[Wien] Units of the momentum matrix elements

[Gavin Abo]

I could be wrong, but I think the values of the complex momentum matrix 
elements in the mommat2 file should be in units of momentum.

In the atomic units (a.u.) system [ 
https://en.wikipedia.org/wiki/Atomic_units ], I believe the momentum 
element values are unitless or dimensionless.

However, to know what the unitless values are for in the a.u. system, I 
think they use labels like a.u. of mass, a.u. of charge, etc. [ 
https://en.wikipedia.org/wiki/Non-SI_units_mentioned_in_the_SI ].  For 
momentum, there is:

a.u. of momentum

To convert between that and SI units, there is [ 
http://physics.nist.gov/cuu/pdf/nonsi_2006.pdf ]:

1 a.u. of momentum = 1.99 x 10^-24 kg*m/s

In the a.u. system, there are Hartree atomic units and Rydberg atomic 
units.  It seems that values such as energy and mass between the two are 
NOT the same in the a.u. system [ 
https://en.wikipedia.org/wiki/Natural_units#Atomic_units ].

However, I tried to do a simple momentum calculation of p = mv with m = 
9.11x10^-31 kg and v = 2x10^6 m/s with Hartree atomic units and Rydberg 
atomic units, and it looks like they gave the same values for momentum [ 
https://github.com/gsabo/Units/blob/master/Momentum%20SI%20And%20Atomic%20Units.pdf 
].

Though, the internal calculations of optic might be using the system of 
Rydberg atomic units [ 
http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg14845.html 
, https://doi.org/10.1186/1754-0429-1-12 (where section 3.2 shows e^2 = 
1/m = 2 and ħ = 1) ].

On 4/18/2017 3:24 AM, Yong Woo Kim wrote:
> Dear Wien2k users,
>
> Hello, I am currently working on obtaining the transition dipole 
> moments of ZnO and Sapphire along specific paths in the Brillouin Zone 
> using optic.
>
> I calculated the momentum matrix elements (the ones in case.mommat2) 
> but I seem to be getting values slightly lower than the ones I found 
> in literature. I tried multiple attempts, using denser k mesh and 
> increasing the energy maximum etc. but wasn't able to reproduce the 
> results.
>
> Until now I thought the units of the values in mommat2 would be in 
> Rydberg atomic units (i.e. in hbar/a0) as written in the userguide, 
> but I wanted to be sure that this is right. It seems that the momentum 
> matrix can be expressed in terms of energy units as well using the 
> Kane parameter, so it would be really helpful if you could confirm me 
> exactly which value is being given.
>
> Thank you very much for your help in advance.
>
> Yours Sincerely,
> Yong Woo Kim