Molecules and potential energy

Question 1

Torsional potential energy

Answer 1

• Rotation about bonds = single most important factor in molecular flexibility
• barrier is low and thermal energy is sufficient to produce rapid rotation

Question 2

Potential energy surfaces

Answer 2

• Description of the way in which molecule potential energy changes as the position of the atoms changes

Question 3

Importance of low energy points

Answer 3

• most stable conformation
• Global = lowest energy point
• Local = other low energy points

Question 4

Stationary points

Answer 4

• At maximum and minima, the derivative of the function in each dimension is 0 - second derivatives are positive at minima, and negative at maxima - Saddle points: zero derivative in each dimension but does not look like a minima or a maxima. The function reaches a maximum in one dimension but a minimum in another. Corresponding to transition states when moving from one minimum to another. Second derivative is both positive and negative

Question 5

Boltzmann distribution

Answer 5

• Describes the population in energy states - k = 1.389e23 J/K (temperature MUST BE IN KELVIN)
• 2.48 kJ/mol at room temp

Question 6

Local Optimization

Answer 6

• As interactions between all atoms in a molecule is very complex, minima are found numerically in a stepwise process
• the slope of the line is followed untill a minimum is reached
• does not find the global minimum, just the nearest local minimum

Question 7

Global optimization

Answer 7

• very difficult
• for example heptadecane has 16 rotatable bonds and three conformations
• Number of conformers thereby = 3^16… calculating the energy of 1/second would take 498 days

Question 8

Systematic Searching

Answer 8

• each rotable bond is rotated and the energy of the confromer recorded.
• Suffers from the combinatoral explosion
• if a molecule with 5 rotable bonds is searched in 36 degree increments the total number will be 360/36^5
• okay for molecules without too many rotable bonds

Question 9

stochastic search methods

Answer 9

thousands of random starting conformations are generated and minimized. Each new minimized structure is compared to the others and only retained if it less.

eventually no new structures will be obtained

no guarantee but extremely likely to find the global minimum