## Syntax

tad N t_event T_lo T_hi delta tmax compute-ID keyword value ...

• N = # of timesteps to run (not including dephasing/quenching)

• t_event = timestep interval between event checks

• T_lo = temperature at which event times are desired

• T_hi = temperature at which MD simulation is performed

• delta = desired confidence level for stopping criterion

• tmax = reciprocal of lowest expected pre-exponential factor (time units)

• compute-ID = ID of the compute used for event detection

• zero or more keyword/value pairs may be appended

• keyword = min or neb or min_style or neb_style or neb_log

min values = etol ftol maxiter maxeval
etol = stopping tolerance for energy (energy units)
ftol = stopping tolerance for force (force units)
maxiter = max iterations of minimize
maxeval = max number of force/energy evaluations
neb values = ftol N1 N2 Nevery
etol = stopping tolerance for energy (energy units)
ftol = stopping tolerance for force (force units)
N1 = max # of iterations (timesteps) to run initial NEB
N2 = max # of iterations (timesteps) to run barrier-climbing NEB
Nevery = print NEB statistics every this many timesteps
neb_style value = quickmin or fire
neb_step value = dtneb
dtneb = timestep for NEB damped dynamics minimization
neb_log value = file where NEB statistics are printed

## Examples

tad 2000 50 1800 2300 0.01 0.01 event
tad 2000 50 1800 2300 0.01 0.01 event &
min 1e-05 1e-05 100 100 &
neb 0.0 0.01 200 200 20 &
min_style cg &
neb_style fire &
neb_log log.neb


## Description

Run a temperature accelerated dynamics (TAD) simulation. This method requires two or more partitions to perform NEB transition state searches.

TAD is described in this paper by Art Voter. It is a method that uses accelerated dynamics at an elevated temperature to generate results at a specified lower temperature. A good overview of accelerated dynamics methods (AMD) for such systems is given in this review paper from the same group. To quote from the review paper: “The dynamical evolution is characterized by vibrational excursions within a potential basin, punctuated by occasional transitions between basins. The transition probability is characterized by p(t) = k*exp(-kt) where k is the rate constant.”

TAD is a suitable AMD method for infrequent-event systems, where in addition, the transition kinetics are well-approximated by harmonic transition state theory (hTST). In hTST, the temperature dependence of transition rates follows the Arrhenius relation. As a consequence a set of event times generated in a high-temperature simulation can be mapped to a set of much longer estimated times in the low-temperature system. However, because this mapping involves the energy barrier of the transition event, which is different for each event, the first event at the high temperature may not be the earliest event at the low temperature. TAD handles this by first generating a set of possible events from the current basin. After each event, the simulation is reflected backwards into the current basin. This is repeated until the stopping criterion is satisfied, at which point the event with the earliest low-temperature occurrence time is selected. The stopping criterion is that the confidence measure be greater than 1-delta. The confidence measure is the probability that no earlier low-temperature event will occur at some later time in the high-temperature simulation. hTST provides an lower bound for this probability, based on the user-specified minimum pre-exponential factor (reciprocal of tmax).

In order to estimate the energy barrier for each event, the TAD method invokes the NEB method. Each NEB replica runs on a partition of processors. The current NEB implementation in LAMMPS restricts you to having exactly one processor per replica. For more information, see the documentation for the neb command. In the current LAMMPS implementation of TAD, all the non-NEB TAD operations are performed on the first partition, while the other partitions remain idle. See the Howto replica doc page for further discussion of multi-replica simulations.

A TAD run has several stages, which are repeated each time an event is performed. The logic for a TAD run is as follows:

while (time remains):
while (time < tstop):
until (event occurs):
run dynamics for t_event steps
quench
run neb calculation using all replicas
compute tlo from energy barrier
update earliest event
update tstop
reflect back into current basin
execute earliest event


Before this outer loop begins, the initial potential energy basin is identified by quenching (an energy minimization, see below) the initial state and storing the resulting coordinates for reference.

Inside the inner loop, dynamics is run continuously according to whatever integrator has been specified by the user, stopping every t_event steps to check if a transition event has occurred. This check is performed by quenching the system and comparing the resulting atom coordinates to the coordinates from the previous basin.

A quench is an energy minimization and is performed by whichever algorithm has been defined by the min_style command; its default is the CG minimizer. The tolerances and limits for each quench can be set by the min keyword. Note that typically, you do not need to perform a highly-converged minimization to detect a transition event.

The event check is performed by a compute with the specified compute-ID. Currently there is only one compute that works with the TAD command, which is the compute event/displace command. Other event-checking computes may be added. Compute event/displace checks whether any atom in the compute group has moved further than a specified threshold distance. If so, an “event” has occurred.

The NEB calculation is similar to that invoked by the neb command, except that the final state is generated internally, instead of being read in from a file. The style of minimization performed by NEB is determined by the neb_style keyword and must be a damped dynamics minimizer. The tolerances and limits for each NEB calculation can be set by the neb keyword. As discussed on the neb, it is often advantageous to use a larger timestep for NEB than for normal dynamics. Since the size of the timestep set by the timestep command is used by TAD for performing dynamics, there is a neb_step keyword which can be used to set a larger timestep for each NEB calculation if desired.

A key aspect of the TAD method is setting the stopping criterion appropriately. If this criterion is too conservative, then many events must be generated before one is finally executed. Conversely, if this criterion is too aggressive, high-entropy high-barrier events will be over-sampled, while low-entropy low-barrier events will be under-sampled. If the lowest pre-exponential factor is known fairly accurately, then it can be used to estimate tmax, and the value of delta can be set to the desired confidence level e.g. delta = 0.05 corresponds to 95% confidence. However, for systems where the dynamics are not well characterized (the most common case), it will be necessary to experiment with the values of delta and tmax to get a good trade-off between accuracy and performance.

A second key aspect is the choice of t_hi. A larger value greatly increases the rate at which new events are generated. However, too large a value introduces errors due to anharmonicity (not accounted for within hTST). Once again, for any given system, experimentation is necessary to determine the best value of t_hi.

Five kinds of output can be generated during a TAD run: event statistics, NEB statistics, thermodynamic output by each replica, dump files, and restart files.

Event statistics are printed to the screen and master log.lammps file each time an event is executed. The quantities are the timestep, CPU time, global event number N, local event number M, event status, energy barrier, time margin, t_lo and delt_lo. The timestep is the usual LAMMPS timestep, which corresponds to the high-temperature time at which the event was detected, in units of timestep. The CPU time is the total processor time since the start of the TAD run. The global event number N is a counter that increments with each executed event. The local event number M is a counter that resets to zero upon entering each new basin. The event status is E when an event is executed, and is D for an event that is detected, while DF is for a detected event that is also the earliest (first) event at the low temperature.

The time margin is the ratio of the high temperature time in the current basin to the stopping time. This last number can be used to judge whether the stopping time is too short or too long (see above).

t_lo is the low-temperature event time when the current basin was entered, in units of timestep. del*t_lo* is the time of each detected event, measured relative to t_lo. delt_lo is equal to the high-temperature time since entering the current basin, scaled by an exponential factor that depends on the hi/lo temperature ratio and the energy barrier for that event.

On lines for executed events, with status E, the global event number is incremented by one, the local event number and time margin are reset to zero, while the global event number, energy barrier, and delt_lo match the last event with status DF in the immediately preceding block of detected events. The low-temperature event time t_lo is incremented by delt_lo.

NEB statistics are written to the file specified by the neb_log keyword. If the keyword value is “none”, then no NEB statistics are printed out. The statistics are written every Nevery timesteps. See the neb command for a full description of the NEB statistics. When invoked from TAD, NEB statistics are never printed to the screen.

Because the NEB calculation must run on multiple partitions, LAMMPS produces additional screen and log files for each partition, e.g. log.lammps.0, log.lammps.1, etc. For the TAD command, these contain the thermodynamic output of each NEB replica. In addition, the log file for the first partition, log.lammps.0, will contain thermodynamic output from short runs and minimizations corresponding to the dynamics and quench operations, as well as a line for each new detected event, as described above.

After the TAD command completes, timing statistics for the TAD run are printed in each replica’s log file, giving a breakdown of how much CPU time was spent in each stage (NEB, dynamics, quenching, etc).

Any dump files defined in the input script will be written to during a TAD run at timesteps when an event is executed. This means the requested dump frequency in the dump command is ignored. There will be one dump file (per dump command) created for all partitions. The atom coordinates of the dump snapshot are those of the minimum energy configuration resulting from quenching following the executed event. The timesteps written into the dump files correspond to the timestep at which the event occurred and NOT the clock. A dump snapshot corresponding to the initial minimum state used for event detection is written to the dump file at the beginning of each TAD run.

If the restart command is used, a single restart file for all the partitions is generated, which allows a TAD run to be continued by a new input script in the usual manner. The restart file is generated after an event is executed. The restart file contains a snapshot of the system in the new quenched state, including the event number and the low-temperature time. The restart frequency specified in the restart command is interpreted differently when performing a TAD run. It does not mean the timestep interval between restart files. Instead it means an event interval for executed events. Thus a frequency of 1 means write a restart file every time an event is executed. A frequency of 10 means write a restart file every 10th executed event. When an input script reads a restart file from a previous TAD run, the new script can be run on a different number of replicas or processors.

Note that within a single state, the dynamics will typically temporarily continue beyond the event that is ultimately chosen, until the stopping criterion is satisfied. When the event is eventually executed, the timestep counter is reset to the value when the event was detected. Similarly, after each quench and NEB minimization, the timestep counter is reset to the value at the start of the minimization. This means that the timesteps listed in the replica log files do not always increase monotonically. However, the timestep values printed to the master log file, dump files, and restart files are always monotonically increasing.

## Restrictions

This command can only be used if LAMMPS was built with the REPLICA package. See the Build package doc page for more info.

N setting must be integer multiple of t_event.

Runs restarted from restart files written during a TAD run will only produce identical results if the user-specified integrator supports exact restarts. So fix nvt will produce an exact restart, but fix langevin will not.

This command cannot be used when any fixes are defined that keep track of elapsed time to perform time-dependent operations. Examples include the “ave” fixes such as fix ave/chunk. Also fix dt/reset and fix deposit.

## Default

The option defaults are min = 0.1 0.1 40 50, neb = 0.01 100 100 10, neb_style = quickmin, neb_step = the same timestep set by the timestep command, and neb_log = “none”.

(Voter2000) Sorensen and Voter, J Chem Phys, 112, 9599 (2000)

(Voter2002) Voter, Montalenti, Germann, Annual Review of Materials Research 32, 321 (2002).