1. 1 F ORCE F IELD O PTIMIZATION for F LUOROCARBON Seung Soon Jang

2. 2 Optimization of van der Waals parameters of Fluorine 2. Crystal structure (A.N. Fitch et al., Z. Kristallogr. 203, 29 (1993)) Density=2.2249 g/cm 3 (T=1.5 K) Tetrafluoromethane (CF 4 ) 3. Enthalpy of sublimation (A. Bondi, J. Chem. Eng. Data 8, 371 (1963), A. Eucken et al., J. Phys. Chem. 41B, 307 (1938))  H sub =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)) Exponential-6 function:

3. 3 a Experimental density @ T=1.5 K is 2.2249 g/cm 3. b Experimental  H sub @ T=76 K is 4.06 kcal/mol. Van der Waals parameters of exponential-6 Density (g/cm 3 ) a  H sub (kcal/mol) b  D0D0 R0R0 C120.084403.8837 F 120.044533.4985 2.2247  0.0475 4.06 130.047203.4480 2.2252  0.0413 4.07 140.049353.4112 2.2244  0.0389 4.06 150.050923.3825 2.2243  0.0360 4.06 160.052463.3589 2.2253  0.0349 4.06 van der Waals Parameters for C and F

4. 4 Isothermal Compressibility The best fit for experimental result where  0 : compressibility at zero pressure V 0 : 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. 5 R0R0 D0D0  C3.88370.0844012.0000 old F3.53800.0211016.0000 new F3.38250.0509215.0000 Thermal expansion The calculated thermal expansion is in good agreement with the experimental observation.

6. 6 Optimization of Valence Force Field Hessian-biased optimization method Expansion of energy of molecule The first derivative of energy: force on atom i-th component The second derivative of energy: Hessian. The mass-weighted Hessian: The vibrational eigenfunctions are obtained from the eigenvalue equation: If the experimental frequency set is available, we can replace theoretical frequency set by experimental one. The force field is determined to minimize the difference between H FF from force field and H QM&exp.

7. 7 1. Bond stretch Harmonic K b R 0 C-C 422.7245 1.5224 F-C535.45831.3354 2. Valence angle bend Cosine harmonic K   0 C-C-C220.8724120.0000 F-C-C129.3900 120.0000 F-C-F160.8744 120.0000 Valence Force Field 3. Dihedral angle torsion Dihedral K d,n d n C-C-C-C3.546413 F-C-C-C3.547013 F-C-C-F2.2211-13

8. 8 Validation of Force Field  geometry Quantum mechanics Molecular mechanics  6-31G* & B3LYP  New Force Field Clockwise  1-165.0-164.9 helicity  2-163.2-163.2  trans minus)  3-165.0-164.9 Counterclockwise  1165.0164.9 helicity  2163.2163.2 (trans plus)  3165.0164.9 RMS difference of atomic position: 0.0346 Å Helical conformation of C 6 F 14

9. 9 Validation of Force Field: Conformational Energy Helical conformation and energy barrier between two energy minima were successfully reproduced. Trans plus Trans minus 

10. 10 Validation of Force Field C2F6C2F6 C3F8C3F8 C 4 F 10 Ref Mulliken Q ESP QRef Mulliken Q ESP QRef Mulliken Q ESP Q Density (g/cm 3 ) 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 Solubility parameter (cal/cm 3 ) 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 Reference data from database of Design Institute for Physical Property Data (DIPPR) Project 801, American Institute of Chemical Engineers (AIChE)