Supporting Information for:
An extension of the Universal Force Field to Metal-Organic Frameworks
Matthew A. Addicoat, Nina Vankova, Ismot Farjana Akter, Thomas Heine*
School of Engineering and Science, Jacobs University Bremen
Campus Ring 1, 28759 Bremen, Germany
*email: [email protected]
Section 1: Covalent radii scans
SI-1.1 Zn4O SBU
Figure S1.1: Optimized metal-metal (black), metal-Ocent (red) and metal-Ocarb (blue)
bond lengths as a function of the covalent radius of the metal atom. Reference (see
text for details) bond lengths are indicated as dashed horizontal lines of the same
colour.
1
SI-1.2 Trimeric oxo-centered SBU
2
3
Figure S1.2: Optimized metal-metal (black), metal-Ocent (red) and metal-Ocarb (blue)
bond lengths as a function of the covalent radius of the metal atom. Reference (see
text for details) bond lengths are indicated as dashed horizontal lines of the same
colour.
4
SI-1.3 MIL-53 SBU
5
Figure S1.3: Optimized metal-metal (black), metal-Ocarb (red) and metal-Ohyd (blue)
bond lengths as a function of the covalent radius of the metal atom. Reference (see
text for details) bond lengths are indicated as dashed horizontal lines of the same
colour.
6
SI-1.4-1 Bare Paddlewheel SBU
7
8
9
10
Figure S1.4-1: Optimized metal-metal (black) and metal-O (red) bond lengths as a
function of the covalent radius of the metal atom. Reference (see text for details)
bond lengths are indicated as dashed horizontal lines of the same colour.
SI-1.4-2 Pyridine capped (pillared) Paddlewheel SBU
11
12
13
14
Figure S1.4-2: Optimized metal-metal (black), metal-O (red) and metal-N (blue) bond
lengths as a function of the covalent radius of the metal atom. Reference (see text
for details) bond lengths are indicated as dashed horizontal lines of the same colour.
15
SI-1.5 MFU-4 (Kuratowski-type) SBU
Figure S1.5: Optimized Cooct-N (black), Cotet-N (red) and Cotet-Cl (blue) bond lengths
as a function of the covalent radius of the cobalt atom. Reference (see text for
details) bond lengths are indicated as dashed horizontal lines of the same colour.
16
Section 2: Standard UFF parameters for linker geometries
17
Figure S2.1-2: UFF geometrical parameters for common linker and pillar molecules,
(DFT data at the BP86/TZP small core level in parentheses).
18
Section 3: Zn4O SBU
Figure S3.1: Optimized metal-metal (black), metal-Ocent (red) and metal-Ocarb (blue)
bond lengths as a function of the covalent radius of the metal atom. Scan
undertaken using GULP and employing a bond order of 0.25 between Zn atoms.
Reference (see text for details) bond lengths are indicated as dashed horizontal lines
of the same colour.
19
Section 4: Re-optimized UFF4MOF parameters with respect to the experimental
MIL-53 SBUs
Table S1 UFF derived structural characteristics (bond lengths and angles), experimental reference
data in parentheses (see the paper for the citations), and calculated maximum percent errors for the
MIL-53 type SBU. The UFF4MOF force field parameters of the type M_6+3 for M = Al, Sc, and Fe and
Cr6f3 for Cr were re-optimized with respect to the experimental MIL-53 SBU geometries and the
thusly chosen values of the M covalent radius are shown in the 2nd column of the table. Standard O_2
C_R and H_ parameters for non-metal atoms (taken from Rappé et al., J. Am. Chem. Soc. 1992) and
bond orders as shown in Fig. 3a in the paper were employed in the calculations.
Metalcenter
Covalent
radius
[Å]
M–M
[Å]
AlIII
1.18
3.37
(3.38)
ScIII
1.44
3.64
(3.65)
CrIII
1.24
Fe6III
1.26
M–Ocarb
M–Ohyd
M–Ohyd–M
Ohyd–M–Ohyd
M–Ocarb–C
[Å]
[Å]
[degree]
[degree]
[degree]
1.93
(1.92)
1.90
(1.89)
124.9
(126.8)
180.0
(179.2)
134.3
(133.4)
2.16
(2.13)
2.11
(2.12/2.06)
119.5
(122.9)
180.0
(176.8)
136.3
(135.0)
3.42
(3.41)
1.98
(1.96)
1.95
(1.95)
123.7
(121.7)
180.0
(180.0)
134.7
(138.8)
Max % error a
3.47
(3.44)
0.87
2.02
(2.01)
1.41
1.98
(1.99)
0.53
122.9
(124.6)
-2.8
180.0
(180.0)
1.8
135.1
(134.9)
-3.0
for
Fe
Sc
Al
Sc
Sc
Cr
a
The maximum % errors are derived after calculating all % errors for the MIL-53 type SBU series. The
% errors are calculated as (XUFF–XExperiment)/XExperiment×100, where XUFF denotes the UFF-predicted and
XExperiment denotes the experimental values of respective bond lengths and angles.
20
Section 5: Comparison of UFF and DFT predicted structural characteristics of the
studied SBUs
Table S2 Comparison of structural characteristics (bond lengths and angles) as predicted by UFF and
DFT (in parentheses) for the trimeric oxo-centered SBU M3O(CO2H)6. The multiplicity, M = (2S + 1),
used in the DFT calculations, and calculated maximum percent errors with respect to DFT are also
shown. Force field parameters employed were M_6+3 for M = Al, Sc, V, Mn and Fe, Cr6f3 for CrIII,
O_2_z for Ocent (UFF4MOF atom types, see Table 1 in the paper), O_2 for Ocarb, C_R and H_ (taken
from Rappé et al., J. Am. Chem. Soc. 1992); bond orders as shown in Fig. 2a in the paper.
Metal
center
M
M–M
M–Ocent
M–Ocarb
M–Ocent–M Ocent–M–Ocarb
M–Ocarb–C
(DFT)
[Å]
[Å]
[Å]
[degree]
[degree]
[degree]
Ocarb–M–
Ocarb(trans)
[degree]
III
Al
1
3.16
(3.04)
1.82
(1.77)
1.89
(1.89)
120.1
(120.0)
95.6
(99.9)
134.2
(127.4)
169.1
(160.1)
ScIII
1
3.34
(3.43)
1.93
(1.98)
2.14
(2.10)
120.1
(120.0)
95.3
(95.0)
133.8
(133.3)
169.6
(170.0)
VIII
7
3.21
(3.24)
1.85
(1.87)
2.03
(1.99)
120.0
(120.0)
96.2
(97.1)
133.0
(130.6)
167.9
(165.8)
CrIII
10
3.20
(3.23)
1.85
(1.86)
2.01
(1.97)
120.0
(118.8)
96.1
(97.1)
133.3
(130.2)
168.1
(165.8)
MnIII
13
FeIII
16
3.26
1.88
2.06
120.0
95.7
133.6
168.9
(3.28/3.35) (1.78/1.98) (1.97/1.99) (122.0/116.2) (97.3/95.8) (130.6/130.3) (165.5/168.3)
Max %
error a
for
3.27
(3.30)
3.95
1.89
(1.90)
2.82
2.07
(2.01)
4.04
120.1
(120.0)
1.6
95.6
(96.5)
-4.3
133.6
(130.9)
5.3
168.9
(167.0)
5.6
Al
Al
Mn
Mn
Al
Al
Al
a
The maximum % errors are derived after calculating all % errors for the M3O(CO2H)6 series. The %
errors are calculated as (XUFF–XDFT)/XDFT×100, where XUFF denotes the UFF-predicted and XDFT denotes
the DFT-predicted value of respective bond lengths and angles.
Table S3 Comparison of structural characteristics (bond lengths and angles) as predicted by UFF and
DFT (in parentheses) for the MIL-53 type SBU. The multiplicity, M = (2S + 1), used in the DFT
calculations, and calculated maximum percent errors with respect to DFT are also shown. Force field
parameters employed were M_6+3 for M = Al, Sc, V, Mn and Fe (UFF4MOF atom types, see Table 1 in
the paper), O_2 C_R and H_ (taken from Rappé et al., J. Am. Chem. Soc. 1992); bond orders as shown
in Fig. 3a in the paper.
Metal
center
M
(DFT)
M–M
[Å]
M–Ocarb
[Å]
M–Ohyd
[Å]
M–Ohyd–M
[degree]
Ohyd–M–Ohyd
[degree]
M–Ocarb–C
[degree]
AlIII
ScIII
CrIII
FeIII
1
1
13
5
3.42 (3.34)
3.64 (3.66)
3.48 (3.45)
3.55 (3.34)
1.98 (1.94)
2.16 (2.15)
2.02 (1.96)
2.08 (1.92)
1.94 (1.86)
2.11 (2.08)
1.98 (1.98)
1.88 (1.89)
123.9 (126.2)
119.5 (122.3)
122.7 (121.6)
121.4 (125.1)
180.0 (179.1)
180.0 (179.4)
180.0 (179.4)
180.0 (179.1)
134.7 (131.6)
136.3 (137.5)
135.1 (132.8)
135.7 (129.4)
6.29
Fe
8.33
Fe
7.94
Fe
-3.0
Fe
0.5
Al and Fe
4.9
Fe
Max % error a
for
a
The maximum % errors are derived after calculating all % errors for the MIL-53 type SBU series. The
% errors are calculated as (XUFF–XDFT)/XDFT×100, where XUFF denotes the UFF-predicted and XDFT
denotes the DFT-predicted value of respective bond lengths and angles.
21
Table S4 UFF derived structural characteristics (bond lengths and angles), DFT reference data in
parentheses, and calculated percent errors for bare M2(CO2H)4 paddlewheels with M = CuII and ZnII.
The UFF calculations include partial charges of +2 per each metal center and -0.5 per each O atom.
Force field parameters employed were M_4+2 for M = CuII and ZnII (UFF4MOF atom types, see Table
1), O_2, C_R and H_ (taken from Rappé et al., J. Am. Chem. Soc. 1992); M-O, C-O and C-H bond orders
as shown in Fig. 4a in the paper.
Metal
center
CuII
ZnII
M–M
M
bond order
(DFT)b
(UFF)
no bond
3
no bond
1
M–M
[Å]
M–O
[Å]
O–M–O (trans)
[degree]
O–M–M
[degree]
C–O–M
[degree]
2.60 (2.47)
2.65 (2.54)
2.02 (1.98)
2.04 (2.04)
169.5 (175.2)
168.0 (173.2)
84.6 (88.0)
83.9 (86.6)
124.4 (117.6)
125.5 (119.0)
5.26
4.33
2.02
0.00
-3.3
-3.0
-3.9
-3.1
5.8
5.5
% error for Cua
% error for Zna
a
calculated as (XUFF–XDFT)/XDFT×100, where XUFF denotes UFF-predicted and XDFT denotes DFT-predicted
values of the respective bond lengths and angles; b M is the multiplicity of the M2(CO2H)4 paddlewheel
SBU, as used in the respective DFT calculation, and is given by the relation M = 2S + 1, where S is the
total spin of the system
Table S5 UFF derived structural characteristics (bond lengths and angles), DFT reference data in
parentheses, and calculated percent errors for pillared M2(CO2H)4(C5H5N)2 paddlewheels with M = CuII
and ZnII. The UFF calculations include partial charges of +2 per each metal center and -0.5 per each O
atom. Force field parameters employed were M_4+2 for M = CuII and ZnII (UFF4MOF atom types, see
Table 1), O_2, C_R, M-N and H_ (taken from Rappé et al., J. Am. Chem. Soc. 1992); M-O, C-O and C-H
bond orders as shown in Fig. 4c.
Metal
center
CuII
ZnII
M–M
M
bond order (DFT)b
(UFF)
no bond
3
no bond
1
% error for Cua
% error for Zna
M–M
[Å]
M–O
[Å]
M–N
[Å]
O–M–O (trans)
[degree]
O–M–M
[degree]
C–O–M
[degree]
O–M–N
[degree]
2.52
(2.60)
2.02
(2.01)
2.14
(2.21)
171.8
(171.4)
85.8
(85.7)
123.3
(119.7)
94.2
(94.3)
2.55
(2.82)
-3.08
-9.57
2.04
(2.08)
0.50
-1.92
2.19
(2.08)
-3.17
5.29
170.9
(165.3)
0.2
3.4
85.3
(82.7)
0.1
3.1
124.0
(122.9)
3.0
0.9
94.7
(97.3)
-0.1
-2.7
a
calculated as (XUFF–XDFT)/XDFT×100, where XUFF denotes UFF-predicted and XDFT denotes DFT-predicted
values of the respective bond lengths and angles; b M is the multiplicity of the M2(CO2H)4(C5H5N)2
paddlewheel SBU, as used in the respective DFT calculation, and is given by the relation M = 2S + 1,
where S is the total spin of the system
Tabble S6 UFF derived structural characteristics (bond lengths and angles), DFT reference data and
calculated percent errors for the Kuratowski-type SBU of MFU-4l(Co4Zn). Force field parameters
employed were Co3+2 and Zn3f2 for Mtet = CoII and ZnII, resp., and M_4+2 for Moct = ZnII (UFF4MOF
atom types, see Table 1), C_R, N_R, Cl and H_ (taken from Rappé et al., J. Am. Chem. Soc. 1992); bond
orders as shown in Fig. 5a. (Moct is ZnII, Mtet is CoII).
Selected structural
characteristics
Znoct–N [Å]
UFF
DFTa
2.17
2.08
4.3
Cotet–N [Å]
2.01
1.97
2.03
Cotet–Cl [Å]
2.01
2.13
-5.63
N–Znoct–N [degree]
90.0
90
0.0
% Error w.r.t. DFTb
22
N–Cotet–N [degree]
101.2
95.6
5.9
N–Cotet–Cl [degree]
116.9
121.2
-3.5
a
calculated as (XUFF–XDFT)/XDFT×100, where XUFF denotes UFF-predicted and XDFT denotes DFTpredicted values of respective bond lengths and angles.
23