VII.C.9.

Configuration changes and contributions to entropy

The rotational contribution to the entropy depends on the product of the moments of inertia. How much does this contribution change as the configuration of a molecule changes? We examine two molecules here: 1,2-dichloroethane (CH₂ClCH₂Cl) and hexane (C₆H₁₄). We use energies and rotational constants from HF/6-31G* calculations.

1,2-dichloroethane (CH₂ClCH₂Cl) can be in a gauche form (Cl-C-C-Cl dihedral angle of +- 60 degrees) or a trans form (Cl-C-C-Cl dihedral angle of 180 degrees). The trans form has the Chlorine and Carbon atoms closer to collinear which results in the larger rotational constant and smaller product of the moments of inertia.

gauche		trans

Results from HF/6-31G* calculations for a temperature of 298.15 K

gauche trans units

Rotational constants A
B
C 0.34194
0.07273
0.06372 0.98541
0.05003
0.04847 cm^-1

Product of moments of inertia 3.023 2.005 10⁶ amu³Å⁶

Entropy S_rot 104.79 103.08 J K^-1 mol^-1

Relative energy 8 0 kJ mol^-1

see section III.A.9 Barriers to internal rotation for more data on 1,2-dichloroethane.

		gauche	trans	units
Rotational constants	A B C	0.34194 0.07273 0.06372	0.98541 0.05003 0.04847	cm^-1
Product of moments of inertia	3.023	2.005	10⁶ amu³Å⁶
Entropy	S_rot	104.79	103.08	J K^-1 mol^-1
Relative energy	8	0	kJ mol^-1

hexane (C₆H₁₄) can be in an extended form or various forms which are more curled up. There are three C-C-C-C dihedral angles in hexane. In the extended form all three dihedral angles are 180 degrees. In the curled (helical) form all three angles are 60 degrees. In the very curled form the dihedral angles are +60, +60, -90. The last angle is different from -60 due to steric repulsion.

extended		curled (helical)		very curled

Results from HF/6-31G* calculations for a temperature of 298.15 K

extended curled very curled units

Rotational constants A
B
C 0.49165
0.03786
0.03655 0.19887
0.05790
0.05776 0.15470
0.07193
0.05803 cm^-1

Product of moments of inertia 7.041748 7.202027 7.418987 10⁶ amu³Å⁶

Entropy S_rot 108.31 108.40 108.52 J K^-1 mol^-1

Relative energy 0 12 21 kJ mol^-1

see section III.A.9 Barriers to internal rotation for data on rotation about the central bond in butane (C₄H₁₀), which should have a potential energy surface for internal rotation similar to hexane.

		extended	curled	very curled	units
Rotational constants	A B C	0.49165 0.03786 0.03655	0.19887 0.05790 0.05776	0.15470 0.07193 0.05803	cm^-1
Product of moments of inertia	7.041748	7.202027	7.418987	10⁶ amu³Å⁶
Entropy	S_rot	108.31	108.40	108.52	J K^-1 mol^-1
Relative energy	0	12	21	kJ mol^-1

For calculating ideal-gas thermochemical properties see section I.D. A brief description of the thermochemical quantities and methods.