electric quadrupole-quadrupole polarizability too small

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zhfan
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electric quadrupole-quadrupole polarizability too small

Post by zhfan » 28 Aug 2014, 03:25

Dear All,

I am new to Dalton and I am trying to calculate frequency dependent electric quadrupole-quadrupole polarizability.
As a practice, I start with this paper "Spectrochimica Acta Part A 55 (1999) 625–638" in which they also use DALTON and calculate polarizability for CO.
The dipole-dipole polarizability is exactly the same to this paper, however, the calculated quadrupole-quadrupole polarizability is very small.
The paper gives around 40 for C_{zz,zz} and what I calculated for C_{zz,zz} is around 6.205 with same method and basis set. Did I mess up the unit?
I attach the output here. Can anyone help me about this?

Thanks,
Fan
Attachments
1-s2.0-S1386142598002662-main(2).pdf
Paper with calculated quadrupole polarizability for CO
(174.05 KiB) Downloaded 443 times
test5_co.out
My DALTON calculation output
(84.28 KiB) Downloaded 382 times
Last edited by zhfan on 29 Aug 2014, 17:50, edited 1 time in total.

sonco
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Re: electric quadrupole-quadrupole polarizability

Post by sonco » 29 Aug 2014, 06:27

Did you check whether it is an origin related problem? Do you have the origin of the coordinate system in the same point in space?

zhfan
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Re: electric quadrupole-quadrupole polarizability

Post by zhfan » 29 Aug 2014, 17:49

Hi Sonia,

Thank you for your reply! I use SOPPA response module. In CO case, I set C-O bond center at (0,0,0) and C-O bond along z direction.
I also tried atom polarizability calculation like He and place the atom at the cartesian coordinate origin. But the SOPPA at MP2 level also gives much smaller quadrupole polarizability value than the correct one. Is there any origin related flag that I need to be careful with since I didn't notice that while reading the manual.

Thanks,
Fan

sauer
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Re: electric quadrupole-quadrupole polarizability too small

Post by sauer » 30 Aug 2014, 10:54

There might be three issues:

a) and as far as I can see, a quadrupole polarizability will depend quadratically on the origin. If you move the origin the change can easily be calculated, if you know the corresponding dipole-quadrupole and dipole-dipole polarizability. But the important point is, which origin was chosen in the calculations by Kedziora, i.e. how they placed the molecule in the coordinate system. Try to run the calculations without specifying an origin, but put the origin of the coordinate system on C and on O and on the center of mass.
b) There might be a conversion factor: Did you try to see whether your results differ by a constant factor from the results in that paper?
c) The definition of a quadrupole moment is not unique: Often one understands the traceless form as quadrupole moment and calls the pure xx, xy and so forth as second electric moment. In addition in Dalton there are spherical second moments. So try to rerun your calculations with the different "second moment" integrals Dalton offers: .CARMOM, .SECMOM, .SPHMOM, .THETA

Good luck
Stephan

michaljz
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Re: electric quadrupole-quadrupole polarizability too small

Post by michaljz » 30 Aug 2014, 17:27

hello,
other than zz,zz tensor components may be easier to reproduce - presumably no one ever puts the
origin off the molecular axis?

and I believe the factor in the expansion (which may enter or not enter the definition) is 6

regards,
Michal
================================================================
Michal Jaszunski tel. +48-22-3432333
Professor, fax +48-22-6326681
Institute of Organic Chemistry,
Polish Academy of Sciences e-mail:
Kasprzaka 44 michal.jaszunski@icho.edu.pl
01-224 Warszawa, POLAND
=================================================================

zhfan
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Re: electric quadrupole-quadrupole polarizability too small

Post by zhfan » 31 Aug 2014, 03:53

Hi Stephan and Michal,

Thank you all for the replies! With your suggestions, I rerun some calculations.
1. I computed C_{yz,yz} and C_{yy,yy} as 2.99 and 10.2 respectively. However, the values in the paper are 32.26 and 18.64. Thank you Michal and Stephan for pointing out the conversion factor. But from the calculation, it seems that it is still not consistent even if considering a factor.
Another issue is that even I change the molecule position (shift/rotate the molecule) in cartesian coordinates, the results are exactly same. This makes me strongly feel that my input may not be correct. As a result, I post my input here and hopefully it is clearer to find out the problem:
Content of the .dal input file
----------------------------------

**DALTON INPUT
.RUN RESPONSE
**INTEGRALS
.PROPRI
**WAVE FUNCTIONS
.HF
.MP2
**RESPONSE
.SOPPA
*LINEAR
.QUADZZ
.QUADYY
.QUADYZ
.FREQUENCIES
3
0.0 0.04557 0.090771
**END OF DALTON INPUT

Content of the .mol file
----------------------------

BASIS
aug-cc-pVTZ
CO
using the pv6z basis
Atomtypes=2
Charge=8.0 Atoms=1
O .0000000000 -.0000000000 2.132221297
Charge=6.0 Atoms=1
C .0000000000 -.0000000000 0.0000000000


2. As recommended by Stephan, I rerun with some "second moments" integrals included. But it seems that as long as I use .QUADZZ in **RESPONSE, the program will automatically use the integral computed with .QUADRU even if I added like .THETA

Thanks,
Fan

taylor
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Re: electric quadrupole-quadrupole polarizability too small

Post by taylor » 31 Aug 2014, 04:26

Can I suggest you run a test where there can be little or no issue with origin, symmetry, etc.? I believe there are calculations from more than 25 years ago by Maroulis and Thakkar on the dipole-dipole, dipole-dipole-quadrupole, and quadrupole-quadrupole polarizabilities of Ne (as well as the dipole-dipole second hyperpolarizability). Those calculations were finite field, employing several point charges to create the desired fields, but I do not think this will compromise the comparison with Dalton results. And the elimination of all the degrees of freedom that arise with less symmetric systems should make this a much simpler case to analyze (generalizing what Michal Jaszunski posted: no-one would put the origin anywhere other than the nucleus in an atomic calculation...).

I \emph{think} the Maroulis and Thakkar reference is cited in
@ARTICLE{Tay89a,
author = {Taylor, P. R. and Lee, T. J. and Rice, J. E. and Alml{\"o}f, J.},
title = {The polarizabilities of neon},
journal = {Chem. Phys. Lett.},
year = {1989},
volume = {163},
pages = {359-365}
}
but I am not sure. Note that the results for gamma in this paper are wrong --- the original results were post-processed through Excel and it turned out this did not yield enough precision. There is an erratum for our gamma results, but this is probably irrelevant to your work.

Best regards
Pete

sauer
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Re: electric quadrupole-quadrupole polarizability too small

Post by sauer » 01 Sep 2014, 09:51

Hej Fan,

if you use the
.QUADMOM
or
.QUADXX and so forth
keywords in *LINEAR you will get only the quadrupoles calculated from the integrals obtained with the .QUADRU option in **INTEGRALS. If you want to use other integrals you have to use the
.PROPRT
keyword in *LINEAR and specify the labels of the integrals yourself. The labels are given in the input section for the one-electron integrals. E.g. for .THETA they are XXTHETA , XYTHETA , XZTHETA , YYTHETA , YZTHETA , ZZTHETA as you can see on page 243 of the present manual.

Good luck
Stephan

zhfan
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Re: electric quadrupole-quadrupole polarizability too small

Post by zhfan » 02 Sep 2014, 21:22

Hi Stephan,

Thank you for your help. So I tried the input like this:

**DALTON INPUT
.RUN RESPONSE
**INTEGRALS
.PROPRI
.THETA
**WAVE FUNCTIONS
.HF
.MP2
**RESPONSE
.SOPPA
*LINEAR
.PROPRT
ZZTHETA ZZTHETA
**END OF DALTON INPUT

However, it gives error like "
At line 2013 of file /scratch/DALTON/DALTON-2013.4-Source/DALTON/rsp/rspmai.F (unit = 11, file = 'DALTON.INP')
Fortran runtime error: Bad value during integer read
Error in /scratch/DALTON/DALTON-2013.4-Source/build/dalton.x, exit code 2"

The program stops when starting to compute response.
I checked the line 2013 of the code and it is:

24 CONTINUE
READ(LUCMD,'(BN,A,I8)')LABEL,IRANK ! <- this line
LLROP( INDPRP(LABEL)) = .TRUE.
OPRANK(INDPRP(LABEL)) = IRANK
GO TO 100

Sorry for this technical problem. But is there something wrong in the input again?

Thanks,
Fan

sauer wrote:Hej Fan,

if you use the
.QUADMOM
or
.QUADXX and so forth
keywords in *LINEAR you will get only the quadrupoles calculated from the integrals obtained with the .QUADRU option in **INTEGRALS. If you want to use other integrals you have to use the
.PROPRT
keyword in *LINEAR and specify the labels of the integrals yourself. The labels are given in the input section for the one-electron integrals. E.g. for .THETA they are XXTHETA , XYTHETA , XZTHETA , YYTHETA , YZTHETA , ZZTHETA as you can see on page 243 of the present manual.

Good luck
Stephan

sauer
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Re: electric quadrupole-quadrupole polarizability too small

Post by sauer » 02 Sep 2014, 21:33

Yes, because as you can see from the line in the code, it tries to read a character string and then an integer and you gave it two character strings. Actually, if you check the manual you can see that you are supposed to give 1 label. So drop the second ZZTHETA and your input is at least conform with the manual. Maybe you have to move the ZZTHEA to the second column, but I am not sure - it is some time ago, that I used the Response code myself.

Good luck
Stephan

P.S. Did you ever contact the authors of this article and asked them for the input file they have used?

zhfan
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Re: electric quadrupole-quadrupole polarizability too small

Post by zhfan » 04 Sep 2014, 02:28

Hi Stephan,

Thank you very much for your help. It works! I think the quadrupole polarizability in the paper is computed with traceless quadrupole operator. What I got using .THETA is exactly three times larger than the values in the paper. I guess this factor of 3 comes from the quadrupole polarizability definition in Buckingham's paper [ref.71 in DALTON manual]. I also tried this to rare gas atoms and it agrees with other calculations. Thanks again for your help.

Fan

sauer
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Re: electric quadrupole-quadrupole polarizability too small

Post by sauer » 04 Sep 2014, 06:47

I am glad to hear this. The definition of higher pole moments is indeed a bit tricky.
Thanks with for your patience with Dalton - I hope that you will continue to use it and cite the new article about it in WIRES. By the way, did you try already also my SOPPA(CCSD) method?
Best regards
Stephan

zhfan
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Re: electric quadrupole-quadrupole polarizability too small

Post by zhfan » 05 Sep 2014, 02:48

I also tried the SOPPA(CCSD) method implemented in DALTON and it agrees with the value in the paper. This is also the case for rare gas atoms. If I get a chance to publish, I will definitely cite the new article.

Thanks,
Fan

zhfan
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Re: electric quadrupole-quadrupole polarizability too small

Post by zhfan » 05 Sep 2014, 02:58

Hi Pete,

Thanks for sending this paper. I am sorry that it took long time to reply since I spent some time to figure out the correct definition of quadrupole polarizability. But now what I calculated for Ne is alpha=2.68 and C=3.61. I use SOPPA(CCSD) and the basis set is d-aug-cc-pCV5Z. I didn't try other basis set yet. But this calculation agrees relatively well with the values in the paper. If I get a chance, I can also try dipole-quadrupole and dipole-dipole hyperpolarizability calculations.

Thanks,
Fan
taylor wrote:Can I suggest you run a test where there can be little or no issue with origin, symmetry, etc.? I believe there are calculations from more than 25 years ago by Maroulis and Thakkar on the dipole-dipole, dipole-dipole-quadrupole, and quadrupole-quadrupole polarizabilities of Ne (as well as the dipole-dipole second hyperpolarizability). Those calculations were finite field, employing several point charges to create the desired fields, but I do not think this will compromise the comparison with Dalton results. And the elimination of all the degrees of freedom that arise with less symmetric systems should make this a much simpler case to analyze (generalizing what Michal Jaszunski posted: no-one would put the origin anywhere other than the nucleus in an atomic calculation...).

I \emph{think} the Maroulis and Thakkar reference is cited in
@ARTICLE{Tay89a,
author = {Taylor, P. R. and Lee, T. J. and Rice, J. E. and Alml{\"o}f, J.},
title = {The polarizabilities of neon},
journal = {Chem. Phys. Lett.},
year = {1989},
volume = {163},
pages = {359-365}
}
but I am not sure. Note that the results for gamma in this paper are wrong --- the original results were post-processed through Excel and it turned out this did not yield enough precision. There is an erratum for our gamma results, but this is probably irrelevant to your work.

Best regards
Pete

xiongyan21
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Re: electric quadrupole-quadrupole polarizability too small

Post by xiongyan21 » 25 Oct 2014, 09:19

I repeated your calculation based on your .out, found the following information:

*** MICROITERATIONS STOPPED DUE TO MAX ITERATIONS REACHED.

*** WARNING : REQUESTED 3 SOLUTION VECTORS NOT CONVERGED
Convergence of RSP solution vectors, threshold = 1.00D-03
---------------------------------------------------------------
(dimension of paired reduced space: 194)
RSP solution vector no. 1; norm of residual 3.88D-04
RSP solution vector no. 2; norm of residual 6.50D-04
RSP solution vector no. 3; norm of residual 1.08D-02


*** RSPCTL WARNING-MAXIMUM NUMBER OF MICROITERATIONS, 60, REACHED,
and got the result
@ FREQUENCY INDEPENDENT SECOND ORDER PROPERTIES

@ -<< ZZQUADRU ; ZZQUADRU >> = 6.205076834683D+00

I changed MAXIT, then got the similar ZZQUADRU

*** THE REQUESTED 3 SOLUTION VECTORS CONVERGED

Convergence of RSP solution vectors, threshold = 1.00D-03
---------------------------------------------------------------
(dimension of paired reduced space: 206)
RSP solution vector no. 1; norm of residual 3.83D-04
RSP solution vector no. 2; norm of residual 6.23D-04
RSP solution vector no. 3; norm of residual 9.97D-04

*** RSPCTL MICROITERATIONS CONVERGED

Final output of second order properties from linear response
------------------------------------------------------------


@ Spin symmetry of operators: singlet

Note that minus the linear response function: - << A; B >>(omega) is printed.
The results are of quadratic accuracy using Sellers formula.

@ FREQUENCY INDEPENDENT SECOND ORDER PROPERTIES

@ -<< ZZQUADRU ; ZZQUADRU >> = 6.205076836041D+00

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