suppmat334. 33KB Jun 05 2011 09:30:47 PM
Supplemental Materials
Yin and MacKerell
Combined Ab initio/Empirical Approach for the Optimzation of Lennard-Jones Parameters
Table S1. Internal geometries for the selected alkanes
Calculated
Experimental1-4
ethane
C-H
1.112
C1-C2
1.533
H-C-H
108.3
H-C-C
110.6
propane
C1-H
1.111
C2-H
1.114
C1-C2
1.530
H-C1-H
108.4
H-C2-H
107.5
C-C-C
112.0
C-C2-H
109.3
C-C1-H
110.6
butane
C1-H
1.111
C2-H
1.114
C1-C2
1.531
C2-C3
1.533
C-C1-H
110.6
C-C2-H
108.7
C-C-C
113.4
Length unit: Å; angle unit: degree.
Numbers in parentheses are experimental errors.
1
Difference
1.112(0.001)
1.534(0.001)
107.5(1.0)
111.2(0.3)
0.000
-0.001
0.8
-0.6
1.107(0.005)
1.115
1.533(0.003)
107.8(0.2)
112.0(0.2)
-
0.003
-0.001
-0.003
-0.3
0.0
-
1.117(0.005)
1.117(0.005)
1.531
1.531
113.3(0.4)
-0.006
-0.003
0.000
0.002
0.1
Table S2. Comparison of calculated and experimental frequencies for ethane
#
Assignment
Calc.
Exp.5-7
1
C-C tor
306
279
2
CH3 rocking
922
822
3
CH3 rocking
922
822
4
C-C str
1002
995
5
CH3 rocking
1113
1190
6
CH3 rocking
1113
1190
7
CH3 asym def
1416
1370
8
CH3 asym def
1416
1388
9
CH3 asym def
1437
1469
10 CH3 asym def
1437
1469
11 CH3 sym def
1437
1460
12 CH3 sym def
1439
1460
13 CH3 sym str
2895
2915
14 CH3 sym str
2909
2915
15 CH3 asym str
2953
2950
16 CH3 asym str
2953
2950
17 CH3 asym str
2964
2974
18 CH3 asym str
2964
2974
Total average %difference
* %difference= ((calc.-exp.)/exp)*100
** average %difference including vibrational modes 1 to 12.
*** average %difference including vibrational modes 13 to 18.
Frequencies in cm-1.
2
%difference*
9.6
12.2
12.2
0.7
6.5
6.5
3.4
2.1
2.2
2.2
1.6
1.5
0.7
0.2
0.1
0.1
0.3
0.3
aver. %diff.
5.1**
0.3***
3.5
Table S3. Comparison of calculated and experimental frequencies for propane
#
Assignment
Calc.
Exp.5-7
1
CCCH tor
224
217
2
CCCH tor
258
265
3
CCC scissor
376
375
4
CH2 rocking
800
748
5
CC stretching
871
868
6
CH3 rocking
949
921
7
CH3 rocking
961
899
8
CC stretching
1062
1049
9
CH3 rocking
1089
1157
10
CH3 rocking
1096
1187
11
CH2 twisting
1214
1278
12
CH2 wagging
1381
1332
13
CH3 sym def
1412
1370
14
CH3 sym def
1412
1385
15
CH3 asym def
1421
16
CH3 asym def
1424
1449
17
CH3 asym def
1425
1459
18
CH3 asym def
1428
1464
19
CH2 scissor
1447
1473
20
CH3 sym str
2895
21
CH3 sym str
2901
2875
22
CH2 sym str
2909
2875
23
CH2 asym str
2929
2915
24
CH3 asym str
2958
2965
25
CH3 asym str
2958
2965
26
CH3 asym str
2960
27
CH3 asym str
2961
2965
Total average %difference
* %difference= ((calc.-exp.)/exp)*100
** average %difference including vibrational modes 13 to 18.
*** average %difference including vibrational modes 20 to 27.
Frequencies in cm-1.
3
%difference*
3.4
2.7
0.3
7.0
0.3
3.1
6.9
1.2
5.9
7.6
5.0
3.7
3.2
2.0
1.7
2.3
2.5
1.8
0.9
1.2
0.5
0.3
0.2
0.1
aver. %diff.
3.4**
0.5***
2.7
Table S4. Comparison of calculated and reference vibrational freqencies for butane
#
Assignment
Calc.
Exp.5-7
1
C2-C3 tor
122
121
2
C1-C2 tor
222
3
C3-C4 tor
258
266
4
CCC scissor
292
5
CCC scissor
394
427
6
CH2 rocking
746
733
7
CH2 rocking
831
8
C2C3 stretch
867
835
9
CH3 rocking
987
944
10
CH3 rocking
992
965
11
C2C3 str
1014
1010
12
C1C2(C3C4) str
1039
1053
13
CH3 rocking
1058
14
CH3 rocking
1109
1148
15
CH2 twisting
1164
1257
16
CH2 twisting
1204
1300
17
CH2 wagging
1294
1293
18
CH2 wagging
1353
19
CH3 sym def
1411
1455
20
CH3 sym def
1413
1455
21
CH3 asym def
1419
22
CH3 asym def
1425
1460
23
CH3 asym def
1426
1462
24
CH3 asym def
1426
1468
25
CH2 sci
1439
1375
26
CH2 sci
1444
1459
27
CH2 sym str
2893
2872
28
CH3 sym str
2898
2853
29
CH3 sym str
2904
2861
30
CH2 sym str
2910
2875
31
CH2 asym str
2924
2912
32
CH2 asym str
2934
2920
33
CH3 asym str
2959
2965
34
CH3 asym str
2959
2965
35
CH3 asym str
2959
2966
36
CH3 asym str
2960
2966
Total average %difference
* %difference= ((calc.-exp.)/exp)*100
** average %difference including vibrational modes 1 to 26.
*** average %difference including vibrational modes 26 to 36.
Frequencies in cm-1.
4
%difference
0.7
3.2
7.6
1.7
3.9
4.6
2.8
0.4
1.3
3.4
7.4
7.4
0.1
3.0
2.9
2.4
2.5
2.8
4.7
1.1
0.7
1.6
1.5
1.2
0.4
0.5
0.2
0.2
0.2
0.2
aver. %diff.
3.0**
0.7***
2.3
Table S5. Conformational energies in the selected alkanes
Experimental3,4,8-14
Calculated
ethane(HCCH)
2.90
propane(HCCC)
V1
V2
butane(CCCC)
180.
120.
60.
gauche(66.47)
0.
Energy unit: kcal/mol
2.88/2.93
3.12/3.13
3.58/3.64
3.12
3.84
0.0
3.47
0.91
0.83
5.22
0.75-0.97
5
Table S7. Alkane internal parameters
Bonds
Kb
b0
CT3 CT3
222.500
1.5300
CT3 CT2
222.500
1.5280
CT2 CT2
222.500
1.5300
H2 CT2
309.000
1.1110
H3 CT3
322.000
1.1110
H4 CT4
322.000
1.1110
Angles
Kθ
θ0
Kub
S0
CT2 CT2 CT2
58.350
113.60
11.16
2.561
CT3 CT2 CT2
58.000
115.00
8.00
2.561
H2 CT2 CT2
26.500
110.10
22.53
2.179
H2 CT2 CT3
34.600
110.10
22.53
2.179
H2 CT2 H2
35.500
109.00
5.40
1.802
H3 CT3 CT2
34.600
110.10
22.53
2.179
H3 CT3 CT3
37.500
110.10
22.53
2.179
H3 CT3 H3
35.500
108.40
5.40
1.802
H4 CT4 H4
35.500
108.40
5.40
1.802
Dihedrals
Kφ
n
δ
CT3 CT2 CT2 CT3
0.1300
1
0.00
X CT2 CT2 X
0.1900
3
0.00
X CT2 CT3 X
0.1600
3
0.00
X CT3 CT3 X
0.1525
3
0.00
L-J
ε
Rmin/2
CT4
0.095
2.11
CT3
0.078
2.04
CT2
0.056
2.01
H4
0.017
1.34
H3
0.024
1.34
H2
0.028
1.34
2
2
Kb: kcal/mol/Å ; Kθ: kcal/mol/degree ; Kub: kcal/mol/Å2; Kφ, ε: kcal/mol; length unit: Å; angle unit:
degree.
6
0.09 H4
0.09
H3 0.09
H3 0.09
H3
-0.36
CT 4
0.09
-0.27 CT3
H4 0.09
0.09
H4
H4 0.09
A
0.09 H3
0.09
H3
0.09
H2
0.09
H2
0.09 H3
H2 0.09
H2 0.09
0.09
0.09
-0.27
CT 3
H3 0.09
H3
CT3
CT 2 -0.18
-0.27
H3
-0.18 CT2
0.09 H2
0.09
H3 0.09
H3
B
-0.27
CT3 CT2 -0.18
0.09 H3
H3
0.09
CT 3 -0.27
H3
H3 0.09
C
D
H2
0.09
-0.27
CT 3
H3 0.09
H3 0.09
H3 0.09
Figure S1. Partial atomic charges and atomic types of the alkanes. A: methane; B: ethane; C: propane
and D: butane.
7
7
Potential Energy, kcal/mol
6
5
B
J
J
4
B
J
B
Ñ
J
3
J
Ñ
Ñ
Ñ
0
H
F
H
F
É
Å
Ç
É
Å
Ç
H
F
É
Å
Ç
J
Ñ
B
J
2
1
Ñ
J
B
J
Ñ
Ñ
Ñ
H
F
Å
É
Ç
B
J
J
H
Ñ
F
Ç
Å
É
Ñ
H
H
F
É
Ç
Å
F
Ç
Å
É
F
H
É
Ç
Å
F
H
Ç
É
Å
F
É
H
Ç
Å
F
É
Ç
Å
H
J
Ñ
F
É
Å
H
Ç
JB
H
F
Ñ
É
Ç
Å
-1
0
30
60
90
120
Dihedral Angle CCCC
150
180
Figure S2. Empirical and ab initio adiabatic energy surfacs for rotation about the CCCC
dihedral in butane. (B): ab initio HF/6-31G(d) (J): total empirical energy (H): electrostatic
(F): L-J (G):dihedral (E): angle (C): bond (A) Urey Bradley
8
115
120
113
118
J
111
B
B
J
J
J
J
J
B
B
B
B
B
B
B
B
B
B
B
109
Angle CCC
Angle HCC
J
J
B
116
B
J
B
B
J
B
114
B
B
J
B
B
J
B
B
J
B
B
J
112
107
110
105
0
30
60
90
120
150
Dihedral Angle HCCC
180
0
30
60
90
120
150
180
Dihedral Angle CCCC
Figure S3. HCC and CCC angle changes as a function of the HCCC and CCCC dihedral
angles, respectively. (B): empirical (J): ab initio..
9
Reference:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
Hoyland, J. R. I. Chem. Phys. 1969, 50, 2775.
Wiberg, K.; Boyd, R. H. J. Am. Chem. Soc. 1972, 94, 5236.
Heenan, P. K.; Bartell, L. S. J. Chem. Phys. 1983, 78, 1270.
Bradford, W. F.; Fitzwater, S.; Bartell, L. S. J. Mol. Struct. 1977, 38, 185.
Schachtschneider, J. H.; Snyder, R. G. Spectrochim. Acta 1963, 19, 117.
Snyder, R. G.; Schachtschneider, J. H. Spectrochim. Acta 1965, 21, 169.
Lifson, S.; Warshel, A. J. J. Chem. Phys. 1968, 49, 5116.
Aufderheide, K. Croat. Chem. Acta 1984, 57, 811.
Hirota, E.; Endo, Y.; Saito, S.; Duncan, J. L. J. Mol. Spectrosc. 1981, 89, 285.
Hirota, E.; Matsumara, C.; Morino, Y. Bull. Chem. Soc. Jpn. 1967, 40, 1124.
Hoyland, J. R. J. Chem. Phys. 1968, 49, 1908.
Compton, D. A.; Montrero, S.; Murphy, W. F. J. Phy. Chem. 1980, 84, 3587.
Rosenthal, L.; Robolt, J. F.; Hummel, J. J. Chem. Phys. 1982, 76, 617.
Banon, A.; Serrano Adan, F.; Santamaris, J. J. Chem. Phys. 1985, 83, 297.
Shipman, L. L.; Burgess, A. W.; Scherage, H. A. J. Phys. Chem. 1976, 80, 52.
10
Yin and MacKerell
Combined Ab initio/Empirical Approach for the Optimzation of Lennard-Jones Parameters
Table S1. Internal geometries for the selected alkanes
Calculated
Experimental1-4
ethane
C-H
1.112
C1-C2
1.533
H-C-H
108.3
H-C-C
110.6
propane
C1-H
1.111
C2-H
1.114
C1-C2
1.530
H-C1-H
108.4
H-C2-H
107.5
C-C-C
112.0
C-C2-H
109.3
C-C1-H
110.6
butane
C1-H
1.111
C2-H
1.114
C1-C2
1.531
C2-C3
1.533
C-C1-H
110.6
C-C2-H
108.7
C-C-C
113.4
Length unit: Å; angle unit: degree.
Numbers in parentheses are experimental errors.
1
Difference
1.112(0.001)
1.534(0.001)
107.5(1.0)
111.2(0.3)
0.000
-0.001
0.8
-0.6
1.107(0.005)
1.115
1.533(0.003)
107.8(0.2)
112.0(0.2)
-
0.003
-0.001
-0.003
-0.3
0.0
-
1.117(0.005)
1.117(0.005)
1.531
1.531
113.3(0.4)
-0.006
-0.003
0.000
0.002
0.1
Table S2. Comparison of calculated and experimental frequencies for ethane
#
Assignment
Calc.
Exp.5-7
1
C-C tor
306
279
2
CH3 rocking
922
822
3
CH3 rocking
922
822
4
C-C str
1002
995
5
CH3 rocking
1113
1190
6
CH3 rocking
1113
1190
7
CH3 asym def
1416
1370
8
CH3 asym def
1416
1388
9
CH3 asym def
1437
1469
10 CH3 asym def
1437
1469
11 CH3 sym def
1437
1460
12 CH3 sym def
1439
1460
13 CH3 sym str
2895
2915
14 CH3 sym str
2909
2915
15 CH3 asym str
2953
2950
16 CH3 asym str
2953
2950
17 CH3 asym str
2964
2974
18 CH3 asym str
2964
2974
Total average %difference
* %difference= ((calc.-exp.)/exp)*100
** average %difference including vibrational modes 1 to 12.
*** average %difference including vibrational modes 13 to 18.
Frequencies in cm-1.
2
%difference*
9.6
12.2
12.2
0.7
6.5
6.5
3.4
2.1
2.2
2.2
1.6
1.5
0.7
0.2
0.1
0.1
0.3
0.3
aver. %diff.
5.1**
0.3***
3.5
Table S3. Comparison of calculated and experimental frequencies for propane
#
Assignment
Calc.
Exp.5-7
1
CCCH tor
224
217
2
CCCH tor
258
265
3
CCC scissor
376
375
4
CH2 rocking
800
748
5
CC stretching
871
868
6
CH3 rocking
949
921
7
CH3 rocking
961
899
8
CC stretching
1062
1049
9
CH3 rocking
1089
1157
10
CH3 rocking
1096
1187
11
CH2 twisting
1214
1278
12
CH2 wagging
1381
1332
13
CH3 sym def
1412
1370
14
CH3 sym def
1412
1385
15
CH3 asym def
1421
16
CH3 asym def
1424
1449
17
CH3 asym def
1425
1459
18
CH3 asym def
1428
1464
19
CH2 scissor
1447
1473
20
CH3 sym str
2895
21
CH3 sym str
2901
2875
22
CH2 sym str
2909
2875
23
CH2 asym str
2929
2915
24
CH3 asym str
2958
2965
25
CH3 asym str
2958
2965
26
CH3 asym str
2960
27
CH3 asym str
2961
2965
Total average %difference
* %difference= ((calc.-exp.)/exp)*100
** average %difference including vibrational modes 13 to 18.
*** average %difference including vibrational modes 20 to 27.
Frequencies in cm-1.
3
%difference*
3.4
2.7
0.3
7.0
0.3
3.1
6.9
1.2
5.9
7.6
5.0
3.7
3.2
2.0
1.7
2.3
2.5
1.8
0.9
1.2
0.5
0.3
0.2
0.1
aver. %diff.
3.4**
0.5***
2.7
Table S4. Comparison of calculated and reference vibrational freqencies for butane
#
Assignment
Calc.
Exp.5-7
1
C2-C3 tor
122
121
2
C1-C2 tor
222
3
C3-C4 tor
258
266
4
CCC scissor
292
5
CCC scissor
394
427
6
CH2 rocking
746
733
7
CH2 rocking
831
8
C2C3 stretch
867
835
9
CH3 rocking
987
944
10
CH3 rocking
992
965
11
C2C3 str
1014
1010
12
C1C2(C3C4) str
1039
1053
13
CH3 rocking
1058
14
CH3 rocking
1109
1148
15
CH2 twisting
1164
1257
16
CH2 twisting
1204
1300
17
CH2 wagging
1294
1293
18
CH2 wagging
1353
19
CH3 sym def
1411
1455
20
CH3 sym def
1413
1455
21
CH3 asym def
1419
22
CH3 asym def
1425
1460
23
CH3 asym def
1426
1462
24
CH3 asym def
1426
1468
25
CH2 sci
1439
1375
26
CH2 sci
1444
1459
27
CH2 sym str
2893
2872
28
CH3 sym str
2898
2853
29
CH3 sym str
2904
2861
30
CH2 sym str
2910
2875
31
CH2 asym str
2924
2912
32
CH2 asym str
2934
2920
33
CH3 asym str
2959
2965
34
CH3 asym str
2959
2965
35
CH3 asym str
2959
2966
36
CH3 asym str
2960
2966
Total average %difference
* %difference= ((calc.-exp.)/exp)*100
** average %difference including vibrational modes 1 to 26.
*** average %difference including vibrational modes 26 to 36.
Frequencies in cm-1.
4
%difference
0.7
3.2
7.6
1.7
3.9
4.6
2.8
0.4
1.3
3.4
7.4
7.4
0.1
3.0
2.9
2.4
2.5
2.8
4.7
1.1
0.7
1.6
1.5
1.2
0.4
0.5
0.2
0.2
0.2
0.2
aver. %diff.
3.0**
0.7***
2.3
Table S5. Conformational energies in the selected alkanes
Experimental3,4,8-14
Calculated
ethane(HCCH)
2.90
propane(HCCC)
V1
V2
butane(CCCC)
180.
120.
60.
gauche(66.47)
0.
Energy unit: kcal/mol
2.88/2.93
3.12/3.13
3.58/3.64
3.12
3.84
0.0
3.47
0.91
0.83
5.22
0.75-0.97
5
Table S7. Alkane internal parameters
Bonds
Kb
b0
CT3 CT3
222.500
1.5300
CT3 CT2
222.500
1.5280
CT2 CT2
222.500
1.5300
H2 CT2
309.000
1.1110
H3 CT3
322.000
1.1110
H4 CT4
322.000
1.1110
Angles
Kθ
θ0
Kub
S0
CT2 CT2 CT2
58.350
113.60
11.16
2.561
CT3 CT2 CT2
58.000
115.00
8.00
2.561
H2 CT2 CT2
26.500
110.10
22.53
2.179
H2 CT2 CT3
34.600
110.10
22.53
2.179
H2 CT2 H2
35.500
109.00
5.40
1.802
H3 CT3 CT2
34.600
110.10
22.53
2.179
H3 CT3 CT3
37.500
110.10
22.53
2.179
H3 CT3 H3
35.500
108.40
5.40
1.802
H4 CT4 H4
35.500
108.40
5.40
1.802
Dihedrals
Kφ
n
δ
CT3 CT2 CT2 CT3
0.1300
1
0.00
X CT2 CT2 X
0.1900
3
0.00
X CT2 CT3 X
0.1600
3
0.00
X CT3 CT3 X
0.1525
3
0.00
L-J
ε
Rmin/2
CT4
0.095
2.11
CT3
0.078
2.04
CT2
0.056
2.01
H4
0.017
1.34
H3
0.024
1.34
H2
0.028
1.34
2
2
Kb: kcal/mol/Å ; Kθ: kcal/mol/degree ; Kub: kcal/mol/Å2; Kφ, ε: kcal/mol; length unit: Å; angle unit:
degree.
6
0.09 H4
0.09
H3 0.09
H3 0.09
H3
-0.36
CT 4
0.09
-0.27 CT3
H4 0.09
0.09
H4
H4 0.09
A
0.09 H3
0.09
H3
0.09
H2
0.09
H2
0.09 H3
H2 0.09
H2 0.09
0.09
0.09
-0.27
CT 3
H3 0.09
H3
CT3
CT 2 -0.18
-0.27
H3
-0.18 CT2
0.09 H2
0.09
H3 0.09
H3
B
-0.27
CT3 CT2 -0.18
0.09 H3
H3
0.09
CT 3 -0.27
H3
H3 0.09
C
D
H2
0.09
-0.27
CT 3
H3 0.09
H3 0.09
H3 0.09
Figure S1. Partial atomic charges and atomic types of the alkanes. A: methane; B: ethane; C: propane
and D: butane.
7
7
Potential Energy, kcal/mol
6
5
B
J
J
4
B
J
B
Ñ
J
3
J
Ñ
Ñ
Ñ
0
H
F
H
F
É
Å
Ç
É
Å
Ç
H
F
É
Å
Ç
J
Ñ
B
J
2
1
Ñ
J
B
J
Ñ
Ñ
Ñ
H
F
Å
É
Ç
B
J
J
H
Ñ
F
Ç
Å
É
Ñ
H
H
F
É
Ç
Å
F
Ç
Å
É
F
H
É
Ç
Å
F
H
Ç
É
Å
F
É
H
Ç
Å
F
É
Ç
Å
H
J
Ñ
F
É
Å
H
Ç
JB
H
F
Ñ
É
Ç
Å
-1
0
30
60
90
120
Dihedral Angle CCCC
150
180
Figure S2. Empirical and ab initio adiabatic energy surfacs for rotation about the CCCC
dihedral in butane. (B): ab initio HF/6-31G(d) (J): total empirical energy (H): electrostatic
(F): L-J (G):dihedral (E): angle (C): bond (A) Urey Bradley
8
115
120
113
118
J
111
B
B
J
J
J
J
J
B
B
B
B
B
B
B
B
B
B
B
109
Angle CCC
Angle HCC
J
J
B
116
B
J
B
B
J
B
114
B
B
J
B
B
J
B
B
J
B
B
J
112
107
110
105
0
30
60
90
120
150
Dihedral Angle HCCC
180
0
30
60
90
120
150
180
Dihedral Angle CCCC
Figure S3. HCC and CCC angle changes as a function of the HCCC and CCCC dihedral
angles, respectively. (B): empirical (J): ab initio..
9
Reference:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
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10