Calculation of d-band center

[jianmin]

Hi Prof. Graeme,

Is there any new progress on the method of calculating the d-band center by VTST (the dosanalyze.pl script)? If there is, I would be glad to use it.

Continue the topic in viewtopic.php?f=2&t=632&p=2070&hilit=center#p2070. According to the guys who put forward this 'd-band model' (Norskov's group), "The d-band center was calculated as the first moment of the projected d-band density of states on the surface atoms referenced to the Fermi level, and the mean squared d-band width was calculated as the second moment.(in J. Chem. Phys. 120 (2004) 10240)" Is this method different from the mothod that you employed? Will you integrate their method, at least as an alternative?

Thanks.

[graeme]

It would certainly be easy enough to add to the script, but you can also do this analytically.

In our script, we calculate the width as:

width = Sqrt( Sum_i (E_i-E_avg)^2 /N )

where E_i are the d-band energies and E_avg is the average d-band level.

If you want

width_fermi = Sqrt( Sum_i (E_i-E_f)^2 /N )

you can take our width and add Sqrt((E_avg-E_f)^2) = |E_avg-E_f|, which is the average position of the d-band with respect to the Fermi level.

And this gets at the heart of the issue. To say that width_fermi is correlated with the average d-band level with respect to the Fermi level (E_avg-E_f) is not a physical principle -- it is by definition. It is (in my view) much stronger to show that the actual width of the distribution correlates with the d-band level.

[jianmin]

Thanks a lot for the explanation. I am learning it.