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A specific HESSIAN calculation carried out with GAMESS software presents this result:

* * * WARNING, MODE 7 HAS BEEN CHOSEN AS A VIBRATION
          WHILE MODE 1 IS ASSUMED TO BE A TRANSLATION/ROTATION.
 PLEASE VERIFY THE PROGRAM'S DECISION MANUALLY!


 MODES 1 TO 6 ARE TAKEN AS ROTATIONS AND TRANSLATIONS.

     FREQUENCIES IN CM**-1, IR INTENSITIES IN DEBYE**2/AMU-ANGSTROM**2

                        1          2         3         4         5         6         7           
       FREQUENCY:       0.04       0.02      0.05      2.43      2.74      4.22     14.57       
    REDUCED MASS:    7.89669    7.90996   7.90399   5.75740   5.67992   5.13823   4.53741
    IR INTENSITY:    0.00002    0.00000   0.00000   0.03626   0.01094   0.09661   0.22220

All frequencies have values greater than zero. However, 1, 2, and 3 frequencies are close to zero. Going the GAMESS recommendation, the frequencies were visualized with Chemcraft.

In this verification: MODES 1, 2, and 3 are TRANSLATIONS MODES 4, 5, AND 6 are ROTATIONS MODE 7 is a VIBRATION

My questions are:

  1. Is it an equilibrium geometry?
  2. Must it once again be optimized?
  3. Is it reliable the calculation?
  4. If this calculation is not realiable, how can this be corrected?

I will appreciate the answer.

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You don't mention your molecule, which would help a lot. I'm trying to figure out how one gets 7 vibrational modes including translations and rotations... 3N will never equal 7, and 3N-5 = 7 would imply 3N = 12, so 4 atoms? If there was only one vibration, then it's a diatomic, but we'd only see 6 modes from 2 atoms.

If you can mention what the molecule is, it will be much easier to answer the question.

  1. While it's a good sign that all the frequencies are positive, usually a geometry optimization shows that forces (gradients) are close to zero before calculating frequencies. So I'd rather see the combination of:
  • negligible forces (GAMESS geometry optimization finished successfully)
  • positive frequencies (Hessian doesn't show negative eigenvalues)
  1. Did the first optimization complete successfully? GAMESS is usually conservative about declaring a completed optimization.

  2. You could mean several things by "reliable." For example, you don't indicate the method / functional / basis set you used to calculate the Hessian. I'd normally suggest something like this for a small molecule:

  • RI-MP2 or modern DFT functional
  • def2-TZVPP or larger basis set (or equivalent, e.g., jun-cc-pVTZ)

Moreover, for frequencies to be accurate, a full geometry optimization is needed first.

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    $\begingroup$ +1. For RI-MP2 one should use def2-TZVPP instead. $\endgroup$ Oct 8 at 8:13
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Your question is quite clear and on point, however it is a bit difficult to reply with the information you provided. I have never used GAMESS myself, so I cannot help you with the specific commands. I do not know on which molecules you are working, but it would be useful to know in order to reply.

If the output is the eigenvalues of the Hessian matrix then either the structure is not optimized or there is some problem with the input.

Since a molecule has 6 (5) degrees of freedom, in an minimum you expect 3N-6(5) non-zero values. I assume you have a diatomic molecule, you would then expect 1 vibrational mode. Since you have 7 positive eigenvalues your structure is clearly not in a minimum; not even in a saddle really.

While the first three could be related to floating point errors, the other three are clearly not zero. This is not an equilibrium geometry and you should optimize it.

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    $\begingroup$ I'm not sure I understand your conclusion. Presumably this is a diatomic molecule which is expected to have 3N-5=1 vibrational mode, 3 translational modes and 3 rotational modes, ie exactly the 7 that the calculation has returned. $\endgroup$
    – Andrew
    Oct 3 at 15:37
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    $\begingroup$ You are right, I am very sorry, I must have had my head in the clouds while answering! $\endgroup$
    – stanton63
    Oct 3 at 15:57
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    $\begingroup$ @Andrew - I haven't used GAMESS much but I don't see how a diatomic would give 7 eigenvalues. Yes, 3(2)-5 = 1, but if GAMESS is showing all the translations and rotations, you'd see 3N = 6 eigenvalues .. only one would be a real vibration. $\endgroup$ Oct 5 at 13:48
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    $\begingroup$ @GeoffHutchison - I'm assuming that one of those is the rotation around the molecular axis that isn't an actual mode for a linear molecule but might get spit out by a calculation method that doesn't know better. I'm not familiar with GAMESS, so I don't know if it eliminates that mode for linear molecules or not. I could be way off base. $\endgroup$
    – Andrew
    Oct 5 at 14:11

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