## INTRODUCTION

Computational chemistry and experimental techniques can be combined into a powerful tool for determining the absolute configuration of chiral molecules.1–10 The conceptually simplest approach is to compare theoretically calculated and experimentally measured specific optical rotations to deduce the absolute stereochemistry. This procedure relies first and foremost on the accuracy of the theoretical model used to compute the optical rotation. Theoretical predictions of optical rotations rely on quantum mechanics11 and require advanced quantum chemical methodologies. Despite tremendous advances in this field, the computer time required for optical rotation calculations remains a bottleneck for routine applications. It is therefore important to strike a reasonable balance between accuracy and efficiency when choosing the theoretical model.

From a computational point of view, density functional theory (DFT) is the simplest electronic structure method that incorporates electron correlation effects. Stephens and coworkers7, 9, 10, 12–15 have assessed the accuracy of the B3LYP exchange-correlation functional16, 17 in optical rotation calculations at the molecular equilibrium geometry. For a test set of 30 chiral molecules with absolute values of experimental sodium D-line specific optical rotations ranging from ∼10–1200° (dm g/cm^{3})^{−1} a mean absolute deviation of 20° (dm g/cm^{3})^{−1} was found.13 For small-angle rotations [absolute value <100° (dm g/cm^{3})^{−1}], the wrong sign was predicted for about 12% of 65 molecules at the sodium D-line.10 Recently, Crawford and Stephens15 compared B3LYP and coupled cluster singles and doubles (CCSD)18 calculations of sodium D-line optical rotations to experimental results for 13 molecules and found that the accuracies of the two models are almost identical (excluding the problematic case of norbornenone) when comparing with liquid-phase experimental data. However, a number of other studies have demonstrated that, at shorter wavelengths than the sodium D-line (589.3 nm), B3LYP and CCSD often differ substantially due to the generally more accurate prediction of excitation energies and rotatory strengths by the latter. For example, at 355 nm, B3LYP predicts specific rotations of methylthiirane, methyloxirane, and fluoro-oxirane to be 131.2,19 18.8,19 and 58.1°20 (dm g/cm^{3})^{−1}, respectively, whereas CCSD gives −96.7,19 −33.3,19 and 0.5°20 (dm g/cm^{3})^{−1} (the aug-cc-pVTZ basis set was used in all cases).

In addition to the purely electronic response at the equilibrium geometry, vibrational, conformational, and solvent effects are often crucial for reliable predictions of optical rotation. Vibrational effects are generally non-neglible21–26 and have been shown to account for as much as 20% of the optical rotation of rigid molecules.22 In the case of methyloxirane, vibrational effects must be taken into account to reproduce the experimental gas phase optical rotation to within a few degrees.27–30 For conformationally flexible molecules, a simple Boltzmann procedure has been applied to average the electronic contributions from different conformations.5, 25, 31–38 Comparing to a rigorous vibrational averaging procedure involving all conformations of 3-chloro-1-butene, Crawford and Allen26 have shown that the simple approach benefits from cancellation of errors. Solvent effects on optical rotations have been modeled by means of continuum methods, both with20, 39 and without14, 28 vibrational contributions. The major problem with the continuum approach is that the chiral solvent configuration induced by the solute may contribute to or even dominate the observed optical rotation.40 It is therefore not surprising that continuum methods in some cases fail to reproduce observed trends. A promising, if computationally expensive, alternative is to combine molecular dynamics (MD) simulation with quantum chemical sampling of the solute and explicit solvent molecules.40–42 In an attempt to keep the computational cost of the MD-based approach at a minimum, Kundrat and Autschbach43, 44 have shown that a simple point charge representation of the solvent molecules (water) may be used to simulate explicit solvent effects in the quantum chemical sampling. As noted by these authors, the MD-based scheme may also be used as an alternative to Boltzmann averaging to account for conformational effects.

In our recent study20 of the gas phase optical rotation of fluoro-oxirane we observed that the main source of discrepancy between vibrationally averaged B3LYP and CCSD results is the difference in electronic contributions at the equilibrium geometry. The dependence of the optical rotation on vibrational degrees of freedom is reasonably well described by B3LYP. As this is also the case for methyloxirane30 and methylthiirane,45 we here assess the accuracy of the following procedure for seven molecules and two wavelengths for which experimental gas phase results are available:

- 1Determine the equilibrium geometry at the B3LYP level of theory.
- 2Calculate the CCSD electronic optical rotation at the B3LYP equilibrium geometry.
- 3Add the zero-point vibrational correction (ZPVC) calculated at the B3LYP level.
- 4For conformationally flexible molecules, perform points 1, 2, and 3 for each low-lying conformer and compute the final optical rotation by Boltzmann averaging.

Using the electronic optical rotation calculated with the approximate coupled cluster singles, doubles, and triples model CC346 by Kongsted et al.28 in point 2, essentially the same procedure has been successfully applied to the difficult case of methyloxirane by Ruud and Zanasi.29 Requiring only a single-point calculation of the optical rotation at the CCSD level of theory, this procedure is significantly less demanding in terms of computer time than a complete CCSD simulation. A somewhat less demanding alternative is obtained by replacing CCSD with the aproximate coupled cluster singles and doubles model CC2,47 and the accuracy of this approach is assessed here as well.