Polarizability anisotropy derivatives

[ankit7540]

I am using DALTON to obtain frequency dependent polarizability of simple molecules like H2. Is it also possible to obtain the derivatives of polarizability anisotropy with respect to the numerical coordinates in DALTON ?
My current approach successfully gives me the polarizabilty (freq. dependent) as following output. Using simple formulae, polarizability anisotropy can be found (for my case, gamma = ((α_zz-α_xx)/3α_iso) and what I am looking for is the derivative of the anisotropy wrt equilibrium nuclear coordinate.

Code: Select all

++++++++++++++++++ Frequency dependent polarizabilities ++++++++++++++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++


Polarizability tensor for frequency 0.000000 au
----------------------------------------------------
Ex Ey Ez

Ex 2.630489 0.000000 0.000000
Ey 0.000000 2.630489 0.000000
Ez 0.000000 0.000000 6.941281

Isotropic polarizability: 4.067419

Polarizability tensor for frequency 0.085645 au
----------------------------------------------------
Ex Ey Ez

Ex 2.653105 0.000000 0.000000
Ey 0.000000 2.653105 0.000000
Ez 0.000000 0.000000 7.159857

Isotropic polarizability: 4.155356


Interatomic separations (in Angstrom):
--------------------------------------

H2 _1 H2 _2
------ ------
H2 _1: 0.000000
H2 _2: 0.750000 0.000000


Max interatomic separation is 0.7500 Angstrom ( 1.4173 Bohr)
between atoms 2 and 1, "H2 _2" and "H2 _1".

Min HX interatomic separation is 0.7500 Angstrom ( 1.4173 Bohr)


Bond distances (Angstrom):
--------------------------

atom 1 atom 2 distance
------ ------ --------
bond distance: H2 _2 H2 _1 0.750000
______________________________________________________________________

[taylor]

It seems there was no reply to your original posting. The derivative of the polarizability (or its anisotropy) with respect to nuclear coordinates is in effect a third derivative of the energy. In fact, for the static case it is exactly that: differentiated twice with respect to electric field and once with respect to nuclear motion. Dalton does not have analytical third derivatives to deal with this case, but the code can handle this by numerical differentiation --- you can look at the documentation under the *NMDDRV directive and its options. I should say however that people have reported some issues with certain calculations (e.g., DFT) when working this way.

If you want the derivatives so that you can obtain a vibrationally averaged polarizability (or anisotropy) you can get these quantities directly by calculating vibrational averages --- this is also documented in the manual. If you want the derivatives for (e.g.) Raman intensities you can either use the numerical differentiation approach I mentioned above, or if you are considering only a diatomic it may be easier to simply calculate the polarizabilities at three geometries around equilibrium and then to use the central difference formula to get the polarizability derivative.

Note that if for some reason you want higher derivatives of the polarizability you will either have to fit it yourself or have the program calculate the numerical derivatives.

Best regards
Pete
P.S. When you post, please upload complete output and error files (the former contains the input files so these are not needed) and upload them separately. Incorporating the files in line creates all sorts of window-size-dependent readability problems, as well as the font being variable width.

[ankit7540]

Thank you very much for the suggestions.
And I will take care while posting in the future.