From chemistry-request |-at-| server.ccl.net Mon Jan 21 09:25:48 2002 Received: from MAIL.AD.Berry.edu ([66.20.28.66]) by server.ccl.net (8.11.6/8.11.0) with ESMTP id g0LEPlI23500 for ; Mon, 21 Jan 2002 09:25:47 -0500 Received: from [10.16.232.24] ([10.16.232.24]) by MAIL.AD.Berry.edu with Microsoft SMTPSVC(5.0.2195.2966); Mon, 21 Jan 2002 09:26:44 -0500 User-Agent: Microsoft-Outlook-Express-Macintosh-Edition/5.02.2022 Date: Mon, 21 Jan 2002 09:25:32 -0500 Subject: SUMMARY: Question pertaining to Vibrational Frequencies From: Gary Breton To: CC: , , , , Message-ID: Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit X-OriginalArrivalTime: 21 Jan 2002 14:26:44.0643 (UTC) FILETIME=[A6D64730:01C1A287] Hello, Thank you so much for all of your responses to my question on vibrational frequencies. The original question is given below: I performed a minimization on a structure using Gaussian 98W (B3LYP/6-311+G**) and followed it up with a frequency calculation at the same level (of course). I obtained a single negative frequency at -27cm-1. I then re-optimized the geometry at the same level but this time ignored symmetry. The new E was lower than the previous by 0.03 kcal/mol. The newfrequency calculation afforded a single negative frequency at -11 cm-1. David Young's "Computational Chemistry" book suggests (page 94) that frequency values with a range of about -20 to 20 cm-1 are essentially zero within the numerical accuracy of most software packages. Is this true for G98 as well? > To sum it all up: Can I take a -11 cm-1 frequency to be inconsequential? or do I need to continue to play with the system until absolutely no negative frequencies are present? I had many requests for a summary of the answers. I provide these below without the names of those responding (which I guess is good etiquette, could be wrong). My final solution? still working on it. I think that my final take home message is the following: small negative frequencies suggest that you are close to a minimum. Probably the energy at this point is NOT very different than the energy at the minimum that you are close to. However, one should do what one can to eliminate this minimum. Suggestions for doing this are given below. Thanks again and best regards to the group members! ****************************************************** A frequncy of -11 cm-1 is a transition state. However, I suspect that your case is "undecided". The number of imaginary freqs gives the curvature of the PES at the stationary point in question. G98 thinks that at your stationary point, with the method (B3LYP) and basis set (6-311+G**) you used the PES is mildly saddle-shaped, but not very different from a minimum. Another method/basis might give a distinct saddle or minimum. Borderline cases like this could require high computational levels to settle. *************************** This imaginary frequency should disappear! To my knowledge, this is not a problem of minimisation. May be you have a methyl group in your molecule that in badly oriented. Just changing its orientation is OK! **************************** I wouldn't worry about a single imaginary frequency as low as 11i cm**-1. It is so low (there's about 350 cm**-1 to a kcal/mole!) that it may well be caused by numerical noise from the integration. You could try integrals(grid=ultrafine) to see if it goes away, but as I said, it doesn't really matter. **************************** One of the most important things to look at, is the six lowest eigenvalues of the Hessian (or frequencies) in absolute sense. In an ideal world, where the QuantumChemical packages would be able to provide geometries with exactly zero gradients, these lowest six should all be zero. The fact that they are not in practice, is (among other factors maybe) due to the fact that the gradient is not exactly zero, but below a certain threshold. Therefore, if your -11 cm-1 is one of these six lowest frequencies, then you can ignore it. NOTE: Gaussian used to be one of the packages that would already filter the output, i.e. the six lowest frequencies were not displayed in the list of frequencies, as I seem to remember. However, at another place in the output, they were displayed. As I haven't done frequency calculations with Gaussian for a few years now, I'm not sure if this is (still) true. Just be careful. ***************************** In my opinion, the small imaginary frequency can be looked as an error > from computation and it is difficult to avoid for some systems. But maybe it is a rotational excited state as well. So please try to change your structure according to the imaginary frequency to find if you can get rid of it. Of course you may try opt=tight, too. ******************************* You are going to get a lot of responses saying the same thing: YES, a freq of -11 may be taken as zero and does not mean you have a saddle. I have done dozens of freq calcs via Gaussian98 at geoms optimized at the B3LYP/6-311++g** level and I usually get anywhere from one to 5 just barely negative frequencies. Perhaps more to the point, when it has been a t-state, the negative freq has always been < -100. ******************************* While a small value like -11cm-1 can arise from a couple of sources I would not suggest you pass it off, especially if it is a mode which would have bearing on any of the chemistry you wish to describe. On the other hand I would agree that making any prediction about the observed frequency of a mode less than 20 wavenumbers based on this calculation is not warranted. So I will make a couple of general comments and help you see the next step. First, there is are two sets of "Frequencies listed" the "low frequencies" and then the normal mode listings including intensities, reduced masses etc. The latter can be given twice if you used the HPmodes option. The first set are the lowest 10 modes from diagonalizing the full 3Natoms by 3Natoms matrix and so there will be 6 low frequency modes, say under 10 wavenumbers and they correspond to overall rotation and translation. Negative values at this point for these modes is not particularly worth note. Then this matrix has the analytic rotation and translation modes projected out and the remaining 3NAtoms-6 modes are determined. At this point only vibrations are left and negative frequencies of any size are harder to dismiss. Second, even with NoSymm you can end up with a symmetric structure because the gradient carries the symmetry of the structure and will not follow anti-symmetric modes downhill. So if the negative frequency is not totally symmetric, i.e. is anything except A1 symmetry, you may only have gotten numerical noise in the re-optimization. Re-optimizing to break the symmetry also requires moving the structure along to lower symmetry, best by displacing along that mode. You can add the displacement vector from the FREQ analysis element by element to the structure. Third, DFT does have more of a problem with numerical precision because of numerical integration. With a low frequency mode like this I have seen use of Int=Grid=UltraFine or one of the higher order angular grids, see the Int keyword, clean up the integration. You would need to use OPT=ReadFC with this Grid followed by FREQ with this same grid to be sure you have it. If your negative frequency is on the Low Freq list and not a normal mode, you are likely fine and it is just numerical. If the structure really is reported as C1 then this may well be real and you should go on to use a better integration grid to sort it out. Or if the structure is still rated as symmetric and this mode breaks symmetry try breaking the symmetry and re-doing the optimization at the lower symmetry. Agreed that modes this low are not going to make large energy differences but if it is a dihedral it can result in opening up a structure by a few degrees, enough to change conclusions. ***************************** i am by no means an expert, but during my calculations on the same level of theory, i had the same problem. what this imaginary freqency means is essentially that you have a very flat poteential energy surface and there are probably more structures to explore. so what you should do is alter the structure and perform a new minimization and see where it takes you. ******************************* You can probably ignore this frequency. Some energy surfaces are fairly flat (especially when a molecule can undergo internal rotations), and frequency calculations "reveal" imaginary frequencies even when you have effectively optimized the geometry. But just to be sure, you might try the following - if the calculation is convenient to do, you could tighten the optimization criteria and repeat the geometry optimization + frequency calculation. (Sorry, but I don't know how you specify these criteria in Gaussian). ******************************** >To sum it all up: Can I take a -11 cm-1 frequency to be inconsequential? Yup. or >do I need to continue to play with the system until absolutely no negative >frequencies are present? Nope. > > as you can see in your example the amount of additional stabilization left in these soft modes is pretty minimal and thus is not worth chasing. *********************************** I prefer to tighten the SCF and the opt convergence criteria, use calcfc, and so on to see if I can remove such -ve frequencies. This can waste a lot of time though, and sometimes you never get rid of them, so you accept you're as close to the minimum as you're going to get. I've had more numerical trouble with DFT than HF/MP*. The -11 is a bit of a problem if you want to use and compare the ZPE and thermochemistry. ********************************** I, too, am uncomfortable with small imaginary frequencies. With the standard HF methods, one could usually rewrite the z-matrix to better represent the internal coordinates to get rid of them or "nudge" the internal coordinate(s) for the imaginary freqs and re-optimize. However, for DFT methods, these tactics are not highly reliable. Nowadays, people (including myself) tend write the input in terms of xyz coordinates and let G98 decide on the redundant internal coordinates so modifying the internal coordinates are a bit more tricky. One possible solution is just to re-order the xyz coordinates (especially the first 3) so that G98 will re-orient the molecule differently in space. Since DFT is a grid-based methods, this "coordinate juggling" procedure will very slightly alter the gradients that are being computed so that in the long run your freqs will all turn out real (hopefully, 8^) ). Of course, this leads to the second solution which is to simply add the option "int=ultrafine" which will give you a finer grid for the DFT calculation. This solution will result in greater CPU time (dependent on size of molecule), but it keeps you > from having to "play games" to get rid of the imaginary freqs. ************************************ Try opt=tight. *********************************** I have heard (second hand from Gaussian) that up to about -50 cm-1 may be considered effectively zero. The problem is more acute with DFT methods compared to Hartree-Fock or post HF methods since the DFT calculations have greater accumulation of rounding errors due to the numerical integration that is required. ************************************** Are you using the ultrafine grid? Try if you are no using!! And maybe this frequency will desapear!