Supporting Information – Modelling Details

Title: Modelling Gas Separation in Metal-Organic Frameworks

Journal: Adsorption

Authors: Brad A Wells and Alan L Chaffee

Affiliation: Cooperative Research Centre for Greenhouse Gas Technologies, School of Chemistry, Monash University, Victoria, Australia.

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Gas Molecules

Gas Geometries

Table 1 details the bond length and bond angle that defines each of the gas molecule geometries.

Gas Molecule / Bond Length / Ǻ / Bond Angle / degrees
Carbon Dioxide / 1.1600 / 180.0
Water / 0.9570 / 104.52
Nitrogen / 1.0977 / -
Hydrogen / 0.7412 / -
Methane / 1.1010 / 109.471

Table 1: Geometrical parameters of gas molecules

Gas Internal Forcefield

To parameterise the gas internal forcefield, each atom is assigned a type. Table 2 shows the atomic parameters of forcefield types for each gas atom.

Gas Molecule / Atom / Forcefield Type / σ / Ǻ / ε
/ kcal mol-1 / Charge
CO2 / C / c2= / 3.9150 / 0.0680 / 0.670
CO2 / O / o1=* / 3.3600 / 0.0670 / -0.335
H2O / H / h1o / 1.0870 / 0.0080 / -0.66
H2O / O / o2* / 3.8400 / 0.0800 / 0.330
N2 / N / n1n / 3.8008 / 0.0598 / 0.000
H2 / H / h1h / 1.4210 / 0.0216 / 0.000
CH4 / C / c40 / 4.0530 / 0.0700 / -0.212
CH4 / H / h1 / 2.8780 / 0.0230 / 0.053

Table 2: Atomic forcefield types of gas molecules

Atomic charges and van der Waals potentials were then assigned by atom type. These are listed in Table 3.

Forcefield Type / σ / Ǻ / ε / kcal mol-1 / Charge
c2= / 3.9150 / 0.0680 / 0.670
o1=* / 3.3600 / 0.0670 / -0.335
h1o / 1.0870 / 0.0080 / -0.66
o2* / 3.8400 / 0.0800 / 0.330
n1n / 3.8008 / 0.0598 / 0.000
h1h / 1.4210 / 0.0216 / 0.000
c40 / 4.0530 / 0.0700 / -0.212
h1 / 2.8780 / 0.0230 / 0.053

Table 3: Gas nonbonding potential parameters

Bond length energies were modelled with a quartic function of the form

V=k2r-r02+k3r-r03+k4r-r04 / 1)

The parameters, in angstroms and kcal/mol for each bond are given in Table 4.

Type I / Type J / r0 / k2 / k3 / k4
o1=* / c2= / 1.1600 / 1161.3421 / -2564.5706 / 3932.8735
h1o / o2* / 0.9570 / 553.2800 / -1278.9600 / 1788.6820
n1n / n1n / 1.0977 / 1651.3730 / -4069.3178 / 5984.9629
h1h / h1h / 0.7412 / 414.2185 / -805.6549 / 914.1296
c40 / h1 / 1.1010 / 345.0000 / -691.8900 / 844.6000

Table 4: Gas bond potential parameters

Bond angle energies were modelled with a quartic function of the form

V=k2θ-θ02+k3θ-θ03+k4θ-θ04 / 2)

The parameters, in degrees and kcal/mol for each gas angle is given in Table 5.

Type I / Type J / Type K / θ0 / k2 / k3 / k4
o1=* / c2= / o1=* / 180.00 / 57.1000 / 0.0000 / 0.0000
h1o / o2* / h1o / 104.5200 / 46.6500 / -11.7046 / -8.7911
h1 / c40 / h1 / 107.6600 / 39.6410 / -12.9210 / -2.4318

Table 5: Gas angle potential Parameters

To increase the accuracy of the forcefield bond-bond, bond-angle and angle-angle terms were also included for some gases. These are of the general form

Vbond-bond=kbbr1-r0,1r2-r0,2 / 3)
Vbond-angle=kbar-r0θ-θ0 / 4)
Vangle-angle=kaaθ1-θ0,1θ2-θ0,2 / 5)

The relevant parameters, in angstroms degrees and kcal/mol are listed in Table 6

Type I / Type J / Type K / kbb / kba / kaa
o1=* / c2= / o1=* / 275.435 / - / -
h1o / o2* / h1o / -10.932 / 23.8488 / -
h1 / c40 / h1 / 5.331 / 18.1030 / -0.3157

Table 6: Gas bond and angle cross-terms

Frameworks

Types were assigned to different atoms following the general type assigning rules in Compass. Types for boron and scandium were added in from the Dreiding and Universal forcefields. Table 7 lists the nonbonding types used, the types of atoms they were used to represent and the van der Waals parameters for that atom type.

Forcefield
Type / Atom / Description / σ / Ǻ / ε / kcal mol-1
b3 / B / Boron in COF-102 / 4.0200 / 0.0950
o2 / O / Oxygen in COF-102 / 3.3000 / 0.08000
c44 / C / sp3 carbon with 4 heavy atoms / 3.8540 / 0.02000
c3a / C / Aromatic carbon / 3.9150 / 0.06800
h1 / H / Generic hydrogen / 2.8780 / 0.02300
cu+2 / Cu / Copper 2+ ion / 2.6500 / 0.04500
o1- / O / Carboxylate oxygen / 3.3000 / 0.05000
c3- / C / Carboxylate carbon / 3.9000 / 0.07000
o_v / O / Oxygen interacting with vanadium in MIL-47 / 3.6270 / 0.38280
v3o / V / Vanadium oxide in MIL-47 / 3.5000 / 0.41278
o_m / O / Oxygen in Zn4O clusters / 3.6270 / 0.07841
zn2o / Zn / Zinc in Zn4O clusters / 3.9800 / 0.54423
sc+3 / Sc / Scandium in Sc-MOF / 3.2950 / 0.01900
o12 / O / Oxygen in nitro group in ZIF-69 / 3.4000 / 0.04800
n3o / N / Nitrogen in nitro group in ZIF-69 / 3.7600 / 0.04800
n2a / N / Aromatic nitrogen / 3.5290 / 0.09600
cl1 / Cl / Chlorine in ZIF-69 / 3.8230 / 0.28600
zn+2 / Zn / Zinc ion / 2.7000 / 0.04700
c4 / C / sp3 carbon in Zn2(BDC)2(TED) / 3.8540 / 0.06200
n3 / N / Tertiary amine in Zn2(BDC)2(TED) / 3.7200 / 0.07500

Table 7: Atom types and nonbonding potentials for framework atoms