FORCE FIELD OPTIMIZATION for FLUOROCARBON
Seung Soon Jang
1
Optimization of van der Waals parameters
of Fluorine
6

R      R0   
 6   

Exponential-6 function: EvdW R   D0 
 exp  1     
   
  6    R0      6  R   


Tetrafluoromethane (CF4 )
1. Frequency (X.-G. Wang et al., J. Chem. Phys.112, 1353 (2000))
2. Crystal structure (A.N. Fitch et al., Z. Kristallogr. 203, 29 (1993))
Density=2.2249 g/cm3 (T=1.5 K)
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))
2
van der Waals Parameters for C and F
Van der Waals parameters of
exponential-6
C
F
Density
(g/cm3)a
Hsub
(kcal/mol)b

D0
R0
12
0.08440
3.8837
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
a Experimental density @ T=1.5 K is 2.2249 g/cm3.
b Experimental Hsub @ T=76 K is 4.06 kcal/mol.
3
Isothermal Compressibility    1  V 
V  P T
Compressibility curves were obtained by differentiating Murnaghan’s
equation of state which were fitted to the each MD simulation result.
Compressibility (Pa-1 at 77K)
3.5e-10
Murnaghan’s equation of state
3.0e-10
Stewart (Experiment @ 77 K)
7/3
y=12
0
0
y=13
y=14
y=15
0
y=16
3  V 
P
 
2   V 
2.5e-10
V 
 
V 
5 / 3 
2/ 3


 V0 

 1      1


 
 V 

2.0e-10
where 0: compressibility at zero pressure
V0: molar volume at zero pressure
: an adjustable parameter
1.5e-10
1.0e-10
5.0e-11
0.0
0.0
0.5
1.0
1.5
2.0
Pressure (GPa)
Stewart (Experiment @ 77 K)
=12
=13
=14
=15
=16
The best fit for experimental result
4
Thermal expansion
3
Molar volume (cm )
55
Bol'Shutkin et al. (experiment)
Fitch (experiment)
New F parameter set
Old F parameter set
50
45
The calculated thermal expansion is in
good agreement with the experimental
observation.
40
35
0
20
40
60
80
Temperature (K)
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
5
Optimization of Valence Force Field
Hessian-biased optimization method
Expansion of energy of molecule
2
3N 
E 

E 
 Ri   
E  E0   
RiR j  



R

R

R
i 1 
i , j 1 
i 0
i
j
3N 
0
The first derivative of energy: force on atom i-th component
The second derivative of energy: Hessian
2E
.
H ij 
Ri R j
Fi 
E
Ri
H ij 
H ij
M i M j 1 / 2
H
The mass-weighted Hessian:
The vibrational eigenfunctions are obtained from the eigenvalue equation:

HQM U  UQM i  i2 , i  1,2,,3N

H QM  UQM U t
If the experimental frequency set is available, we can replace theoretical frequency set by
experimental one.
H QM &exp  UexpU t

H QM &exp  M i M j
1 / 2 H QM &exp
The force field is determined to minimize the difference between HFF from
force field and HQM&exp.
6
Valence Force Field
1. Bond stretch
Harmonic
1
Eb R   K b R  R0 2
2
C-C
F-C
Kb
422.7245
535.4583
R0
1.5224
1.3354
2. Valence angle bend
Cosine harmonic
1
Ea    C cos  cos 0 2
2
K  C sin 2  0
C-C-C
F-C-C
F-C-F
0
120.0000
120.0000
120.0000
K
220.8724
129.3900
160.8744
3. Dihedral angle torsion
1
Dihedral Ed    K d ,n 1  d cos n 
2
C-C-C-C
F-C-C-C
F-C-C-F
Kd,n
3.5464
3.5470
2.2211
d
1
1
-1
n
3
3
3
7
Helical conformation of C6F14
Validation of Force Field
f1
f2
f3
geometry
Quantum mechanics
6-31G* & B3LYP
Molecular mechanics
New Force Field
Clockwise
helicity
trans minus)
f1
f2
f3
-165.0
-163.2
-165.0
-164.9
-163.2
-164.9
Counterclockwise
helicity
(trans plus)
f1
f2
f3
165.0
163.2
165.0
164.9
163.2
164.9
RMS difference of atomic position:
0.0346 Å
8
Validation of Force Field: Conformational Energy
f
1.6
Quantum calculation
Force Field
Energy
(kcal/mol)
Energy
(kcal/mol)
1.4
1.6
Quantum calculation
Force Field
1.2
1.4
1.0
1.2
0.8
1.0
0.6
0.8
Trans
plus
Trans
minus
0.4
0.6
0.2
0.4
0.0
0.2
140
0.0
140
160
180
200
220
Dihedral angle (degree)
160
180
200
220
Helical conformation and energy barrier between two energy minima were
Dihedral angle (degree)
successfully reproduced.
9
Validation of Force Field
Density and Solubility Parameter of small fluorocarbons
 U 
    m 
 Vm 
0.5
 H vap  RT 

 
V
m


C2F6
Density
(g/cm3)
Solubility
parameter
(cal/cm3)0.5
0.5
C3F8
C4F10
Ref
Mulliken
Q
ESP Q
Ref
Mulliken
Q
ESP Q
Ref
Mulliken
Q
ESP Q
1.60
1.66
± 0.03
1.63
± 0.07
1.61
1.66
± 0.05
1.61
± 0.06
1.60
1.65
± 0.06
1.59
± 0.06
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
Reference data from database of Design Institute for Physical Property Data (DIPPR) Project 801,
American Institute of Chemical Engineers (AIChE)
10