# Why is MP2 failing to calculate proper IR frequencies for [Co(CO)4]- and [Fe(CO)4]2-?

I was doing some IR calculations on different 3d transition metal carbonyl complexes during some practical courses where we were introduced to effective core potentials. While doing this we found that MP2 has some problem with the calculation of at least the asymmetrical $\nu_\text{CO}$ band (that was the only one we were interested in).

We made the calculations for $\ce{[Ti(CO)6]^2-}$, $\ce{[V(CO)6]-}$, $\ce{[Cr(CO)6]}$, $\ce{[Mn(CO)6]+}$ in octahedral symmetry and $\ce{[Fe(CO)4]^2-}$, $\ce{[Co(CO)4]-}$ and $\ce{[Ni(CO)4]}$ in tetrahedral symmetry. The method was MP2, as stated in the title, and the basis set was 6-31G(d). The program we used was Gaussian$~$09 Rev. A.02 but that was not the problem, as I did calculations with other programs with similar results. All optimized structures are considered to be true minima as there either is no imaginary frequency or it is calculated to be $\ge -50~\mathrm{cm^{-1}}$ with was stated to be a problem of the insufficient DFT grid but not further questioned.

The following graphic shows that most of the calculated values are acceptable and near their experimental values but two of them, namely $\ce{[Co(CO)4]-}$ and $\ce{[Fe(CO)4]^2-}$ differ significantly from the experimental values by nearly $300\ldots1000~\mathrm{cm^{-1}}$.

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After this I varied some parameters of the calculation that could influence this deviation as was:

• additional diffuse functions for the better description of ions
• tight optimization criteria (T) as this might reduce the imaginary frequency
• no frozen core (F) just to try it
• solvents: PCM(DCM), PCM(Heptane) as experimental values aren't taken in gas phase
• I also optfreq'ed with B3LYP/6-31G(d)/MDF10 (B) to see if it's the method itself

The results can be seen in the following table: $$\begin{array}{cccccccc} \hline \text{Basis~Set} & \mathrm{Solv.} & \mathrm{d(MC)} & \mathrm{d(CO)} & \nu_\text{CO}(calc.) & \mathrm{Int.} & \nu_\text{CO}(exp.) & \Delta\nu_\text{CO}\\ & & \mathrm{Ang.} & \mathrm{Ang.} & \mathrm{cm^{-1}} & \mathrm{km\, mol^{-1}} & \mathrm{cm^{-1}} & \mathrm{cm^{-1}}\\ \hline \mathrm{E}/6{-}31\mathrm{G}^\ast & & 1.802 & 1.184 & 2830 & 2.0\cdot10^5 & 1890 & 940\\ \mathrm{EFT}/6{-}31\mathrm{+G}^\ast & & 1.799& 1.187& 2966& 2.7\cdot10^5 & 1890 & 1076\\ \mathrm{E}/6{-}31\mathrm{+G}^\ast & & 1.800 & 1.187 & 2996 & 2.9\cdot10^5 & 1890 & 1106\\ \mathrm{E}/6{-}31\mathrm{+G}^\ast & \mathrm{DCM} & 1.795 & 1.186 & 4671 & 0.0 & 1890 & 2781\\ \mathrm{E}/6{-}31\mathrm{G}^\ast & \mathrm{Hept.} & 1.799 & 1.184 & 3203 & 4.3\cdot10^5 & 1890 & 1223\\ \hline \mathrm{BE}/6{-}31\mathrm{G}^\ast & & 1.767 & 1.169 & 1978 & 1322 & 1890 & 88\\ \hline \end{array}$$

What can be seen:

• Within MP2 there is no significant effect on $\ce{M-C}$- or $\ce{C=O}$-bond lengths.
• The diffuse functions shift the frequency to higher wave numbers and the impact of the solvent is big to huge. As without the solvents the deviation was calculated to be somewhere around $+1000~\mathrm{cm^{-1}}$ it is now at $+2800~\mathrm{cm^{-1}}$!
• Also the intensities are horribly wrong ... they are somewhere around $2$ to $4\cdot10^5~\mathrm{km\, mol^{-1}}$ instead of somewhere around 1000 or in the special case of DCM they are completely zero.
• B3LYP predicts everything within common error ranges

• "All optimized structures are considered to be ground states". You probably meant "true minima" out there rather then "ground states". – Wildcat Jul 21 '15 at 19:29
• @PH13, the failure of MP2 might be due the multi-reference character of a molecular specie. The quick way to check that in Gaussian would be to run single-point CCSD calc requesting the T1 diagnostic (T1Diag). If T1 is bigger than 0.02, you might have a multi-reference situation for which neither MP2 nor CC are reliable. DFT is also unreliable in this case, but it might work sort of by accident. :D – Wildcat Jul 21 '15 at 21:31
• 1st row TM have always been problematic for a HF reference wf, mainly because of strong static correlation effects as mentioned. MP2 is not expected to work well. Typically, hybrid-functional are also expected to have larger errors than GGAs for 1st row TM, but at least they can deal better with static correlation. With such small basis sets, all kind of effects can occur. – hokru Jul 23 '15 at 8:49
• Transition metal chemistry is a graveyard for MP2 :D ||| I think the better question is almost, why MP2 is not failing for the other complexes ;) – Martin - マーチン Jul 23 '15 at 11:27
• Could you please check by a simple CAS(2,2), 2 electrons in 2 orbitals, the occupation numbers? This would be a indication for the reliability or not of the HF determinant used for MP2. – user17738 Jul 26 '15 at 20:17

Some months later but here we go...

I agree with most of the comments that multiconfigurational effects should be present for this system, and maybe they are very strong. But I tend to think that this is not the cause of the huge difference with experimental values. The fact that B3LYP returns reasonable values should be taking into account. Surely it "could be" just a coincidence but let's face it, I is very unprovable that all the results are reasonable due to coincidence (it is very simple to check it out, just try some others well proved functionals).

My guess is that you found the correct nuclear coordinates for the minimum of the PES, but the SCF part of the calculation have serious problems and it converged to some unreasonable electronic "state". This would imply that the MP2 results are ridiculous. As HF and B3LYP are very different in the SCF part, B3LYP converged correctly.

You could try different initial guesses (Hückel, PA, a previous converged calculation) and different methods (like RHF, OHF, UHF etc.). Other basis sets can also help (a little larger if possible). I would try to avoid effective core potentials! (I understand that this can be a problem for your teaching purposes). Convergence method is of course of main importance (consider quadratic or very damped convergence) . I found almost impossible that calculating inner electrons correlation helps in this case.

Of course that the refinements that you tried are useful, but I think that just to improve quantitatively the results.

I hope that the ideas above help you. I would like to know if you effectively solved your problem.

Regards

• Thank you for your answer. My current plan is to further investigate on that during this summer. Besides all comments to my question, your answer gives me other good points to look at. – pH13 - Yet another Philipp Mar 3 '16 at 12:22
• @pH13, If it is not a problem for you, it would be interesting that you share the output file to play with it, I'm curious about what happened. If a nuclei coordinate file (XYZ file or something like that). – user1420303 Mar 3 '16 at 14:38