Recommendations for Velocity Adjustment in Surface Hopping

Abstract

This study investigates velocity adjustment directions after hopping in surface hopping dynamics. Using fulvene and a protonated Schiff base (PSB4) as case studies, we investigate the population decay and reaction yields of different sets of dynamics with the velocity adjusted in either the nonadiabatic coupling, gradient difference, or momentum directions. For the latter, in addition to the conventional algorithm, we investigated the performance of a reduced kinetic energy reservoir approach recently proposed. Our evaluation also considered velocity adjustment in the directions of approximate nonadiabatic coupling vectors. While results for fulvene are susceptible to the adjustment approach, PSB4 is not. We correlated this dependence to the topography near the conical intersections. When nonadiabatic coupling vectors are unavailable, the gradient difference direction is the best adjustment option. If the gradient difference is also unavailable, a semiempirical vector direction or the momentum direction with a reduced kinetic energy reservoir becomes an excellent option to prevent an artificial excess of back hoppings. The precise velocity adjustment direction is less crucial for describing the nonadiabatic dynamics than the kinetic energy reservoir's size.

Nuclear Quantum Effects on Nonadiabatic Dynamics of a Green Fluorescent Protein Chromophore Analogue: Ring-Polymer Surface-Hopping Simulation

“…In particular, Ṙ k ′ = λ i j Ṙ k while the global scaling factor λ ij is calculated using the expression λ i j = { true false( V i false( boldR̅ false) − V j false( boldR̅ false) false) + K false( boldR̅ false) K false( boldR̅ false) ( V i ( R̅ ) ≥ V j ( R̅ ) ) K false( boldR̅ false) false( V j false( boldR̅ false) − V i false( boldR̅ false) false) + K false( boldR̅ false) ( V i ( R̅ ) < V j ( R̅ ) ) where K ( R̅ ) is the kinetic energy of the centroid. Even though FSSH usually scales velocity components in the direction of nonadiabatic coupling vectors, some recent works indicate that the velocity adjustment direction is much less important than the size of kinetic energy reservoir . By combining some simple algorithms, the velocity rescaling can obtain satisfactory results.…”

“…In our original implementation, only hops from higher to lower state are allowed while all back hops are rejected to avoid so-called frustrated hops considering that back hops usually play minor roles during the excited-state deactivation of photoexcited molecules. , To check whether such approximation is valid, we have run RPSH-CA simulations at 50 K with 1 bead and 10 beads with an algorithm recently proposed by Toldo et al considering back hops properly . In short, the velocity adjustment is still made in velocity direction, but hops from state i to j are accepted if the energy gap satisfies the inequality and the first condition of eq K false( boldR̅ false) N D F − false( V j false( boldR̅ false) − V i false( boldR̅ false) false) ≥ 0 in which N DF is the number of vibrational degrees of freedom.…”

“…In particular, while the global scaling factor λ ij is calculated using the expression where K ( R̅ ) is the kinetic energy of the centroid. Even though FSSH usually scales velocity components in the direction of nonadiabatic coupling vectors, some recent works indicate that the velocity adjustment direction is much less important than the size of kinetic energy reservoir . By combining some simple algorithms, the velocity rescaling can obtain satisfactory results.…”

“…By combining some simple algorithms, the velocity rescaling can obtain satisfactory results. In the present work, we adopted a reduced kinetic energy reservoir approach proposed by Toldo et al for its easy implementation and effectiveness . In the near future, we will explore the accuracy of scaling velocities of beads in the direction of nonadiabatic coupling vectors evaluated for centroids.…”

Quantum Quality with Classical Cost: Ab Initio Nonadiabatic Dynamics Simulations Using the Mapping Approach to Surface Hopping

“…The main aspect that differs between most FSSH algorithms lies in the way in which the nuclear velocities are rescaled at a hop. While it is generally agreed upon that rescaling along the nonadiabatic coupling vector (NACV) is the correct thing to do, ,− many other schemes are used in practical implementations of FSSH . In particular, rescaling all degrees of freedom equally, which is often referred to as rescaling “along the velocity vector”, is probably the most commonly used. − Additionally, an upward hop must be aborted if there is insufficient nuclear kinetic energy, often referred to as a “frustrated hop”.…”