixed number of total trajectories in the GNN approach, the accuracy of the transition state ensemble decreases as the number of trajectories per committor probability estimate increases. This quantitatively demonstrates the benefit of individual committor probability realizations over committor probability estimates. Furthermore, when the least squares score of the GNN approach is applied to individual committor probability realizations, the likelihood score still provides a better approximation to the true transition state surface. Finally, the polymorph transition in terephthalic acid demonstrates that the new half-trajectory likelihood scheme estimates the transition state location more accurately than likelihood schemes based on the probability of being on a transition path.
authors.affiliation: Centre Européen de Calcul Atomique Moléculaire (CECAM), Ecole Normale Supérieure, 46 Allée d'Italie, 69364 Lyon Cedex 7, France. bpeters@cecam.org
authors.forename: Baron
authors.initials: B
authors.lastname: Peters
authors.forename: Gregg T
authors.initials: GT
authors.lastname: Beckham
authors.forename: Bernhardt L
authors.initials: BL
authors.lastname: Trout
mesh_terms: D000465:Algorithms; D053263:Gene Regulatory Networks; D016013:Likelihood Functions; D015233:Models, Statistical; D009415:Nerve Net; D011336:Probability