Dear Giuseppe, Understanding the negative values is quite simple actually.
Imagine two compatible Hilbert spaces. Let's say Cartesian coordinates and spherical coordinates. Let's be in 2D to make things simple. Transforming a coordinate like d=135 degrees and r=1 cm (which are both positive numbers) will give you 0.707107y, -0.707107x so it is possible to have a transformation that gives you negative values, although you start with positive values. Mathematically speaking, as long as you are dealing with spaces that obey closure/completeness you can choose whatever to represent your results. The KS states constitute a complete set (assuming you have infinite/enough virtual orbitals calculated), so you can choose it to describe your results, but it is very important to remember that the interpretation should be adapted to new situation. O.k. This part needs a risky allegory. Imagine a particle that can move only in a line. The Hilbert space spanned by the corresponding Hamiltonian will then be on a line as well, say it consists of +X and -X When you add a perturbation to the system, say a slight perturbation in the Y direction, the new Hilbert space is +X,-X,+Y and -Y Since this is a perturbation, the magnitude of the Y component is negligible in comparison to magnitude of X component. The result is almost exactly equivalent to re-adjusting the length of the X in the previous calculation. So let's assume your Hilbert space remains the same in both cases. When you want to represent the perturbed result using +X and -X Hilbert space, irrespective if you have a constraint in the system that restricts the particle to move only in +X direction, when you "project" the +Y or -Y component in your perturbed system to the vectors spanning the unperturbed Hilbert space, you will see a -X. So what can be the values that will serve our best interest in our case? After a lengthy discussion, and I totally agree with it, the most physically useful value we come up with are the oscillator strengths. So, those values are to be interpreted as corrections to the oscillator strengths due to transitions that "look like" mentioned elements. (In a vaguely similar manner how a movement in Y direction looks like -X, but since we are talking about a Hilbert space that obeys closure and can span both Hamiltonians, this time the resemblance is more "exact") and I would advise you to use more virtual states, otherwise you will have too much spilling (i.e. error due to not satisfying closure) Baris On Fri, May 25, 2012 at 11:19 AM, Giuseppe Mattioli <giuseppe.mattioli at ism.cnr.it> wrote: > > Dear all > I've performed a TDDFT calculation of the absorption spectrum of a molecule, > and I am playing around > with the new (QE 5.0) "stage 2" calculations, which should indicate the > contribution of virtual > states to the absorption coefficients, as explained in > > my_Espresso/5.0/TDDFPT/Examples/CH4-BOND > > The "stage 2" calculation has been pointed on the first absorption band found > by turbo_spectrum.x; my > molecule has 98 occupied states, and 10 unoccupied have been calculated by > pw.x (nband=108) and I > suppose to be quite satisfied (for all I know of this molecule) with these > lines > > ? ? ?98 ? 1 ? ? 0.28374685E+04 ? -0.82400471E+04 ? 2.33588 > ? ? ?98 ? 2 ? ? 0.27984762E+04 ? -0.82731097E+04 ? 2.34525 > ? ? ?98 ? 3 ? ?-0.52066456E-05 ? ?0.13245374E-04 ? 0.00000 > ? ? ?98 ? 4 ? ?-0.93634066E-05 ? ?0.23337916E-04 ? 0.00000 > ? ? ?98 ? 5 ? ? 0.52748267E-05 ? -0.14618050E-04 ? 0.00000 > ? ? ?98 ? 6 ? ?-0.78431969E+01 ? ?0.20124113E+02 ?-0.00570 > ? ? ?98 ? 7 ? ?-0.78379694E+01 ? ?0.20102365E+02 ?-0.00570 > ? ? ?98 ? 8 ? ?-0.10283141E-04 ? ?0.18715947E-04 ? 0.00000 > ? ? ?98 ? 9 ? ?-0.29200741E-04 ? ?0.36618310E-04 ? 0.00000 > ? ? ?98 ?10 ? ? 0.38666959E-05 ? -0.12074233E-04 ? 0.00000 > > which seem to indicate that the onset of the absorption spectum can be > attributed to single-particle > transitions involving the highest occupied state and the first and second > virtual states (I daresay > HOMO connected with LUMO and LUMO+1...). > > But what about these lines? > > ? ? ?92 ? 1 ? ?-0.67396365E+03 ? ?0.17328962E+04 ?-0.49124 > ? ? ?92 ? 2 ? ?-0.68404352E+03 ? ?0.17306015E+04 ?-0.49059 > ? ? ?92 ? 3 ? ? 0.94419011E-05 ? -0.60010033E-04 ? 0.00000 > ? ? ?92 ? 4 ? ?-0.18274042E-04 ? ?0.26892556E-04 ? 0.00000 > ? ? ?92 ? 5 ? ?-0.51970803E-04 ? ?0.11972278E-03 ? 0.00000 > ? ? ?92 ? 6 ? ?-0.38956134E+01 ? ?0.48423966E+01 ?-0.00137 > ? ? ?92 ? 7 ? ?-0.38946693E+01 ? ?0.48428589E+01 ?-0.00137 > ? ? ?92 ? 8 ? ?-0.20625070E-01 ? -0.59183925E-04 ? 0.00000 > ? ? ?92 ? 9 ? ?-0.17290402E-02 ? -0.34538054E-04 ? 0.00000 > ? ? ?92 ?10 ? ? 0.59116529E-05 ? -0.18839515E-04 ? 0.00000 > > That is, what do negative (and not so small) coefficients means? > > Thank you in advance > > Giuseppe > > -- > ******************************************************** > - Article premier - Les hommes naissent et demeurent > libres et ?gaux en droits. Les distinctions sociales > ne peuvent ?tre fond?es que sur l'utilit? commune > - Article 2 - Le but de toute association politique > est la conservation des droits naturels et > imprescriptibles de l'homme. Ces droits sont la libert?, > la propri?t?, la s?ret? et la r?sistance ? l'oppression. > ******************************************************** > > ? Giuseppe Mattioli > ? CNR - ISTITUTO DI STRUTTURA DELLA MATERIA > ? v. Salaria Km 29,300 - C.P. 10 > ? I 00015 - Monterotondo Stazione (RM) > ? Tel + 39 06 90672836 - Fax +39 06 90672316 > ? E-mail: <giuseppe.mattioli at ism.cnr.it> > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum
