Dear Baris Thank you. I should read the answer another couple o' times, and then I may possibly post further questions...:-) Giuseppe
On Monday 28 May 2012 18:33:00 O. Baris Malcioglu wrote: > 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 > > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum -- ******************************************************** - 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>
