Ab initio prediction of optical rotation: Comparison of density functional theory and Hartree‐Fock methods for three 2,7,8‐trioxabicyclo[3.2.1]octanes

Abstract

We report ab initio calculations of the frequency-dependent electric dipole-magnetic dipole polarizabilities, beta(nu), at the sodium D line frequency and, thence, of the specific rotations, [alpha](D), of 2,7,8-trioxabicyclo[3.2.1]octane, 1, and its 1-methyl derivative, 2, using the Density Functional Theory (DFT) and Hartree-Fock/Self-Consistent Field (HF/SCF) methodologies. Gauge-invariant (including) atomic orbitals (GIAOs) are used to ensure origin-independent [alpha](D) values. Using large basis sets which include diffuse functions DFT [alpha](D) values are in good agreement with experimental values (175.8 degrees and 139.2 degrees for (1S,5R)-1 and -2, respectively); errors are in the range 25-35 degrees. HF/SCF [alpha](D) values, in contrast, are much less accurate; errors are in the range 75-95 degrees. The use of small basis sets which do not include diffuse functions substantially lowers the accuracy of predicted [alpha](D) values, as does the use of the static limit approximation: beta(nu) approximately beta(o). The use of magnetic-field-independent atomic orbitals, FIAOs, instead of GIAOs, leads to origin-dependent, and therefore nonphysical, [alpha](D) values. We also report DFT calculations of [alpha](D) for the 1-phenyl derivative of 1, 3. DFT calculations find two stable conformations, differing in the orientation of the phenyl group, of very similar energy, and separated by low barriers. Values of [alpha](D) predicted using two different algorithms for averaging over phenyl group orientations are in good agreement with experiment. In principle, the absolute configuration (AC) of a chiral molecule can be assigned by comparison of the optical rotation predicted ab initio to the experimental value. Our results demonstrate the critical importance of the choice of ab initio methodology in obtaining reliable optical rotations and, hence, ACs, and show that, at the present time, DFT constitutes the method of choice.

Formation and temperature stability of G‐quadruplex structures studied by electronic and vibrational circular dichroism spectroscopy combined with ab initio calculations

“…15 These functionals yield vibrational rotational strengths in better agreement with experimental observations compared to calculations at the Hartree-Fock (HF) level, with a minimal increase in computation time. 16 In this study we newly used a combination of VCD spectroscopy and ab initio calculations to address the open question of the formation and determination of the G-quadruplex structure in solution, which is not always the same as in a crystal. 17 For our study, we choose the sequence of five runs GGG which was characterized biophysically before.…”

Optical rotation: Recent advances in determining the absolute configuration

“…47 The systematic investigations of specific rotations using DFT however did not occur until Cheeseman et al 18 developed the computer code for this method as a part of Gaussian suite of programs. Using this code, Cheeseman and colleagues 48,50,[72][73][74] undertook systematic studies to determine the level of accuracy one can obtain using quantum mechanical methods and to discern the origin of differences between the experimental observations and theoretical predictions. In their first report 48 on this subject, they investigated specific rotations predicted at both the HF and DFT levels of theory using 38 different basis sets, static limit method, and GIAOs for methyloxirane and trans-dimethylthiirane.…”

“…In their first report 48 on this subject, they investigated specific rotations predicted at both the HF and DFT levels of theory using 38 different basis sets, static limit method, and GIAOs for methyloxirane and trans-dimethylthiirane. In later studies, 50,[72][73][74] they implemented frequency-dependent specific rotation calculation using DFT and investigated a large number of molecules. The general conclusions obtained from their studies are: 1) calculated specific rotations converge slowly as the size of basis set is increased; 2) the differences between HF and DFT predictions are large and DFT results are more accurate than HF results; 3) large basis sets containing diffuse functions and DFT are needed to achieve reliable results; 4) static limit method predictions are not as reliable as the dynamic method predictions; and 5) two basis sets, aug-cc-pVDZ and 6-311++G(2d,2p), are suggested to provide the best compromise of accuracy and computational cost.…”

“…As mentioned earlier, such calculations were shown 48,[72][73][74] to give approximate estimates. Recently, Grimme 49 reported DFT predictions of specific rotation for bromochlorofluoromethane, but GIAOs were not used here so the results became origin-dependent.…”

Synthesis, chiroptical properties, and their theoretical simulation of some highly rotating benzotricamphor derivatives

“…In spite of all these progresses, some difficulties are still present. In fact, Stephens et al18 claiming that the ab initio calculation of the OR (and of ECD) provides a reliable answer only by the use of TDDFT method with extended basis sets (i.e., including diffuse functions) propose the use of the TDDFT method with the state‐of‐the‐art hybrid functional B3LYP19–21 and an extended basis set (aug‐cc‐pVDZ or higher) as a reliable and largely applicable22–57 calculation technique. Clearly, such a recipe makes compulsory the use of powerful computing systems when big‐sized molecules (i.e., those having applicative interest and most common for the practicing organic chemist) are treated: this represents a clear obstacle to the diffusion of these methods among nonspecialists.…”