Molecular Modelling Flashcards
What is molecular modelling?
> Molecular modelling = molecular mechanics = force field calculations.
> Unlike quantum mechanics (accurate but slow), this approach does not solve the electronic Schrodinger equation).
> It is an empirical approach, atom-atom interactions are described using some suitable mathematical expressions and electron-electron and electron-nuclei interactions are ignored → this approach is much FASTER than quantum mechanics (and gives results that are almost as good).
What are we looking for when we model molecular systems?
> We are looking for the MINIMUM ENERGY of the molecule.
Why are we allowed to ignore electron-electron interactions?
> BORN-OPPENHEIMER APPROXIMATION: nuclei are much heavier than atoms, therefore, electrons move on a much faster timescale. → We can consider nuclei to be stationary and electrons to be moving in the constant potential energy field of the nuclei.
> Can also postulate that electrons move so fast that there is an average distribution of electrons around each nucleus (molecular mechanics).
How are diatomic molecules modelled>
> Harmonic approximation: the molecule is represent s 2 balls connect by a spring.
> Energy is calculated using Hooke’s law. The structure with the best geometry is the lowest energy structure.
What is Hooke’s Law and what are its limits?
E= 1/2 k(x-x0)2
where k=force constant
x0= the ideal interatomic distance (equilibrium bond length).
> With Hooke’s law, the molecule never dissociates. (even with the atoms at infinite separation, the molecule remains bound).
> The harmonic potential (i.e. Hooke’s law) can be used only for intermolecular distances of x0 ± 10%.
What is steric energy?
> Steric energy is a measure of strain in the molecules’ bond lengths (and angles, torsional angles etc.).
How do you calculate and interpret the force of a molecule?
F= -∂E/∂x = -k(x-x0)
> If x=xo then F=0 → the net force = 0, atoms are in their ideal positions and there is no movement.
> If x0→ the force drives the atom to the right towards x0.
> If x>x0 the F<0 → the force drives the atom to the left towards x0.
What is meant by the term “minimisation of energy”?
> Minimisation of energy is the procedure of searching for the best (minimum energy) structure with force F=0.
What is the Lennard-Jones potential?
E = 4 Ɛ[ (σ/r)12 - (σ/6)6]
> It describes both the equilibrium bond length and dissociation.
What is a force field?
> Force field= combination of equations and their parameters used to describe interatomic interactions.
What are the advantages and disadvantages of quantum mechanics (QM)?
> Advantages:
→ rigorous description of electron-electron and electron- nuclei interactions.
→ from 1st principals (does not require experimental input).
→ Can cope with new unexpected structures.
→ only method to use if interested in electronic properties.
> Disadvantages:
→ Slow
→ Solving Schrodinger equation requires approximations which lower QM accuracy.
What are the advantages and disadvantages of molecular mechanics (MM)?
> Advantages:
→ very fast
→ applicable to large systems
→ allows dynamics of molecules to be studied (evolution of the structure over time).
→If properly parameterised it can be as accurate as QM.
> Disadvantages:
→ parameters of the force field need to be properly chosen (hard).
→ QM of experiment needs to be done first.
→Non-transferable, cannot cope with new unknown structures.
→ Applicable for describing atoms but not electronic properties.
When can QM be used?
>QM should be used to describe electronic properties of: → molecular orbitals → electronic states → light absorption → charge transfer → bond rearrangements (mechanisms)
When can MM be used?
→ large molecules especially biomolecules
→ dynamics of molecules
→ molecules in solution
→ some inorganic solids (e.g. Si)
When can both methods be used?
→ Small/medium molecules
→ some inorganic solids
The energy of a molecular system is given by a sum of intramolecular and intermolecular interactions, what are these interactions?
> Intramolecular = all ‘chemical’ interactions between atoms within 1 molecule. Depends only on the geometry of each molecule.
> Intermolecular = All interactions between atoms of different molecules: non-bonded and electrostatic.
What is the Valence force field?
> Molecules are not fixed, they undergo bond stretching, bond bending (change of angle) and torsion (change of dihedral angle) - a typical valence force field includes all of these terms.
> E= Estretch + Ebend + Etorsion
How is the stretching term dealt with?
> Stretching - changing the bond length
> Most simple form for the bond stretching term is the harmonic oscillator (Hooke’s law).
> For a molecule containing many atoms, the stretch term is the sum of stretch contributions over all bonds between the atoms.
> Can also use the Morse potential: Estretch(rij)= Dij[1-e^-aij(rij-rij0)]2
where Dij = dissociation energy (binding strength) and aij= strength of the potential
(describes dissociation better than quadratic but is less easy computationally)
> Can also use a Cubic potential:
Estretch (rij) = 1/2 kij (rij-rij0)2 (1-2(rij-rij0))
> or the Quartic potential:
Estretch (rij) = 1/2 k1 (ij)(rij-rij0)2 + 1/2 k2(ij) (rij-rij0)4
> These expressions are better at describing the anharmonicity of bonds (important for the calculations of vibrational frequencies).
Note: the HARMONIC POTENTIAL = most widely used because it is mathematically the simplest.
How do we know if there is a bond between 2 atoms?
> Check the distance, there is a cut off distance (rij ± 10-20%) beyond which atoms are considered to be not chemically bound and the stretching interaction does not apply.
How is the bending term dealt with?
> Bending term= changing the bond angle
> Ebend (θ ijk) - 1/2 kijk(θijk - θijk0)2
where θijk0 = the natural (ideal) angle between atoms ijk.
> For a molecule containing many atoms, the bending term is the sum of the contributions over all angles between all bonded atoms.
> Again, more complex forms can be used such as quartic or cosine:
Ebend (θijk) - Kijk/2sin^2θijk(cosθ ijk-θcosijk0)^2
How is the torsional term dealt with?
> Torsional term= changing the dihedral angle.
> Harmonic potential:
Etorsion (χijkl) = 1/2 kijkl (χijkl-χijkl0)^2
This expression implies that there is 1 preferred value for a torsional (dihedral) angle (suitable for improper torsions but not suitable for proper torsions).
What are proper and improper torsions?
> Proper torsion= not restricted and a full 360° rotation around the j0k bond is possible (e.g. rotation around the c-c bond in ethane).
> Improper torsion= the values taken by the dihedral angles are restricted (e.g. in benzene c-c-c-c ~0, atom are all in the same plane).
What expression can be used to describe the periodicity of a torsional angle?
Etorsion (χ)= 1/2Vijkl [1-cos(nχ-ϒ)]
where:
n=periodicity of torsion
Vijlk= force constant (the height difference between the maxima and minima in the torsional potential)
ϒ= the phase factor which determines where the torsional potential passes through a minimum.
> For ethane, all minima have equal depths (not always the case). A more general expression that accounts for several minima of unequal depths:
Etorsion (χ)= 1/2 ΣVn [1-cosχ-ϒ)]
n=a number from 1 to some value (depending on the force field).
How do different types of force fields differ?
> Force fields differ in:
→choice of equations
→choice of atom types (united or all atom)
→choice of parameters
