Supporting Information
Modeling Adsorption and Self-Diffusion of Methane in LTA
Zeolites: the Influence of Framework Flexibility
A. García-Sánchez1,2, D. Dubbeldam2, S. Calero1*
Department of Physical, Chemical, and Natural Systems. University Pablo de Olavide. Ctra. Utrera km. 1.
41013 Seville, Spain, Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe
Achtergracht 166, 1018 WV, Amsterdam, The Netherlands.
*
E-mail: [email protected]
University Pablo de Olavide(1), University of Amsterdam(2).
Table S1: Energy potentials and force field parameters used in this work based on the force field reported
by Nicholas et al.1
Force Field Parameters
Valence Potential Parameters
i) Bond Stretch:
U bond (r ) 
kr
r  r0 2
2
Si-Ozeo Bond Stretch (Harmonic Bond)
kr/kB = 300724.7766358210 (K/Å2)
r0= 1.61 Å
Al-Oa Bond Stretch (Harmonic Bond)
kr/kB = 300724.7766358210 (K/Å2)
r0= 1.61 Å
ii) Bond Angle Bend: (Ozeo-Si-Ozeo)
U Obend
Si O ( ) 
k
  0 2
2
Ozeo-Si-Ozeo Bond Angle Bend (Harmonic Bend)
 0 = 109.50
kθ/kB = 69537.44416550520 (K/rad2)
Oa-Al-Oa Bond Angle Bend (Harmonic Bend)
 0 = 109.50
kθ/kB = 69537.44416550520 (K/rad2)
iii) Bond Angle Bend: (Si-Ozeo-Si)
USibend
OSi ( ) 
k1
  0 2  k2   0 3  k3   0 4
2
2
2
Si-Ozeo-Si Bond Angle Bend (Quartic Bend)
k1/kB=5462.50557(K/rad2)
k2/kB=-17157.8055(K/rad3)
k3/kB=13351.6726(K/rad4)
 0 =149.50
k3/kB=13351.6726(K/rad4)
 0 =149.50
Al-Oa-Si Bond Angle Bend (Quartic Bend)
k1/kB=5462.50557(K/rad2)
k2/kB=-17157.8055(K/rad3)
iv) Bond Angle Coupling:
U U  B (r ) 
kr
rSiSi  r0 2
2
Si-Ozeo-Si Urey-Bradley Term (Harmonic Urey-Bradley)
kr/kB = 27488.73770226310 (K/Å2)
r0= 3.1261 Å
Al-Oa-Si Urey-Bradley Term (Harmonic Urey-Bradley)
kr/kB = 27488.73770226310 (K/Å2)
r0= 3.1261 Å
v) Dihedral Angle:
k

U torsion ( ,  , ' )  S    (1  cos(3 )) S  '
2

Si-Ozeo-Si-Ozeo Torsion (Smoothed three cosine dihedral)
k/kB = -352.419714131579 (K)
Si-Ozeo-Al-Ozeo Torsion (Smoothed three cosine dihedral)
k/kB = -352.419714131579 (K)
Al-Ozeo-Si-Ozeo Torsion (Smoothed three cosine dihedral)
k/kB = -352.419714131579 (K)
vi) Nonbonded Potential Parameters (Lennard Jones Potential)
q (e-)
Atom
ε/kB (K)
Si
81.76308187
3.962387454
1.1
Al
81.76308187
3.962387454
0.8
OSi
29.4338257
3.062219744
-0.55
OAl
29.4338257
3.062219744
-0.609146341
Si
81.76308187
3.962387454
1.1
Na
--
--
0.536585366
Ca
--
--
1.073170732
The Ozeo oxygen atom has two types: (a) OSi connected to two silicon atoms, and (b) OAl connected to an
aluminium.
The smoothing function S() is defined as:
1


S       2 off  2  3on
off

off  on 

with
 on =1700 and off =1800.
  on
  on
Table S2: Energy potentials and force field parameters used in this work based on the force field reported
by Hill and Sauer2,3.
Force Field Parameters
i) Bond Stretch:
U bond(r )  k2 r  r0   k3 r  r0   k4 r  r0 
2
3
4
Si-O Bond Stretch (CFF Quartic Bond)
k2/kB = 231017.255 (K/Å2) k3/kB = -338387.114 (K/Å3)
k4/kB = 223109.917 (K/Å4) r0= 1.6104 Å
Si-Oa Bond Stretch (CFF Quartic Bond)
k2/kB = 248642.816 (K/Å2) k3/kB = -18468.957 (K/Å3)
k4/kB=1082265.698 (K/Å4) r0= 1.6157 Å
Al-Oa Bond Stretch (CFF Quartic Bond)
k2/kB = 165400.667 (K/Å2) k3/kB = -171605.009 (K/Å3)
k4/kB = 1101564.816 (K/Å4) r0= 1.7193 Å
ii)Bond Angle Bend:
U angle( )  k2    0   k3    0   k4    0 
2
3
4
O-Si-O Bond Bending (Bond Angle Bend) (CFF Quartic Bend)
k2/kB = 41248.441 (K/rad2)
k3/kB = -18408.470 (K/rad3) k4/kB = 58854.427 (K/rad4) θ0= 112.02000
Oa-Si-O Bond Bending (Bond Angle Bend) (CFF Quartic Bend)
k2/kB = 44318.985 (K/rad2)
k3/kB = -28705.144 (K/rad3) k4/kB = 46537.881 (K/rad4) θ0= 112.42790
Oa-Al-Oa Bond Bending (Bond Angle Bend) (CFF Quartic Bend)
k2/kB= 150991.986 (K/rad2) k3/kB = -16387.793 (K/rad3) k4/kB = 33846.084 (K/rad4) θ0= 113.40000
Oa-Si-Oa Bond Bending (Bond Angle Bend) (CFF Quartic Bend)
k2/kB = 77589.386 (K/rad2)
k3/kB = -34550.792 (K/rad3) k4/kB = 11890.672 (K/rad4) θ0= 110.61200
Si-O-Si Bond Bending (Bond Angle Bend) (CFF Quartic Bend)
k2/kB = 10417.396 (K/rad2)
k3/kB = 13863.996 (K/rad3)
k4/kB = 5531.891 (K/rad4)
θ0= 173.76510
Al-Oa-Si Bond Bending (Bond Angle Bend) (CFF Quartic Bend)
k2/kB = 5206.006 (K/rad2)
k3/kB = 6358.982 (K/rad3)
k4/kB = 4530.887 (K/rad4)
θ0= 162.40000
iii) Bond Bond:
U bondbond(r , r ' )  kbb' r  r0 r 'r '0 
Al-Oa-Si Bond-Bond (Bond Coupling) (CFF Bond Bond Cross)
kbb’ /kB = 41850.643 (K/Å2)
r’0= 1.6157 Å
r0= 1.7193 Å
Oa-Si-O Bond-Bond (Bond Coupling) (CFF Bond Bond Cross)
kbb’ /kB = 23023.294 (K/Å2)
r0= 1.6157 Å
r’0= 1.6104 Å
Si-O-Si Bond-Bond (Bond Coupling) (CFF Bond Bond Cross)
kbb’ /kB = 76426.043 (K/Å2)
r0= 1.6104 Å
r’0= 1.6104 Å
Oa-Al-Oa Bond-Bond (Bond Coupling) (CFF Bond Bond Cross)
kbb’ /kB = -28434.412 (K/Å2)
r0= 1.7193 Å
r’0= 1.7193 Å
Oa-Si-Oa Bond-Bond (Bond Coupling) (CFF Bond Bond Cross)
kbb’ /kB = 76426.043 (K/Å2)
r0= 1.6157 Å
r’0= 1.6157 Å
iv) Bond-Angle:
U bondangle(r , , r ' )    0 kr r  r0   kr ' r 'r '0 
Al-Oa-Si Bond-Bend (Bond-Bend Coupling) (CFF Bond Bend Cross)
kr /kB = 4612.610 (K/Å/rad)
kr’ /kB = 6918.160 (K/Å/rad) θ0= 162.40000
b0= 1.7193 Å b’0=1.6157 Å
Oa-Si-O Bond-Bend (Bond-Bend Coupling) (CFF Bond Bend Cross)
kr /kB = 10125.881 (K/Å/rad) kr’/kB =39231.890 (K/Å/rad) θ0= 112.42790
b0= 1.6157 Å b’0=1.6104 Å
O-Si-O Bond-Bend (Bond-Bend Coupling) (CFF Bond Bend Cross)
kr /kB = 39313.462 (K/Å/rad) kr’/kB= 39313.462 (K/Å/rad) θ0= 112.02000
b0= 1.6104 Å b’0=1.6104 Å
Si-O-Si Bond-Bend (Bond-Bend Coupling) (CFF Bond Bend Cross)
kr /kB = 4649.244 (K/Å/rad)
kr’/kB = 4649.244 (K/Å/rad)
θ0= 173.76510
b0= 1.6104 Å b’0=1.6104 Å
Oa-Al-Oa Bond-Bend (Bond-Bend Coupling) (CFF Bond Bend Cross)
kr /kB = 55430.774 (K/Å/rad) kr’/kB =55430.774 (K/Å/rad) θ0= 113.40000
b0= 1.7193 Å b’0=1.7193 Å
Oa-Si-Oa Bond-Bend (Bond-Bend Coupling) (CFF Bond Bend Cross)
kr/kB= 117789.368 (K/Å/rad) kr’/kB=117789.368(K/Å/rad) θ0= 110.61200
b0= 1.6157 Å b’0=1.6157 Å
v) Angle- Angle:
U angleangle( , ' )  k '    0  ' '0 
O-Si-O-O Bend-Bend (Bend Coupling) (CFF Bend Bend Cross)
kθθ’ /kB = -3171.792 (K/rad2)
θ0= 112.02000
θ'0= 112.02000
O-Si-Oa-O Bend-Bend (Bend Coupling) (CFF Bend Bend Cross)
kθθ’ /kB = 9680.532 (K/rad2)
θ0= 112.42790
θ'0= 112.42790
vi) Torsion:
U torsion , , '  S  k1 1  cos  k2 1  cos 2   k3 1  cos 3 S  '
Al-Oa-Si-O Bend-Torsion-Bend (Torsion) (Smoothed CFF Dihedral)
k1 /kB = 1106.52913 (K)
k2 /kB = 378.82356 (K)
k3 /kB = -248.38909 (K)
Si-O-Si-Oa Bend-Torsion-Bend (Torsion) (Smoothed CFF Dihedral)
k1 /kB = 19.97780 (K)
k2 /kB = 6.69282 (K)
k3 /kB = -123.43972 (K)
Si-O-Si-O Bend-Torsion-Bend (Torsion) (Smoothed CFF Dihedral)
k1 /kB = 15.39851 (K/Å2)
k2 /kB = -5.28380 (K/Å2)
k3 /kB = 40.45884 (K/Å2)
Si-Oa-Al-Oa Bend-Torsion-Bend (Torsion) (Smoothed CFF Dihedral)
k1 /kB = 3061.48615 (K/Å2)
k2 /kB = -286.93570 (K/Å2)
k3 /kB = -745.67050 (K/Å2)
Al-Oa-Si-Oa Bend-Torsion-Bend (Torsion) (Smoothed CFF Dihedral)
k1 /kB = 935.83711 (K/)
k2 /kB = -11.62437 (K)
k3 /kB = -218.64883 (K)
vii) Angle-Angle Torsion:
U angleangletorsion ( , , ' )  k ' cos     0  ' '0 
O-Si-Oa-Al Bend-Torsion-Bend (Bend Coupling Torsion) (Smoothed CFF Bend Torsion Cross)
kθθ’/kB = 4260.004 (K/rad2)
θ0= 112.42790
θ'0= 162.40000
Oa-Si-O-Si Bend-Torsion-Bend (Bend Coupling Torsion) (Smoothed CFF Bend Torsion Cross)
kθθ’/kB = -5243.093 (K/rad2)
θ0= 112.42790
θ'0= 173.76510
O-Si-O-Si Bend-Torsion-Bend (Bend Coupling Torsion) (Smoothed CFF Bend Torsion Cross)
kθθ’/kB = -2272.036 (K/rad2)
θ0= 112.02000
θ'0= 173.76510
Oa-Al-Oa-Si Bend-Torsion-Bend (Bend Coupling Torsion) (Smoothed CFF Bend Torsion Cross)
kθθ’/kB = -9067.208 (K/rad2)
θ0= 113.40000
θ'0= 162.40000
Oa-Si-Oa-Al Bend-Torsion-Bend (Bend Coupling Torsion) (Smoothed CFF Bend Torsion Cross)
kθθ’ /kB = -5499.131 (K/rad2)
θ0= 110.61200
θ'0= 162.40000
Nonbonded Potential Parameters (CFF 9-6 Potential: U (r )  p1  p2
r9 r6
Atom
p1/kB (K Å9)
p2/kB (K Å6)
q (e-)
Si
94057219.175
0.0
2.05
Al
10316687.74
0.0
1.75
O
40076506.50
0.0
-1.025
Oa
28891069.825
0.0
-1.2
Na
--
--
1.0
Ca
--
--
2.0
(1)
Nicholas, J. B.; Hopfinger, A. J.; Trouw, F. R.; Iton, L. E. J. Am. Chem. Soc. 1991, 113,
(2)
(3)
Hill, J. R.; Sauer, J. Journal of Physical Chemistry 1994, 98, 1238.
Hill, J. R.; Sauer, J. Journal of Physical Chemistry 1995, 99, 9536.
4792.