Quantum ESPRESSO Workshop
June 25-29, 2012
The Pennsylvania State University
University Park, PA
Real Time TDDFT
Curtesy of
Davide Ceresoli
Istituto di Scienze e Tecnologie Molecolari CNR
c/o Dipartimento di Chimica Fisica ed Elettrochimica
Università degli studi di Milano
davide.ceresoli@istm.cnr.it
Optical excitations: real-time TDDFT
In principle, TDDFT is an exact reformulation of time-dependent quantum
mechanics. However, in practice we have to adopt some approximations:


Adiabatic approximation: (i.e. without memory effect)
LDA / GGA
 self-interaction error
 wrong asymptotic limit of XC potential
 local/semilocal functional
Real time TDDFT
Real-time propagation scheme of TDDFT is a simple, efficient, and direct
approach to obtain optical properties.
Calculate dynamic polarizability and polarization under time-dependent external
perturbation
Flowchart:
(a) apply a perturbative electric field along three directions
(b) propagate the TDKS wavefunctions
(c) calculate time-dependent dipole moment / angular momentum
(d) finally obtain the dipole / rotational strength function via Fourier
transform
Real time TDDFT: flowchart
(a) apply a perturbative electric field along three directions
(b) propagate the TDKS wavefunctions
First-order Crank-Nicholson integration method
Ax=b
: solved by conjugated-gradient squared method (CGS)
Δt = 2 attosecond. Integration for 20 fs (→ 0.2 eV resolution)
Real time TDDFT: flowchart
(c) calculate time-dependent dipole moment / angular momentum
(d) obtain the dipole/rotational strength function via Fourier transform
Dynamic polarizability
Dipole strength function
Averaged in 3 directions
Complex rotatory strength function
Rotational strength function
Real time TDDFT with QE
1- Run SCF calculation (SiH4-scf.in)
&control
prefix = 'sih4'
calculation = 'scf', restart_mode = 'from_scratch'
pseudo_dir = './pseudo/', outdir = './scratch/'
/
&system
ibrav = 1, celldm(1) = 20.0
nat = 5, ntyp = 2
ecutwfc = 25
nosym = .true.
/
&electrons
diagonalization = 'david', conv_thr = 1.0d-8
/
ATOMIC_SPECIES
Si
28.08550 Si.pz-vbc.UPF
H
1.00000 H.pz-vbc.UPF
ATOMIC_POSITIONS angstrom
Si
0.000000000
0.000000000
H
0.859674551
0.859674551
H
-0.859674551
-0.859674551
H
-0.859674551
0.859674551
H
0.859674551
-0.859674551
K_POINTS automatic
1 1 1
0 0 0
0.000000000
0.859674551
0.859674551
-0.859674551
-0.859674551
./pw.x <SiH4-scf.in >SiH4-scf.out
Real time TDDFT with QE
2- Run TDDFT propagation (SiH4-tddft_x.in)
&inputtddft
job = 'optical'
prefix = 'sih4'
tmp_dir = './scratch/'
dt = 2.0
nstep = 5000
e_direction = 1
e_strength = 0.01
/
!
!
!
!
attoseconds (1e-18 s)
5000-10000 typically
1=x, 2=y, 3=z
E-field strength (1/Angstrom)
./tddft.x <SiH4-tddft_x.in >SiH4-tddft_x.out
3- Extract dipole dynamics, calculate optical absorption
grep ^DIP SiH4-tddft_x.out >dip_x.dat
python plot_optical_absorption.py x
Check time-step, and energy range in python script!
Let's plot the results (SiH4)
gnuplot> plot 'dip_x.dat' us 3:5
Let's plot the results (SiH4)
9.4 eV
7.7 eV
gnuplot> plot 'sih4_x.dat'
Let's take another view
gnuplot> set log y
gnuplot> plot 'sih4_x.dat' us (1239.8419/$1):2
Exercise: aromatic vs. conjugated
Aromatic
Conjugated
C6H6
Fulvene
Benzene
C10H8
Naphtalene
Azulene
Aromatic vs. conjugated





Pick one molecule
Run SCF
Run TDDFT // x, run TDDFT // y
(optional) Run TDDFT // z
Plot optical absorption, find maximum λmax of absorption
Note: 20 Ry cutoff, 4 Å vacuum!!!
Results: benzene
7.33 eV
8.35
eV
6.1
eV
$ paste benzene_[xyz].dat >benzene_tot.dat
gnuplot> plot 'benzene_tot.dat' us 1:(($2+$4+$6)/3)
Results: fulvene
5.32
eV
3.1
eV
6.91
eV
Results: naphtalene
6.00
eV
7.99
eV
4.28
eV
7.12
eV
Results: azulene
5.22
eV
2.44
eV
Comparison to experiments
Calc. (nm)
Expt. (nm)
Intensity
203
254
weak
169
204
strong
148
184
strong
Naphtalene
Benzene
Calc. (nm)
Expt. (nm)
Intensity
289
312
weak
206
289
strong
174
--
weak
155
220
strong
Comparison to experiments: λmax
Benzene
λmax = 254 nm (expt.)
λmax = 203 nm (calc.)
Naphtalene
λmax = 312 nm (expt.)
λmax = 289 nm (calc.)
Fulvene
λmax = 370 nm (expt.)
λmax = 399 nm (calc.)
Azulene
λmax = 690 nm (expt.)
λmax = 508 nm (calc.)
What color is azulene?
Let's convert wavelength into approximate RGB:
$ python wave2RGB.py
From wikipedia:
Not absorbed
“TD-ALDA” azulene
Absorbed
Not absorbed
Absorbed
“Real” azulene
Essential bibliography

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




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Yabana and Bertsch, Time-dependent local-density approximation in real time,
Phys. Rev. B 54, 4484 (1996)
Yabana and Bertsch, Application of the time-dependent local density approximation to optical
activity, Phys. Rev. A 60, 1271 (1999)
Yabana, Nakatsukasa, Iwata and Bertsch, Real-time, real-space implementation of the linear
response time-dependent density-functional theory,
Physica status solidi (b) 243, 1121 (2006)
Castro, Appel, Oliveira, Rozzi, Andrade, Lorenzen, Marques, Gross and Rubio, Octopus: a tool
for the application of time-dependent density functional theory,
Physica status solidi (b) 243, 2465 (2006)
Marques, Castro, Bertsch and Rubio, Octopus: a first-principles tool for excited electron-ion
dynamics, Comput. Phys. Commun. 151 60-78 (2003)
Castro, Marques and Rubio, Propagators for the time-dependent Kohn-Sham equations,
J. Chem. Phys 121, 3425 (2004)
Andrade, Botti, Marques and Rubio, Time-dependent density functional theory scheme for
efficient calculations of dynamic (hyper)polarizabilities,
J. Chem. Phys 126, 184106 (2007)
Xiaofeng Qian, Ju Li, Xi Lin, and Sidney Yip, Time-dependent density functional theory with
ultrasoft pseudopotentials: Real-time electron propagation across a molecular junction,
Phys. Rev. B 73, 035408 (2006)
Codes:
http://www.phys.washington.edu/
users/bertsch/V2.1.tar