Table 1 Descriptors, model coefficients, and responding values determined by Dirichlet–Laplace for dopant-modified MgO.

From: Using statistical learning to predict interactions between single metal atoms and modified MgO(100) supports

 

Descriptors

Coefficients

Au/Na-MgO

Au/Al-MgO

1

\({\mathrm{wr}}_{\mathrm{p}}^{\mathrm{m}} \times \left| {\frac{{{\mathrm{IE}}_2^{\mathrm{m}} - {\mathrm{IE}}_2^{\mathrm{s}}}}{{{\mathrm{IE}}_2^{\mathrm{s}} - {\mathrm{IE}}_1^{\mathrm{d}}}}} \right|\)

11.99

0.98

0.30

2

\(\left( {{\mathrm{NVal}}^{\mathrm{m}}} \right)^3 \times \left| {\frac{{{\mathrm{IE}}_2^{{\mathrm{dn}}}}}{{{\mathrm{IE}}_1^{\mathrm{m}} - {\mathrm{IE}}_2^{\mathrm{s}}}}} \right|\)

0.00003

0.34

0.14

3

\(\left( {{Z}^{\mathrm{m}} - {Z}^{\mathrm{d}}} \right)^2 \times \left| {\frac{{{\mathrm{IE}}_2^{\mathrm{m}} - {\mathrm{IE}}_2^{\mathrm{s}}}}{{{\mathrm{IE}}_1^{\mathrm{o}} - {\mathrm{IE}}_2^{{\mathrm{dn}}}}}} \right|\)

−0.0002

−0.15

−0.89

4

\(\left| {{\textstyle{{{\mathrm{EN}}_{\mathrm{P}}^{\mathrm{m}} - {\mathrm{EN}}_{\mathrm{P}}^{\mathrm{s}}} \over {{\mathrm{EN}}_{\mathrm{P}}^{\mathrm{o}} - {\mathrm{EN}}_{\mathrm{P}}^{\mathrm{d}}}}}} \right| \times \left| {{\textstyle{{{\mathrm{IE}}_{\mathrm{2}}^{\mathrm{m}} - {\mathrm{IE}}_{\mathrm{1}}^{\mathrm{d}}} \over {{\mathrm{IE}}_{\mathrm{1}}^{\mathrm{s}} - {\mathrm{IE}}_{\mathrm{2}}^{\mathrm{d}}}}}} \right|\)

−1.69

−0.31

−0.69

5

\(\sqrt {\left| {{\textstyle{{{\mathrm{EN}}_{{\mathrm{MB}}}^{\mathrm{m}} - {\mathrm{EN}}_{{\mathrm{MB}}}^{\mathrm{o}}} \over {{\mathrm{EN}}_{{\mathrm{MB}}}^{\mathrm{s}} - {\mathrm{EN}}_{{\mathrm{MB}}}^{\mathrm{o}}}}}} \right|} \times \left| {{\textstyle{{{\mathrm{IE}}_1^{\mathrm{s}} - {\mathrm{IE}}_1^{{\mathrm{dn}}}} \over {{\mathrm{IE}}_1^{\mathrm{m}}}}}} \right|\)

−6.30

−1.76

−1.17

6

\(\left| {\frac{{{\mathrm{IE}}_1^{\mathrm{m}} - {\mathrm{IE}}_2^{\mathrm{s}}}}{{{\mathrm{IE}}_2^{\mathrm{m}} - {\mathrm{IE}}_2^{\mathrm{d}}}}} \right| \times \left| {\frac{{{\mathrm{IE}}_1^{\mathrm{m}} - {\mathrm{IE}}_2^{{\mathrm{dn}}}}}{{{\mathrm{IE}}_2^{\mathrm{m}} - {\mathrm{IE}}_1^{{\mathrm{dn}}}}}} \right|\)

−3.09

−0.88

−0.09

7

\(\left| {\frac{{{\mathrm{IE}}_1^{\mathrm{m}} - {\mathrm{IE}}_2^{\mathrm{d}}}}{{{\mathrm{IE}}_2^{\mathrm{s}} - {\mathrm{IE}}_1^{\mathrm{d}}}}} \right| \times \left( {{\mathrm{NVal}}^{\mathrm{m}} - {\mathrm{NVal}}^{\mathrm{d}}} \right)\)

0.04

0.83

0.47

8

\(\left| {\frac{{{\mathrm{IE}}_2^{\mathrm{d}}}}{{{\mathrm{IE}}_2^{\mathrm{m}}}}} \right| \times \left| {\frac{{{\mathrm{EA}}^{\mathrm{m}}}}{{{\mathrm{EA}}^{{\mathrm{dn}}}}}} \right|\)

−0.002

−0.03

−0.09

9

\(\left| {\frac{{{\mathrm{IE}}_1^{\mathrm{o}} - {\mathrm{IE}}_1^{\mathrm{d}}}}{{{\mathrm{IE}}_2^{\mathrm{m}}}}} \right| \times \left| {\frac{{{\mathrm{IE}}_2^{\mathrm{m}} - {\mathrm{IE}}_2^{\mathrm{s}}}}{{{\mathrm{IE}}_1^{{\mathrm{dn}}} - {\mathrm{IE}}_2^{{\mathrm{dn}}}}}} \right|\)

−0.16

−0.03

−0.34

10

\(\left| {\frac{{{\mathrm{IE}}_2^{\mathrm{o}} - {\mathrm{IE}}_2^{\mathrm{d}}}}{{{\mathrm{IE}}_2^{\mathrm{m}}}}} \right| \times \left| {\frac{{{\mathrm{IE}}_2^{\mathrm{m}} - {\mathrm{IE}}_2^{\mathrm{s}}}}{{{\mathrm{IE}}_2^{\mathrm{s}} - {\mathrm{IE}}_1^{{\mathrm{dn}}}}}} \right|\)

−0.10

−0.09

−0.33

11

Intercept

0.84

0.84

0.84

Δ(ΔEads)

–

–

−0.26

−1.83

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