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esmuigors

Member

Registered: 2026-02-06

Posts: 2

Hyper-Rayleigh scattering computation

Dear Dr. Lu and others,

I am currently investigating more thoroughly the output of Gaussian for Polar=DCSHG, particularly the computation of  HRS-averaged β in dipole orientation. I am typically using my own custom scripts. When I learned that Multiwfn does possess this ability as well (and much more), I computed the HRS-averaged β with it to get a reliable reference value.

Multiwfn uses a more general formula (from Plaquet et al., 2008). My script previously used the simpler formula from Verbiest, Clays and Rodriguez, 2009; I have now reimplemented the formula from Multiwfn manual, but the computed value of <β_HRS > changed only marginally. It is approximately equal to Multiwfn output.

However, what is peculiar is that it is equal to Multiwfn output only if I use component values for the static case to compute the <β_HRS >, not the dynamic one. In the case attached, the dynamic value of squared components <β_ZZZ>^2 and <β_XZZ>^2 is about 9 times higher than the static one. Here are the results for N,N-dimethylnitroaniline:

    --------------Multiwfn    -------My script   
        ---------------------------Static    -------Dynamic
<β_ZZZ>2    8.297E+05    8.293E+05    7.427E+06
<β_XZZ>2    2.017E+05    2.001E+05    1.578E+06

My question is, can this be the case? If so, maybe a note in the output would suffice in future versions of Multiwfn...

Personally I would still use the static value (as in the Multiwfn output) because most of the current density functionals still get the resonance values wrong due to simplicity and adiabaticity of their kernels.

P.S. There is a misprint on page 334 in the Multiwfn Manual, in the formula for <β_XZZ>^2. The term with coefficient +3/35 should have β_ζηη squared, as in the source publication (Plaquet et al., 2008).

P.P.S. I can send You the input and output of Gaussian calculation I used here if You fancy it.

sobereva

Tian Lu (Multiwfn developer)

From: Athens, Greece

Registered: 2017-09-11

Posts: 2,194

Website

Re: Hyper-Rayleigh scattering computation

The result is not necessarily wrong. Hyperpolarizability (beta) is often sensitive to frequency of incident light, static and dynamic beta at certain frequencies can easily differ by several times. Given that < β_HRS > contains squared beta components, it is not surprising that < β_HRS > calculated based on static and dynamic beta differ by nearly one order of magnitude.

It is indeed a misprint in the manual, I will fixed it. Thank you for pointing out.

esmuigors

Member

Registered: 2026-02-06

Posts: 2

Re: Hyper-Rayleigh scattering computation

Yes, indeed they are different (2.5 times in magnitude for this case). I was actually pointing out to the fact that Multiwfn only outputs one quantity and does not elaborate which one it is Maybe You can add this note to the output...

Thank You for the great software!

Last edited by esmuigors (2026-02-09 10:59:13)