# Convergence issue in Gaussian

I have been struggling with geometry optimization of a prostaglandin molecule (20 carbon atoms). I finally got the optimization, all right. Then I did the Frequency job on the optimized structure (I opened the Optimization job .LOG file scrolled up to the last geometry (highest number) and launched the Frequency job from there). Below is my route line from the .gjf file:

# freq=noraman cphf=noread b3lyp/6-31g(d) geom=connectivity


The Frequency job terminated normally and that's what I got in the Frequency job .LOG file:

          Item               Value     Threshold  Converged?
Maximum Force            0.000005     0.000450     YES
RMS     Force            0.000001     0.000300     YES
Maximum Displacement     0.013516     0.001800     NO
RMS     Displacement     0.003867     0.001200     NO
Predicted change in Energy=-2.250043D-08


Unfortunately, there is no statement: "Stationary point found", however according to Gaussian manual: "A stationary point is found when the Maximum Force and RMS Force are two orders of magnitude smaller than the thresholds shown, regardless of the values of the displacements."

Is not it just the case? If so, why wouldn't Gaussian kindly state that the stationary point was found?

• Just few suggestions for finding a stationary point. You can add some additional angular flexibility into the basis by changing it to, say, 6-31G(2df,p) or even switch to more modern Ahlrichs' def2 bases (Def2SVP to start from). Besides, you'd better use UltraFine integration grid and tight optimization criteria and do geometry optimization and frequency calculation in a single run: Opt=Tight Freq Int=UltraFine. – Wildcat Aug 28 '16 at 20:34
• Generally, you need all the 4 parameters to converge. However, displacement values may be large unrelated to the question wheater your geometry is stationary or not. It is a judgement call and you should have your chemical insight into the system to see wheater these values raise a red flag or not. – Greg Aug 29 '16 at 7:14
• Thank you so much Greg and @Wildcat. Opt=Tight and Int=Ultrafine did the trick! Stupid question: if I want to double check after an Opt-Freq job and just do the Freq job, I should of course skip the Opt=Tight, shouldn't I? How about Int=Ultrafine - should I always put it in the Freq job for this .chk or .log file? I mean, is it mandatory? – Ricardo Moreno Aug 30 '16 at 7:13
• @RicardoMoreno, yes, you should use the same integration grid for geometry optimization and frequency calculation. And yes, you can skip the Opt keyword for frequency calculations when an input geometry is already optimized (at the very same level of theory, of course, and using the same settings). – Wildcat Aug 30 '16 at 8:51
• But even if you include the Opt keyword in frequency calculations for an already optimized input geometry it would not harm: the program will just run 1 geometry optimization cycle and then switch to frequency calculation. Note though that a better approach for separate geometry optimization and frequency calculations is to save the checkpoint file for geometry optimization, then read the optimized geometry from it to start frequency calculations. – Wildcat Aug 30 '16 at 8:54

Is not it just the case?

Looks like it is indeed not the case. I think the phrase OP quoted from the manual, which says that the optimization stops when

The Maximum Force and RMS Force are two orders of magnitude smaller than the thresholds shown, regardless of the values of the displacements.

can be interpreted a bit differently, but I guess that algoritmically it is implemented in a pretty simple way: the above mentioned quantities should be at least 100 times smaller that the corresponding thresholds. And this is not the case for the calculation under consideration: Maximum Force value (0.000005) is not 100 times smaller (but only 90) than the threshold (0.000450).

• Thank you Wildcat. You are absolutely correct. It is 90 times less and not 100. It is all about precision. Thank you! – Ricardo Moreno Aug 30 '16 at 6:54

The actual answer to this question is that the Hessian is calculated analytically for DFT methods when you do a frequency calculation, but it is estimated when performing a geometry optimization. Therefore, in some cases, the optimization will show a converged structure but the frequency analysis shows that it is not below the convergence thresholds when the analytical Hessian is generated. The best option is to continue from the checkpoint file of the frequency calculation using freq opt=ReadFC guess=Read. This is all discussed on the Gaussian website here.

Oftentimes, the structure optimized from the analytical Hessian is nearly identical to the one from the approximated Hessian, but you simply don't know in advance how big this difference will be. In large, flexible molecules (ones that can have moderate displacements even at low forces), I have seen that the optimization can sometimes actually have a long way to go after continuing from the analytical Hessian.