Mr. Maidur,

You can pay attention to the attachment.

Dear madam thank you very much for your response.

I think what you mentioned here is static hyperpolarizability, but I was looking for frequency dependent hyperpolarizability. Could you please have a look at my output file and suggest me which components I've to choose for the calculations. Kindly help me out. Looking for your answer.

Mr. Maidur,

In general, all equations that we have discussed are based on fundamental works by James Clerk Maxwell about polarizability, known from about 180 years.

So:

P(3)=B.X*(3)(-3w;w,w,w)(E*w)*3 B=1/4 (THG)

P(3)=B.X*(3)(-2w;w,w,0)(E*w)*2.E0 B=3/2 (EFISHG)

The equation to 'Chi'*(3) is given in my last posting. It includes ijkl-values, which for the so-called ''dynamic'' case are listed below to each frequency in your output.

Dear Bojidarka B. Ivanova,

I really didn't understand your answer, I just want to know the third order hyperpolarizability components from my output file, which components I've to consider? And please tell me whether I had computed the hyperpolarizability correctly or not. Please do reply madam.

Mr. Maidur,

Let us first clarify what are: '2nd', '3rd', 'static', 'dynamic', your datablock/set of; And what would you like to compute, in fact?

1. Your output file contains 'hyperpolarizability (gamma) tensor components' of the 2nd order (or g(ijkl)). The tensor is the sum of the vibrational, electronic and dipolar contributions. These values can be used, to calculate 'third-order nonlinear optical susceptibility' or 'chi(3)' (or X3 in my postings).

2. The so-called off-resonant limit, highlights those (hyper)polarizability values, which correspond to electronic properties and neglect the motion of nuclei; Or neglect the 'vibrational contribution'. The dominant longitudinal component of the static gamma is approximation to off-resonant dynamic gamma. The component is (g)ijkl=g(zzzz) in the output file. If you have a relatively large and uniaxial molecule (like organics, for example) you can use these values as "dynamic" gamma. Thus 'Chi(3)' can be approximated as g(zzzz) as a dynamic 3rd nonlinear optical effect for such cases:

........

Gamma(-2w;w,w,0) w= 532.0nm:

(au) (10**-36 esu) (10**-61 SI)

...............................

zzzz -0.233807D+09 -0.117761D+06 -0.145787D+06

.........

A reduction part of the electron density distribution at different frequencies is calculated. This reduction is the so-called "dynamic" gamma. But there are not 'dynamic' computations. These are static calculations (At w=0). When w is not '0', the computations are presented as ''dynamic'' ones.

3. THG susceptibilities as '3rd' order NLO effect.

It is given by 'Chi(3)IJKL(-3w;w,w,w)' (IJKL denotes macroscopic, while ijkl denotes microscopic). It is 3D fourth rank tensor with 81 components. Depending on the symmetry of the molecular object and medium some of these components are equal and/or '0'. So, if you would like to calculate THG in solution, for example, due to random orientation of the molecules,

Chi(3)IJKL(-3w;w,w,w) = N.Fg(IJKL),

The diagonal componets are given by the equation, which you already have with my first posting (attachment). It is necessary to replace g(ijkl)s to obtain 'Chi(3)'. However, as far as these are data in solution, you should calculate gammas in equilibrium or nonequilibrium solution.

4. Due to experimental THG measurements of optical field polarized parallel and perpendicular to the static field, you can compute theoretically g(p)-parallel as well.

It is given for the dynamic case by:

g(p)=(1/15)sum(g(iijj)+g(ijij)+g(ijji)), where i,j=x,y and z.

In this case you should distinguish g(ijkl) at w different from '0'.

In the static case the equation is given by:

= (1/5) sum(g(iijj)(0)).

5. To EFISH as '3rd' order NLO effect.

'Chi(3)' is given by 'Chi(3)(2w;w,w,0)'. The tensor consists of 3 independent elements and the equations can be found in the literature.

g(EFISH)= (mu.beta/5kT)+g0(-2w;w,w,0)

mu-molecular dipole moment

beta - polarizability tensor analog

k,T- known consts

6. dc Kerr effect

g(xxxx)(-w;0,0,w)-g(xyyx)(-w;0,0,w)

7. DFWM

g(xxxx)(-w;w,w,-w)

8. CARS effect

g(xxxx)(-2w1+w2;w1,w1,-w2)

The values in your output to 'g||' represent directly the 'parallel isotropic average' values as mentioned above. The perpendicular is also given:

.........

Gamma(-2w;w,w,0) w= 532.0nm:

(au) (10**-36 esu) (10**-61 SI)

|| -0.272119D+09 -0.137058D+06 -0.169677D+06

_|_ -0.881530D+08 -0.444000D+05 0.964596D+03

.........

As s described above, you should recognize with literature, that is devoted to the polarization effects, in general, and NLO properties of molecules (organics and metal-organics mainly due to large divergence of molecular symmetry) to determine what data you have. Then you should calculate gammas (gTHG, gEFISH, ...) and 'chi(3)' of interest, depending on the molecular symmetry, medium (gas-phase, solution) and more.

Dear Bojidarka B. Ivanova, I thank you very very much for your precious answer. Could you please suggest me where can I study the full background theory what you had mentioned above. Please give some reference materials to study these hyperpolarizabilities in detail. I realized there is so much to study thoroughly. Once again thank you so much. 

Mr. Maidur,

You might be paying attention to:

(i) I. Khoo, Liquid Crystals, Wiley, 1995, pages 1-297.

(ii) G. Wagniere, Linear and Nonlinear Properties of Molecules, VCH, 1993, pp. 1-193.

(iii) H. Nalwa, S. Miyata, Nonlinear Optics of Organic Molecules and Polymers, 1997, pp. 1-883.

(iv) Molecular aggregation: structure analysis and molecular simulation of crystals and liquids, Gavezzotti, A. Oxford Univ. Press, 2007, pp. 1-425.

In particular, ref. (iii) is very suitable to study this matter. It has rather a textbook character, in spite of, the given original references typical of monographs. There are given the matrix transformations according the symmetry, however, not to all groups. So, according to the molecular symmetry of your object and/or the space group (if you study crystals) you should perform the corresponding transformations in order to obtain 'Chi(3)'s.

The (ii) also gives the equations in details, despite, the context does not represent physically oriented treatment, but rather chemically oriented one. It is associated with molecular factors, electronic, molecular and crystal sructure effects on the response of the matter upon irradiation. Scarce attention has been payed, however, to the effect of environmetal factors on the molecular reactivity, electronic redistribution, structural changes and response, meaning solvation effects, stacking effects, molecular conformational effects; tautomerism, structural intramolecular rearrangement and formation of new C-C (C-X) bond/s upon irradiation; metal-ligand bond formation and CT effects; CT effects to the environment on the NLO response; ES geometry transformation; perturbation of the electronic structure; and dynamics in ES and GS; and many more chemical processes and reactions in GS and ES. All they are associated, however with valence electrones, and thus they affact the LO and NLO responses.

More details you may find in the original Maxwell's and Kerr's works known from about 190 years as I have already written as well as, while THG (3rd harmonic), EFISH and SHG (2nd harmonic) - in works from about 80 years, if you can find them.

In addition, you can use ref (v) to details about 'Chi(3)'. Ref. (v) has been outlined NLO effects upon IR irradiation. The reference section treats sources about 50's from the last Century. The description, however, follows a monograph style. So, it does not so suitable to study this topic. It has been addressed to infrared science, in general, and methodological instrumentation contributions associated with generation of far-IR irradiation via NLO methods. But most probably should be useful to anyway to you.

(v) Y. Shen, Nonlinear Infrared Generation, Springer Verlag, 1977, pp. 1-279.

I thank you very much dear madam, your answers were really helpful to me.. Thank you again..

Dear madam,

                          Does Gamma (-2w;w,w,0) corresponds to third harmonic generation parameter? because somewhere I read that (-2w;w,w,0) is related to electric field induced second harmonic generation (EFITHG) and (-3w;w,w,0) related to third harmonic generation (THG). But, in my output file I got only Gamma (-2w;w,w,0), and I need to calculate Gamma for THG i.e. at (-3w;w,w,w), how can I get this? Please kindly guide me madam, I will be grateful to you. Thank you very much for your replies.

Mr. Maidur,

The answer to your question is given above un my postings. For THG of molecular crystals you can use hexadecapole moments (http://www.gaussian.com/g_tech/g_ur/k_population.htm). If the tensor transformations to your crystalline system absent from ref. (iii), then you should carry out it according the symmetry of your crystal. 'Matrix transformations' is topic to your BSc education in more then one courses, furthermore. The linear optical and nonlinear optical phenomena in molecular systems is expressed by only one equation.

RG doe not represent University.

Ok madam I am working on it, Could you please tell me one thing.. Can I claim Gamma (-2w;w,w,0) as second hyperpolarizability for THG processes. If no, kindly suggest me how can I compute Gamma (-3w;w,w,w) using Gaussian 09. So far I could compute only Gamma (-2w;w,w,0), and I need to know the dynamic hyperpolarizability, but as you suggested I can't use hexadecapole moments for frequency dependent calculations. Please comment on this madam. I thank you for your kind response.

Dear Shivaraj Maidur,

Unfortunately there is no option to compute THG processes or second hyperpolarizability (-3w;w,w,w) using Gaussian program, you may have to use Gamess or Dalton for such type of calculations. Thank you for your question on RG.

Best wishes,

Please watch the video.. here is the link..

https://www.youtube.com/watch?v=VEQ0VRt2hdA