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.

6

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.

7

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)