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

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

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

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

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

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)

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.

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.

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

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)

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.

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