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Composition of the response charge density in terms of ground state KS orbitals

Posted: March 9th, 2010 | Author: obm | Filed under: Physics/Theories, TDDFT | Tags: , , | No Comments »

In the code I calculate the response charge density at a given frequency from

\rho^{\prime}(\omega)=2\sum_{v}\left(\left|Q_{m}^{T}\right>\left<\phi_v\right|\right).W_m(\omega)(1)

where \phi_v is the ground state KS orbitals and Q_{m}^{T} is the matrix that contains Krylov subspace of q in real space

q_{v}=\frac{1}{2}\left( x_v+y_v \right)

Q_{m}=\left[q^1,q^2,\dots,q^m \right]

(m is the number of Lanczos iterations)

For visualisation purposes I calculate

n^{\prime}(\vec{r},\omega)=\left<\vec{r}\right|\rho^{\prime}\left|\vec{r}\right>

where \vec{r} are the points that span the simulation box.

In principle I can also use this operator to obtain the overlap of response charge density at a specific frequency to ground state orbitals.

F=\left<\phi^c\right|\rho^{\prime}\left|\phi^v\right>

where F contains the contribution of a valance->conduction transition to the response charge density.

from the construction of (1) any two-photon processes is zero, thus the ith element can be calculated as

F^ij=2\left<(Q_{m}^{T})^i\phi^j\right>.W_m(\omega)

where index ij is the transition index and j runs through the unoccupied states

Ultrasoft Pseudopotentials

I start with the normalized space

1=\left<\phi\right|S\left|\phi\right>

and go to cross-term

\left<\phi^c\right|S\left|\phi^v\right>

then I add the response operator to the left of S operator

F=\left<\phi^c\right|\rho^{\prime}S\left|\phi^v\right>

F=\left<\phi^c\right|2\sum_{v}\left(\left|Q_{m}^{T}\right>.W_m(\omega)\left<\phi_v\right|\right)S\left|\phi^v\right>

since ground state KS orbitals are orthogonal to each other

\left<\phi_v\right|S\left|\phi^v\right>=\delta^v

F=2\left<\phi^c\right|\left|Q_{m}^{T}\right>.W_m(\omega)

Thus it appears that no addition of S matrix is necessary.

Dry Flav without water: Test on the cell size dependence of the spectra

Posted: February 16th, 2010 | Author: obm | Filed under: Project 21: Extreme, TDDFT | Tags: | No Comments »

The following spectra is obtained for the dry system without counter-ion

The cell-size has no significant impact on the spectra of the dry system. The M-T correction does not work, since the cell size is not at least twice the molecule size.

Example input file:

&CONTROL
 calculation = "scf",
 restart_mode="from_scratch",
 prefix="flav-14-nowat-nocl-x2",
 pseudo_dir = "/u/cm/mbaris/work/arrigo/pseudo/"
 outdir="./out"
/
&SYSTEM
 ibrav=8,
 celldm(1)=37.794538
 celldm(2)=1.0
 celldm(3)=0.75
 nat=53,
 ntyp=3,
 ecutwfc=25.0,
 ecutrho=200.0,
 tot_charge=1.0
 occupations="smearing",
 smearing="gaussian",
 degauss=0.006
/
&ELECTRONS
 diagonalization = "cg"
 electron_maxstep = 50,
 tqr=.true.
/
ATOMIC_SPECIES
 C   12.011  C.pbe-van_bm.UPF
 O   16.00   O.pbe-van_bm.UPF
 H   1.001   H.pbe-van_bm.UPF
ATOMIC_POSITIONS (angstrom)
H      16.022422    8.404178    4.026815
H      16.927685    5.434648    2.237667
H      14.746682    3.281691    1.359805
H      10.229997    3.426490    1.603412
H      11.849385    5.171335    0.566569
H      12.384277    3.542142    1.022973
O      10.665086    4.279735    1.982355
O      12.659925    7.182996    4.571237
O      16.462485    6.291544    2.537711
H      15.173886    5.567365    4.038213
H      14.870297    7.913472    2.112808
O      15.071861    8.237275    4.170719
H      12.596159    8.423016    2.813131
H      12.796823    4.959934    3.511343
C      11.928708    4.470731    1.405801
O      14.875801    3.751071    2.205858
H      14.410707    5.360034    0.955741
C      15.187645    6.001185    2.989469
C      14.553003    7.461131    3.121187
C      13.008388    7.475260    3.162092
O      12.571817    6.611538    2.187258
C      12.876253    5.208181    2.444845
C      14.354138    5.030383    2.071934
H       8.221876    3.334249    5.640921
H       9.458457   13.276892    5.709185
H       4.658234    6.122102    6.725152
H      14.055153   13.956144    4.956817
H      10.915334    5.178283    4.960759
H       6.806275    8.872129    5.448724
H       6.445641    4.601972    6.539093
H       9.439671   10.941687    5.060393
H      14.344719   11.546695    4.865238
H      13.538306    9.221439    5.004162
O       9.383525    8.744544    5.025901
O       8.894354    4.064138    5.738343
O      10.332657   13.506396    5.370300
O       5.096403    7.003869    6.303451
O      12.960550   13.824802    5.203096
C      10.738854    8.618018    4.931856
C       8.577166    7.648407    5.406602
C      11.321160    7.294758    4.831180
C       8.318398    5.251129    5.780359
C      11.073399   12.356283    5.173758
C       9.179369    6.372297    5.447613
C       6.398120    6.752775    6.016743
C      12.493869   12.540966    5.143188
C      11.373125    9.907093    4.943921
C      10.496861    6.146920    5.064049
C       7.222102    7.841186    5.575991
C       6.927668    5.447613    6.087758
C      10.569993   11.097001    5.025261
C      13.265356   11.384291    5.019503
C      12.818361   10.091406    4.991848
K_POINTS {gamma}

Casimir Effects: Physical Manifestations of the quantum vacuum.

Posted: January 19th, 2010 | Author: obm | Filed under: Seminar Notes | Tags: | No Comments »

Today, Robert J. Jaffe gave a very inspiring talk on Casimir effect. He started from the classical grounded planes and ended up describing a method for calculating more general shapes. Some highlights from his talks are:

  • Divergences removed using renormalization theory lead to unphysical results, as there are no terms in the expansion that can cancel the divergence.
  • Divergences often result from unphysical conditions imposed on the system, like unphysical boundary conditions. For example assuming a metal to be rigid at every frequency is unphysical.
  • The transition from VdW to Casimir forces is continuous, and can be approximated by adding retardation effects to Quantum-Relativistic calculation of VdW.
  • Using T matrices and dynamical polarizability of the system, just like how engineers use them to identify material based on their radar signature, Casimir forces can be calculated.
  • Dark energy/Casimir correlation is overstated, S matrix theories show casimir effects even without vacuum.
  • Many different methods of calculating casimir forces each lead to interesting physics
  • Experimental manifestations?

T. Emigetal et Al. PRL 99 170403 (2007) might be interesting to read.

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