1 Introduction
2 Methods
2.1 Adsorption isotherm calculations
2.2 Force fields
2.3 Point charge calculation methods
3 Results and discussion
3.1 IRMOF-1
Charge set | Method | Zn | O1 | O2 | C1 | C2 | C3 | H |
---|---|---|---|---|---|---|---|---|
Manz and Sholl (2010) | DDEC | 1.121 | − 0.658 | − 1.398 | 0.762 | − 0.058 | − 0.148 | 0.122 |
Manz and Sholl (2010) | DDEC uncompensated | 1.32 | − 0.68 | − 1.68 | 0.79 | − 0.16 | − 0.05 | 0.12 |
Strathclyde (this work) | DDEC | 0.9864 | − 0.5512 | − 1.0220 | 0.5786 | − 0.0139 | − 0.1237 | 0.1490 |
Campana et al. (2009) | REPEAT | 1.28 | − 0.61 | − 1.57 | 0.52 | 0.14 | − 0.18 | 0.17 |
Manz and Sholl (2010) | Hirshfeld | 0.42 | − 0.22 | − 0.34 | 0.18 | − 0.01 | − 0.02 | 0.04 |
Manz and Sholl (2010) | ISA | 1.27 | − 0.66 | − 1.59 | 0.73 | − 0.08 | − 0.10 | 0.15 |
Manz and Sholl (2010) | Bader | 1.30 | − 1.13 | − 1.23 | 1.37 | 0.11 | 0.22 | − 0.16 |
Yang and Zhong (2006b) | CHELPG | 1.501 | − 0.724 | − 1.846 | 0.667 | 0.072 | − 0.132 | 0.140 |
Yazaydin et al. (2009b) | CHELPG | 1.333 | − 0.641 | − 1.564 | 0.558 | 0.106 | − 0.167 | 0.162 |
Sagara et al. (2004) | CHELPG | 1.31 | − 0.63 | − 1.79 | 0.62 | 0.05 | − 0.12 | 0.12 |
Dubbeldam et al. (2007) | CHELPG | 1.275 | − 0.60 | − 1.50 | 0.475 | 0.125 | − 0.15 | 0.15 |
Mu et al. (2010) | CHELPG | 1.637 | − 0.757 | − 1.996 | 0.671 | 0.079 | − 0.122 | 0.125 |
Fischer et al. (2009) | MSK | 1.515 | − 0.708 | − 1.884 | 0.606 | 0.193 | − 0.234 | 0.190 |
Babarao et al. (2007) | RESP | 1.10 | − 0.56 | − 0.98 | 0.53 | − 0.02 | − 0.10 | 0.12 |
Belof et al. (2009) (1) | MSK | 1.8529 | − 1.0069 | − 2.2568 | 1.0982 | − 0.1378 | − 0.0518 | 0.1489 |
Belof et al. (2009) (2) | MSK | 1.8833 | − 1.0144 | − 2.2684 | 1.1457 | − 0.1787 | − 0.0659 | 0.1729 |
Tafipolsky et al. (2007) | MSK | 1.26 | − 0.67 | − 1.44 | 0.68 | 0.06 | − 0.16 | 0.16 |
Wilmer and Snurr (2011) (1) | EQeq | 1.16 | − 0.70 | − 1.50 | 0.69 | 0.07 | − 0.13 | 0.19 |
Wilmer et al. (2012a) (2) | EQeq | 1.211 | − 0.482 | − 0.968 | 0.321 | − 0.064 | − 0.024 | 0.053 |
Wilmer et al. (2012a) | Qeq | 0.450 | − 0.479 | − 0.225 | 0.612 | 0.033 | − 0.121 | 0.146 |
Xu and Zhong (2010) | CBAC | 1.583 | − 0.802 | − 1.93 | 0.797 | 0.041 | − 0.139 | 0.100 |
Average | 1.2747 | − 0.6802 | − 1.4752 | 0.6858 | 0.0170 | − 0.1009 | 0.1223 | |
Standard deviation | 0.3614 | 0.1979 | 0.5395 | 0.2656 | 0.1015 | 0.0903 | 0.0750 |
3.2 MIL-47
Charge set | Method | V | O1 | O2 | C1 | C2 | C3 | H |
---|---|---|---|---|---|---|---|---|
Nazarian et al. (2016) | DDEC | 2.010 | − 0.657 | − 0.833 | 0.734 | − 0.118 | − 0.056 | 0.111 |
Finsy et al. (2009) | CHELPG | 1.68 | − 0.52 | − 0.60 | 0.56 | 0.00 | − 0.15 | 0.12 |
Yazaydin et al. (2009b) | CHELPG | 1.770 | − 0.611 | − 0.662 | 0.644 | 0.320 | − 0.153 | 0.149 |
Wilmer et al. (2012a) | REPEAT | 1.570 | − 0.533 | − 0.592 | 0.635 | 0.004 | − 0.136 | 0.153 |
Wilmer and Snurr (2011) | EQeq | 1.377 | − 0.591 | − 0.701 | 0.689 | 0.059 | − 0.131 | 0.179 |
Ramsahye et al. (2007) | Mulliken | 1.207 | − 0.496 | − 0.596 | 0.604 | − 0.071 | − 0.068 | 0.146 |
Average | 1.6023 | − 0.5680 | − 0.6640 | 0.6443 | 0.0323 | − 0.1157 | 0.1430 | |
Standard deviation | 0.2858 | 0.0617 | 0.0936 | 0.0614 | 0.1540 | 0.0426 | 0.0245 |
3.3 UiO-66
Charge set | Method | Zr | O1 | O2 | O3 | C1 | C2 | C3 | H1 | H2 |
---|---|---|---|---|---|---|---|---|---|---|
Nazarian et al. (2016) | DDEC | 2.5730 | − 0.6761 | − 1.2300 | − 1.2370 | 0.7470 | − 0.1040 | − 0.0760 | 0.1180 | 0.4810 |
Wu et al. (2012) | CBAC | 2.2576 | − 0.6324 | − 1.3024 | − 1.1494 | 0.8046 | 0.0486 | − 0.1314 | 0.1076 | 0.4426 |
Yang et al. (2011) | CHELPG | 2.008 | − 0.582 | − 1.179 | − 0.741 | 0.625 | − 0.002 | − 0.121 | 0.127 | 0.495 |
Ghosh et al. (2014) | REPEAT | 2.4490 | − 0.6983 | − 1.4330 | − 0.7187 | 0.7623 | 0.0430 | − 0.1599 | 0.1460 | 0.4380 |
Average | 2.3219 | − 0.6472 | − 1.2861 | − 0.961525 | 0.7347 | − 0.004 | − 0.1221 | 0.1247 | 0.4642 | |
Standard deviation | 0.2462 | 0.0514 | 0.1102 | 0.2700 | 0.0771 | 0.0707 | 0.0348 | 0.0163 | 0.0282 |
3.4 CuBTC
Charge set | Method | Cu | O | C1 | C2 | C3 | H |
---|---|---|---|---|---|---|---|
Nazarian et al. (2016) | DDEC | 0.920 | − 0.567 | 0.691 | − 0.164 | 0.031 | 0.117 |
Zang et al. (2013) | DDEC | 0.8682 | − 0.5436 | 0.6500 | − 0.0079 | − 0.1229 | 0.1339 |
Wilmer et al. (2012a) | REPEAT | 0.940 | − 0.572 | 0.704 | − 0.088 | − 0.073 | 0.131 |
Wilmer and Snurr (2011) | EQeq | 0.86 | − 0.59 | 0.6 | − 0.04 | − 0.06 | 0.25 |
Huang et al. (2012) | CBAC | 1.065 | − 0.652 | 0.792 | 0.036 | − 0.148 | 0.094 |
Castillo et al. (2008) | Empirical (set IV) | 1.248 | − 0.624 | 0.494 | 0.130 | − 0.150 | 0.156 |
Liu et al. (2009) (1) | CHELPG | 1.105 | − 0.659 | 0.937 | − 0.320 | 0.000 | 0.150 |
Liu et al. (2009) (2) | CHELPG | 1.082 | − 0.725 | 0.824 | − 0.061 | − 0.004 | 0.153 |
Yang and Zhong (2006a) | CHELPG | 1.098 | − 0.665 | 0.778 | − 0.092 | − 0.014 | 0.109 |
Yazaydin et al. (2009a) (1) | CHELPG | 1.000 | − 0.587 | 0.680 | − 0.033 | − 0.110 | 0.137 |
Yazaydin et al. (2009b) (2) | CHELPG | 1.130 | − 0.645 | 0.741 | − 0.070 | − 0.091 | 0.145 |
Babarao et al. (2009) | MSK | 1.026 | − 0.671 | 0.879 | − 0.197 | 0.028 | 0.123 |
Fischer et al. (2009) | MSK | 1.030 | − 0.574 | 0.573 | 0.215 | − 0.364 | 0.209 |
Average | 1.0286 | − 0.6211 | 0.7187 | − 0.0532 | − 0.0829 | 0.1468 | |
Standard deviation | 0.1110 | 0.0531 | 0.1248 | 0.1364 | 0.1056 | 0.0417 |
3.5 Co-MOF-74
Charge set | Method | Co | O1 | O2 | O3 | C1 | C2 | C3 | C4 | H |
---|---|---|---|---|---|---|---|---|---|---|
Haldoupis et al. (2015) | DDEC | 1.165 | − 0.702 | − 0.617 | − 0.715 | 0.760 | − 0.237 | 0.381 | − 0.175 | 0.141 |
Yazaydin et al. (2009a) | CHELPG | 1.139 | − 0.684 | − 0.645 | − 0.731 | 0.832 | − 0.292 | 0.315 | − 0.110 | 0.176 |
Haldoupis et al. (2015) | LoProp | 1.4753 | − 0.7493 | − 0.6876 | − 0.8359 | 0.6104 | − 0.1258 | 0.2245 | − 0.1772 | 0.2657 |
Wilmer and Snurr (2011) | EQeq | 0.164 | − 0.532 | − 0.473 | − 0.586 | 0.423 | − 0.180 | 0.209 | − 0.108 | 0.083 |
Wilmer et al. (2012a) | REPEAT | 1.066 | − 0.648 | − 0.626 | − 0.676 | 0.848 | − 0.340 | 0.309 | − 0.087 | 0.157 |
Mercado et al. (2016) | REPEAT | 1.189 | − 0.720 | − 0.696 | − 0.785 | 0.846 | − 0.308 | 0.391 | − 0.177 | 0.177 |
Average | 1.0331 | − 0.6726 | − 0.6241 | − 0.7215 | 0.7199 | − 0.2471 | 0.3049 | − 0.1390 | 0.1666 | |
Standard deviation | 0.4483 | 0.0768 | 0.0807 | 0.0868 | 0.1712 | 0.0821 | 0.0761 | 0.0417 | 0.0596 |
3.6 Sifsix-2-Cu-I
Charge set | Cu | Si | N | F1 | F2 | C1 | H1 | C2 | H2 | C3 | C4 |
---|---|---|---|---|---|---|---|---|---|---|---|
Pham (CHELPG) | 0.286 | 1.748 | − 0.060 | − 0.537 | − 0.566 | 0.142 | 0.155 | − 0.324 | 0.175 | 0.251 | − 0.160 |
DDEC CP2K | 0.770 | 1.923 | − 0.211 | − 0.580 | − 0.594 | 0.077 | 0.136 | − 0.203 | 0.158 | 0.160 | − 0.075 |
REPEAT VASP | − 0.162 | 2.070 | 0.148 | − 0.523 | − 0.634 | − 0.019 | 0.163 | − 0.288 | 0.194 | 0.317 | − 0.147 |
DDEC VASP | 0.760 | 1.855 | − 0.209 | − 0.568 | − 0.581 | 0.073 | 0.137 | − 0.199 | 0.157 | 0.167 | − 0.082 |
CHELPG (clusters) | 0.7742 | 2.8916 | − 0.3288 | − 0.4753 | − 0.7022 | 0.2313 | 0.0044 | − 0.3291 | 0.1620 | 0.3734 | − 0.1584 |
DDEC (clusters) | 0.9690 | 2.0139 | − 0.2445 | − 0.6465 | − 0.6342 | 0.1058 | 0.1042 | − 0.1603 | 0.1332 | 0.1834 | − 0.0930 |
Average | 0.5662 | 2.0836 | − 0.1509 | − 0.5550 | − 0.6186 | 0.1017 | 0.1166 | − 0.2506 | 0.1632 | 0.2420 | − 0.1192 |
Standard deviation | 0.4227 | 0.4120 | 0.1703 | 0.0581 | 0.0495 | 0.0830 | 0.0586 | 0.0722 | 0.0203 | 0.0880 | 0.0400 |
4 Conclusions
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The variation in the values of the framework point charges, for any given MOF, is much larger than the variation in the adsorption isotherms themselves. This is particularly the case for QM-derived charges, which suggests that the main property controlling adsorption predictions is the overall electrostatic potential induced by the framework on the adsorbate molecules. As a consequence, assessing the suitability of point charge determination methods solely on the basis of the charges themselves may lead to erroneous conclusions. We recommend diagnosing the suitability of charge sets by comparing predicted isotherms against reference data, whenever possible.
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Charges derived from periodic QM calculations yielded isotherms that were consistent with each other for all charge determination methods, with the exception of Bader and Hirshfeld. This was the case regardless of the details of the underlying QM calculation. In particular, it is noteworthy that consistent charges were obtained from both DDEC (an electron density partitioning method) and REPEAT (an electrostatic potential fitting method) for all MOFs analysed here. It is hard to draw definitive conclusions for other charge determination methods (e.g. LoProp, ISA) due to the small number of instances analysed. As such, we would recommend this approach as the most reliable for obtaining framework charges for adsorption simulations, at least when the size of the unit cell does not make such calculations prohibitive.
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Framework charges derived from QM cluster calculations were comparatively less reliable—while several sets yielded isotherms in agreement with each other and with periodic charges, there was a significant degree of variation in some cases. Moreover, with one or two exceptions, it was not possible to predict which sets would lead to discrepant isotherms simply by examining the charge values. This means that care should be taken when using charges calculated by this approach, and consistency checks should be sought whenever possible.
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Charges calculated using methods that fit the electrostatic potential (such as CHELPG or REPEAT) or that partition the electron density (such as DDEC or ISA) generally yield isotherms that are statistically consistent with each other. A clear exception are Bader charges, which strongly overestimate the electrostatic potential, and hence the adsorbed amounts. Charges determined from population analysis (e.g. Mulliken) appear to be less reliable, although there are not enough examples in our study to confirm this observation. The decreased reliability of Mulliken charges is reinforced by their significant dependence with the basis set size as reported in the literature.
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Semi-empirical approaches, like EQeq or CBAC, can provide reasonable alternatives to QM-based charges when computational expense is an important limitation (e.g. large-scale screening). However, in some cases, predictions from this class of methods can lead to rather unexpected results (e.g. water in UiO-66). Given the wide variability in MOF framework structures and surface chemistries (including functionalization), we recommend that any charges obtained from semi-empirical methods be validated against reference isotherms obtained from periodic QM charges for prototypical MOFs.
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Water isotherms are much more sensitive to details of the electrostatic interactions than CO2 isotherms. This was rather expected, due to the significant difference in polarity between these two adsorbates. This effect is emphasised in MOFs that contain open metal sites, as these provide rather strong adsorption sites for water molecules. In such MOFs, attempts to adjust framework point charges (or, indeed, LJ parameters) to implicitly account for coordination bonds at the unsaturated metal site are unlikely to lead to physically consistent adsorption behaviour.