« 6. Calculation of correlation functions :: Contents :: 8. Optimization of clusters »

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].

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

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

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

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

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

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

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

« 6. Calculation of correlation functions :: Contents :: 8. Optimization of clusters »