Which test illustrates SHG calculation in Dalton

[xiongyan21]

I wish to calculate SHG, Kerr effect, etc. of organic molecules, but I am not familiar with the related inputs in DALTON.
Could you please tell me which test in Dalton illustrates them?

Thanks.

Very Best Regards!

[magnus]

For SCF and MCSCF there is rsp_2ndharm and I suggest that you also take a look at section 30.1.4 in the manual. For CC there is cc_rsp_betafreq and cc_rsp_betafreq2, and the relevant section in the manual is 32.4.

[xiongyan21]

Dear all
Could you please tell me the relationship between data expressed in terms of esu. and a.u.?
Thanks a lot.
Very Best Regards!

[taylor]

All of the fundamental constants needed for units conversion are listed in the file
DALTON/include/codata.h
in the Dalton source tree. My experience is that it is usually better to calculate the conversion factors oneself from these, rather than rely on other people who may not be using the same data or the same precision.

Best regards
Pete

[xiongyan21]

Thanks a lot.
I have found the reference of codata recommended indexed there, and will carefully read it.

Very Best Regards!

[xiongyan21]

I began from using DALTON 2016.2 to calculate Beta by HF of aniline, the .dal file was form Pehf_beta in DALTON test, and the geometry was optimized by B3LYP with 6-311G++(2d,2p) employing GAMESS. Here the basis set is 6-31G.

The error is ~/dalton2016.2/build/basis
Note: The following floating-point exceptions are signalling: IEEE_DIVIDE_BY_ZERO
STOP ERROR: potential input file not found
aniline.tar.gz has been copied to /applications/computation5/dalton2016.2/build
Output is in ~/dalton2016.2/build/aniline.log as requested in input.

input
**DALTON
.RUN RESPONSE
.PEQM
**WAVE FUNCTIONS
.HF
**RESPONSE
*QUADRATIC
.DIPLEN
.FREQUE
2
0.00 0.006
**END OF

What causes the error?

Very Best Regards!

[magnus]

The error message tells you what is wrong:

STOP ERROR: potential input file not found

It's because you took the dal file from a polarizable embedding test which requires a potential input file. Removing the ".PEQM" keyword will disable polarizable embedding.

[xiongyan21]

Thanks a lot.
It works!

Very Best Regards!
...
======================================================================
--- L I N E A R R E S P O N S E F U N C T I O N S ---
======================================================================

The -<<A;B>>(omega_b) functions from vectors generated
in a *QUADRA calculation of <<A;B,C>>(omega_b,omega_c)

Note: the accuracy of off-diagonal elements will be linear
in the convergence threshold THCLR = 1.00D-03


Perturbation symmetry. KSYMOP: 1
Perturbation spin symmetry.TRPLET: F
Orbital variables. KZWOPT: 1300
Configuration variables. KZCONF: 0
Total number of variables. KZVAR : 1300

@ Singlet linear response function in a.u.

@ A operator, symmetry, frequency: XDIPLEN 1 -0.000000
@ B operator, symmetry, frequency: XDIPLEN 1 0.000000

@ Value of linear response -<<A;B>>(omega): 72.779263824219

@ Singlet linear response function in a.u.

@ A operator, symmetry, frequency: YDIPLEN 1 -0.000000
@ B operator, symmetry, frequency: XDIPLEN 1 0.000000

...

Results from quadratic response calculation
--------------------------------------------

@ B-freq = 0.000000 C-freq = 0.000000 beta(X;X,X) = 1.73000832
...
@ B-freq = 0.006000 C-freq = 0.000000 beta(X;X,X) = 1.73021905
...
Total CPU time used in RESPONSE: 49.12 seconds
Total wall time used in RESPONSE: 49.17 seconds


.-------------------------------------------.
| End of Dynamic Property Section (RESPONS) |
`-------------------------------------------'

Total CPU time used in DALTON: 1 minute 2 seconds
Total wall time used in DALTON: 1 minute 2 seconds


Date and time (Darwin) : Tue Mar 3 14:47:41 2020
Host name : ...

GAMESS implementing some correction to dynamic polarizability of polyatomic molecules, also using TDHF, gives the following in terms of a.u.
Beta tensor [in au]( -0.006000; 0.006000, 0.000000)
x y z
xx. 1.733832 ...

This should be compared with experimental work.

[xiongyan21]

Using coupled cluster method and 6-31G with Dalton2016.2, the following could be obtained

....
+---------------------------------------------------------------------------------------+
! FINAL CCSD RESULTS FOR THE FIRST HYPERPOLARIZABILITIES !
+---------------------------------------------------------------------------------------+


A operator B operator C operator property
------------------------------------------------------------------------------------------------------

XDIPLEN (unrel.) -0.0000 XDIPLEN (unrel.) 0.0000 XDIPLEN (unrel.) 0.0000 0.53430526
-0.0120 0.0060 0.0060 0.53061585
...
CPU and wall time for CC : 7874.921 4867.660


Date and time (Darwin) : Wed Mar 4 14:34:52 2020
Host name : ...

and the input is
**DALTON INPUT
.RUN WAVE FUNCTIONS
**INTEGRAL
.DIPLEN
**WAVE FUNCTIONS
.CC
*CC INPUT
.CCS
.CC2
.CCSD
*CCFOP
.DIPMOM
*CCLR
.OPERATOR
XDIPLEN XDIPLEN
YDIPLEN YDIPLEN
ZDIPLEN ZDIPLEN
.FREQUE
2
0.00 0.006
.DISPCF
6
*CCQR
.OPERATOR
XDIPLEN XDIPLEN XDIPLEN
YDIPLEN YDIPLEN YDIPLEN
ZDIPLEN ZDIPLEN ZDIPLEN
.MIXFRE
2
0.00 0.006
0.00 0.006
**END OF DALTON INPUT


Could professors and doctors comment on the various calculated results and how they could be compared with experimental data？

Very Best Regards!

[xiongyan21]

I previously had a reference on the comparison of theoretical and experimental hyperpolarizabilities in JCP, where some conventions were introduced, and I will read it carefully.

[xiongyan21]

I understand a factor, making esu an energy unit, should be included to transform esu into energy unit a.u.

[taylor]

First, would you please not post outputs or output fragments inline! It makes messages very difficult to read in some browsers and on some machines. There are perfectly good mechanisms for attaching files.

Second, atomic units are a system of units, like SI. In a. u. certain fundamental quantities are defined as unity, which greatly simplifies manipulations within electronic structure programs. The atomic unit of energy is the hartree, with the symbol E_h. The atomic unit of length is the bohr with the symbol a₀, etc. Where there is no agreed name for a particular atomic unit for some quantity one often just uses "a.u." to indicate this particular system of units.

Third, I think you have to accept that this forum is primarily related to the use and capabilities of the Dalton program. Commenting "on the various calculated results and how they could be compared with experimental data" is a bit beyond the scope of the forum, unless you are lucky enough to find another user or developer with exactly the right background to comment. And I am certainly no expert on SHG. But I do know a bit about basis sets and about electron corrrelation, and I regret to say that CC results with a 6-31G basis set for any property for any molecule are likely to be utter garbage. I have posted so many times about the deficiencies of these basis sets that I am not prepared to do it again here. And in a basis set without polarization functions inclusion of correlation via any orbital-based method is utterly pointless. Description of electric properties in a basis set without polarization functions (and typically diffuse ones) is equally pointless. So I am afraid this level of calculation will only give anything vaguely resembling experiment because of massive error cancellation. That may work in some cases, but the problem is that it doesn't always work...

Best regards
Pete

[xiongyan21]

Dear Dr. Olsen
If I wish to include solvation into TDHF, in addition to .PEQM, what keywords should be added?

Thanks a lot.
Very Best Regards!

[magnus]

Polarizable embedding is a QM/MM type embedding so it requires that you explicitly include statistical sampling of structures, e.g., through molecular dynamics. I recommend this tutorial paper if you're interested: https://onlinelibrary.wiley.com/doi/ful ... /qua.25717

Of course the easy way to include solvation in Dalton is to use PCM. For this I recommend that you start by taking a look at chapter 14 in the Dalton manual.

[xiongyan21]

Thanks a lot.

There are references on the hyperpolarizabilies of paranitroaniline in solutions, but I have not found that of aniline in solutions.

Very Best Regards!

[taylor]

It appears my earlier posting was not clear. It does not matter which correlation treatment you use (you said you would try ACCD, but what I write here applies to any treatment of dynamical electron correlation, starting with MP2 and climaxing with full CI): unless you have a basis set with polarization functions the calculation is an exercise in pointlessness. It is simply a waste of computer time. This has been known since before I was born. The absolute smallest basis set in size that can give even qualitatively sensible answers is something split-valence plus polarization. Like cc-pVDZ, or perhaps pc-1. Note that 6-31G**blahblah will not do, and nor will replacing 6-31 with 6-311 (the former is hopelessly compromised by the constraints in s and p exponents and the latter turns out in practice to be simply double-zeta in the core). In addition, any property that involves an electric field perturbation requires additional attention to the basis set to ensure that the wave function can respond to the applied perturbation. There are many many papers and reviews in which these topics have been revisited again and again.

I repeat, your calculation is fundamentally flawed if you use a basis set like 6-31G. Starting to look at things like solvent effects is heading in the wrong direction: if you cannot describe the free molecule adequately, it is useless to start looking at subtle effects like solvation.

Best regards
Pete

[xiongyan21]

Sorry for this abbreviation.
ACCD is aug-cc-pvdz, and the experimental data of PNA were obtained in solutions.

[xiongyan21]

CC2 and aug-cc-pvdz gives
+--------------------------------------------------------------------------------------+
! FINAL CC2 RESULTS FOR THE FIRST HYPERPOLARIZABILITIES !
+--------------------------------------------------------------------------------------+


A operator B operator C operator property
------------------------------------------------------------------------------------------------------

XDIPLEN (unrel.) -0.0000 XDIPLEN (unrel.) 0.0000 XDIPLEN (unrel.) 0.0000 0.90796725
-0.0120 0.0060 0.0060 0.90362549



------------------------------------------------------------------------------------------------------
6-31G gives
+--------------------------------------------------------------------------------------+
! FINAL CC2 RESULTS FOR THE FIRST HYPERPOLARIZABILITIES !
+--------------------------------------------------------------------------------------+


A operator B operator C operator property
------------------------------------------------------------------------------------------------------

XDIPLEN (unrel.) -0.0000 XDIPLEN (unrel.) 0.0000 XDIPLEN (unrel.) 0.0000 1.2190352
-0.0120 0.0060 0.0060 1.2166503
------------------------------------------------------------------------------------------------------

HF and aug-cc-pvdz using Dalton2016.2 gives
...
@ B-freq = 0.000000 C-freq = 0.000000 beta(X;X,X) = 1.05916178

[xiongyan21]

Unit changing factors can be found in references.

[xiongyan21]

Aug-cc-pvdz and CCSD gives the following with Dalton2016.2


+---------------------------------------------------------------------------------------+
! FINAL CCSD RESULTS FOR THE FIRST HYPERPOLARIZABILITIES !
+---------------------------------------------------------------------------------------+


A operator B operator C operator property
------------------------------------------------------------------------------------------------------

XDIPLEN (unrel.) -0.0000 XDIPLEN (unrel.) 0.0000 XDIPLEN (unrel.) 0.0000 0.44961733
-0.0120 0.0060 0.0060 0.44481616



------------------------------------------------------------------------------------------------------


------------------------------------------------------------------------------------------------------
...

Total CPU time used in DALTON: 118 hours 12 minutes 18 seconds
Total wall time used in DALTON: 69 hours 59 minutes 9 seconds


Date and time (Darwin) : Thu Mar 12 03:50:51 2020
Host name : ...

The values of beta(x,x,x) of gaseous aniline is more than three times greater than that obtained by experiment SHG of liquid aniline in reference.
I will try to find the experimental result of gaseous aniline, and try PCM in aniline if the parameters existing.

Very Best regards!

[xiongyan21]

When I try to include aniline into aniline solvation with PCM, the following error appears
... *******************************************************************
*********** Output from DALTON general input processing ***********
*******************************************************************

--------------------------------------------------------------------------------
Overall default print level: 0
Print level for DALTON.STAT: 1

HERMIT 1- and 2-electron integral sections will be executed
"Old" integral transformation used (limited to max 255 basis functions)
Wave function sections will be executed (SIRIUS module)
Static molecular property section will be executed (ABACUS module)
--------------------------------------------------------------------------------

** LOOKING UP INTERNALLY STORED DATA FOR SOLVENT = C6H5NH2 **
Optical and physical constants:
EPS= 6.890; EPSINF= 2.506; RSOLV= 2.800 A; VMOL= 91.150 ML/MOL;
TCE= 8.50000D-04 1/K; STEN= 42.790 DYN/CM; DSTEN= 0.7310; CMF= 0.9720


-----------------------------------
Input for PCM solvation calculation
-----------------------------------
ICOMPCM = 0 SOLVNT=C6H5NH2 EPS = 6.8900 EPSINF= 2.5060
RSOLV = 2.8000

ICESPH = 0 NESFP = 0
OMEGA = 40.0000 RET = 0.2000 FRO = 0.7000

IPRPCM= 0

NON-EQ = F NEQRSP =F

--- SEVERE ERROR, PROGRAM WILL BE ABORTED ---
Date and time (Darwin) : Thu Mar 12 09:40:30 2020
Host name : appledeMac-mini.local

@ MPI MASTER, node no.: 0
@ Reason: ILLEGAL KEYWORD IN PCMCAV

Total CPU time used in DALTON: 0.00 seconds
Total wall time used in DALTON: 0.00 seconds


QTRACE dump of internal trace stack

========================
level module
========================
2 DALTON_GNRLI
1 DALTON main
========================

The input is **DALTON INPUT
.RUN WAVE FUNCTION
.RUN PROPERTIES
*PCM
.SOLVNT
WATER
.NPCMMT
0
.NESFP
5
.ICESPH
2
.NEQRSP
*PCMCAV
.RIN
1.7
2.0
1.4
1.6
1.2
.INA
1
2
3
4
5
.AREATS
0.50
**WAVE FUNCTION
.HF
**PROPERTIES
.OPTROT
*ABALNR
.FREQUE
1
.0773178
.THRESH
8.0D-4
**END OF INPUT

Perhaps it is not feasible, and explicit solvation should be applied.

Very Best Regards!

[xiongyan21]

It seems there is few published reliable SHG data of pesticides.
Very Best Regards!

[xiongyan21]

I use 6-311G++(2d,2p) and mp2 with GAMESS to optimize initially linear HF dimer, get an nonlinear, planar equilibrium geometry, but its beta(zzz)es become zero or nearly zero. Whether is it correct?

From the dimer optimized structure, 276.76 pm is the distance between the two Fs, 92 pm is the length of each of the F-H bond, and 185.71 pm is the intermolecular hydrogen bond length. These agree with those in reference Benchmark calculations with correlated molecular wave functions. VII. Binding energy and structure of the HF dimer, where the dimer has no intermolecular hydrogen bond.

[taylor]

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. Hartree-Fock and most DFT functionals that I am aware of will only give sensible-looking results through cancellation of errors.
2) The inclusion of diffuse functions in calculations is essential, including diffuse polarization functions. Basis sets such as 6-311G 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

[xiongyan21]

I first used B3LYP 6-311G++(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 in terms of a.u.

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'' Frequency-dependent 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.

Very Best Regards!