Singular Matrix

(It is not necessary to upload input files, they can be found in the output file.)

cymantren
Posts: 34
Joined: 11 Jan 2014, 13:59
First name(s): Alfred
Last name(s): Güthler
Affiliation: privat
Country: Germany

Singular Matrix

Hello everybody,

I tried to do follow a mode in a WALK transition state calculation, but got this message: ".. Solution not obtained to linear equations" --> Appendix

First of all, I am not quite sure, if the input is corect, and if, why does this message appeares ?
What I actually wanted to do, is to follow the 12-mode, which showed - in an former calculation - to be imaginary. That means this is an transition state.

Please give me some hints, how I can solve the problem, the technical problem and that problem relating to DALTON, namly treating a transition state correctly, if one knowes which mode is imaginary.

Kind regards

Alfred
WALK_modfol_TiB5_631gdp_optim_1.out

taylor
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: Singular Matrix

This has nothing to do with the type of walk you are doing, I think, because the SCF calculation has not converged, so you have not even reached the geometry optimization step yet. The problem is perhaps that you specify the occupancy as if the point group is of order 4, but the program detects only Cs symmetry. This is readily seen because at the start of the SCF calculation the total charge on the molecule is given as 16. You need to specify the occupancy according to the symmetry the program finds.

Unrelated to the specifics of your convergence problems, but perhaps worth noting, is that unless you are trying to reproduce the results of someone else's calculation, the choice of a 6-31G** basis set is a guarantee of poor to useless results especially given that your molecule contains a transition metal.

Best regards
Pete

cymantren
Posts: 34
Joined: 11 Jan 2014, 13:59
First name(s): Alfred
Last name(s): Güthler
Affiliation: privat
Country: Germany

Re: Singular Matrix

Dear Mr.Taylor,

I have no experience with that kind of calculation and so it was only a try. However I came across the fact, that this special system represents an transition state,so I actually don't need to do a walk-calculation, because the transition state is already found.
Concerning your statement that I use the C2v- group, but the program detects Cs, I wonder why this is the case. Why does the program detects Cs, but the system really is C2v, is a fact I do'nt understand. At least I can follow, that this can produce problems with the size of the B-Matrix and this leads to this failure message.
You also gave a solution to this, namly relating the IRREP's of C2v to those of Cs ! I will try.

Regarding to your last statement: I use the very old but simple 6-31G**Basis-set, not for reproducing results, but to make a basis for new results. The ano-basis set is able to simulate this old 6-31G**, but I have now yet any idea how to use it. Another reason for that is, that I also use a different program to later do more sophisticated calculations (MECP, conic-inetrsections..). So I want to compare the results. This program also uses dalton-hermit to calculate some integrals.

Finally I know, that the produced results are very poor and have less meaning, however there are still in use. Moreover they could be prone to error, compared with the new basis-sets, especialy with transition-metals. But - I have no idea about using the ANO's.
Despite this fact I wanted to stay with these sets, because of the above mentioned reason. Later, when the results are more relaible, I will turn to better basis.sets.

Nevertheless, thank you for your statement.

Best Regards

Alfred

cymantren
Posts: 34
Joined: 11 Jan 2014, 13:59
First name(s): Alfred
Last name(s): Güthler
Affiliation: privat
Country: Germany

Re: Singular Matrix

Dear Mr. Taylor,

sorry for the "typos":

".. I have NO yet any idea how to use it "
"..especially.."
"..want to stay.."
" reliable"

Kind regards

Alfred

taylor
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: Singular Matrix

If I look at your posted output it has
``` Content of the .mol file ---------------------------- BASIS 6-31G** Title optim TiB5 dublet at 6-31G**/HF C2v Atomtypes=2 Charge=22.0 Atoms=1 Ti 0.00 0.00 1.29 Charge=5.0 Atoms=5 B 0.00 0.00 -3.25 B 0.00 2.67 -2.06 B 0.00 -2.67 -2.06 B 0.00 3.79 0.79 B 0.00 -3.75 0.79 ```
and this certainly does not have C2v symmetry. Should the fourth boron have y-coordinate -3.79? Or the third boron y-coordinate 3.75? In such cases the structure would have C2v symmetry. I should note though that a structure given to only two decimal places is very unlikely to be a stationary point although it might be a crude approximation to one.

If you are not including dynamical correlation an ANO basis may be overkill for your needs. Jensen's pc-N basis sets are available for all elements up to Kr and should be satisfactory for SCF, DFT, and MCSCF calculations. Another good alternative would be the def2- series such as def2-TZVP, which are available for all elements up to Rn.

Best regards
Pete

cymantren
Posts: 34
Joined: 11 Jan 2014, 13:59
First name(s): Alfred
Last name(s): Güthler
Affiliation: privat
Country: Germany

Re: Singular Matrix

Dear Mr. Taylor,

you are again right. The molecule is in the xy-plane and Ti und one Boron are located at the z-axis, whereas the other three B-Atoms are in the xy-plane. The last B should be of course 3.79 and is a typo. Tha'ts the reason why the program detects Cs instead of C2v.
I supposed that the Cs -sym is maybe used, because looking for an transition-state, it is better to turn the symmetry of - or use Cs, better C1. However the system could also be similar to a Bipyramid, which has no Cs -sym. DALTON uses subgroups of D2h, but a Biparamid has D4h-sym. To think about this is not necessary because the sym. of the transition state is C2v.

In the WALK module one uses:
......
*WALK
.MODFOL
.INDEX
1
.MODE
12
...
It is also possibel to do the same input, but with "*OPT " ?
Maybe it is not sensible to turn the symmetry detection on, because one does'nt really know, in which direction the system reacts ? So, "Nosymmetry" in the mol file ?

This leads me to my question:
How can one follow a mode which is imaginary, but wants to get rid of this mode and find the corresponding structure. How this can be done ?
What I know is, that looking at the ouput and visualize the vibration, with e.g. molden, one has to change the geometry according to this mode. Are there other possibilities ?

Best Regards
Alfred

cymantren
Posts: 34
Joined: 11 Jan 2014, 13:59
First name(s): Alfred
Last name(s): Güthler
Affiliation: privat
Country: Germany

Re: Singular Matrix

..correction,

.....in the YZ-PLANE !

taylor
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: Singular Matrix

If you are not at a stationary point (and as we discussed before, with a geometry given to only two decimals you are not) the program should figure out how to walk downhill to a minimum. You can use .OPTIMIZE, which is relatively economical, or .WALK, which is more computationally demanding but is very robust.

There is need for care here. If, either because you explicitly ask the program to use symmetry, or you specify "Nosymmetry" but your starting geometry has some symmetry, then because the gradient is symmetry-conserving (at least in exact arithmetic) the walk will retain that symmetry because there is no gradient information about how the symmetry might be lowered. In your case, if your starting geometry has C2v symmetry the the optimization will converge to a stationary point that has that same symmetry. This stationary point may have your desired Hessian index (that is, no negative eigenvalues for a minimum, one for a transition state) within that symmetry, but until the full Hessian is calculated there is no information about the sign of the other eigenvalues of the Hessian. A point that appears to be a minimum when symmetry is imposed may have multiple negative eigenvalues of the full Hessian. At the risk of labouring the point, I reiterate that the key here is the symmetry of the starting geometry, not whether symmetry is explicitly used in the calculation.

Nature does not seem to be as fond of symmetry as I am when it comes to transition states. Despite what we like to show students when presenting e.g. the Woodward-Hoffman rules, most chemical reactions seem to involve transition states with decidedly unsymmetrical geometries. If you are looking for a transition state it is probably safest to use an unsymmetrical starting geometry. If you start from a minimum to walk up to a transition state, say with mode-following, then the first step will probably break the symmetry, but this is not guaranteed --- it depends on the symmetry of the mode being followed. If you are looking for a minimum, then with .WALK it is safe to use symmetry as long as .TOTSYM is not specified, as the program will seek a minimum using the original symmetry, but if the stationary point found is not a minimum when the full Hessian is calculated, the program will break the symmetry and re-optimize.

Finally, you are looking at a molecule of the form XY5, where the obvious symmetrical structures are the trigonal bipyramid (D3h) and the square pyramid (C4v). These groups share as a common Abelian subgroup C2v, and there is usually a pathway preserving symmetry corresponding to "Berry pseudorotation" between such conformers. I would suggest, therefore, that for this case it should be possible to give the program a starting structure that is slightly distorted from one of the high-symmetry conformers, and simply allow the program to determine a minimum in C2v. You can then decide whether an optimization in lower symmetry would be advisable, based on the full Hessian. Finally, consistent with what was noted above, if you give the program a geometry that is D3h- or C4v-symmetric, then the optimization will maintain this, which may not be what you want! It is unlikely that one would specify an input geometry to such accuracy that exact D3h symmetry would be maintained, but this is not an issue for C4v, which does not depend on irrational numbers to specify the geometry.

Best regards
Pete

hjaaj
Posts: 395
Joined: 27 Jun 2013, 18:44
First name(s): Hans Jørgen
Middle name(s): Aagaard
Last name(s): Jensen
Affiliation: Universith of Southern Denmark
Country: Denmark

Re: Singular Matrix

I agree with Pete's comments, but perhaps two clarifications are useful:

1. Remember to used .INDEX 0 if you want to find a minimum

2. Even when you want a better basis set for your final results, you will save time by doing a pre-optimization with a smaller basis set, and then switch to a better basis in the end. In particular I do not know how good/bad 6-31G** is for Ti.

hjaaj
Posts: 395
Joined: 27 Jun 2013, 18:44
First name(s): Hans Jørgen
Middle name(s): Aagaard
Last name(s): Jensen
Affiliation: Universith of Southern Denmark
Country: Denmark

Re: Singular Matrix

PS. I recommend that you switch to the newest version of Dalton.

cymantren
Posts: 34
Joined: 11 Jan 2014, 13:59
First name(s): Alfred
Last name(s): Güthler
Affiliation: privat
Country: Germany

Re: Singular Matrix

Dear Mr. Taylor and Mr. Jensen

I thank you very much for your informative reply. I changed to the def2-TZVP -Basisset and the geometry according to the v12-mode.
For years I used the OPTIMIZE -Module, because it contains first - and second order methods. Using only WALK means that one is sure about the symmetry. I fact that' s not really the case, but I started from my former findings, which were calculated by DFT. Now, I am not so convinced again, that ONLY DFT can lead to correct results. The methods should fit the demandings of the system and not vice versa. However I think that MCSCF and MRCI have the advantage, that one can be certain about the symmetry of the system. That means for me, knowing wich state I investigate, is crucial. The molecule has in C2v , 2^A1 sym. That's the end or the beginning of the calculation.

Finally I used this older version of DALTON, because I have an old laptop and use Debian 9.12. On this system all of my programs work, which was'nt the case before, with a newer version of debian (Buster). Therefore I'm urged to keep on it. But with this old debain-system, the new DALTON-version could work also. I wanted to stay with a version, because I had the experience that when there is a new version of debian and I installed it , I had to reinstall everything., Libraries, programs .. After that, some things don't work.
So I keep on this older system - at least on my latop.

Best Greetings
and kind regards

Alfred

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