Computational Chemistry
 

III. Molecular mechanics in chemistry: 
 
 
 

Topics of this lecture:
 
• Modeling of atomic motion in a molecule based on potential energy description.

• Molecular Mechanics:

Study of atomic motions in molecules and their effect on other objects based on energy discription.

I. Atomic motions in a molecule:

 

• Atoms are not rigidly positioned.
 
• External and internal forces can induce atomic motions.
 
• Some motions have chemical effect.

 

Example:

Binding of a drug to a protein can induce an atomic motion in protein that leads to the change of the 3D shape of that protein.

This shape change makes a chemically important cavity inaccessible to other molecules.


 

Drug Binding Induced Conformation Change in Protein.
 
 
 
 
 
II. The effect of motions are described by energy:
 

 

• Energy measures the ability to do work.
 
• Motion is associated with energy.
 
• There are two types of energy:
 
• Kinetic energy -- motional energy.
Kinetic energy is related to the speed and mass of a moving object. The higher the speed and the heavier the object is, the bigger work it can do.
 
• Potential Energy -- "positional" energy.
 

Potential energy description:



Water falls from higher ground to lower ground. In physics such a phenomenon is modeled by potential energy description:

Objects move from higher potential energy place to lower potential energy place.
 


 
Atomic motions in molecules are also modeled by this potential energy description.
 

 
• Different types of bond motions are modeled by different energy functions.
 
• Energy terms are additive.
 
• The total energy determines overall effect.

 
 
 
 III. Energy terms for a molecule:
 
 
• There are four type of bond motions important in chemical compounds:
 
 
• The total energy of motions is:

Energy = Stretching Energy +
               Angle Bending Energy +
               Torsion Energy +
               Non-Bonded Interaction Energy
 

 
• Stretching Energy:
 



The stretching energy equation is based on Hooke's law. The "k_b" parameter controls the stiffness of the bond spring, while "r_o" defines its equilibrium length.



Stretching energy as a function of bond length
 
 
 
 

• Angle Bending Energy:
 
 




The bending energy equation is also based on Hooke's law



      Angle bending energy as a function of angular displacement
 
 
• Torsion Energy:
 
 



 

The torsion energy is modeled by a simple periodic function, as can be seen in the following plot:


Torsion energy as a function of bond rotation angle.
 
 
 

• Nonbonded Energy:
 
The non-bonded energy represents the pair-wise sum of the energies of all possible interacting non-bonded atoms i and j:





The non-bonded energy accounts for repulsion, van der Waals attraction, and electrostatic interactions.
 

• van der Waals attraction occurs at short range, and rapidly dies off as the interacting atoms move apart.
 
• Repulsion occurs when the distance between interacting atoms becomes even slightly less than the sum of their contact distance.
 
• Electrostatic energy dies out slowly and it can affect atoms quite far apart.

van der Waals energy as a function of atom-atom separation.
 
 
Average energy scale for various interactions:
 

Energy Term	Scale (kcal/mol)
Bond stretching	100
Angle Bending	10
Torsion	1
Hydrogen Bond	2
Electrostatic interaction	0.5
Van der Waals	0.1

 

Average bond energies in units of kJ/mol (1kJ/mol=0.239 kcal/mol):

A. Single bonds:
 

	S	P	O	N	C	H
H	339	318	463	389	414	436
C	259	264	351	293	347
N		209	201	159
O		351	138
P	230	213
S	213

 

B. Multiple bonds:
 

N=N	418		C=C	611
N=N	946		C=C	837
C=N	615		C=O (in CO2)	803
C=N	891		C=O (as in H2C=O)	745
O=O	498		C=O	1075

 

Homework assignment