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
What are your ideas why MP2 fails with this special task?
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 $\endgroup$ – Wildcat Jul 21 '15 at 21:31