Metal-organic frameworks (MOFs) attract a lot of interest due to their unique structure-dependent properties. Their internal pores comparable to the size of small molecules are naturally refined for various absorbance effects. Possessed properties lie in a foundation of multiple applications, such as catalysis, gas storage/separation and especially – clean energy related ones. Theoretical calculations are a usual way of decreasing experimental costs while investigating properties of new materials, especially at a design stage. Electronic structure calculations like density functional theory (DFT) in most cases provide an appropriate accuracy in matching experimentally measured data such as adsorbate interaction energies. However, as in the case of experimental studies, large-scale materials screening studies with DFT calculations are rather time-consuming, and it can be carried out only for structures with relatively small unit cell. Here we would like to present a theoretical and experimental results describing calculation of electron density in metal-organic frameworks. We built a model trained to predict partial charges on MOF atoms based on DFT calculations. The relative error of the model allows us to conclude that models do not decrease the level of accuracy and do not superinduce additional error comparing to DFT. At the same time, computational cost of the model is several orders of magnitude less. Models also demonstrated transferability and allowed to make prediction e.g. for MOFs containing metals not presented in the train set. We have also built a force-field (FF) of two-centered and three-centered interatomic potentials constructed using predicted charges. The FF proved to reproduce MOF crystal structure. As a final test, we have applied the developed model and FF to a new synthesized lanthanide-containing MOFs to estimate influence of supramolecular effects on metal complexation selectivity. As a result, we’ve built a model predicting one of basic MOF properties within relatively small computational time and tested it on experimental data, both obtained from literature sources and self-investigated.

1. Metal-organic frameworks: from
database to supramolecular
effects in complexation
Artem Mitrofanov, Vadim Korolev, Ekaterina Marchenko, Nickolay Eremin,
Nickolay Andreadi, Petr Matveev, Natalia Borisova, Valery Tkachenko
Science Data
Software, LLC
Lomonosov
Moscow State University
1

2. MOFs
• Metal ions or clusters
• Organic ligands
• 1D, 2D or 3D structures
• Often porous materials
Fig. from doi:10.1126/science.1083440. 2

3. MOF usage
• Catalysis
• Gas purification or separation
• Luminescent properties
• Supercapacitors
• Semiconductors
• Gas storage
3

4. MOF properties
• Structure
• Nature of metal ion or cluster
• …
• Partial charges
• …
• Functional properties
4

5. CORE database
Computation-Ready, Experimental (CoRE) Metal-
Organic Frameworks Database
• 838 structures (without DDEC partial atomic
charges) and another with 502 structures (with
DDEC partial atomic charges) now more
D. Nazarian, J. Camp, Y.G. Chung, R.Q. Snurr, D.S. Sholl,
"Large-Scale Refinement of Metal Organic Framework
Structures Using DFT," Chemistry of Materials, 2016
5

6. CORE database
6

7. Machine learning
• Descriptors:
• Intrinsic elemental properties of the corresponding site
• Structural descriptors of site characterized its local environment
• XGBoost:
• 10-fold cross-validation
• 10% external test set
7

8. ML charges
MAE: 0.0096
8

9. 9

10. Very preliminary conclusions
• We built a model for MOF partial charges calculation, adding no
additional error to DFT ones
• …how to apply it?
10

11. Ln-containing MOFs
11

12. Interatomic potentials
Morse potential
V(r)=𝐷 𝑀[exp(−2𝛼(𝑟 − 𝑟0) − 2exp(−𝛼(𝑟
− 𝑟0))]
Ln-O potentials were fitted earlier:
Eremin, N. N.; Marchenko, E. I.; Petrov, V. G.; Mitrofanov, A.
A.; Ulanova, A. S. Solid Solutions of Monazites and Xenotimes
of Lanthanides and Plutonium: Atomistic Model of Crystal
Structures, Point Defects and Mixing Properties. Comput.
Mater. Sci. 2019, 157, 43–50.
12

13. SEHTEF (Y4H12C36O24)
Parameter Value from database Calculated value Difference, %
a, Å 10.838800 11.077384 2.20
b, Å 10.942100 11.070761 1.18
c, Å 15.591800 15.753738 1.04
α 90.00 90.00 0.00
β 90.00 89.99 -0.01
γ 100.51 100.80 0.29
V, Å3 1818.13 1897.73 4.38
SEHSUU (Er4H12C36O24)
Parameter Value from database Calculated value Difference, %
a, Å 10.801000 10.804109 0.03
b, Å 10.906000 10.914457 0.08
c, Å 15.550000 15.558781 0.06
α 90.00 90.00 0.00
β 90.00 90.00 0.00
γ 100.4 100.4 0.00
V, Å3 1801.62 1804.53 0.16
AFUPEX (Tm4H12C36O24)
Parameter Value from database Calculated value Difference, %
a, Å 10.815800 11.038927 2.06
b, Å 10.933100 11.045046 1.02
c, Å 15.551400 15.729286 1.14
α 90.00 90.00 0.00
β 90.00 90.0 0.00
γ 100.56 100.78 0.22
V, Å3 1807.83 1883.98 4.21 13

14. Let’s complicate the task…
14

15. … and compare with the experiment
GEGDED WEHHEY
Cell
param.
Experiment Calculated Difference Experiment Calculated Difference
a, Å 12.247300 12.247309 0.000009 12.160000 12.160009 0.000009
b, Å 25.914000 25.914024 0.000024 26.331000 26.331027 0.000027
c, Å 25.914100 25.914123 0.000023 26.468000 26.468026 0.000026
α,° 90.0 90.0 0.0 90.0 90.0 0.0
β,° 90.0 90.0 0.0 90.0 90.0 0.0
γ,° 90.0 90.0 0.0 90.0 90.0 0.0
V, Å3 8224.527193 8224.54819 0.020997 8474.655521 8474.679058 0.023537
15

16. Perhaps, the charges are unimportant
16
-750
-700
-650
-600
-550
-500
-450
-400
-350
-300
La Pr Nd Sm Eu Gd Tb Dy
ΔH, eV (with ML charges)
ΔH, eV (with EQEq charges)

17. Preliminary conclusions
• We built a model for MOF partial charges calculation, adding no
additional error to DFT ones
• We built a set of interatomic two-body potentials for MOF geometry
and thermochemistry calculations
• Available on https://arxiv.org/abs/1905.12098
• …how to apply it?
17

18. Liquid-liquid extraction
18
DAqueous phase DOrganic phase

19. Distribution ratios
19
La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
0,00
0,05
0,10
0,15
0,20
0,25
0,30
Distibutionratio
0,1 M
0,01 M
0,25 M

20. Enthalpies of formation
20
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
La Pr Nd Pm Sm Eu Er Lu

21. Results and conclusions
• We built a model for MOF partial charges calculation, adding no
additional error to DFT ones
• We built a set of interatomic two-body potentials for MOF geometry
and thermochemistry calculations
• Available on https://arxiv.org/abs/1905.12098
• We used the models to explain extraction process
21

22. Thank you!
On Web:
scidatasoft.com
Slides:
https://www.slideshare.net/valerytkachenko16
Contact us:
info@scidatasoft.com