This may be too late to be useful to you, but I would make the following points:
1) Calculated polarizabilities and particularly hyperpolarizabilities are usually strongly affected by the inclusion of correlation effects. HartreeFock and most DFT functionals that I am aware of will only give sensiblelooking results through cancellation of errors.
2) The inclusion of diffuse functions in calculations is essential, including diffuse polarization functions. Basis sets such as 6311G are the worst place to start because they are fundamentally poor descriptions of the atomic electronic structure. Augmenting them is not the way to go. Better basis sets are needed from the start.
3) For hyperpolarizabilities there are vibrational as well as electronic contributions that can be significant in polyatomic molecules.
4) Comparison with experiments is a much trickier business than looking at a published experimental number. It is very often the case that the uncertainties given in experimental papers are derived purely from the precision of the original measurement. But the original measurement is not the measurement of the hyperpolarizability! It is a measurement of something (light scattering, SHG, birefringence) from which the experimentalists deduce a hyperpolarizability. Such analysis of experiment includes all sorts of assumptions that may or may not be warranted, and whose influence on the uncertainties in the final result are often ignored. One should be very careful about understanding exactly how the final result was obtained from the original experiment, and what sources of uncertainty might arise.
Best regards
Pete
Which test illustrates SHG calculation in Dalton

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Re: Which test illustrates SHG calculation in Dalton
I first used B3LYP 6311G++(2d,2p) by GAMESS to optimize HF, and then used NWCHEM7.0.0, GAMESS and Dalton2016.2 to calculate the hyperpolarizability of HF.
Dalton2016.2 using the same basis set and c2v symmetry gives
ZDIPLEN (unrel.) 0.0000 ZDIPLEN (unrel.) 0.0000 ZDIPLEN (unrel.) 0.0000 8.8915460
0.1312 0.0656 0.0656 9.7304868
NWCHEM gives
CCSD Lambda Response polarizability / au
Frequency = 0.0000000 / au
Wavelength = Infinity / nm
beta(Z,Z,Z) = 9.739286463 / au
...
CCSD Lambda Response polarizability / au
Frequency = 0.0656000 / au
Wavelength = 694.5633079 / nm
...
CCSD Quadratic Response
Static Hyperpolarizability ''' ''Why still called static?'''''

beta(Z,Z,Z) = 8.461760589 / au
The original NWCHEM QA test using the following geometry
symmetry c2v
H 0 0 0
F 0 0 1.7328795 (This perhaps should be almost one half.)
gives
CCSD Quadratic Response
Static Hyperpolarizability

...
beta(Z,Z,Z) = 8.630759039 / au
1 H 1.0000 0.00000000 0.00000000 1.55959155
2 F 9.0000 0.00000000 0.00000000 0.17328795
GAMESS HF gives using basis set accdz and c2v symmetry
Beta tensor [in au]( 0.131200; 0.065600, 0.065600)
x y z
...
zz. 0.000000 0.000000 10.171063
Reference'' Frequencydependent hyperpolarizability of hydrogen fluoride'' gives(calculated)
static beta(z,z,z)=8.058
SHG beta(z,z,z)=9.430 at Re=1.7328 a.u. (This perhaps should be almost one half.)
Very Best Regards!
Dalton2016.2 using the same basis set and c2v symmetry gives
ZDIPLEN (unrel.) 0.0000 ZDIPLEN (unrel.) 0.0000 ZDIPLEN (unrel.) 0.0000 8.8915460
0.1312 0.0656 0.0656 9.7304868
NWCHEM gives
CCSD Lambda Response polarizability / au
Frequency = 0.0000000 / au
Wavelength = Infinity / nm
beta(Z,Z,Z) = 9.739286463 / au
...
CCSD Lambda Response polarizability / au
Frequency = 0.0656000 / au
Wavelength = 694.5633079 / nm
...
CCSD Quadratic Response
Static Hyperpolarizability ''' ''Why still called static?'''''

beta(Z,Z,Z) = 8.461760589 / au
The original NWCHEM QA test using the following geometry
symmetry c2v
H 0 0 0
F 0 0 1.7328795 (This perhaps should be almost one half.)
gives
CCSD Quadratic Response
Static Hyperpolarizability

...
beta(Z,Z,Z) = 8.630759039 / au
1 H 1.0000 0.00000000 0.00000000 1.55959155
2 F 9.0000 0.00000000 0.00000000 0.17328795
GAMESS HF gives using basis set accdz and c2v symmetry
Beta tensor [in au]( 0.131200; 0.065600, 0.065600)
x y z
...
zz. 0.000000 0.000000 10.171063
Reference'' Frequencydependent hyperpolarizability of hydrogen fluoride'' gives(calculated)
static beta(z,z,z)=8.058
SHG beta(z,z,z)=9.430 at Re=1.7328 a.u. (This perhaps should be almost one half.)
Very Best Regards!
Last edited by xiongyan21 on 22 Mar 2020, 07:15, edited 3 times in total.

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 First name(s): yan
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Re: Which test illustrates SHG calculation in Dalton
I use the specific GAMESS input making software waMacMolPlt to redraw the molecule, then use mp2 and 6311G++(2d,2p) to find the following equilibrium geometry of HF having c2v geometry.
DALTO2016.2 gives
++
! FINAL CCSD RESULTS FOR THE FIRST HYPERPOLARIZABILITIES !
++
A operator B operator C operator property

ZDIPLEN (unrel.) 0.0000 ZDIPLEN (unrel.) 0.0000 ZDIPLEN (unrel.) 0.0000 8.6941344
0.1312 0.0656 0.0656 9.5090740

With GAMESS
...
Beta tensor [in au]( 0.000000; 0.000000, 0.000000)
x y z
zx. 0.704144 0.000000 0.000000
zz. 0.000000 0.000000 9.926728
Beta tensor [in au]( 0.131200; 0.065600, 0.065600)
x y z
xz. 0.848328 0.000000 0.000000
zx. 0.679234 0.000000 0.000000
zz. 0.000000 0.000000 10.603235
The above reference gives (calculated)
SHG beta(zzz)=9.430 beta(zxx)=1.107 beta(xzx)=1.276
static beta(zzz)=8.722,8.750 beta(zxx)=1.045,1.102
one indexed data there:static beta(zzz)=9.838, beta(zxx)=0.802
SCF:beta(zzz)=8.808, beta(zxx)=0.434
NWCHEM7.0.0 gives
CCSD Lambda Response polarizability / au
Frequency = 0.0656000 / au
Wavelength = 694.5633079 / nm
...
Cpu & wall time / sec 0.2 0.2
CCSD Quadratic Response
Static Hyperpolarizability

beta(X,Z,X) = 0.581141625 / au
beta(Z,X,X) = 0.581141625 / au
beta(Z,Z,Z) = 8.275124709 / au

CCSD Lambda Response polarizability / au
Frequency = 0.0000000 / au
Wavelength = Infinity / nm

Cpu & wall time / sec 0.1 0.1
CCSD Quadratic Response
Static Hyperpolarizability

beta(Z,X,X) = 0.770738651 / au
beta(Z,Z,Z) = 9.518810663 / au

Cpu & wall time / sec 13.1 13.5
Very Best Reards!
DALTO2016.2 gives
++
! FINAL CCSD RESULTS FOR THE FIRST HYPERPOLARIZABILITIES !
++
A operator B operator C operator property

ZDIPLEN (unrel.) 0.0000 ZDIPLEN (unrel.) 0.0000 ZDIPLEN (unrel.) 0.0000 8.6941344
0.1312 0.0656 0.0656 9.5090740

With GAMESS
...
Beta tensor [in au]( 0.000000; 0.000000, 0.000000)
x y z
zx. 0.704144 0.000000 0.000000
zz. 0.000000 0.000000 9.926728
Beta tensor [in au]( 0.131200; 0.065600, 0.065600)
x y z
xz. 0.848328 0.000000 0.000000
zx. 0.679234 0.000000 0.000000
zz. 0.000000 0.000000 10.603235
The above reference gives (calculated)
SHG beta(zzz)=9.430 beta(zxx)=1.107 beta(xzx)=1.276
static beta(zzz)=8.722,8.750 beta(zxx)=1.045,1.102
one indexed data there:static beta(zzz)=9.838, beta(zxx)=0.802
SCF:beta(zzz)=8.808, beta(zxx)=0.434
NWCHEM7.0.0 gives
CCSD Lambda Response polarizability / au
Frequency = 0.0656000 / au
Wavelength = 694.5633079 / nm
...
Cpu & wall time / sec 0.2 0.2
CCSD Quadratic Response
Static Hyperpolarizability

beta(X,Z,X) = 0.581141625 / au
beta(Z,X,X) = 0.581141625 / au
beta(Z,Z,Z) = 8.275124709 / au

CCSD Lambda Response polarizability / au
Frequency = 0.0000000 / au
Wavelength = Infinity / nm

Cpu & wall time / sec 0.1 0.1
CCSD Quadratic Response
Static Hyperpolarizability

beta(Z,X,X) = 0.770738651 / au
beta(Z,Z,Z) = 9.518810663 / au

Cpu & wall time / sec 13.1 13.5
Very Best Reards!
Last edited by xiongyan21 on 23 Mar 2020, 02:56, edited 5 times in total.

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Re: Which test illustrates SHG calculation in Dalton
Perhaps owing to the network traffic problem, I just can read Dr. Taylor's suggestion. Augccpvdz already adds diffuse, but for HF, only daugccpvdz works, e.g, NWCHEM7.0.0 will give large discrepencies. NWCHEM 7.0.0 has impemented a new coupled cluster method though quantum computing algorithm to address correlation effects.
Prof. Grodon's article compared the effects of basis sets when using explicit solvation, important for solutions and aggregates.
Previously, 631G is just for warming up exercises, and for the inquiry of units conversion, and agreements of different softwares with the same method, and I answered a question on Feb, 8, 2016 entitled Cannot obtain hyperpolarizabilities with CC3 on this forum, saying CBS and FCI will get the best results.
Reference Ab initio variational calculation of dynamic polarizabilities and hyperpolarizabilities I. Polarizability and quadratic hyperpolarizability of water, carbon monoxide and hydrogen fluoride gives the transformed experimental beta parallel of 5.45 at 694nm, i.e., from reference Measurements of second and thirdorder nonlinear polarizabilities for HF and HCI , containing another kind factor to change unit a.u. into esu.
Dalton2016.2 HF gives, using daugccpvdz,
Bfreq = 0.065600 Cfreq = 0.065600 beta(Z;Z,Z) = 8.06145767
Bfreq = 0.065600 Cfreq = 0.065600 beta(Z;X,X) = 0.11285876
Bfreq = 0.065600 Cfreq = 0.065600 beta(X;Z,X) = 0.00022904
beta parellel=1/5(3*8.061462*0.112859+4*0.00022904)=4.79
GAMESS gives
beta parellel=1/5(3*10.603235+2*0.679234+4*0.848328)=7.31
NWCHEM7.0.0 gives
beta parallel1/5(3*8.275+2*0.5811+4*0.5811)=5.66
Beta parallel is calculated based on Prof. Jorgensen's article, Frequencydependent hyperpolarizability of hydrogen fluoride.
I am trying to calculate this for HF aggregates and organic molecules in solutions.
Very Best Regards!
Prof. Grodon's article compared the effects of basis sets when using explicit solvation, important for solutions and aggregates.
Previously, 631G is just for warming up exercises, and for the inquiry of units conversion, and agreements of different softwares with the same method, and I answered a question on Feb, 8, 2016 entitled Cannot obtain hyperpolarizabilities with CC3 on this forum, saying CBS and FCI will get the best results.
Reference Ab initio variational calculation of dynamic polarizabilities and hyperpolarizabilities I. Polarizability and quadratic hyperpolarizability of water, carbon monoxide and hydrogen fluoride gives the transformed experimental beta parallel of 5.45 at 694nm, i.e., from reference Measurements of second and thirdorder nonlinear polarizabilities for HF and HCI , containing another kind factor to change unit a.u. into esu.
Dalton2016.2 HF gives, using daugccpvdz,
Bfreq = 0.065600 Cfreq = 0.065600 beta(Z;Z,Z) = 8.06145767
Bfreq = 0.065600 Cfreq = 0.065600 beta(Z;X,X) = 0.11285876
Bfreq = 0.065600 Cfreq = 0.065600 beta(X;Z,X) = 0.00022904
beta parellel=1/5(3*8.061462*0.112859+4*0.00022904)=4.79
GAMESS gives
beta parellel=1/5(3*10.603235+2*0.679234+4*0.848328)=7.31
NWCHEM7.0.0 gives
beta parallel1/5(3*8.275+2*0.5811+4*0.5811)=5.66
Beta parallel is calculated based on Prof. Jorgensen's article, Frequencydependent hyperpolarizability of hydrogen fluoride.
I am trying to calculate this for HF aggregates and organic molecules in solutions.
Very Best Regards!
Last edited by xiongyan21 on 26 Mar 2020, 22:44, edited 1 time in total.

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Re: Which test illustrates SHG calculation in Dalton
I am a bit lost now as to what your question is, or at least what it seems to have evolved into. Are you asserting that three programs that claim to do exactly the same calculation give different results? If so there are ways to check this (certainly in the static limit this can be done using finitefield methods).
If your concern is the lack of agreement between calculation and experiment, I attempted to point out some issues in this respect in my earlier posting. But this is already perhaps going beyond the function of the Dalton mailing forum, which is focussed more in assisting people to use the program. If no computational method gives satisfactory agreement with experiment for your purposes, I don't see how we can do more to help!
Best regards
Pete
If your concern is the lack of agreement between calculation and experiment, I attempted to point out some issues in this respect in my earlier posting. But this is already perhaps going beyond the function of the Dalton mailing forum, which is focussed more in assisting people to use the program. If no computational method gives satisfactory agreement with experiment for your purposes, I don't see how we can do more to help!
Best regards
Pete
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