Polarizability anisotropy derivatives

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ankit7540
Posts: 26
Joined: 05 Sep 2015, 10:49
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Last name(s): RAJ
Affiliation: National Chiao Tung University
Country: Taiwan, Province of China

Polarizability anisotropy derivatives

Post by ankit7540 » 23 Sep 2015, 09:19

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 = ((αzzxx)/3αiso) 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
______________________________________________________________________
Last edited by ankit7540 on 04 Nov 2015, 11:20, edited 1 time in total.
Best regards.
Ankit

taylor
Posts: 532
Joined: 15 Oct 2013, 05:37
First name(s): Peter
Middle name(s): Robert
Last name(s): Taylor
Affiliation: Tianjin University
Country: China

Re: Polarizability anisotropy derivatives

Post by taylor » 30 Oct 2015, 14:00

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
Posts: 26
Joined: 05 Sep 2015, 10:49
First name(s): ANKIT
Last name(s): RAJ
Affiliation: National Chiao Tung University
Country: Taiwan, Province of China

Re: Polarizability anisotropy derivatives

Post by ankit7540 » 31 Oct 2015, 08:15

Thank you very much for the suggestions.
And I will take care while posting in the future. :-)
Best regards.
Ankit

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