Lecture 5 – frontier applications and developments

Question 1

• What sort of simulations are possible that are of key interest in QD

Answer 1

• Surface chemistry and biological application

Question 2

Notes from paper 1

Conclusion is that MCTDH is particularly efficient for computing dissociation probabilities compared to many large … calcualtions on individual …

Computational resources grow exponentially with …

Can choose initial wavefunction of H₂molecule to be whatever you want (e.g. v=1 vib state and v=10 rot state, can represents any desired quantum state)

Shows MCTDH gives … … as more expensive DVR method

Answer 2

Notes from paper 1

Conclusion is that MCTDH is particularly efficient for computing dissociation probabilities compared to many large DVR calcualtions on individual states

Computational resources grow exponentially with DOFs

Can choose initial wavefunction of H₂molecule to be whatever you want (e.g. v=1 vib state and v=10 rot state, can represents any desired quantum state)

Shows MCTDH gives same result as more expensive DVR method

Question 3

Assume adiabatic … … and ignore electron-hole excitations in metal

R would not like this as his research is based on understanding how electron-hole excitations in metals influence surface chemistry

Basically, says electron stay in … (CB) no promotion of electrons as CO hits surface – experimentally poor approximation

Fitting … … , here via DFT calculations for CO in many different geometries and fit in to …-…-… form that MCTDH needs to work – very complex step (time consuming)

Answer 3

Assume adiabatic BO PESs and ignore electron-hole excitations in metal

R would not like this as his research is based on understanding how electron-hole excitations in metals influence surface chemistry

Basically, says electron stay in GS (CB) no promotion of electrons as CO hits surface – experimentally poor approximation

Fitting Global PESs, here via DFT calculations for CO in many different geometries and fit in to sum-of-products form that MCTDH needs to work – very complex step (time consuming)

Question 4

Overall summary

… : ihd/dt = H

… describes how wavefunction evolves with time and relates to calculation of … properties

Solved various methods for solving this:

… /non … dynamics

Answer 4

Overall summary

TDSE: ihd/dt = H

TDSE describes how wavefunction evolves with time and relates to calculation of dynamic properties

Solved various methods for solving this:

BOA/non BOA dynamics

Question 5

Overall summary 2

BOA dynamics

• Wavefunction moving on a … electronic (often GS) surface
• DVR
  
  • Wavefunction encoded as value of a wavefunction on a certain amount of … …
  • Solve … to get eigenstates and … (E’s), then use these to solve TDSE
  • Adv: simple to perform calculations
  • Disadv: grid representation scales … (f = DOFs) means fitting wavefunction in to memory available can be very challenging.
  • … … on many states takes a long time

Answer 5

Overall summary 2

BOA dynamics

• Wavefunction moving on a single electronic (often GS) surface
• DVR
  
  • Wavefunction encoded as value of a wavefunction on a certain amount of grid points
  • Solve TIDSE to get eigenstates and eigenvalues (E’s), then use these to solve TDSE
  • Adv: simple to perform calculations
  • Disadv: grid representation scales N^f (f = DOFs) means fitting wavefunction in to memory available can be very challenging.
  • Individual DVR on many states takes a long time

Question 6

Overall summmary 3

Non-adiabatic dynamics

• Dynamics where … dynamic surface is concerned, where at certain configurations … … states energies interact and cause … between states.
• Adiabatic vs …
  
  • HF/wavefuntion theory gives … states
    
    • Adiabatic: Coupling between them carried by … (NACME – non adiabatic coupling matrix elements), how much does one electronic state overlap with the derivative of another
    • In regions where 2 states very close, goes to infinity, calculation of which very challenging
    • Diabatic: coupling carried out by … … term
    • Much nicer behaved (… )
    • Problem is that they don’t come out of HF, must convert via … (cumbersome and different matrix for each system)

Answer 6

Overall summmary 3

Non-adiabatic dynamics

• Dynamics where >1 dynamic surface is concerned, where at certain configurations close electronic states energies interact and cause transitions between states.
• Adiabatic vs diabatic
  
  • HF/wavefuntion theory gives adiabatic states
    
    • Adiabatic: Coupling between them carried by KE (NACME – non adiabatic coupling matrix elements), how much does one electronic state overlap with the derivative of another
    • In regions where 2 states very close, goes to infinity, calculation of which very challenging
    • Diabatic: coupling carried out by potential energy term
    • Much nicer behaved (smooth)
    • Problem is that they don’t come out of HF, must convert via diabatization (cumbersome and different matrix for each system)

Question 7

Overall summary 4

• Methods for propagating … on these states
  
  • AIMS: more … but can analyse much larger systems e.g. … dynamics in a complex environment
  • … : very accurate simulations for small organic molecules (~…s atoms)

Answer 7

Overall summary 4

• Methods for propagating wavefunctions on these states
  
  • AIMS: more approximate but can analyse much larger systems e.g. chromophores dynamics in a complex environment
  • MCTDH: very accurate simulations for small organic molecules (~10s atoms)