Concise Physical Chemistry

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

312 CLASSICAL MOLECULAR MODELING

between SBE and HATOM [the enthalpy input to drive hydrogen and graphite into

the atomic state (Section 19.2) for the strainless molecule] is

fH^298 (strainless)=− 675. 77 −(− 655 .94)=− 19 .83 kcal/mol

A similar sum of normal bond enthalpies gives a different result for the normal

molecule:

NBE+HATOM=
fH^298 (normal)+MH=− 67. 81 + 48. 63 =− 19 .18 kcal/mol.

The new term MH (molar heat content) arises from a slightly different way of defining

the normal bond energies; they should be represented by an arrow going all the way to

the bottom of the energy wells in the real molecule. Positive enthalpies—consisting

primarily of the zero point energies of vibration (Section 18.2), with a contribution

from thesteric energy—and small statistical factors add up to a positive correction

of 48.63 kcal/mol. The difference between HFS and HFN is an accumulated strain

energy:

INHERENT SIGMA STRAIN (SI) =HFN - HFS 0.65

The partial MM4 output for ethane (File 19.1) illustrates some other features of the

MM procedure and the full file provides more. SeeSTATISTICAL THERMODY-

NAMICS ANALYSISfrom the MM4 output and Nevins et al. (1996 b, pp. 703–707)

for more detail.

19.8 THE OUTSIDE WORLD

In any molecular modeling enterprise, we seek to compare physical properties pre-

dicted by the model with the same properties measured by experiment. One obvious

choice is bond lengths as measured by X-ray crystallography. Agreement is usually

good but not perfect. Even assuming that the impossible task of removing all defects

from the model has been achieved, the X-ray crystallographer and the MM modeler

are not really looking at the same thing. The idea of a model as developed so far

implies an isolated gas-phase species, but molecules in crystals are subjected to pow-

erful forces holding them in the crystalline state due to the sum of forces exerted by

their neighbors.

Somewhat surprisingly, these forces do not influence bond lengths very much.

Agreement between X-ray bond lengths and MM4 lengths is usually within about

0.002A. Simple bond angles, being weaker, are distorted by a few degrees, and ̊

torsional angles, being weaker still, are distorted more. X-rays are scattered by

electrons, so crystallographic structures represent the centers of electron densities

which tend to be the same as the location of the nuclei, but which may be displaced

in some chemical bonds. For example, the difference between the C H bond length