Homework Problem Set 2

Chemistry 380.37
May 2013
Dr. Jean M. Standard
May 16, 2013
Homework Problem Set 2
1. Indicate whether it would be appropriate to carry out a molecular mechanics calculation using a typical
organic/biological force field (such as MMFF or Amber) to determine the minimized energy for the molecular
systems listed below.
a. porphyrin
b. ferrocene
c. a small protein such as BPTI
d. IF 5
e. the water pentamer, (H 2 O) 5
2. A researcher is interested in using molecular mechanics to study molecules containing amine functional groups.
The force field that the researcher is using has no energy term to describe the torsional motion of amines, so the
researcher constructs a new set of parameters to describe the amine torsional motion using experimental data from
the molecule CH 3 NH 2 . The researcher uses the following functional form for the energy of torsional rotation of
the C-N bond:
U torsion = k torsion ( ω − ω eq ) 2 ,
where k torsion is a constant, ω eq is the equilibrium value of the torsional angle, and ω is the torsional angle.
Is the form that the researcher chose € for the torsional energy a reasonable one Explain. If not, sketch a form
that would be more appropriate.
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3. In most force fields, the interaction between two nonbonded atoms is described using a function called the
Lennard-Jones 6-12 potential. It has the general form
U nb = − a
r 6 + b
r 12 ,
where a and a are constants which depend on the two interacting atoms and r is the distance between them. For
example, for two carbon atoms interacting, € a = 745 and b = 2524840 (these parameters yield energy in kcal/mol
if the distance is expressed in angstroms).
a. Sketch the nonbonded energy as a function of distance for the case of two carbon atoms.
b. At approximately what distance does the minimum energy occur for this particular nonbonded interaction
c. Which of the two terms in the expression for the nonbonded energy is responsible for the attractive part of
the interaction Which term is responsible for the repulsive part of the interaction
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2
4. A computational chemist working at DrugsRUs, Inc. performed an energy minimization using the Amber force
field on the lactic acid molecule and found that the lowest energy conformer had an energy of 19.856 kcal/mol.
Upon carrying out a literature search, the chemist found a journal article from 1995 in which a study using the
MMFF force field determined the global minimum for lactic acid to be 3.898 kcal/mol. Is there something
wrong with the DrugsRUs chemist’s work Explain.
5. The part of a particular MM3-like force field that describes stretching energy for an O-H single bond is given by
the following expression:
U s = 380( r − r eq ) 2 − 75( r − r eq ) 3 ,
where r is the O-H bond distance , r eq= 1.044 Å, and the stretching energy U s is expressed in kcal/mol. Notice
that in many force fields based € on MM3, the harmonic stretching energy is corrected by an anharmonic term like
the cubic one shown above. A molecule is built on the computer with an initial O-H bond distance of 1.320 Å.
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a. What is the stretching energy of the O-H bond with r = 1.320 Å
b. What is the gradient of the energy with respect to the O-H bond at r = 1.320 Å
c. What is the curvature at r = 1.320 Å
d. Using the Newton-Raphson method for geometry optimization, carry out one step to determine the new
value of r.
e. Calculate the gradient at the new value of r determined in part (d). If the tolerance for reaching the
minimum is that the absolute value of the gradient be less than or equal to 0.1 kcal/mol-Å, is the
optimization complete
6. Consider the energies of the axial and equatorial forms of t-butylcyclohexane.
a. Which form would you expect to be higher in energy, the axial or equatorial Why
b. Do molecular mechanics calculations agree with your qualitative expectations Use the data below to verify
the relative energies of the two forms.
Energy of t-butylcyclohexane calculated using MM3 and Amber force fields (kcal/mol)
Force Field Bonds Angles Torsions Nonbonded Total
Axial
MM3 1.517 4.281 5.458 6.625 18.313
Amber 0.732 4.434 1.837 4.303 11.305
Equatorial
MM3 1.394 1.969 3.755 5.892 13.312
Amber 0.584 1.465 0.311 3.989 6.350
c. From the force field data given in part (b), what element of the force field shows the largest change when
comparing the axial and equatorial conformations Why do you suppose this is