Beta vector which is the part of first hyperpolarizability can be calculated from
(βx2 +βy2 + βz2 )^1/2 How can we get βi where i=x,y,z.
I am confused, where there are different parameters discussed in different articles. Please suggest the formula and parameter for calculating β vector.
Also, they have given, βi = 1/3 Σ j=x,y,z (βijj+βjij+βjji) where i ≠ j Is it correct parameter to follow??
Kindly suggest me...
Mr. Perumal,
Can you upload your route section (input) and output data which you have taken to calculate betai?
Hello Anna,
β=(βx2 +βy2 + βz2 )^1/2,
β= [(β xxx + βxyy +βxzz )2 + (βyyy+βyzz +βyxx )2 + (βzzz+ βzxx +βzyy )2 ]1/2
Gaussian 09 gives the output file as follows, (see the file).
Thank you,
V.Mohankumar
Dr.Bojidarka B. Ivanova,
Thank you for your reply.
I hereby attach the output of the calculations for your perusal.
Also, I got confused in the parameters they are used.
βi = 1/3 Σ j=x,y,z (βijj+βjij+βjji) where i ≠ j Is it correct parameter to follow??
Kindly reply..
-Muthuraja.
Dear Mohankumar,
Thank you for your reply.
I want to calculate vector part of first hyperpolarizability.
Kindly Suggest a method for obtaining the same...
Mr. Perumal,
Two sets polarization tensor components are displayed in your output file. You should consider the quadrupole moment and octapole moments to calculate the beta values. They are specified as xxx, yyy, zzz values in a tabular form.
The data presented as 'end' of your Gaussian output file account for the nuclear motion in the calculation of electrical properties (or vibrational contribution). The vibration contribution using FTP, for example, applied to molecular systems (organics) shows a weak correction to 3 or even 4 decimal signs of the values.The beta tensor components of organic dyes, for example, (some of our systems) have magnitude order from (-7000)-(-10000). So, a contribution to the 3 or 4 decimal sign (meaning -10000.00XX) can be neglected.
The vibrational contribution is important to consider inorganic anions in external electric field or in general inorganics like NaCl, for example. Or to sistems where there is induced CT in external electric field. These are mainly ionic compounds, non-covalently bonded systems. Because of the computation of ijk tensor components (or XXX, YYY ...) by Gaussian includes computation of the energy of the system in absence and then in presence of an external electric field. The results are obtained from numerical differentiation in the energy values.
Your output:
...........
Quadrupole moment (field-independent basis, Debye-Ang):
XX= -15.9480 YY= -23.5499 ZZ= -25.3210
XY= 0.0001 XZ= -0.0022 YZ= -0.0003
Traceless Quadrupole moment (field-independent basis, Debye-Ang):
XX= 5.6583 YY= -1.9436 ZZ= -3.7147
XY= 0.0001 XZ= -0.0022 YZ= -0.0003
Octapole moment (field-independent basis, Debye-Ang**2):
XXX= 0.0001 YYY= -16.6006 ZZZ= 0.0117 XYY= 0.0002
XXY= -1.6543 XXZ= 0.0127 XZZ= 0.0000 YZZ= 1.6044
YYZ= 0.0106 XYZ= -0.0009
Hexadecapole moment (field-independent basis, Debye-Ang**3):
XXXX= -99.9378 YYYY= -114.5932 ZZZZ= -21.6732 XXXY= 0.0003
XXXZ= -0.0109 YYYX= 0.0001 YYYZ= 0.0030 ZZZX= -0.0016
ZZZY= -0.0005 XXYY= -38.6972 XXZZ= -31.1812 YYZZ= -25.5530
....................................
Dr. Bojidarka B. Ivanova,
For calculating 'β'
β=(βx2 +βy2 + βz2 )^1/2
βi = 1/3 Σ j=x,y,z (βijj+βjij+βjji) where i ≠ j
where i=x,y,z.
which means
βx = 1/3 Σ (βxyy+βyxy+βyyx+βxzz+βzxz+βzzx+βxyz)
Is it correct parameter to follow??
Dr. Bojidarka B. Ivanova,
Thank you once again for your reply.
Kindly comment the above answer and let me suggest the parameters
Mr. Perumal,
The parameters are shown above (ijk=xyz components). These values are electronic polarizability/hyperpolarizability.
Urea is a covalently bonded system. In external electric field there is not dissociation of the covalent bond and systems cannot be regarded as ensemble of independent different changed species. Or it is not ensemble of ions. So, the polarization effect of the valent p-electrons is governed, rather then the atomic motion in covalently bonded systems. The covalent skeleton of a molecule can be stable under even more extremal conditions.
You have given equations in your posting, which, in fact, represent average hyperpolarizability.
The b(vec) is the equation b=(bx.bx+by.by+bz.bz)1/2 (your equation). The bx, by, bz are computed using equation b(i)=1/5(Bijj + Bjij +Bjji) in your posting.
The vector and average equations can be found in ref. 1.
If you would like to compute polarizabilities with separates x,y components at given frequency, then there is needed to add in your route section only: 'cphf=xy'. The 'cphf=rdfreq' is used when the computations should account for given frequency/nm. The output ijk=xyz data have the same format. Then b(vec) data correspond to the frequency/nm used in your input.
You have used polar=DCSHG to extra frequency-dependent CPHF, but this option implies CPHF=RdFreq, too (http://www.gaussian.com/g_tech/g_ur/k_polar.htm).
Ref. 1. A group-dipole interaction model of the molecular polarizability and the molecular first and second hyperpolarizabilities, K. Sundberg, The Journal of Chemical Physics 66, 114 (1977); doi: 10.1063/1.433657
Dr. Bojidarka B. Ivanova,
Many thanks to you.
I will go through the reference, if any doubts means, I may come again...
yes you can used gauusian09:
and you can calculate the first hyperpolariability Beta like this
β=(βx2 +βy2 + βz2 )^1/2,
β= [(β xxx + βxyy +βxzz )2 + (βyyy+βyzz +βyxx )2 + (βzzz+ βzxx +βzyy )2 ]1/2
Gaussian 09 or 03
you can calculate vector of the first hyperpolarizability by using : The b(vec) is the equation b=(bx.bx+by.by+bz.bz)1/2 (your equation). The bx, by, bz are computed using equation b(i)=1/5(Bijj + Bjij +Bjji) in your posting.
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