# [Pw_forum] Phonon omega or nu? Factors of 2pi

Johannes Moeller j.moeller1 at physics.ox.ac.uk
Fri Sep 21 16:21:06 CEST 2012

```Thanks very much for your reply Saurabh,

That's what I thought as well, though if the "omega" output by Espresso is a linear frequency it should be

Energy = h (energy-s) * nu (/s)

rather than hbar. This is not what I would naturally do if I was a given a number "omega". So if this indeed is correct, I think the naming of the phonon output frequency should be revised.

Best wishes,
Johannes

From: Saurabh Bajaj <sbajaj at caltech.edu<mailto:sbajaj at caltech.edu>>
Date: 21 September 2012 15:02:25 GMT+01:00
To: PWSCF Forum <pw_forum at pwscf.org<mailto:pw_forum at pwscf.org>>
Subject: Re: [Pw_forum] Phonon omega or nu? Factors of 2pi
Reply-To: PWSCF Forum <pw_forum at pwscf.org<mailto:pw_forum at pwscf.org>>

Yes, you are right. The numbers with units /cm are wavenumbers (nu-bar).
Frequency, nu (/s) = c (cm/s) * nu-bar (/cm)
Lamda (cm) = 1/nu-bar (/cm)
Energy = hbar (energy-s) * nu (/s)

Saurabh Bajaj
California Institute of Technology

On Fri, Sep 21, 2012 at 9:25 AM, Johannes Moeller <j.moeller1 at physics.ox.ac.uk<mailto:j.moeller1 at physics.ox.ac.uk>> wrote:
Hello all,

A quick question about the definition of the phonon frequency omega. Is the omega output by Espresso an angular or a linear frequency (omega/2pi)? I.e. is this converted into an energy by multiplying by hbar or h?

Comparing simple vibrational modes of molecules (eg. of CO2) in cm^-1 to experimental values gives good agreement with experimental data, which are usually referred to as a liner frequency nu or 1/lambda rather than an angular frequency omega. This suggests that the value that Espresso outputs is nu and not omega(2pi*nu) as the name implies?

The values output by Espresso in THz and cm^-1 seem to be related simply by a factor of c (no factors of 2pi). I'm using QE 5.01 but I don't think this is version specific.

Many thanks,
Johannes

-------------------------------
Johannes Moeller
Department of Physics
University of Oxford
Oxford OX1 3PU, UK

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Johannes Moeller
Department of Physics
University of Oxford