Ph.-DOS /transmission eigen values

[Dipankar Saha]

How can I get some states, at negative energy values....in the Ph.-DOS diagram??
(Even though the "Acoustic  sum rule" is checked.....!!!!)

Best_
Dipankar

[Dipankar Saha]

In ATK..... whatever "transmission eigen values"  that we get ......., how they are related to
the Trace[G^r  Sigma₁  Sigma₂ G^a] .....??

Thanks & Regards__
Dipankar

[Julian Schneider]

Most likely, the atomic positions in your structure are not accurately optimized before calculating the PhononDOS.
If that still does not help, and if you are using classical potentials with a long range (e.g. Coulomb interactions) then you need to increase the maximum interaction range parameter to be larger than the largest cutoff distance of the potential.

[Dipankar Saha]

Most likely, the atomic positions in your structure are not accurately optimized before calculating the PhononDOS.
If that still does not help, and if you are using classical potentials with a long range (e.g. Coulomb interactions) then you need to increase the maximum interaction range parameter to be larger than the largest cutoff distance of the potential.

Thank you Julian for your reply....../ Optimization May not be the reason in this case.... / However, I didn't get that.... while using classical potetials...... how can I  "increase the maximum interaction range parameter"  (Because, in calculator, all I have .... "potentialSet=     " and  "calculator=   ").....??

[Julian Schneider]

The maximum interaction range is an optional parameter that can be set in the DynamicalMatrix analysis object. When calculating the dynamical matrix, this parameter specifies the distance around a displaced central atom (i) in which the derivative of the forces on atoms (j)  are taken into account to calculate d^2 U / dr_i dr_j .
If this parameter is not specified, the default values are used (which are the covalent distances multiplied by a fuzz factor of 4.0).  In most cases this works well, but when e.g. a classical potential is used, which has a large cutoff radius (e.g. CoulombDSF (http://www.quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/ref.coulombdsf.html) with a default of 9 Angstrom), then the maximum interaction range parameter has to be increased to be larger than this cutoff radius, i.e. larger than 9 Angstrom, to avoid discontinuities.
You can find out if large cutoff values are used by your potential, if you send the script to the Editor with the "Script details" parameter set to "Show defaults". Then all the details of the classical potential are reflected in the script.
Which exact potential are you using?

Apart from that, negative frequencies might also occur if you are sitting exactly at a local maximum (e.g. due to symmetries in your structure). In this case, small random displacements to the atoms followed by another accurate geometry optimization should lead you to a minimum.

[Dipankar Saha]

Thanks a lot Julian for this detailed answer......    / It's actually  the parameterization of SW.... (i.e., StillingerWeber_MoS_2013) ..../ I could not really follow the steps....as you said, like... "if you send the script to the Editor with the "Script details" parameter set to "Show defaults"...then all the details of the classical potential are reflected in the script...." ; but still looking at source paper, I find that they....fitted the phonon spectrum with SW parameters for the two-body and the three body(angle bending as well) potentials.....with a max. cut-off of  4.27 Ang.  / In such a case... should I need to change the default "atomic_displacement=0.01*Angstrom" in dynamical matrix..??

Regards_
Dipankar

[Julian Schneider]

For the Stillinger-Weber and Tersoff-potentials the default values usually work well. You don't need to specify the maximum interaction range in the DynamicalMatrix parameters.

In your case, I'd rather suspect that there is something odd with the structure. Negative frequencies mean that there are soft modes present in the system, either by atoms sitting in a local saddle point.
You could try to calculate the phonon bandstructure (without checking Accoustic sum rule and Symmetrize) and then the location of the negative frequencies might give you some hints. If the negative frequencies occur at gamma, then you might need to increase the maximum interaction range, if the negative frequencies occur elsewhere, then it is likely that your structure is not in a local minimum.

[Dipankar Saha]

Thanks a lot.... Julian..... 

That's a nice way.....!!!  / Let me....try that....   I will let you know...

Best _
Dipankar

[Dipankar Saha]

Interestingly.... making the "acoustic_sum_rule=   ",  symmetrize=  " True or False... produces no change in  dispersion...!!!  / On the other hand .... "max_interaction_range= " set to default.... or, a very specific range of values ..... could only provide the reqd. Ph-DOS... (otherwise it's arbitrary)!!!

Instead...I went for further opti. of the strcut. ...which somewhat soothes out the density states at negative energy values(see, the attachment)...../ So your guess, that it is due to the struct.  ....seems to be correct....   

[Dipankar Saha]

In ATK..... whatever "transmission eigen values"  that we get ......., how they are related to
the Trace[G^r  Sigma₁  Sigma₂ G^a] .....??

Besides, it will be of great help ....if you can please comment on this.....!!! 

[Dipankar Saha]

 Dr. Julian Schneider,

For any particular energy 'E', one way to find the Transmission co-eff. is......

T(E) = Summation of [t_k t_k^dagger delta(E-Ek)] for all 'k' states at energy 'E'

Which is again same as.....  Trace[Gr  Sigma1  Sigma2 Ga]   ....

On the other hand, we have transmission eigen values of the transmission matrix...which can also be summed up...
for getting the transmission co-efficient...

1) How can one get these t_k s (or, as you say transmission amplitudes).....??

Actually, why I'm looking for this...is simply to find an analogy...with the ideal transmisson....either 0 or, 1.

2) Is it incorporated through the delta function....??

[Anders Blom]

See http://quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/ref.transmissioneigenvalues.html

[Dipankar Saha]

Dr. Anders Blom,

To be more specific,
can I extract the individual channel contributions form the total transmission....??
If yes.... then, which is the parameter...I should look into ??

Thanks in advance......

Best_
Dipankar

[Anders Blom]

That is precisely what the transmission eigenvalues are

[Dipankar Saha]

Okay....  / Thanks a lot...!!!