Concise Physical Chemistry

c19 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

FINDING THERMODYNAMIC PROPERTIES 311

three-dimensional diagrams (visualization) on the computer screen to appeal to the

pictorial thinking favored by many chemists. Indeed, the drawing may be made to

mimic the familiar wooden ball-and-stick models, with the difference that we expect

it to be more accurate.

19.7 FINDING THERMODYNAMIC PROPERTIES

Suppose that, with some labor, we have arrived at a collection of force parameters

sufficient to describe a real molecule at its optimized geometry. Suppose further that

we have arrived at a set of bond enthalpies that enables us to write idealized “heats”

of formation as (a) a sum of bond energies SBE derived from a set of molecules

taken to bestrainlessand (b) another sum of bond energies NBE derived from a set

of molecules taken to benormal. Some of the resulting information available from

a computational run using MM4 for ethane is shown in File 19.1. The difference

HEAT OF FORMATION AND STRAIN ENERGY CALCULATIONS

(UNIT = KCAL/MOLE)

( # = TRIPLE BOND)

NORMAL (BE) AND STRAINLESS (SBE) ENTHALPY OF INCREMENTS

(CONSTANTS AND SUMS OF INCREMENTS)

BOND OR STRUCTURE NO ----NORMAL---- --STRAINLESS--

C-C SP3-SP3 1 -89.2005 -89.2005 -84.0718 -84.0718

C-H ALIPHATIC 6 -105.7262 -634.3572 -98.4375 -590.6250

C-METHYL (ALKANE) 2 -0.0964 -0.1928 -0.5379 -1.0758

-----------------------------------------------------------------------

NBE = -723.7505 SBE = -675.7726

HEAT OF FORMATION OF ELEMENTS (HATOM) = -655.9401 KCAL/MOLE

IN STANDARD STATE FROM ATOMS

MOLAR HEAT CONTENT OF COMPOUND (MH) = 48.6328 KCAL/MOLE

(STERIC + ZPE + THERMAL ENERGIES)

PARTITION FUNCTION CONTRIBUTION (PFC)

CONFORMATIONAL POPULATION INCREMENT (POP) 0.00 (ASSUMED VALUE)

TORSIONAL CONTRIBUTION (TOR) 0.00 (ASSUMED VALUE)

----------------

PFC = 0.00 (ASSUMED VALUE)

HEAT OF FORMATION (HFN) AT 298.2 K = -19.18 KCAL/MOLE

(HFN = MH + NBE + PFC - HATOM)

STRAINLESS HEAT OF FORMATION FOR SIGMA SYSTEM (HFS) = -19.83

(HFS = SBE - HATOM)

INHERENT SIGMA STRAIN (SI) = HFN - HFS 0.65

SIGMA STRAIN ENERGY (S) = POP + TOR + SI 0.65

FILE 19.1 Partial MM4 enthalpy output for ethane. (Units are kcal/mol.)