Fundamentals of Medicinal Chemistry

Energy

Time

(a) Butane

(b)

Energy

0 60 120 180 240 300 360

Degrees of rotation

Skew or gauche

CH 3

H

HH

H

CH 3

HH

CH 3

CH 3

H H

Staggered

HHHCH^3

CH 3

H

H H

Eclipsed

CH 3

H H

CH 3

Figure 5.7 (a) Molecular dynamics trajectory for the rotation of the C 2 –C 3 bond in butane at

600 using the CAChe program. Moving the cursor along the energy trajectory causes the

structure of butane on the right to assume the corresponding conformation. Reproduced from

W. B. Smith,Introduction to Theoretical Organic Chemistry and Molecular Modelling, 1996, by

permission of Wiley–VCH, Inc. (b) A plot of the change in energy with rotation about the C 2 –C 3

bond in butane showing the corresponding conformations

system. In molecular modelling termsECrepresents the total potential and

kinetic energy of all the particles (nuclei and electrons) in the structure andHis

the Hamiltonium operator acting on the wave functionC. Operators are math-

ematical methods of converting one function into another function in order to

find a solution or solutions of the original function. For example, differentiation

is an operator that transforms an equation representing a function into its first

derivative.

Schrodinger equations for atoms and molecules use the the sum of the potential

and kinetic energies of the electrons and nuclei in a structure as the basis of a

description of the three dimensional arangements of electrons about the nucleus.

Equations are normally obtained using the Born–Oppenheimer approximation,

which considers the nucleus to be stationary with respect to the electrons. This

approximation means that one need not consider the kinetic energy of the nuclei

in a molecule, which considerably simplifies the calculations. Furthermore, the

106 COMPUTER AIDED DRUG DESIGN