Binding Energy Estimation of Metal Organic Frameworks
by All-Electron Mixed-Basis Program TOMBO
R. Sahara1,2, R. Note2, H. Mizuseki2, K. Ohno3, M.H.F. Sluiter1, and Y. Kawazoe2
Delft, the Netherlands, 2IMR , Tohoku University, Japan, 3Yokohama National University, Japan
• Metal-Organic Frameworks (the self-assembly of
metal-ions & bridging organic ligands)
• Constructed by light elements
=> High gravimetric hydrogen capacity
• Many kinds of organic ligands
=> Controlling the binding energy
Uptake hydrogen significant at both low and room
Ligand
temperature
+
⇒
Metal Cluster
BDC benzenedicarboxylic acid
IRMOF-8
MOF-5
(IRMOF-1)
Cutoff energy dependence of structural
optimization and its calculation time:
-1082
-1086
-1088
{
{
◎Reduction of number of PW, which is necessary
for standard planewave based approaches.
◎Study of properties affected by core level such
as XPS and hyper fine structures [2].
AOs of SiH4:
1s, 2s, 2p
1s, 2s, 2p, 3p
1s, 2s, 2p, 3s
-7906
-7908
200
400
600
800
1000
-7912
0
200
400
600
800
1000
Cutoff planewaves, eV
Cutoff planewaves, eV
Figure: Cutoff energy dependence of structural optimization for
(a) methane and (b) silane. 400eV of PW is good enough for
convergence. The effectiveness is clear for methane including
elements in second row (carbon).
Estimation of the binding energy:
(1) without ligand, Li
Model (a)
[1] K. Ohno, K. Esfarjani, and Y. Kawazoe, Computational Materials Science: From
ab initio to Monte Carlo Methods, Springer Series in Solid-State Sciences Vol. 129
(Springer-Verlag, Berlin, Heidelberg, 1999), 42-46.
[2] M. S. Bahramy, M.H.F. Sluiter, and Y. Kawazoe, Phys. Rev. B73 (2007), 045111.
[3] http://www-lab.imr.edu/~marcel/tombo/tombo.html
◎Mixed-basis approach:
＋ Atomic orbitals (AO)
Plane wave (PW)
(b)
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-1092
0
TOhoku Mixed-Basis Orbitals ab initio simulation
package “TOMBO”, which has been developed by our
research group, is a tool for first principles calculations
based on “all-electron mixed basis approach” [1-3].
◎All-electron:
Core
Valence
-7904
-1090
What is TOMBO ?
One-electron wave function is expressed as:
(a)
-1084
2,6-NDC naphtalenedicarboxylic acid
Formation of TOMBO and advantages:
-7902
AOs of CH4:
1s
1s, 2s
1s, 2s, 2p
Total energy, eV
MOF as hydrogen storage materials:
Total energy, eV
1TU
(b)
C-C
(c)
length [Å]
C6H6-H2
C-H
H-H
Total energy
[eV]*
Model (a)
2.790
1.389
1.097
0.771
-6292.6301
Model (b)
2.679
1.389
1.097
0.770
-6292.6280
Model (c)
2.623
1.390
1.097
0.770
-6292.6159
(*Binding energies are estimated as negative
and they are not stable with hydrogen.)
(2) with ligand, Li
Model (a-1)
length [Å]
mean C-C
C6H6-Li
(b-2)
(b-1)
(a-2)
Li-H2
mean H-H
EB of H2 [eV]
n=0
1.398
1.755
-
(0.768)
-
Model (a-1)
1.398
1.772
1.964
0.777
0.3179
Model (a-2)
1.398
1.760
1.958
0.777
0.3375
Model (b-1)
1.397
1.803
2.000
0.776
0.2747
Model (b-2)
1.397
1.803
2.001
0.776
0.2739
Charge density difference plot:
(i)
(a)
(b)
Figure: (a) Construction of AOs from atomic radial
wave function and (b) Kohn-Sham wave functions.
Purpose of the present study:
Estimating the binding energy of hydrogen molecules
on MOF-5 using C6H6-Li (simplest model of MOF-5).
=> Effect of ligand, Li
Calculation conditions: LDA, Ecut PW=400eV,
Ecut AO=2000eV, cell=12Å.
[email protected]
[email protected]
(ii)
(iii)
(iv)
Figures: Charge density difference plot for Model (a-2) (Fig.(i)
and (ii)) and Model (b-1) (Figs. (iii) and (iv)). Figs. (i) (iii) are
for +0.01 e/Å3 and (ii) (iV) are for -0.01 e/Å3 .
Conclusion:
Binding energy of hydrogen molecules on C6H6-Li as a simplest
model of MOF-5 are estimated. Ligand, Li, is found to be
effective to enhance the binding energy of hydrogen.