Dear Professor Claudio,

Thank you for your quick response. I was doing a TDSHF calculation, but I started first with an IPA (with DG). The SHG-IPA result seems to be quite convincing over a large number of laser frequencies. The next approximation level I am using is TD-Hartree. At TD Hartree, I encountered this "on the fly" situation. I am aware that a static dielectric function should be calculated first to figure out the screening, but I did not find any one in yambo community to use on the fly situation, so I was in a bit of dilemma. It is not mentioned anywhere also... I am pasting a snippet of my TDDFT calculation. The simulation time used in our calculation is larger than the noise in polarization vs time plot. Can you please comment on this?

[05.01] Initialization

======================

Dephasing Time [fs]: 32.910594

Sampling Time [fs]: 8.3213347

Total simulation time [fs]: 55.000000

[05.02] Messaging

=================

---General---

Integrator :CRANKNIC

Simulation time [fs]: 55.000000

Step length [fs]: 0.01000

NE Steps : 5501

Correlation :TDDFT

Damping [eV]: 0.2000000

Dephasing [fs]: 6.5821189

Efield :SOFTSIN

Efield FWHM [fs]: 2.0000000

Efield Amplitude [V/m]:0.13725E+7

Frequencies range : 0.5000000 6.0000000

Frequencies steps : 10

Frequency step : 0.5500000

Use Dipoles :no

Induced Field :no

Force Snd Order Dipoles :no

Lenght of G vectors in each direction: 0.94663934 0.94663934 0.22166123

Lenght of G vectors in each direction: 0.94663934 0.94663934 0.22166123

[WF] Performing Wave-Functions I/O from ./SAVE

[WF loader] Normalization (few states) min/max :0.5012E-14 0.9963

[WARNING] Covariant Dipoles not in 3d. Assuming non periodic system.

Using forth order approximation for covariant dipoles

[WF] Performing Wave-Functions I/O from ./SAVE

[FFT-Oscillators/R space] Mesh size: 7 7 25

[WR./SAVE//ndb.dip_iR_and_P]--------------------------------

Brillouin Zone Q/K grids (IBZ/BZ): 144 144 144 144

RL vectors (WF): 601

Fragmentation :yes

Electronic Temperature [K]: 0.2000000

Bosonic Temperature [K]: 0.2000000

X band range : 1 33

X band range limits : 33 1

X e/h energy range [ev]:-1.0000000 -1.0000000

RL vectors in the sum : 601

[r,Vnl] included :no

Using shifted grids :no

Using covariant dipoles:yes

Using G-space approach :no

Using R-space approach :no

Direct v evaluation :no

Field momentum norm :0.10000E-4

Wavefunctions

erdew, Burke & Ernzerhof(X)+Perdew, Burke & Ernzerhof(C)

- S/N 009235 -------------------------- v.04.03.02 r.00134 -

[WR./SAVE//ndb.Overlap]-------------------------------------

Brillouin Zone Q/K grids (IBZ/BZ): 144 144 144 144

RL vectors (WF): 601

Fragmentation :yes

Electronic Temperature [K]: 0.2000000

Bosonic Temperature [K]: 0.2000000

X band range : 1 33

X band range limits : 33 1

X e/h energy range [ev]:-1.0000000 -1.0000000

RL vectors in the sum : 601

[r,Vnl] included :no

Using shifted grids :no

Using covariant dipoles:yes

Using G-space approach :no

Using R-space approach :no

Direct v evaluation :no

Field momentum norm :0.10000E-4

Wavefunctions

erdew, Burke & Ernzerhof(X)+Perdew, Burke & Ernzerhof(C)

- S/N 009235 -------------------------- v.04.03.02 r.00134 -

Lenght of G vectors in each direction: 0.94663934 0.94663934 0.22166123

[WF] Performing Wave-Functions I/O from ./SAVE

[FFT-NL] Mesh size: 7 7 25

[05.03] External/Internal QP corrections

========================================

[QP apply] Ind. Gap Correction [ev]: 1.8400000

[WARNING] HXC collisions not found. Potential is computed on the fly.

* * * Polarization * * *

==========================

Volume : 1441.94978746 bohr^3

Direction: 1

Numer of k-points per string : 12

Numer of different strings : 12

Electronic Phase : -0.04064865 mod(2)

Ionic Phase : -0.00000011 mod(1)

Total Phase : -0.04064876 mod(1)

Polarization : -0.31153870 mod( 7.66416224) (e/Volume).bohr

Polarization : -0.00021605 mod( 0.00531514) e/bohr^2

Polarization : -0.01236147 mod( 0.30410436) C/m^2

Direction: 2

Numer of k-points per string : 12

Numer of different strings : 12

Electronic Phase : 0.02316682 mod(2)

Ionic Phase : 0.00000011 mod(1)

Total Phase : 0.02316693 mod(1)

Polarization : 0.17755513 mod( 7.66416224) (e/Volume).bohr

Polarization : 0.00012314 mod( 0.00531514) e/bohr^2

Polarization : 0.00704517 mod( 0.30410436) C/m^2

The total polarization has module 1 !!

Initial Polarization :-.27762E-3 0.10664E-3 0.0000

[WR./SAVE//ndb.Nonlinear]-----------------------------------

Brillouin Zone Q/K grids (IBZ/BZ): 144 144 144 144

RL vectors (WF): 601

Global Gauge :length

[RT] Time steps : 5501

[RT] Time step [fs]: 0.01000

[NL] Damping [fs]: 0.2000000

[NL] Bands ange : 24 33

[NL] Energy range : 0.5000000 6.0000000

[NL] Number of freqs : 10

[NL] Force 2nd approx :no

[NL] Use DIPOLES :no

[NL] Induced Field :no

[RT] Integrator :CRANKNIC

[NL] Correlation :TDDFT

[FIELDs] Type :SOFTSIN

[FIELDs] Versor : 1.0000000 0.0000000 0.0000000

[FIELDs] Intensity [kWCMm2]: 500.00000

[FIELDs] Damping [fs]: 82.682747

[FIELDs] Frequency range [eV]: 0.100000 0.100000

[FIELDs] Frequency steps : 1

[FIELDs] Frequency step [eV]: 0.0000000