“On‐the‐fly” Crystal: How to reliably and automatically characterize and construct potential energy surfaces

Abstract

In this work, the code, developed previously by the authors to find “holes” as well as legitimate transition states in existing potential energy surface (PES) functions [JPC Lett. 11, 6468 (2020)], is retooled to perform on‐the‐fly “direct dynamics”‐type PES explorations, as well as automatic construction of new PES functions. In all of these contexts, the chief advantage of over other methods is its ability to globally map the PES, thereby determining the most relevant regions of configuration space quickly and reliably—even when the dimensionality is rather large. Here, is used to generate a uniformly spaced grid of density functional theory (DFT) or ab initio points, truncated over the relevant regions, which can then be used to either: (a) hone in precisely on PES features such as minima and transition states, or; (b) create a new PES function automatically, via interpolation. Proof of concept is demonstrated via application to three molecular systems: water (HO), (reduced‐dimensional) methane (CH), and methylene imine (CHNH).

Development of Parallel On-the-Fly Crystal Algorithm for Global Exploration of Conical Intersection Seam Space

“…), the scaling of the grid size is polynomial with respect to the dimensionality. The latter scaling has been explored in detail in some of our past publications. ,− In practice, a small number of grid points extending across the entire configuration space in a single direction are needed, but this can depend greatly on the system.…”

“…Many of the uses described above, especially (but not exclusively) PES construction, have been made possible or improved by the recent development of on-the-fly Crystal , whose basic operation is as follows: for any new lattice points generated, Crystal sends the coordinates of the system as input to an external software package which performs the quantum mechanical (QM) calculations. The corresponding energy calculated by the QM package is returned to Crystal and used for continuing the exploration.…”

“…In this manner, Crystal has been found to be well suited for a wide range of purposes�such as discovering (in addition to PES minima) energetically accessible TSs and reaction pathways up to a predetermined energy cutoff, analyzing existing PES surfaces for "holes" and other features, and even constructing new PESs. 25,27−29 Many of the uses described above, especially (but not exclusively) PES construction, have been made possible or improved by the recent development of on-the-fly Crystal, 25 whose basic operation is as follows: for any new lattice points generated, Crystal sends the coordinates of the system as input to an external software package which performs the quantum mechanical (QM) calculations. The corresponding energy calculated by the QM package is returned to Crystal and used for continuing the exploration.…”

“…To address this challenge, in this work we developed the parallel on-the-fly Crystal algorithm to globally explore the CI seam space. The Crystal algorithm ,− (Figure ) was originally developed to globally explore extended regions of phase space and was then adapted to find TSs and other features in the configuration spaces of ground-state PESs. ,− One of Crystal’s most notable features is its ability to handle simultaneous displacements along a large number of d.o.f.s, without the need for evaluating nuclear gradients or defining collective variables (as is the case with metadynamics , ). Such displacements are performed on a multidimensional lattice of grid points spanning the configuration space.…”

“…First, the configurational space volume that must be searched can scale exponentially with respect to the number of d.o.f.s in the system (if conventional methods are used). Second, on-the-fly PES calculations using electronic structure methods are often necessary because it is difficult to accurately parametrize analytical PESs of multiple intersecting states without conformational sampling a priori . Thus, mitigating the exponential scaling of the number of PES evaluations with respect to the number of d.o.f.s is the central challenge for the development of global search algorithms. − …”