1. 龙讯教程
How to simulate ultrafast dynamics
using rt-TDDFT in Pwmat?

2. Ultrafast dynamics are dynamics in the time scale of ~100fs.
It mostly involves carrier dynamics (the movement of electron). Thus it
cannot be described by ground state molecular dynamics, instead
rt-TDDFT simulation is needed.
It can be: the dynamics after a system suddenly loses an electron (e.g., due to
femtosecond laser beam caused ionization); or exciting one electron from
valence band to one conduction band state; a collision of a very fast ion…
We are interested in what happens following the initial event
Hot carrier cooling

3. PWmat has two approaches to simulate such ultrafast carrier dynamics:
Real-time time dependent density functional theory (rt-TDDFT)
Good for relatively small system (e.g., less than 100 atoms)
Can add oscillating electric field, simulate the initial excitation process
Include electron-electron interaction and electron-phonon interaction
Can include the detailed balance between states (goes beyond Ehrenfest dynamics)
Can include the finite dephasing time
Non-adiabatic molecular dynamics (NAMD)
Good for large systems (e.g., > 100 atoms)
It is an approximation method, it ignores the effects of carrier dynamics to
nuclear dynamics
It first performs a ground state MD (classical trajectory, with job=NAMD),
then do actual NAMD as a post-processing (using the utility codes).
It only include electron-phonon interaction, no electron-electron interaction
It include the detailed balance and finite dephasing time in a matrix formalism

4. One example: using rt-TDDFT to study carrier dynamics
occupied
states
Time (fs)
Orbital energy (eV)

5. In this simulation, we first relax a molecule C2O2H6 in a large box
The atomic configuration is stored in atom.config
We also do a SCF calculation, so it has OUT.WG, OUT.RHO. We copy them into IN.WG, IN.RHO

6. Now, we carry out a JOB=TDDFT calculation.
A few important things: (1) We have used IN.OCC=T for the occupation
(2) We have used TDDFT_BOLTZMANN to turn on the Boltzmann factor
(3) We have used IN.WG=T and IN.RHO=T (from the JOB=SCF calculation)

7. This is the IN.OCC
Here, we have 13 states with occupation number 1 (with spin=1, each orbital is occupied with 2 electron)
But the fourth orbital is an occupation number 0.5 (e.g, only 1 electron for spin=1).
That is why, in etot.input, the NUM_ELECTRON=25.
This will effectively remove one electron from the original system (e.g., to simulate the process of
laser or electron beam induced ionization process).
In the TDDFT calculation, at the first step, it will do a SCF calculation with the above constraint occupation
numbers. So, after the first step, the wave function and charge density will be changed. This is the correct
procedure to describe sudden ionization (since the final state after this fast ionization process is a many
body eigenstate, or say a many-body adiabatic state, which is represented by the SCF solution).
If for some reason, one likes to simulate an even faster process, where one electron disappear extreme
fast, the electronic system cannot response, to relax to an electronic many-body adiabatic state, then one
should use IN.OCC_T=T, instead of IN.OCC=T.

8. TDDFT_BOLTZMANN = 1, 3, 300., -1
This line control the implementation of Boltzmann factor
The first 1 means the Boltzmann factor is turned on, 0 means it is not used
3: means where the kinetic energy goes.
When used the Boltzmann factor, the total energy is not conserved (the electronic
energy will lose some energy, and such energy should be given to the phonon kinetic
energy). Here 0: do not rescale the nuclear kinetic energy (let the total energy not conserved);
1: scale the nuclear velocity uniformly to conserve the energy; 2: scale the nuclear energy so
its kinetic energy always correspond to the temperature T (300, the third number) (total energy
not conserve); 3: conserve the total energy, and give the energy to nuclear according to electron phonon
coupling <psi_i|dH/dR|psi_j>.
Recommend: for isolated system, use 3; for an embedded system with thermal bath, use 2.
The fourth number: tau
If tau>0, this is the dephasing time (in fs) between all adiabatic states i and j.
If tau<0, the tau_i,j between adiabatic state i,j equals (tau_i*tau_j)^0.5, while
tau_i are given in IN.BOLTZMANN_TAU:
It is a good idea to use IN.BOLTZMANN_TAU, especially for the highest few adiabatic state to use
small tau_i for good TDDFT convergence.

9. Then you run PWmat
It take about 1.5 hours
to finish 1000 steps
on 4 GPU.

10. Orbital energy (eV) Time (fs) Post-processing after TDDFT run
Run the utility file: > plot_TDDFT.x
Choose 1 (for E,DOS).
It will generate file: plot.TDDFT.E, and plot.TDDFT.DOS
plot.TDDFT.E has the adiabatic state eigen energies, with the form:
t1, E1,E2,E3,……EN
………………….
tN, E1,E2, E3,….EN
Plot it out (e.g., using gnuplot), it looks like:
Ei is the adiabatic
state eigen energy
Orbital energy (eV)
Time (fs)

11. occupation state-13 (VBM) state-4 Time (fs) plot.TDDFT.DOS
It has the format:
t1,o(1),o(2),o(3),……o(N)
………..
tN,o(1),o(2),o(3),…..o(N)
O(i)=sum_j |C(i,j)|2 occ(j) the total occupation on adiabatic state ϕi(t)
Ψj(t)=sum_j C(i,j) ϕi(t)
Plot them out, they might look like:
occupation
state-4
state-13 (VBM)
state-12
Time (fs)
One can see that, the occupation of the fourth state (the state with a hole) very quickly increase to 2,
while the top of valence band states 12,13, occupation reduces, eventually the hole is in state-13.
This is a hot carrier (hole) cooling process.

12. The molecule configurations are in file MOVEMENT
MDSTEPS
One can also plot the total energy and potential energy in file MDSTEPS
Energy (eV)
potential energy
total energy
Time (fs)
One see that, overall, the potential energy decreases, as the hot
carrier (hole) cool, but there are large oscillations, since the extra
kinetic energy went to the phonon modes which cause the hot
carrier transition (through the electron-phonon coupling)
The molecule configurations are in file MOVEMENT