Interactions

Question 1

Describe the rationale in the process of choosing a potential.

Answer 1

• type of interaction (Van der Waals, coulombic or metallic)
• accuracy (chemistry or statistical mechanics)
• simulation time
• computational capability

Question 2

Name an example for a potential for noble gases, metals, molecules.

Answer 2

• Noble metals: Lennard-Jones potential only considers Van der Waals Force
• Metals : Embedded-Atom method (EAM) takes into account the effect of e-cloud/ M-EAM takes into account the bond angle
• Molecules: AMBER, a type of cluster potential that takes into account the intra and inter molecular interactions
- intra: bending, stretching, torsion
- inter: Van der Waals and couloumb

Question 3

Explain the Born-Oppenheimer approximation.

Answer 3

• BO approximation is an assumption that the motion of nuclei and e- can be separated due to their significant difference in mass (nuclei&raquo_space; e- ).
• Due to this the wave function can then be expressed separately in terms of e- position and nuclear position.
• This separation allows an easier solution for the wave function, which leads to the formulation of Electronic Schrodinger Equation

(Hₑ + V) ψ = Eₑψ

Question 4

Benchmark for a good force field

Answer 4

• Structure - within few percent
• Thermodynamics - within few percent
• Dynamics - within 20%

Question 5

Describe the terms in EAM

Answer 5

Energy = Pair Potential + Influence of e- cloud

Question 6

Describe the terms in MEAM

Answer 6

Energy = Pair Potential + Influence of e- cloud + Bond (Length and Angle)

Question 7

Describe the Cluster Potential for Molecules

Answer 7

Combination of different force field to map the geometry . and interaction of molecules

Question 8

List the terms in a cluster potential for molecules and sketch them

Answer 8

E = E,bonded + E,nonbonded

where:
E,bonded = E,bond + E,angle + E,torsion
E,bond = ΣKb (l - lo)²
E,angle = ΣKa (l - lo)²
E,torsion = ΣΣ ½Vn [1 + cos (nω - γ)]

E,nonbonded = E,electrostatics + E,vanderwaals

Question 9

State Heisenberg’s uncertainty principle and explain the equation

Answer 9

The momentum and position cannot be accurately determined at the same time.

ΔxΔp ≥ ℏ/2

Question 10

Classical Schrödinger Equation

Answer 10

Hψ = Eψ

Question 11

Compare MOT versus DFT

Answer 11

MOT → LCAO → quantum chemistry → >N⁶ → precise

DFT → e- density → materials science → N⁴ → fast

Question 12

Enumerate applications of DFT

Answer 12

• Compare ground state energy of different crystals to determine their relative stability
• Band structure calculation for electronic properties
• Relax and analyze defect structures using optimization algorithms List the terms in a cluster potential for molecules and sketch them

Question 13

Write down and sketch the Lennard-Jones potential

Answer 13

U(r) = 4ℇ [ (σ/r)¹² - (σ/r)⁶ ]

Question 14

Write down Coloumb Potential

Answer 14

U(r) = qi qj/ 4πℇₒrij