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# pair_style pace command

Accelerator Variants: pace/kk, pace/extrapolation/kk

# pair_style pace/extrapolation command

## Syntax

    pair_style pace ... keyword values ...

- one or more keyword/value pairs may be appended

      keyword = product or recursive or chunksize
        product = use product algorithm for basis functions
        recursive = use recursive algorithm for basis functions
        chunksize value = number of atoms in each pass

    pair_style pace/extrapolation

## Examples

    pair_style pace
    pair_style pace product chunksize 2048
    pair_coeff * * Cu-PBE-core-rep.ace Cu

    pair_style pace
    pair_coeff * * Cu.yaml Cu

    pair_style pace/extrapolation
    pair_coeff * * Cu.yaml Cu.asi Cu

## Description

Pair style pace computes interactions using the Atomic Cluster Expansion (ACE), which is a general expansion of the atomic energy in multi-body basis functions. (Drautz19). The pace pair style provides an efficient implementation that is described in this paper (Lysogorskiy21).

In ACE, the total energy is decomposed into a sum over atomic energies. The energy of atom i is expressed as a linear or non-linear function of one or more density functions. By projecting the density onto a local atomic base, the lowest order contributions to the energy can be expressed as a set of scalar polynomials in basis function contributions summed over neighbor atoms.

Only a single pair_coeff command is used with the pace style which specifies an ACE coefficient file followed by N additional arguments specifying the mapping of ACE elements to LAMMPS atom types, where N is the number of LAMMPS atom types:

- ACE coefficient file (.yaml or .yace/.ace format)

- N element names = mapping of ACE elements to atom types

Only a single pair_coeff command is used with the pace style which specifies an ACE file that fully defines the potential. Note that unlike for other potentials, cutoffs are not set in the pair_style or pair_coeff command; they are specified in the ACE file.

The pair_style pace command may be followed by the optional keyword product or recursive, which determines which of two algorithms is used for the calculation of basis functions and derivatives. The default is recursive.

The keyword chunksize is only applicable when using the pair style pace with the KOKKOS package on GPUs and is ignored otherwise. This keyword controls the number of atoms in each pass used to compute the atomic cluster expansion and is used to avoid running out of memory. For example if there are 8192 atoms in the simulation and the chunksize is set to 4096, the ACE calculation will be broken up into two passes (running on a single GPU).

## Extrapolation grade

Calculation of extrapolation grade in PACE is implemented in pair_style pace/extrapolation. It is based on the MaxVol algorithm similar to Moment Tensor Potential (MTP) by Shapeev et al. and is described in (Lysogorskiy23). In order to compute extrapolation grade one needs to provide:

1. ACE potential in B-basis form (.yaml format) and

2. Active Set Inverted (ASI) file for corresponding potential (.asi format)

Calculation of extrapolation grades requires matrix-vector multiplication for each atom and is slower than the usual pair_style pace recursive, therefore it is not computed by default. Extrapolation grade calculation is involved by fix pair, which requests to compute gamma, as shown in example below:

    pair_style  pace/extrapolation
    pair_coeff  * * Cu.yaml Cu.asi Cu

    fix pace_gamma all pair 10 pace/extrapolation gamma 1

    compute max_pace_gamma all reduce max f_pace_gamma
    variable dump_skip equal "c_max_pace_gamma < 5"

    dump pace_dump all custom 20 extrapolative_structures.dump id type x y z f_pace_gamma
    dump_modify pace_dump skip v_dump_skip

    variable max_pace_gamma equal c_max_pace_gamma
    fix extreme_extrapolation all halt 10 v_max_pace_gamma > 25

Here extrapolation grade gamma is computed every 10 steps and is stored in f_pace_gamma per-atom variable. The largest value of extrapolation grade among all atoms in a structure is reduced to c_max_pace_gamma variable. Only if this value exceeds extrapolation threshold 5, then the structure will be dumped into extrapolative_structures.dump file, but not more often than every 20 steps.

On all other steps pair_style pace recursive will be used.

When using the pair style pace/extrapolation with the KOKKOS package on GPUs product B-basis evaluator is always used and only linear ASI is supported.

See the pair_coeff page for alternate ways to specify the path for the ACE coefficient file.

## Core repulsion

The ACE potential can be configured to initiate core-repulsion from an inner cutoff, seamlessly transitioning from ACE to ZBL. The core repulsion factor can be accessed as a per-atom quantity, as demonstrated in the example below:

    pair_style  pace
    pair_coeff  * * CuNi.yaml Cu Ni

    fix pace_corerep all pair 1 pace corerep 1

In this case, per-atom f_pace_corerep quantities represent the fraction of ZBL core-repulsion for each atom.

## Mixing, shift, table, tail correction, restart, rRESPA info

For atom type pairs I,J and I != J, where types I and J correspond to two different element types, mixing is performed by LAMMPS with user-specifiable parameters as described above. You never need to specify a pair_coeff command with I != J arguments for this style.

This pair style does not support the pair_modify shift, table, and tail options.

This pair style does not write its information to binary restart files, since it is stored in potential files. Thus, you need to re-specify the pair_style and pair_coeff commands in an input script that reads a restart file.

This pair style can only be used via the pair keyword of the run_style respa command. It does not support the inner, middle, outer keywords.

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## Restrictions

This pair style is part of the ML-PACE package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

## Related commands

pair_style snap, fix pair

## Default

recursive, chunksize = 4096,

(Drautz19) Drautz, Phys Rev B, 99, 014104 (2019).

(Lysogorskiy21) Lysogorskiy, van der Oord, Bochkarev, Menon, Rinaldi, Hammerschmidt, Mrovec, Thompson, Csanyi, Ortner, Drautz, npj Comp Mat, 7, 97 (2021).

(Lysogorskiy23) Lysogorskiy, Bochkarev, Mrovec, Drautz, Phys Rev Mater, 7, 043801 (2023) / arXiv:2212.08716 (2022).