# [Pw_forum] virtual states in TDDFT (turbo_lanczos.x) calculations

Giuseppe Mattioli giuseppe.mattioli at ism.cnr.it
Tue May 29 11:10:58 CEST 2012

```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
>
> 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
> >
> > --
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> >
> >   Giuseppe Mattioli
> >   CNR - ISTITUTO DI STRUTTURA DELLA MATERIA
> >   v. Salaria Km 29,300 - C.P. 10
> >   I 00015 - Monterotondo Stazione (RM)
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> >   E-mail: <giuseppe.mattioli at ism.cnr.it>
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--
********************************************************
- Article premier - Les hommes naissent et demeurent
libres et ègaux en droits. Les distinctions sociales
ne peuvent être fondèes que sur l'utilitè commune
- Article 2 - Le but de toute association politique
est la conservation des droits naturels et
imprescriptibles de l'homme. Ces droits sont la libertè,
la propriètè, la sùretè et la rèsistance à 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>

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