A4 -Aleena

Accurate vs precise

accuracy is about being right, precision is about being consistent

basis sets

a set of functions used to represent the molecular orbitals φ. χ is some undefined basis function and c is an expansion coefficient

C6 correction schemes

E = E(DFT) + E(disp)
E(disp) = -ΣC₆^AB/r⁶ where C₆ depends on elemental pairs A and B

Shortcomings of C6 correction

• choice needed for how the damping is handled

• dispersion coefficients for atoms in different environments are treated as the same

solutions to C6 correction shortcomings

environment-dependent C6 coefficients: atoms get ‘squeezed’, polarisability decreases, C6 decreases

Draw a diagram for the SCF cycle used to solve Kohn-Sham equations and obtain the ground state density and total energy

Electron correlation

• reduces coulomb energy between electrons as motion of each individual e- is correlated with the motion of all others

• correlations represent deviations from the mean-field approximation caused my complex interactions

electron exchange

must be symmetric under exchange of any 2 e- as they are fermions. Asymmetry reduces Coulomb energy by increasing spatial separation

Dimensionality of PES for non linear molecules

3N-6

Dimensionality of PES for linear molecules

3N-5

One limitation of PESs

systems with large numbers of atoms have a high dimensionality which is difficult to compute or visualise

examples of classical approaches in computational chemistry

Force fields, molecular mechanics, interatomic potentials

examples of quantum approaches to computational chemistry

Ab initio, HF, DFT

How are MLIPs (Machine Learning Interatomic Potentials) made

1. assemble a set of reference points that serve as training data for the properties we seek to learn

2. represent the training data in terms of atomic environments using appropriate descriptors

3. Train the machine

4. Test, validate and iteratively improve MLIP

5. Apply MLIP

Kohn-Sham DFT

• made DFT practical and useable

• big problem with previous density based techniques was an accurate determination of Te[n]