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!

References

(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.

Sugars comprise a very important class of organic compounds for a variety of reasons, including dietary needs. On the chemical side, their stereochemical variations give rise to interesting
conformational questions. While sugar structures are a well-studied dating back to Fischer, most of these studies are in the solid or solution phase, and these phases can certainly play a role in dictating conformational preferences. This is seen in the differences in conformational distribution with different solvents. Only recently has instrumentation been developed (see these posts for some earlier applications: A, B, C) that can provide structural information of sugars in the gas phase. Cocinero and co-workers describe just such an analysis of fructose.¹

Using a combination of laser ablation Fourier transform microwave spectroscopy and quantum chemical computations, they have examined the gas-phase structure of this ketose. There are
quite a number of important conformational and configurational isomers to consider, as shown in Scheme 1. Fructose can exist in a pyranose form (6-member ring) with the anomeric carbon being α or β. An alternative cyclic form is the 5-member ring furanose form, which again has the two options at the anomeric position. Both the 5- and 6-member rings can ring flip, giving rise to 4 pyranose and 4 furanose forms. Of course there is also the
acyclic form.

Scheme 1. Major Frucotse isomers

The observed microwave spectrum is quite simple, showing evidence of only a single isomer. In comparing the microwave rotational constants and the quartic centrifugal distortion constants with those obtained from MP2 and M06-2x computations, it is clear that the only observed isomer is the β-pyranose isomer in its ²C₅ conformation.

Both MP2 and M06-2x (with a variety of TZ basis sets) predict this isomer to be the lowest energy form by about 2.5 kcal mol^-1. This structure is shown in Figure 1. Interestingly, B3LYP predicts the open chain configuration as the most stable isomer, with the β-pyranose isomer about 0.5 kcal mol^-1 higher in energy. The authors strongly caution against using B3LYP for any sugars.

Figure 1. MP2/maug-cc-pVTZ optimized structure of β-fructopyranose.

This most stable furanose isomer displays five intramolecular hydrogen bonds that account for its stability over all other possibilities. However, the pyranose form of fructose is very rare in nature, and the Protein Data Bank has only four examples. The furanose form is by far the more commonly found isomer (as in sucrose). Clearly, hydrogen bonding to solvent and other solvent interactions alter the conformational distribution.

References

(1) Cocinero, E. J.; Lesarri, A.; Ecija, P.; Cimas, A.; Davis, B. G.; Basterretxea, F. J.; Fernandez, J. A.; Castano, F. "Free Fructose is Conformationally Locked," J. Am. Chem. Soc. 2013, 135, 2845-2852, DOI: 10.1021/ja312393m.

InChIs:

β-fructopyranose:
InChI=1S/C5H10O6/c6-2-1-11-5(9,10)4(8)3(2)7/h2-4,6-10H,1H2
InChIKey=FFDHYUUPNCCTDA-UHFFFAOYSA-N

Myśliwiec and Stępień report on a new method for creating buckybowls.¹ The usual way had been to build from the inside outward. They opt instead to build from the outside in and have constructed the heterosubstitued bowl chrysaorole 1.

1

B3LYP/6-31G** optimizations reveal two conformers that are very close in energy: one has the butyl chains outstretched (1a) and one has the butyl arms internal or pendant (1b). These structures are shown in Figure 1. The depth of this bowl (1.96 Å) is quite a bit larger than in corranulene (0.87 Å). The agreement between the computed and experimental ¹³C and ¹H chemical shifts are excellent, supporting the notion that this gas phase geometry is similar to the solution phase structure. Though 1 is strained, 53.4 kcal mol^-1 based on B3LYP/6-31G** energies for Reaction 1 (which uses the parent of 1 – replacing the butyl groups with hydrogens), on a per sp² atom basis, it is no more strained than corranulene.

1a

1b

Figure 1. B3LYP/6-31G** optimized geometries of two conformers of 1.

This new synthetic strategy is likely to afford access to more unusual aromatic structures.

References

(1) Myśliwiec, D.; Stępień, M. "The Fold-In Approach to Bowl-Shaped Aromatic Compounds: Synthesis of Chrysaoroles," Angew. Chem. Int. Ed. 2013, 52, 1713-1717, DOI:10.1002/anie.201208547.

InChI

1: InChI=1S/C54H45N3/c1-4-7-16-55-49-19-31-10-12-33-21-51-45-27-39(33)37(31)25-43(49)44-26-38-32(20-50(44)55)11-13-34-22-52-46(28-40(34)38)48-30-42-36(24-54(48)57(52)18-9-6-3)15-14-35-23-53(47(45)29-41(35)42)56(51)17-8-5-2/h10-15,19-30H,4-9,16-18H2,1-3H3
InChIKey=VUUJVETWVYQACL-UHFFFAOYSA-N