1 FORCE FIELD OPTIMIZATION for FLUOROCARBON Seung Soon Jang
1
FORCE FIELD OPTIMIZATION for FLUOROCARBON
Seung Soon Jang
2
Optimization of van der Waals parametersof Fluorine
2. Crystal structure (A.N. Fitch et al., Z. Kristallogr. 203, 29 (1993))
Density=2.2249 g/cm3 (T=1.5 K)
Tetrafluoromethane (CF4 )
3. Enthalpy of sublimation (A. Bondi, J. Chem. Eng. Data 8, 371 (1963), A. Eucken et al., J. Phys. Chem. 41B, 307 (1938))
Hsub=4.06 kcal/mol at 76 K
4. Isothermal compressibility (J. W. Stewart et al., J. Chem. Phys. 28, 425 (1958))
5. Thermal expansion (D. N. Bol’Shutkin et al., Acta Cryst. B28, 3542 (1972))
1. Frequency (X.-G. Wang et al., J. Chem. Phys.112, 1353 (2000))
6
0
00 6
16
6
R
R
R
RexpDREvdW
Exponential-6 function:
3
a Experimental density @ T=1.5 K is 2.2249 g/cm3.b Experimental Hsub @ T=76 K is 4.06 kcal/mol.
Van der Waals parameters of exponential-6 Density
(g/cm3)a Hsub
(kcal/mol)b
D0 R0
C 12 0.08440 3.8837
F
12 0.04453 3.4985 2.2247 0.0475
4.06
13 0.04720 3.4480 2.2252 0.0413
4.07
14 0.04935 3.4112 2.2244 0.0389
4.06
15 0.05092 3.3825 2.2243 0.0360
4.06
16 0.05246 3.3589 2.2253 0.0349
4.06
van der Waals Parameters for C and F
4
Pressure (GPa)
0.0 0.5 1.0 1.5 2.0
Co
mp
ress
ibili
ty (
Pa-1
at
77K
)
0.0
5.0e-11
1.0e-10
1.5e-10
2.0e-10
2.5e-10
3.0e-10
3.5e-10
Stewart (Experiment @ 77 K)y=12y=13y=14y=15y=16
Stewart (Experiment @ 77 K)=12=13=14=15=16
Isothermal CompressibilityTP
V
V
1
The best fit for experimental result
11
2
332
035
037
0
0
///
V
V
V
V
V
VP
where 0: compressibility at zero pressure V0: molar volume at zero pressure : an adjustable parameter
Compressibility curves were obtained by differentiating Murnaghan’s equation of state which were fitted to the each MD simulation result.
Murnaghan’s equation of state
5
R0 D0
C 3.8837 0.08440 12.0000
old F 3.5380 0.02110 16.0000
new F 3.3825 0.05092 15.0000
Thermal expansion
Temperature (K)
0 20 40 60 80
Mo
lar
volu
me
(cm
3)
35
40
45
50
55
Bol'Shutkin et al. (experiment)Fitch (experiment) New F parameter setOld F parameter set
The calculated thermal expansion is in good agreement with the experimental observation.
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Optimization of Valence Force Field
Hessian-biased optimization method
ii R
EF
N
j,iji
ji
N
ii
i
RRRR
ER
R
EEE
3
1 0
23
1 00 Expansion of energy of molecule
jiij RR
EH
2
The first derivative of energy: force on atom i-th component
The second derivative of energy: Hessian .
The mass-weighted Hessian:
H21 /
ji
ijij
MM
HH
The vibrational eigenfunctions are obtained from the eigenvalue equation:
N,,,i,UU iiQMQM 3212 H
If the experimental frequency set is available, we can replace theoretical frequency set by experimental one.
tQMQM UUH
texpexp&QM UUH exp&QM/ji
exp&QM MM HH 21
The force field is determined to minimize the difference between HFF from force field and HQM&exp.
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1. Bond stretch
Harmonic 202
1RRKRE bb
Kb R0 C-C 422.7245 1.5224 F-C 535.4583 1.3354
2. Valence angle bend
Cosine harmonic
02
202
1
sinCK
coscosCEa
K 0
C-C-C 220.8724 120.0000F-C-C 129.3900 120.0000 F-C-F 160.8744 120.0000
Valence Force Field
3. Dihedral angle torsion
Dihedral ncosdKE n,dd 12
1 Kd,n d nC-C-C-C 3.5464 1 3F-C-C-C 3.5470 1 3F-C-C-F 2.2211 -1 3
8
Validation of Force Field
geometry Quantum mechanics Molecular mechanics6-31G* & B3LYPNew Force FieldClockwise1 -165.0 -164.9helicity2 -163.2 -163.2trans minus)3 -165.0 -164.9
Counterclockwise1165.0 164.9helicity2 163.2 163.2(trans plus)3 165.0 164.9
1 23
RMS difference of atomic position:0.0346 Å
Helical conformation of C6F14
9
Validation of Force Field: Conformational Energy
Helical conformation and energy barrier between two energy minima were successfully reproduced.Dihedral angle (degree)
140 160 180 200 220
Energy (kca
l/mol)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6Quantum calculationForce Field
D ih e d ra l a n g le (d e g re e )
1 4 0 1 6 0 1 8 0 2 0 0 2 2 0
En
erg
y (k
cal/m
ol)
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
1 .4
1 .6Q u a n tu m c a lc u la t io nF o rc e F ie ld
Transplus
Transminus
10
Validation of Force Field
C2F6 C3F8 C4F10
RefMulliken
QESP Q Ref
Mulliken Q
ESP Q RefMulliken
QESP Q
Density
(g/cm3)1.60
1.66
± 0.03
1.63
± 0.071.61
1.66
± 0.05
1.61
± 0.061.60
1.65
± 0.06
1.59
± 0.06
Solubility parameter(cal/cm3)0.5
6.33
± 0.19
6.76
± 0.22
6.56
± 0.49
6.02
± 0.60
6.41
± 0.31
6.24
± 0.28
5.76
± 0.29
6.24
± 0.23
5.88
± 0.23
Density and Solubility Parameter of small fluorocarbons
5050 .
m
vap.
m
m
V
RTH
V
U
Reference data from database of Design Institute for Physical Property Data (DIPPR) Project 801, American Institute of Chemical Engineers (AIChE)