Archive for the 'vibrational frequencies' Category

Structure of 2-oxazoline

A recent reinvestigation of the structure of 2-oxazoline demonstrates the difficulties that many computational methods can still have in predicting structure.

Samdal, et al. report the careful examination of the microwave spectrum of 2-oxzoline and find that the molecule is puckered in the ground state.1 It’s not puckered by much, and the barrier for inversion of the pucker, through a planar transition state is only 49 ± 8 J mol-1. The lowest vibrational frequency in the non-planar ground state, which corresponds to the puckering vibration, has a frequency of 92 ± 15 cm-1. This low barrier is a great test case for quantum mechanical methodologies.

And the outcome here is not particularly good. HF/cc-pVQZ, M06-2X/cc-pVQZ, and B3LYP/cc-pVQZ all predict that 2-oxazoline is planar. More concerning is that CCSD and CCSD(T) with either the cc-pVTZ or cc-pVQZ basis sets also predict a planar structure. CCSD(T)-F12 with the cc-pVDZ predicts a non-planar ground state with a barrier of only 8.5 J mol-1, but this barrier shrinks to 5.5 J mol-1 with the larger cc-pVTZ basis set.

The only method that has good agreement with experiment is MP2. This method predicts a non-planar ground state with a pucker barrier of 11 J mol-1 with cc-pVTZ, 39.6 J mol-1 with cc-pVQZ, and 61 J mol-1 with the cc-pV5Z basis set. The non-planar ground state and the planar transition state of 2-oxazoline are shown in Figure 1. The computed puckering vibrational frequency does not reproduce the experiment as well; at MP2/cc-pV5Z the predicted frequency is 61 cm-1 which lies outside of the error range of the experimental value.


Planar TS

Figure 1. MP2/cc-pV5Z optimized geometry of the non-planar ground state and the planar transition
state of 2-oxazoline.


(1) Samdal, S.; Møllendal, H.; Reine, S.; Guillemin, J.-C. "Ring Planarity Problem of 2-Oxazoline Revisited Using Microwave Spectroscopy and Quantum Chemical Calculations," J. Phys. Chem. A 2015, 119, 4875–4884, DOI: 10.1021/acs.jpca.5b02528.


2-oxazoline: InChI=1S/C3H5NO/c1-2-5-3-4-1/h3H,1-2H2

MP &vibrational frequencies Steven Bachrach 15 Jun 2015 1 Comment

Anharmonic corrections to vibrational frequenices

Vibrational frequencies are routinely computed within most QM codes assuming the harmonic approximation. To correct for the neglect of higher order terms (anharmonicity), along with correcting for the inherent approximations of whatever quantum mechanical method is used, the harmonic frequencies are typically corrected by using a multiplicative scaling factor. The values of the scaling factor is method-dependent: a different scaling factor is need for every method and basis set combination! Nonetheless, this is a simple approach to computing often quite reasonable vibrational frequencies.

Anharmonic corrections can also be computed, and this is usually done using perturbation theory, which requires computing the third and often fourth derivatives, a mightily expensive proposition for reasonably large molecules even with DFT, let alone with some wavefunction-based post-HF method.

Jacobsen and co-workers1 examined a set of 176 molecules that include 2738 vibrational modes, using HF, MP2, B3LYP and PBE0 with the 6-31G(d) or 6-31+G(d,p) basis sets. The unscaled anharmonic frequencies are much better than the unscaled harmonic frequencies; for example, using B3LYP/6-31+G(d), the root mean square deviation (RMSD) for the harmonic frequencies is 78 cm-1 and 36 cm-1 for the anharmonic frequencies. But the scaled harmonic frequencies are just as good as the scaled anharmonic frequencies; using the same QM method, the RMSD for the scaled harmonic frequencies is 38 cm-1 and 36 cm-1 for the scaled anharmonic frequencies.

These authors suggest that accurate anharmonic corrections require very accurate potential energy surfaces, and so they recommend that unless you are using a very highly accurate computational model, there is no point in computing anharmonic frequencies; scaled harmonic frequencies will suffice!


(1) Jacobsen, R. L.; Johnson, R. D.; Irikura, K. K.; Kacker, R. N. "Anharmonic Vibrational Frequency Calculations Are Not Worthwhile for Small Basis Sets," J. Chem. Theor. Comput. 2013, 9, 951-954, DOI: 10.1021/ct300293a.

vibrational frequencies Steven Bachrach 25 Mar 2013 No Comments