Supplementary Information for
“Scaling Properties of Binding Energies for NHx on Transition Metal
Complexes”
Ying Wang, Joseph H. Montoya, Charlie Tsai, Mårten S. G. Alquist, Jens K. Nørskov,
Felix Studt
Electronic energy data
In this supplement, we include data corresponding to the results of the selfconsistent plane wave calculations done in Quantum Espresso.1 In table S1, we
show the raw electronic energy output for each cluster (these energies are in eV, all
other anergies are in kJ/mol), along with the states in which N, NH, and NH2 are
bound to the metal site. We also include the gas-phase reference energies calculated
for N2 and H2, from which the binding energy of the N, NH, and NH2 molecules can
be calculated according to Equation 3 in the main text.
Electronic energies, molecular clusters (eV)
[(YCH2CH2)3Z]X
[(YCH2CH2)3Z]X-N
[(YCH2CH2)3Z]X-NH
[(YCH2CH2)3Z]X-NH2
X = Mo, Y = NH, Z = N
-4365.58
-4365.58
-4661.06
-4677.98
X = Mo, Y = NH, Z = P
-4302.49
-4580.72
-4597.26
-4614.51
X = Mo, Y = S, Z = N
-4426.91
-4705.63
-4721.94
-4739.05
X = Mo, Y = S, Z = P
-4364.42
-4641.73
-4658.76
-4676.00
X = Ru, Y = NH, Z = N
-3038.34
-3314.38
-3331.77
-3349.97
X = Ru, Y = NH, Z = P
-2975.52
-3250.79
-3268.35
-3286.83
X = Ru, Y = S, Z = N
-3100.55
-3376.27
-3393.62
-3411.89
X = Ru, Y = S, Z = P
-3038.23
-3312.92
-3330.67
-3349.20
X = Os, Y = NH, Z = N
-3271.42
-3548.91
-3565.60
-3583.60
X = Os, Y = NH, Z = P
-3208.50
-3485.29
-3502.31
-3520.68
X = Os, Y = S, Z = N
-3333.02
-3610.04
-3626.78
-3644.87
X = Os, Y = S, Z = P
-3270.60
-3546.92
-3563.91
-3582.35
X = Fe, Y = NH, Z = N
-5817.56
-6093.51
-6110.69
-6128.78
X = Fe, Y = NH, Z = P
-5754.33
-6029.45
-6046.84
-6065.18
X = Fe, Y = S, Z = N
-5879.09
-6154.96
-6171.95
-6190.08
X = Fe, Y = S, Z = P
-5816.43
-6091.44
-6108.70
-6127.07
Electronic energies, gas-phase references (eV)
N2
H2
-555.06
-32.94
Table S1. Electronic energies of [(YCH2CH2)3Z]X, [(YCH2CH2)3Z]X-N,
[(YCH2CH2)3Z]X-NH and [(YCH2CH2)3Z]X-NH2 for each of 16 complexes. Reference
electronic energies of gas-phase species N2 and H2 are listed at the end of this table. All
values are given in eV.
We tabulate the values of E(Y3ZX-N), E(Y3ZX-NH), and E(Y3ZX-NH2) as
calculated according to Equation 3 in the main text in Table S2 below.
Binding energies (kJ/mol)
Standard deviation (kJ/mol)
E(Y3ZX-N)
E(Y3ZX-NH)
E(Y3ZX-NH2)
σ(Y3ZX-N)
σ(Y3ZX-NH)
σ(Y3ZX-NH2)
[(NHCH2CH2)3N]Mo
-187.2
-141.1
-184.3
21.1
18.2
19.2
[(SCH2CH2)3N]Mo
-113.3
-98.9
-159.4
14.4
14.4
19.2
[(NHCH2CH2)3P]Mo
-66.2
-73.0
-147.8
23.0
18.2
16.3
[(SCH2CH2)3P]Mo
22.1
-31.7
-105.6
25.0
20.2
17.3
[(NHCH2CH2)3N]Ru
144.0
55.7
-110.4
20.2
16.3
14.4
[(SCH2CH2)3N] Ru
172.8
89.3
-82.6
22.1
18.2
15.4
[(NHCH2CH2)3P] Ru
217.0
112.3
-80.6
33.6
21.1
16.3
[(SCH2CH2)3P] Ru
273.6
149.8
-48.0
32.6
22.1
17.3
[(NHCH2CH2)3N]Os
4.8
-16.3
-163.2
19.2
12.5
14.4
[(SCH2CH2)3N] Os
49.0
24.0
-132.5
18.2
13.4
14.4
[(NHCH2CH2)3P] Os
72.0
18.2
-163.2
25.0
16.3
15.4
[(SCH2CH2)3P] Os
116.2
66.2
-122.9
25.0
17.3
14.4
[(NHCH2CH2)3N]Fe
151.7
83.5
-72.0
25.0
19.2
21.1
[(SCH2CH2)3N] Fe
160.3
110.4
-48.0
25.0
19.2
17.3
[(NHCH2CH2)3P] Fe
230.4
144.0
-35.5
33.6
25.9
25.0
[(SCH2CH2)3P] Fe
242.9
163.2
-15.4
31.7
23.0
21.1
Table S2. Binding energies of Y3ZX-N, Y3ZX-NH, and Y3ZX-NH2 for each cluster, along
with the estimated standard deviation of each quantity. Calculated error estimates are
the standard deviation of an ensemble of 2000 exchange correlation functionals
provided within the BEEF framework. Note that all units are in kJ/mol.
Principal Component Analysis of the BEEF Ensemble
Figure 2 of the main text displays values of E(Y3ZX-NH) and E(Y3ZX-NH2)
plotted against values of the descriptor energy E(Y3ZX-N). In addition, the figure
shows results of a principal component analysis on the BEEF2 ensemble in the form
of ellipses with their major and minor axes corresponding to the PCA vectors
corresponding to each binding energy pair.3 In Figure S1 below, we show the
complete set of 2000 sampled energies from the BEEF ensemble for a particular
cluster configuration which contains Y=N, Z=N, X=Fe.
The largest principal
component, which corresponds to the major axis, represents the direction of
maximum variability, and the magnitudes of each vector are determined by the
variance along that direction. With perfect correlation, the PCA ellipse converges to
a line, while a PCA ellipse corresponding to uncorrelated data should form a circle.
Figure S1. Scatter plot representing the BEEF ensemble calculation. Black points
represent 2000 binding energies provided in the BEEF ensemble. The green ellipse
represents the result of the principal component analysis (PCA), in which the major
and minor axes are defined by the PCA vectors.
Scaling analysis using Jaguar code
In the main text, we allude to a replication of our DFT analysis performed
using the Jaguar software package4 and the B3LYP functional.5,6 Figure S2 shows
the results of that analysis, in which we find that the slope remains nearly identical.
Figure S2. All Density Functional Theory (DFT) calculations in this figure were carried
out with the Jaguar 7.9 program package by Schrödinger LLC. Becke’s threeparameter hybrid functional and the LYP correlation functional (B3LYP) were used
with the LACVP** core potential and basis set.
References
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T. Bligaard and K. W. Jacobsen, Phys. Rev. B, 2012, 85, 235149.
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Jacobsen, T. Bligaard and J. K. Nørskov, Science, 2014, 345, 197–200.
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