Normal frequencies of vibration of a molecule

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Hello,
I am new in computational chemistry. I was calculating by "Moller Plesset Second Order perturbation theory -MP2-" (using GAMESS) molecular parameters of Cs3Cl2-. Among them i found two complex frequencies of vibration. My question is now, what is the physical meaning of those complex frequencies?
My aim was actually to evaluate thermodynamic functions of that ion using the rigid-rotator-harmonic oscillator approximation. I am wondering if this approximation still hold for such an ion with a complex frequency, is it really a rigid one?
 

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  • #2
SpectraCat
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Hello,
I am new in computational chemistry. I was calculating by "Moller Plesset Second Order perturbation theory -MP2-" (using GAMESS) molecular parameters of Cs3Cl2-. Among them i found two complex frequencies of vibration. My question is now, what is the physical meaning of those complex frequencies?
My aim was actually to evaluate thermodynamic functions of that ion using the rigid-rotator-harmonic oscillator approximation. I am wondering if this approximation still hold for such an ion with a complex frequency, is it really a rigid one?
Imaginary frequencies means that the geometry optimization landed you at a transition state (i.e. a point on the potential energy surface with negative curvature). So by definition, you are not at a stable minimum, and thus much of your analysis will be non-sensical. What I recommend is to make a small distortion of the geometry along one of the imaginary modes, turn off symmetry and re-run the geometry optimization and frequency analysis. If the geometry optimization converges (i.e. ends without an error message), then you can run the frequency calculation, which should yield no imaginary frequencies if you are at a stable minimum.

It is important to note that, even if you end up at a stable minimum, there is no guarantee that you will have found the lowest energy structure .. there may be multiple structural isomers with different energies, but with such a simple system, there should not be too many. You should try to use any external knowledge you may have about the system to try to predict whether the structure you find is likely to be the global minimum.

One other word of advice ... if you are calculating an anion .. you really need to be using diffuse functions in your basis set, or you will likely get incorrect results.
 
  • #3
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adding to spectracat suggestions..
imaginary freq. means that there is some transition states..
also thermodynamics properties depend on temp. than freq.
have fun with computing..(boring thing is you have wait till you calc. finishes..)..
here we use G03 or G09.
 
  • #4
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..(boring thing is you have wait till you calc. finishes..)..
here we use G03 or G09.
Thank you! Actually, the calculation of those molecular parameters by GAMESS is the more boring one. For thermodynamic functions it is faster, i use a simple software called "Openthermo" which is based on rigid-rotator harmonic oscillator approximation. Of course thermodynamic function depends on temperature.
 
  • #5
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Imaginary frequencies means that the geometry optimization landed you at a transition state (i.e. a point on the potential energy surface with negative curvature). So by definition, you are not at a stable minimum, and thus much of your analysis will be non-sensical. What I recommend is to make a small distortion of the geometry along one of the imaginary modes, turn off symmetry and re-run the geometry optimization and frequency analysis. If the geometry optimization converges (i.e. ends without an error message), then you can run the frequency calculation, which should yield no imaginary frequencies if you are at a stable minimum.

It is important to note that, even if you end up at a stable minimum, there is no guarantee that you will have found the lowest energy structure .. there may be multiple structural isomers with different energies, but with such a simple system, there should not be too many. You should try to use any external knowledge you may have about the system to try to predict whether the structure you find is likely to be the global minimum.

One other word of advice ... if you are calculating an anion .. you really need to be using diffuse functions in your basis set, or you will likely get incorrect results.
Thank you!
For that ion Cs3Cl2+, i found also that it has other isomers which are in U-shape geometry and even pyramid ones. And I thought that to determine which one is the most equilibrium structure, i should take the one with a lower energy. Am i right? (I am really enjoying this computational chemistry)
 
  • #6
SpectraCat
Science Advisor
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Thank you!
For that ion Cs3Cl2+, i found also that it has other isomers which are in U-shape geometry and even pyramid ones. And I thought that to determine which one is the most equilibrium structure, i should take the one with a lower energy. Am i right? (I am really enjoying this computational chemistry)
Yes, that is correct. Glad you are having fun :wink:
 
  • #7
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Thank you!
For that ion Cs3Cl2+, i found also that it has other isomers which are in U-shape geometry and even pyramid ones. And I thought that to determine which one is the most equilibrium structure, i should take the one with a lower energy. Am i right? (I am really enjoying this computational chemistry)
There is a sentence you really never expect to hear outside of this forum, a lab, or... that's it! :smile: I'm not being sarcastic when I say it warms my heart to hear someone excited by personal triumph in science. Mind keeping us posted on how this proceeds? I'd be curious for one.
 
  • #8
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There is a sentence you really never expect to hear outside of this forum, a lab, or... that's it! :smile: I'm not being sarcastic when I say it warms my heart to hear someone excited by personal triumph in science. Mind keeping us posted on how this proceeds? I'd be curious for one.
Oh nice to hear someone who is interested too! Dear Frame Dragger, actually i am workig on thermodynamic properties (Enthalpy of dissociation) of tri- and penta -atomic ions that have been found experimentally over the CsCl vapors. My task is to use ab initio computational methods and check if my results agree other obtained using estimated molecular parameters. I have already calculated enthalpies of dissociation of the two tri-atomic ions Cs2Cl+ and CsCl2-. My results agree at +-5% with other pre-obtained results. I would add that i worked on a similar work (Concerning the part of thermodynamic functions only), on RbI ions, and the results are going to be exposed (probably) in the coming international conference of pure and applied chemistry (ICPAC).
 
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  • #9
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Oh nice to hear someone who is interested too! Dear Frame Dragger, actually i am workig on thermodynamic properties (Enthalpy of dissociation) of tri- and penta -atomic ions that have been found experimentally over the CsCl vapors. My task is to use ab initio computational methods and check if my results agree other obtained using estimated molecular parameters. I have already calculated enthalpies of dissociation of the two tri-atomic ions Cs2Cl+ and CsCl2-. My results agree at +-5% with other pre-obtained results. I would add that i worked on a similar work (Concerning the part of thermodynamic functions only), on RbI ions, and the results are going to be exposed (probably) in the coming international conference of pure and applied chemistry (ICPAC).
Well, probable congratulations then! Double-checking and finding such a close agreement must be fantastic. :smile: Chemistry really is the playground of the physicist.
 
  • #10
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Well, probable congratulations then! Double-checking and finding such a close agreement must be fantastic. :smile: Chemistry really is the playground of the physicist.
thank you!
 
  • #11
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Hello,
I am wondering if this approximation still hold for such an ion with a complex frequency, is it really a rigid one?
Someone told me that there is other approximation (other than rigid-rotator-harmonic oscillator) that can be used to calculate thermodynamic functions of molecules with complex vibrational frequencies. Among them he cited me the "Non-Rigid-Rotator-Harmonic oscillator but i have no clue about that. Is there anyone who knows something or who has a document that can be useful? Do exist software for that? Give me links please if possible
 
  • #12
SpectraCat
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Someone told me that there is other approximation (other than rigid-rotator-harmonic oscillator) that can be used to calculate thermodynamic functions of molecules with complex vibrational frequencies. Among them he cited me the "Non-Rigid-Rotator-Harmonic oscillator but i have no clue about that. Is there anyone who knows something or who has a document that can be useful? Do exist software for that? Give me links please if possible
You are mixing two problems:

1) If a molecule has imaginary frequencies, then it is at a transition state, not a stable minimum. In your case, I guess that means that your geometry optimization "failed", and you need to adjust the geometry (perhaps by breaking symmetry somewhere) and restart it. However, if you are interested in looking at chemical reactions, you may be trying to optimize to a transition state.
With regards to thermochemistry, there are statistical mechanical methods to calculate the thermodynamic functions of transition states, and they aren't really much more complicated than for a stable geometry, you just need to take into account that one of your "internal" degrees of freedom has been "used up" as the reaction coordinate, and deal appropriately with that negative force constant (it tells you the curvature at the top of the barrier, which in turn tells you about how "loose" or "tight" the transition state is).

2) If your molecule has large-amplitude motions (low-frequency, large-amplitude vibrations), or if it has an internal rotor, or if there is significant anharmonicity to one of the higher-frequency normal modes, then you need to use some sort of non-rigid model to account for the deviation of the density of rovibrational state from the ideal case (all vibrations are perfectly harmonic normal modes, molecule is a rigid rotator). These can be made arbitrarily complicated in my experience, but a good place to start is to look up the Morse potential, vibration-rotation coupling, and centrifugal distortion. The classic spectroscopic texts by Gerhard Herzberg are THE reference for this material, but they are most useful after you have already absorbed the basics in my experience. "Molecular Quantum Mechanics" by Atkins and Friedman gives a good introduction to the basics, as do many other graduate level texts ("Molecular Symmetry and Spectroscopy" by Harris and Bertolucci springs to mind). Those models I mentioned should encompass most of what you need to handle for the non-ideality of the simple molecules you mentioned in your earlier posts.
 
  • #13
alxm
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SpectraCat covered most of the issues here, but just to clarify (since it's been said twice): An imaginary frequency corresponds to a transition-state, if you're at a stationary point, i.e. where the gradient (forces) are zero (or close to it). This being directly analagous to the http://en.wikipedia.org/wiki/Second_derivative_test" [Broken] we all know from basic calculus. If you're not at a stationary point, then your frequencies don't mean much. There is an additional force on the atoms, and so they can't act as a harmonic oscillator.

As said, re-optimize the geometry with a different starting guess to get a stationary point (it's not really common that they converge to transition states when you're looking for a minimum, it's usually the other way around). If symmetry is on (it is by default in most codes), turn it off (e.g. keyword 'nosymm' in Gaussian), because you might be constraining the structure to a symmetric but incorrect structure. Likewise if you have any constrained distances or angles, of course.

Some caveats: As mentioned, you'll need diffuse functions. For a heavy element like Cesium, relativistic effects are significant. At the very least you should also use an ECP as well. When calculating frequencies, one tends to get a lot of systematic errors, so the results are usually improved by applying a http://pubs.acs.org/doi/abs/10.1021/jp048233q" [Broken].

If you do get results within 5%, it's probably due to error cancellation. (i.e. 'luck'). An MP2 calculation for such a molecule just won't be that good in general.
 
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