Table 1 Energies per ion of the lowest energy structures obtained for differently sized supercells of O3-Na2/3[Li1/6Fe1/6Co1/6Ni1/6Mn1/3]O2 with the different heuristics implemented in GOAC (all calculations performed on 128 physical CPU cores and using 128 OpenMP threads)

From: Optimization of Coulomb energies in gigantic configurational spaces of multi-element ionic crystals

    

Energy per ion [eV]

\(\sqrt{3}\)-Cell

NConf

tC [s]

tR [h]

GD

MC

SA

REMC

GA

HY

2 × 2 × 1

1031

0.0

1

−22.080

−22.080

−22.080

−22.080

−22.080

−22.080

2 × 2 × 2

1064

0.0

1

−22.071

−22.082

−22.096

−22.096

−22.096

−22.096

4 × 4 × 1

10132

0.1

1

−22.040

−22.027

−22.087

−22.087

−22.042

−22.087

4 × 4 × 2

10269

0.5

2

−22.013

−22.006

−22.096

−22.096

−21.772

−22.040

6 × 6 × 1

10303

0.5

2

−22.003

−22.078

−22.083

−21.814

−22.029

8 × 8 × 1

10543

1.6

4

−21.975

−22.031

−22.022

−21.625

−21.986

6 × 6 × 2

10611

1.9

8

−21.984

−22.040

−22.031

−21.589

−21.992

6 × 6 × 3

10920

3.8

16

−21.970

−22.018

−22.006

−21.548

−21.975

  1. Even though energy differences appear to be small as they are scaled per ion to allow for comparisons, they are very significant (usually more than 1 eV) when the energy of a whole supercell is considered. The table also shows the total number of configurations (NConf) of the different combinatorial problems along with the required time to calculate the Coulomb matrices and expansion coefficients (tC). The run times for each heuristic were limited to tR for the shown problems. Minimum energies found for each of the problem sizes are highlighted in bold.