Manual:Output

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At first you may be quite happy that you have mastered the input file, and octopus runs without errors. However, eventually you (or your thesis advisor) will want to learn something about the system you have managed to describe to Octopus.

1 Ground State DFT
2 Time Dependent DFT
3 References

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Ground State DFT

Octopus sends some relevant information to the standard output (which you may have redirected to a file). Here you will see energies and occupations of the eigenstates of your system. These values and other information can also be found in the file static/info.

However Octopus also calculates the wavefunctions of these states and the positions of the nuclei in your system. Thus it can tell you the density of the dipole moment, the charge density, or the matrix elements of the dipole moment operator between different states. Look at the values that the Output variable can take to see the possibilities.

For example, if you include


Output = wfs_sqmod + potential

in your inp file, octopus will create separate text files in the directory static with the values of the square modulus of the wave function and the local, classical, Hartree, and exchange/correlation parts of the Kohn-Sham potential at the points in your mesh.

You can specify the formatting details for these input files with the OutputHow variable and the other variables in the Output section of the Reference Manual. For example, you can specify that the file will only contain values along the x, y, or z axis, or in the plane x=0, y=0, or z=0. You can also set the format to be readable by the graphics programs OpenDX, gnuplot or MatLab. OpenDX can make plots of iso-surfaces if you have data in three-dimensions. However gnuplot can only make a 3-d plot of a function of two variables, i.e. if you have the values of a wavefunction in a plane, and 2-d plots of a function of one variable, i.e. the value of the wavefunction along an axis.

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Time Dependent DFT

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Optical Properties

A primary reason for using a time dependent DFT program is to obtain the optical properties of your system. You have two choices for this, linear response theory a la Jamorski, Casida & Salahub ^[1], or explicit time propogation of the system after a perturbation, a la Yabana & Bertsch ^[2]. You may wish to read more about these methods in the paper by Castro et al.^[3]

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Linear Response Theory

Linear response theory is based on the idea that a small (time-dependent) perturbation in an externally applied electric potential $δ v (r,ω)$ will result in a (time-dependent) perturbation of the electronic density $δρ(r,ω)$ which is linearly related to the size of the perturbation: $\delta \rho (r, \omega ) = \int d^{3} r' \chi (r, r'; \omega) \delta v (r, \omega )$ . Here, obviously, the time dependence is Fourier transformed into a frequency dependence, $ω$ . The susceptibility, $χ(r, r';ω)$ , is a density-density response function, because it is the response of the charge density to a potential that couples to the charge density of the system. Because of this it has poles at the excitation energies of the many-body system, meaning that the induced density also has these poles. One can use this analytical property to find a related operator whose eigenvalues are these many-body excitation energies. The matrix elements of the operator contain among other things: 1) occupied and unoccupied Kohn-Sham states and energies (from a ground state DFT calculation) and 2) An exchange-correlation kernel, $f_{xc}(r, r', \omega) = {{\delta v_{xc}[n(r,\omega)]}\over{\delta n(r',\omega)}}\mid_{\delta v_{ext} = 0}$ .

Petersilka and Casida are two different approximations for these matrix elements, which we cannot find exactly (I think).

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Casida

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Petersilka

^[4]

"Petersilka means single-pole in frequency space, while Casida means the solution of the full matrix equation in momentum space. Unofficially speaking, these methods are clearly much faster (an order of magnitude) than propagating in time, but it turns out that they are terribly sensitive to the quality of the unoccupied states. This means that it is very hard to converge the excitation energy for one requires a very large simulation box (much larger than when propagating in real time). We still don't understand this fully. The implementation seems to be correct, though. You you try it out, I would also like to listen to your conclusions ;)" -- Miguel, Nov. 02

"Currently the oscillation forces calculated through the Petersilka approximations and in the eigenvalue-differences file are not given (they are all zeros). As a result, the result of oct-broad for those two cases is meaningless.

However, the full calculation (Casida's equations) is not much more costly than the Petersilka approximation, we have speeded that up quite a bit. And in this case the strengths are given properly, so that the spectrum given in spectrum.casida is correct. Since this is actually the "good" calculation, we have neglected the other options, I am afraid." --Al, Apr. 06

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Electronic Excitations by means of Time Propogation

see Time_Dependent#Delta_kick_-_Calculating_an_Absorption_Spectrum

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References

↑ {{{authors}}}, Dynamic polarizabilities and excitation spectra from a molecular implementation of time-dependent density-functional response theory: N2 as a case study, The Journal of Chemical Physics 5134-5147 (1996) [1]
↑ {{{authors}}}, Time-dependent local-density approximation in real time, Physical Review B 4484 - 4487 (1996) [2]
↑ {{{authors}}}, octopus: a tool for the application of time-dependent density functional theory, physica status solidi (b) 243 2465-2488 (2006) [3]
↑ {{{authors}}}, Excitation Energies from Time-Dependent Density-Functional Theory, Phys. Rev. Lett. 76 1212--1215 (1996) [4]