7. Estimation of effective cluster interaction

7.1. Theoretical backgrounds

Estimation of ECI using the least-squares technique

See [lsf1] and [lsf2].

Cross validation (CV) score

See [cv1], [cv2] and [cv3].

[lsf1]

D de Fontaine, Solid State Physics 47, Academic Press, (1994).

[lsf2]

Z W Lu, S H Wei, A Zunger, S Frota-Pessoa and L G Ferreira, Phys. Rev. B 44, 512 (1991).

[cv1]

M Stone, J. R. Stat. Soc. Ser. B. Methodol. 36, 111 (1974).

[cv2]

A van de Walle and G Ceder, J. Phase Equilib. 23, 348 (2002).

[cv3]

N A Zarkevich and D D Johnson, Phys. Rev. Lett. 92, 255702 (2004).

7.2. lsf

• Estimating ECI from DFT energies and correlation functions for the DFT structures using the least-squares technique.

• Estimating the CV score.

Input files

• LS.in

• ENERGY

• CORRELATION

Output

• ECI

• Residual sum of squares

• CV score

• diagonal terms of precision matrix

7.3. wlsf

• Estimating ECI from DFT energies and correlation functions for the DFT structures using the weighted least-squares technique.

• In addition to the estimation of the ECI, the weighted CV (WCV) score is evaluated.

Input files

• LS.in

• ENERGY

• CORRELATION

• WEIGHT

Output

• ECI

• WCV score

7.4. LS.in

LS.in specifies clusters for estimating ECIs.

• first line : number of all clusters

• after second line : indexes of clusters in cluster.out

• Sample

  53
  1
  2
  3
  4
  5
  6 7 8 11
  

7.5. statistic

• Examining variances of clusters and correlations between clusters.

Input files

• STAT.in

• CORRELATION

Output files

• statistic.out

7.6. STAT.in

7.6.1. NALLCLUSTER tag

Number of all clusters.

• Default : none

• Example : NALLCLUSTER = 53

7.6.2. CUTCO tag

Truncation value for correlations between clusters. One cluster is output out of the two clusters with strong correlation.

• Default : 1.0

• Example : CUTCO = 0.95

7.6.3. CUTVAR tag

Truncation value for variances of clusters. Clusters with variances less than CUTVAR are output.

• Default : 0.0

• Example : CUTVAR = 0.05