electric quadrupolequadrupole polarizability too small

 Posts: 8
 Joined: 28 Aug 2014, 03:05
 First name(s): Fan
 Last name(s): Zheng
 Affiliation: UPENN
 Country: United States
electric quadrupolequadrupole polarizability too small
Dear All,
I am new to Dalton and I am trying to calculate frequency dependent electric quadrupolequadrupole 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 dipoledipole polarizability is exactly the same to this paper, however, the calculated quadrupolequadrupole 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
I am new to Dalton and I am trying to calculate frequency dependent electric quadrupolequadrupole 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 dipoledipole polarizability is exactly the same to this paper, however, the calculated quadrupolequadrupole 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

 1s2.0S1386142598002662main(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.

 Posts: 87
 Joined: 06 Sep 2013, 13:49
 First name(s): Sonia
 Last name(s): Coriani
 Affiliation: DTU Chemistry
 Country: Denmark
Re: electric quadrupolequadrupole polarizability
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?

 Posts: 8
 Joined: 28 Aug 2014, 03:05
 First name(s): Fan
 Last name(s): Zheng
 Affiliation: UPENN
 Country: United States
Re: electric quadrupolequadrupole polarizability
Hi Sonia,
Thank you for your reply! I use SOPPA response module. In CO case, I set CO bond center at (0,0,0) and CO 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
Thank you for your reply! I use SOPPA response module. In CO case, I set CO bond center at (0,0,0) and CO 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

 Posts: 51
 Joined: 27 Aug 2013, 16:37
 First name(s): Stephan P. A.
 Last name(s): Sauer
 Affiliation: Department of Chemistry, University of Copenhagen
 Country: Denmark
 Contact:
Re: electric quadrupolequadrupole polarizability too small
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 dipolequadrupole and dipoledipole 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
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 dipolequadrupole and dipoledipole 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

 Posts: 7
 Joined: 15 Nov 2013, 11:46
 First name(s): Michal
 Last name(s): Jaszunski
 Affiliation: ICHO PAN
 Country: Poland
Re: electric quadrupolequadrupole polarizability too small
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. +48223432333
Professor, fax +48226326681
Institute of Organic Chemistry,
Polish Academy of Sciences email:
Kasprzaka 44 michal.jaszunski@icho.edu.pl
01224 Warszawa, POLAND
=================================================================
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. +48223432333
Professor, fax +48226326681
Institute of Organic Chemistry,
Polish Academy of Sciences email:
Kasprzaka 44 michal.jaszunski@icho.edu.pl
01224 Warszawa, POLAND
=================================================================

 Posts: 8
 Joined: 28 Aug 2014, 03:05
 First name(s): Fan
 Last name(s): Zheng
 Affiliation: UPENN
 Country: United States
Re: electric quadrupolequadrupole polarizability too small
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
augccpVTZ
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
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
augccpVTZ
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

 Posts: 600
 Joined: 15 Oct 2013, 05:37
 First name(s): Peter
 Middle name(s): Robert
 Last name(s): Taylor
 Affiliation: Tianjin University
 Country: China
Re: electric quadrupolequadrupole polarizability too small
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 dipoledipole, dipoledipolequadrupole, and quadrupolequadrupole polarizabilities of Ne (as well as the dipoledipole 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: noone 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 = {359365}
}
but I am not sure. Note that the results for gamma in this paper are wrong  the original results were postprocessed 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
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 = {359365}
}
but I am not sure. Note that the results for gamma in this paper are wrong  the original results were postprocessed 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

 Posts: 51
 Joined: 27 Aug 2013, 16:37
 First name(s): Stephan P. A.
 Last name(s): Sauer
 Affiliation: Department of Chemistry, University of Copenhagen
 Country: Denmark
 Contact:
Re: electric quadrupolequadrupole polarizability too small
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 oneelectron 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
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 oneelectron 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

 Posts: 8
 Joined: 28 Aug 2014, 03:05
 First name(s): Fan
 Last name(s): Zheng
 Affiliation: UPENN
 Country: United States
Re: electric quadrupolequadrupole polarizability too small
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/DALTON2013.4Source/DALTON/rsp/rspmai.F (unit = 11, file = 'DALTON.INP')
Fortran runtime error: Bad value during integer read
Error in /scratch/DALTON/DALTON2013.4Source/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
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/DALTON2013.4Source/DALTON/rsp/rspmai.F (unit = 11, file = 'DALTON.INP')
Fortran runtime error: Bad value during integer read
Error in /scratch/DALTON/DALTON2013.4Source/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 oneelectron 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

 Posts: 51
 Joined: 27 Aug 2013, 16:37
 First name(s): Stephan P. A.
 Last name(s): Sauer
 Affiliation: Department of Chemistry, University of Copenhagen
 Country: Denmark
 Contact:
Re: electric quadrupolequadrupole polarizability too small
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?
Good luck
Stephan
P.S. Did you ever contact the authors of this article and asked them for the input file they have used?

 Posts: 8
 Joined: 28 Aug 2014, 03:05
 First name(s): Fan
 Last name(s): Zheng
 Affiliation: UPENN
 Country: United States
Re: electric quadrupolequadrupole polarizability too small
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
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

 Posts: 51
 Joined: 27 Aug 2013, 16:37
 First name(s): Stephan P. A.
 Last name(s): Sauer
 Affiliation: Department of Chemistry, University of Copenhagen
 Country: Denmark
 Contact:
Re: electric quadrupolequadrupole polarizability too small
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
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

 Posts: 8
 Joined: 28 Aug 2014, 03:05
 First name(s): Fan
 Last name(s): Zheng
 Affiliation: UPENN
 Country: United States
Re: electric quadrupolequadrupole polarizability too small
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
Thanks,
Fan

 Posts: 8
 Joined: 28 Aug 2014, 03:05
 First name(s): Fan
 Last name(s): Zheng
 Affiliation: UPENN
 Country: United States
Re: electric quadrupolequadrupole polarizability too small
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 daugccpCV5Z. 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 dipolequadrupole and dipoledipole hyperpolarizability calculations.
Thanks,
Fan
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 daugccpCV5Z. 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 dipolequadrupole and dipoledipole 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 dipoledipole, dipoledipolequadrupole, and quadrupolequadrupole polarizabilities of Ne (as well as the dipoledipole 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: noone 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 = {359365}
}
but I am not sure. Note that the results for gamma in this paper are wrong  the original results were postprocessed 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

 Posts: 290
 Joined: 24 Sep 2014, 08:36
 First name(s): yan
 Last name(s): xiong
 Affiliation: CENTRAL CHINA NORMAL UNIVERSITY
 Country: China
Re: electric quadrupolequadrupole polarizability too small
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 = 1.00D03

(dimension of paired reduced space: 194)
RSP solution vector no. 1; norm of residual 3.88D04
RSP solution vector no. 2; norm of residual 6.50D04
RSP solution vector no. 3; norm of residual 1.08D02
*** RSPCTL WARNINGMAXIMUM 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 = 1.00D03

(dimension of paired reduced space: 206)
RSP solution vector no. 1; norm of residual 3.83D04
RSP solution vector no. 2; norm of residual 6.23D04
RSP solution vector no. 3; norm of residual 9.97D04
*** 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
*** MICROITERATIONS STOPPED DUE TO MAX ITERATIONS REACHED.
*** WARNING : REQUESTED 3 SOLUTION VECTORS NOT CONVERGED
Convergence of RSP solution vectors, threshold = 1.00D03

(dimension of paired reduced space: 194)
RSP solution vector no. 1; norm of residual 3.88D04
RSP solution vector no. 2; norm of residual 6.50D04
RSP solution vector no. 3; norm of residual 1.08D02
*** RSPCTL WARNINGMAXIMUM 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 = 1.00D03

(dimension of paired reduced space: 206)
RSP solution vector no. 1; norm of residual 3.83D04
RSP solution vector no. 2; norm of residual 6.23D04
RSP solution vector no. 3; norm of residual 9.97D04
*** 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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