Force Fields and Simulations

Question 1

For a diatomic molecule the potential energy only depends on

Answer 1

one variable - the bond length

Question 2

Plotting oscillator potential to approximate potential energy represents

Answer 2

how often energy varies as a function of the distortion of the bond length from its equilibrium value

Question 3

1 d potential energy (E) =

Answer 3

f(l) = 1/2 * k (l-l0)^2 for bond length l, min bond length l0 and bond force constant k

Question 4

If potential energy is a function of more than one variable we have a…

Answer 4

potential energy surface

Question 5

potential energy wells correspond to

Answer 5

lowest energy states for reactants and products

Question 6

Saddle point on PES correspond to

Answer 6

transition state for reaction

Question 7

hypersurface depends on

Answer 7

many variables

Question 8

molecules spend most of the time in

Answer 8

potential wells on PES

Question 9

energy minima on PES are

Answer 9

STABLE CONFORMATIONS

Question 10

Anti conformation (180) is more stable than gauche (60) because

Answer 10

reduced steric hindrance

Question 11

PES calculated by considering

Answer 11

rotation about backbone dihedral angles

Question 12

To calculate potential energy of molecular system write

Answer 12

as a sum of all the different contributions from bond stretching/bending, dihedral angle distortions and nonbonded interaction (eg steric repulsion and van der Waals) and electrostatic interaction

Question 13

Can use computational algorithms to minimise

Answer 13

steric energy and find stable conformations corresponding to minima on the PES

Question 14

High force constant for bond corresponds to

Answer 14

stiff bonds where distortion from equilibrium value corresponds to large energies

Question 15

Energy in torsional motion of dihedral angle =

Answer 15

sum up to number of terms (n) in series expansion of: (force constants / 2)*(1+cos(nangle))

Question 16

2 neutral atoms approaching at long distances

Answer 16

attract each other through dispersion interactions and repel at close distances

Question 17

Lennard jones potential

Answer 17

epsilon is well depth and sigma is distance where attractive and repulsive energies cancel equation on cheat sheet

Question 18

Energy due to electrostatic interactions can be given by

Answer 18

a charge-charge interaction equation on cheat sheet

Question 19

in some force fields electrostatic interactions can be represents by

Answer 19

bond dipoles. equation on cheat sheet

Question 20

Steric energy should not be compared between

Answer 20

molecules. Compared between different conformation of a molecule instead.

Question 21

Individual force fields are not normally needed because

Answer 21

so similarin different molecules so can use the same parameters

Question 22

making force fields:

Answer 22

using computational fitting procedures. using experimental data, using other calculations eg monte carlo (details on pg 10-11)

Question 23

Structure with the lowest energy is the most stable and therefore the

Answer 23

most abundant structure.

Question 24

IF first derivative of energy is 0 and second derivative is > 0

Answer 24

miminmum

Question 25

Formal derivation of minimisation algorithm

Answer 25

start at x. x(min) = x + delta x. differential of x(min) = 0. expand as taylor series. equation. Find x(min) as roughly x - E’/E’’.

Question 26

For higher dimensions replace E’ by

Answer 26

vector (force vector)

Question 27

For higher dimensions replace E’’ by

Answer 27

hessian matrix, giving a vector of small changes for each iteration.

Question 28

Boltzmann Law gives

Answer 28

relative population of states with different energies.

Question 29

If more than 2 states in system we can use boltzman distribution to find

Answer 29

probability of each state

Question 30

partition function is the

Answer 30

sum over boltzmann factors for each energy level and energy of lowest energy state is subtracted from each energy level

Question 31

To find probability of different conformations:

Answer 31

Find energy relative to lowest energy state for each conformation. Work our Boltzmann factor for each conformation. Sum up boltzmann factor to give partition function. Work out probability of each level using partition. Us relative energy to get correct partition function.

Question 32

Uses of Molecular mechanics (3)

Answer 32

finding global energy minima, conformational searching and modelling of interactions between molecules.

Question 33

Advantages of MM over QM: (2):

Answer 33

MM faster, possible for large molecules, simple organic molecule stuctures are better for MM as poor representation of dispresion in Qm

Question 34

Disadvantages of MM over QM: (3)

Answer 34

No account of electrons, not good where electronic effects dominate over steric effects, and polarisability not taken into account in most force fields.

Question 35

Limitations of MM(4):

Answer 35

in large molecules, the number of accessible conformations is great, the number of molecular arrangements grows exponentially as the number of molecules increases. if only considering energy minima then ignore entropy and free energy, molecules are moving all the time so sampling diff energy states.

Question 36

Average energy =

Answer 36

average over representation number of states. equation on cheat sheet.

Question 37

Velocity Verlet algorithm

Answer 37

breaks time down into a sequence of small discrete time-steps (delta t). method on page 18. delta t is very small and should be 1/20 of the fastest motion in system.

Question 38

Leapfrog algorithm

Answer 38

velocities are half a time step behind the positions but then leap ahead by half a time step. Algorithm of pg 18

Question 39

Monte carlo simulation

Answer 39

uses random numbers to make small changes from current configuration, calculating Blotzmann factor for energy change and acceptingrejecting the change. diagram on pg 19

Question 40

MC vs MD (5):

Answer 40

Both generate energy states according to their Bolztmann weights. Only coordinates enter MC, md has velocities and forces. Md good for big molecules. More good.free programs available for MD.

Question 41

LARGE molecules hard to simulate via MC because

Answer 41

hard to generate MC mobes that sample conformational space efficiently

Question 42

Mc has many advantages over MD such as

Answer 42

use of special MC moves and use of thermodynamic ensembles for simulation. Even possible to have MC moves whree molecules appear/disappear. Move can be used to speed up simulation of mixing or demixing in a binary mixture of 2 liquids.

Question 43

When simulating bulk systems with many molecules avoid

Answer 43

serious problem caused by fact we can only simulate a few hundred molecules (at most a few thousand).

Question 44

For a small system surface molecules dominate over

Answer 44

bulk molecules

Question 45

Periodic boundary conditions

Answer 45

employed alongside minimum image convention

Question 46

when simulating in the bulk it is usually necessary to

Answer 46

conserve certain quantities that define the thermodynamic ensemble used. important ensembles on page 21

Question 47

Thermodyanmic properties can be obtained using

Answer 47

MC and MD techniques. examples on page 22

Question 48

increasing the temperature in MC will

Answer 48

change the moves that are accepted with additional moves to higher energy configurations being accepted

Question 49

For MD temperature can be obtained from velocities in a simulation by the

Answer 49

equipartition principle equation on page 22

Question 50

dihedral angle distributions plot the

Answer 50

frequency of dihedral angles occuring during a simulation.

Question 51

Can take natural log of the dihedral angle distribution to obtain the

Answer 51

torsional free energy

Question 52

Radial distribution function g(r) shows

Answer 52

the average structure in a liquid. 1st peak corresponds to solvation shell, 2nd solvation shell is less well defined. g(r) decays to 1 at long distances as no long range structure in a liquid

Question 53

Bulk diffusion coefficient can be estimated in MD simulation from the

Answer 53

mean squared displacement at long times or the velocity autocorrection function equation on page 23

Question 54

Molecular mechanics is for single molecules and

Answer 54

solids and ‘clusters’

Question 55

MC and MD for

Answer 55

single molecules and fluids