## Nonlinear response definition in Dalton

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dawsphys
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Joined: 31 Oct 2014, 00:07
First name(s): Nathan
Middle name(s): J
Last name(s): Dawson
Affiliation: Case Western Reserve University
Country: United States

### Nonlinear response definition in Dalton

I was hoping someone could spell out how the nonlinear response is defined.

There are typically two evenly used conventions for the power series response coefficients. Ignoring tensor and freq jazz for simplicity, the two usual definitions begin with

(1) p = polarizability*E + hyperpol*E*E + 2nd_hyperpol*E*E*E + ...

(2) p = polarizability*E + (1/2)*hyperpol*E*E + (1/6)*2nd_hyperpol*E*E*E + ...

Which one does Dalton use?

The reason is because the MCSCF of an H-atom gave me a cubic response of approx 630 for the static gamma_zzzz. The accepted answer from Coulston about 80 years ago was approx. 222 a.u. from the first definition (about 1333 from the second definition). If I do a quick three-level model with sum rules I get about 118 (known to be this low for 1/r potentials). If Dalton uses the second definition then I would feel more comfortable with getting about 105 for the first definition rather than 650 (which sounds off). Anybody know why it is still way off from the static perturb method from Coulston? Below is the .dal file used

**DALTON INPUT
.RUN RESPONSE
.DIRECT
**WAVE FUNCTIONS
.MCSCF
*CONFIGURATION INPUT
.SYMMETRY
1
.SPIN MULTIPLICITY
2
.INACTIVE
0 0 0 0
.CAS SPACE
4 2 2 0
.ELECTRONS
1
**RESPONSE
*LINEAR
.DIPLNZ
*CUBIC
.DIPLNZ
.THCLR
1.0D-5
**END OF DALTON INPUT

olav
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Joined: 28 Aug 2013, 06:20
First name(s): Olav
Last name(s): Vahtras

### Re: Nonlinear response definition in Dalton

It is the second definition, i.e. the beta value is the second derivative of the dipole moment, gamma is the third derivative of the dipole moment.

Regards,
Olav

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