CCL:G: How to calculate Hyperpolarizability using G03

[Sahan Thanthiriwatte <sahanchem###gmail.com>]

 Hi Veerpandian,

First hyperpolarizability (Beta) is a third rank tensor
 that can be described by a 3x3x3 matrix. The 27 components of the 3D matrix can
 be reduced to 10 components due to the Kleinman symmetry. It can be given in the
 lower tetrahedral format. It is obvious that the lower part of the 3x3x3 matrix
 (cube) is a tetrahedral. 
 
you can exploit #P and POLAR keywords to compute hyperpolarizability in
 Gaussian. 

For an example: ‘#P B3LYP/6-31G** POLAR gives you the
 10 components of lower tetrahedral tensor. The 10 components of this tensor is
 Bxxx, Bxxy, Bxyy, Byyy, Bxxz, Bxyz, Byyz, Bxzz, Byzz, and Bzzz;
 respectively.
 
The the total hyperpolarizability (Btot) can be calculated using following
 equations. 

1) The components of beta can be calculated using the
 following equation

B_i = B_iii + 1/3 sum (B_ijj+B_jij+B_ijj)  i =
 x,y,z
 
Using the x, y and z components of B, the magnitude of the first
 hyperpolarizability tensor can be calculated.

B_tot =
 (Bx^2+By^2+Bz^2)^1/2

The complete equation for calculating the magnitude
 of B from Gaussian output is given as follows.
 
b_tot =
 {(b_xxx+b_xyy+b_xzz)^2+(b_yyy+b_yzz+yxx)^2+(b_zzz+b_zxx+b_zyy)^2}^1/2

Since
 the values of the first hyperpolarizability tensors of the output file of
 Gaussian are reported in atomic units (a.u.), the calculated values should be
 converted into electrostatic units (1 a.u. = 8.6393x10^-33 esu).
 
you can find more details form 
J. Mol. Struc. (Theochem)
 y2002,v617,pp169–175
http://dx.doi.org/10.1016/S0166-1280(02)00419-0

Regards,
-Sahan-
 
/*---------------------------*/
K. Sahan Thanthiriwatte, Ph.D.
Center
 for Computational Molecular Science & Technology,
School of Chemistry and
 Biochemistry
Georgia Institute of Technology
Atlanta, GA 30332
 Tel: 404-496-8244, Fax: 404-894-7452


On Mon, Jan 10, 2011 at 4:52 AM,
 veera pandian ponnuchamy veera.pandi33[a]gmail.com <owner-chemistry]^[ccl.net> wrote:
 >
> Sent to CCL by: "veera pandian ponnuchamy"
 [veera.pandi33(_)gmail.com]
> I am a beginner in computational chemistry doing my M.Sc
 project on prediction of hyperpolarizability of organic molecule using Gaussian
 03/09. When I use polar=enonly in the route section, the program completed
 successfully. I dont know which value I have to take from the output to get the
 hyperpolarizability? Whether my keyword is right or wrong? Any suggestions will
 be helpful
 >
> Thanks in advance.
>
> By
>
 Veerpandian.P
>
>
>
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