Optical Rotation from Coupled Cluster and Density Functional Theory: The Role of Basis Set Convergence

On the choice of coordinate origin in length gauge optical rotation calculations

In this work, we explore the issue of origin dependence in optical rotation (OR) calculations in the length dipole gauge (LG) using standard approximate methods belonging to density functional theory (DFT) and coupled cluster (CC) theory. We use the origin-invariant LG approach, LG(OI), that we recently proposed as reference for the calculations, and we study whether a proper choice of coordinate origin and molecular orientation can be made such that diagonal elements of the LG-OR tensor match those of the LG(OI) tensor. Using a numerical search algorithm, we show that multiple spatial orientations can be found where the LG and LG(OI) results match. However, a simple analytical procedure provides a spatial orientation where the origin of the coordinate system is close to the center of mass of the molecule. At the same time, we also show that putting the origin at the center of mass is not an ideal choice for every molecule (relative errors in the OR up to 70% can be obtained in out test set). Finally, we show that the choice of coordinate origin based on the analytical procedure is transferable across different methods and it is superior to putting the origin in the center of mass or center of nuclear charge. This is important because the LG(OI) approach is trivial to implement for DFT, but not necessarily for nonvariational methods in the CC family. Therefore, one can determine an optimal coordinate origin at DFT level and use it for standard LG-CC response calculations.

Finding reliable methodology for optical rotation and correct predictions of (s)-methyloxirane and (1R,5R)-β-pinene

Theoretical calculations of optical rotation (OR), although important to predict absolute configurations (ACs) and corroborate experiments, require efficient methodology able to reproduce enantiomer specificity and real OR values. Also, troublesome molecules are recurring in the literature, such as (S)-methyloxirane and (1R,5R)-β-pinene. This study evaluates DFT functionals B3LYP, CAM-B3LYP, ωB97X-D, M06-2X, and PBE0 considering basis sets aug-cc-pVDZ, aug-cc-pVTZ, 6-311++G(2d,p), and 6-311++G(3df,2p) in OR prediction of 42 rigid organic molecules assessing cases with wrong enantiomeric determination comparing to available experimental data at wavelengths 355, 589, and 633 nm. Functionals CAM-B3LYP and ωB97X-D with aug-cc-pVTZ are indicated here to reproduce experimental values more accurately considering fewer number of wrong AC predictions, normalized RMSD values below 0.70, and a good approximation to experimental values in hierarchical cluster analysis. Methyloxirane AC was reproduced in CAM-B3LYP and PBE0, with [ α ] 355 = 6 . 94 $$ {\left[\alpha \right]}_{355}=6.94 $$ for CAM-B3LYP/aug-cc-pVTZ close to experimental value [ α ] 355 = 7 . 49 ± 0 . 30 $$ {\left[\alpha \right]}_{355}=7.49\pm 0.30 $$ . Good results were found for AC of β-pinene in M06-2X, CAM-B3LYP, and ωB97X-D while the latter in 6-311++G(3df,2p) obtained OR values of [ α ] 589 = 3 . 44 $$ {\left[\alpha \right]}_{589}=3.44 $$ and [ α ] 689 = 4 . 20 $$ {\left[\alpha \right]}_{689}=4.20 $$ close to experimental values [ α ] 589 = 2 . 8 $$ {\left[\alpha \right]}_{589}=2.8 $$ and [ α ] 689 = 4 . 66 ± 0 . 60 $$ {\left[\alpha \right]}_{689}=4.66\pm 0.60 $$ . The two molecules aforementioned are, for the first time, reported to give valid theoretical OR values in such simple methodologies. OR calculations were all performed after geometry optimization at the same level of theory, and analysis of different functional combinations for each step in β-pinene showed it can interfere with AC prediction even in rigid molecules.

Comparative Study of Vibrational Raman Optical Activity with Different Time-Dependent Density Functional Approximations: The VROA36 Database

A new database, VROA36, is introduced to investigate the performance of computational approaches for vibrational Raman optical activity (VROA) calculations. The database is composed of 36 molecules with known experimental VROA spectra. It includes 93 conformers. Normal modes calculated with B3LYP-D3(BJ)/def2-TZVP are used to compute the VROA spectra with four functionals, B3LYP-D3(BJ), ωB97X-D, M11, and optimally tuned LC-PBE, as well as several basis sets. SimROA indices and frequency scaling factors are used to compare calculated spectra with each other and with experimental data. The four functionals perform equally well independently of the basis set and usually achieve good agreement with the experimental data. For molecules in near- or at-resonance conditions, the inclusion of a complex (damped) linear response approach is important to obtain physically meaningful VROA intensities. The use of any of the tested functional approximations with the def2-SVPD Gaussian-type basis set, or a basis of similar flexibility, can be recommended for efficient and reliable theoretical VROA studies.

Basis Set Dependence of Optical Rotation Calculations with Different Choices of Gauge

In this work, the basis set dependence of optical rotation (OR) calculations is examined for various choices of gauge/level of theory. The OR is calculated for a set of 50 molecules using B3LYP and CAM-B3LYP and 17 molecules using coupled cluster with single and double excitations (CCSD). The calculations employ the correlation-consistent basis sets, aug-cc-pVζZ with ζ = D, T, Q. An inverse-power extrapolation formula is then utilized to obtain OR values at the complete basis set (CBS) limit. We investigate the basis set convergence for these methods and three choices of gauge: length gauge (with gauge-including atomic orbitals, LG(GIAOs), for DFT), the origin-invariant length gauge [LG(OI)], and the modified velocity gauge (MVG). The results show that all methods converge smoothly to the CBS limit and that the LG(OI) approach has a slightly faster convergence rate than the other choices of gauge. While the DFT methods reach gauge invariance at the CBS limit, CCSD does not. The significant difference between the MVG and LG(OI) results at the CBS limit, 26%, indicates that CCSD is not quite at convergence in the description of electron correlation for this property. On the other hand, gauge invariance at the CBS limit for DFT does not lead to the same OR values for the two density functionals, which is also due to electron correlation incompleteness. A limited comparison to gas-phase experimental OR values for the DFT methods shows that CAM-B3LYP seems more accurate than B3LYP. Overall, this study shows that the LG(OI) approach with the aug-cc-pVTZ basis set for DFT, and with the CBS(DT) extrapolation for CCSD, provides a good cost/accuracy balance.

Origin invariant full optical rotation tensor in the length dipole gauge without London atomic orbitals

We present an origin-invariant approach to compute the full optical rotation tensor (Buckingham/Dunn tensor) in the length dipole gauge without recourse to London atomic orbitals, called LG(OI). The LG(OI) approach is simpler and less computationally demanding than the more common length gauge (LG)-London and modified velocity gauge (MVG) approaches, and it can be used with any approximate wave function or density functional method. We report an implementation at the coupled cluster with single and double excitations level (CCSD), for which we present the first simulations of the origin-invariant Buckingham/Dunn tensor in the LG. We compare LG(OI) and MVG results on a series of 22 organic molecules, showing good linear correlation between the approaches, although for small tensor elements, they provide values of opposite sign. We also attempt to decouple the effects of electron correlation and basis set incompleteness on the choice of gauge for specific rotation calculations on simple test systems. The simulations show a smooth convergence of the LG(OI) and MVG results with the basis set size toward the complete basis set limit. However, these preliminary results indicate that CCSD may not be close to a complete description of the electron correlation effects on this property even for small molecules and that basis set incompleteness may be a less important cause of discrepancy between choices of gauge than electron correlation incompleteness.

Structure Elucidation and Confirmation of Phloroglucinols from the Roots of Garcinia dauphinensis by Comparison of Experimental and Calculated ECD Spectra and Specific Rotations

Eight phloroglucinols from Garcinia dauphinensis were recently reported to have good to moderate antiplasmodial and anticancer activities, consistent with other phloroglucinol derivatives isolated from natural sources. Chiroptical properties were previously calculated and compared to experimental data for compound 2 as a means to deduce its absolute configuration. Tentative assignments for the remaining compounds were also reported based on these data. In order to arrive at stereochemical assignments for phloroglucinols 1 and 3-8, ECD spectra and specific rotations were computed for all stereoisomers of each compound. Molecular orbital analyses were also carried out for the most energetically favorable conformers of each compound. Absolute configurations are reported for all eight phloroglucinols for the first time.

Modeling Complex Solvent Effects on the Optical Rotation of Chiral Molecules: A Combined Molecular Dynamics and Density Functional Theory Study

The challenge of assigning the absolute stereochemical configuration to a chiral compound can be overcome via accurate ab initio predictions of optical rotation, a sensitive molecular property that is further complicated by solvent effects. The solvent's "chiral imprint"-the transfer of the chirality from the solute to the surrounding achiral solvent-is explored here using conformational averaging and time-dependent density-functional theory. These complex solvent effects are taken into account via simple averaging over a molecular dynamics trajectory together with the explicit quantum mechanical consideration of the solvent molecules within the solute's cybotactic region and implicit modeling of the bulk solvent. We consider several axes along which the system's optical rotation varies, including the sampling of the dynamical trajectory, the quality of the one-electron basis set, and the use of continuum solvent models to account for bulk effects.

A Density Functional Theory Study of Optical Rotation in Some Aziridine and Oxirane Derivatives

We present time-dependent density functional theory (TDDFT) calculations of the electronic optical rotation (ORP) for seven oxirane and two aziridine derivatives in the gas phase and in solution and compare the results with the available experimental values. For seven of the studied molecules it is the first time that their optical rotation was studied theoretically and we have therefore investigated the influence of several settings in the TDDFT calculations on the results. This includes the choice of the one-electron basis set, the exchange-correlation functional or the particular polarizable continuum model (PCM). We can confirm that polarized quadruple zeta basis sets augmented with diffuse functions are necessary for converged results and find that the aug-pc-3 basis set is a viable alternative to the frequently employed aug-cc-pVQZ basis set. Based on our study, we cannot recommend the generalized gradient functional KT3 for calculations of the ORP in these compounds, whereas the hybrid functional PBE0 gives results quite similar to the long-range correct CAM-B3LYP functional. Finally, we observe large differences in the solvent effects predicted by the integral equation formalism of PCM and the SMD variant of PCM. For the majority of solute/solvent combinations in this study, we find that the SMD model in combination with the PBE0 functional and the aug-pc-3 basis set gives the best agreement with the experimental values.

Full optical rotation tensor at coupled cluster with single and double excitations level in the modified velocity gauge

This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10%-20% with CAM-B3LYP and 20%-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(-)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistent with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials.

Theory and algorithms for chiroptical properties and spectroscopies of aqueous systems

Chiroptical properties and spectroscopies are valuable tools to study chiral molecules and assign absolute configurations. The spectra that result from chiroptical measurements may be very rich and complex, and hide much of their information content. For this reason, the interplay between experiments and calculations is especially useful, provided that all relevant physico-chemical interactions that are present in the experimental sample are accurately modelled. The inherent difficulty associated to the calculation of chiral signals of systems in aqueous solutions requires the development of specific tools, able to account for the peculiarities of water-solute interactions, and especially its ability to form hydrogen bonds. In this perspective we discuss a multiscale approach, which we have developed and challenged to model the most used chiroptical techniques.

Chiroptical properties of 2,2'-bioxirane

The two enantiomers of 2,2'-bioxirane were synthesized, and their chiroptical properties were thoroughly investigated in various solvents by polarimetry, vibrational circular dichroism (VCD), and Raman optical activity (ROA). Density functional theory (DFT) calculations at the B3LYP/aug-cc-pVTZ level revealed the presence of three conformers (G₊ , G_- , and cis) with Gibbs populations of 51, 44, and 5% for the isolated molecule, respectively. The population ratios of the two main conformers were modified for solvents exhibiting higher dielectric constants (G_- form decreases whereas G₊ form increases). The behavior of the specific optical rotation values with the different solvents was correctly reproduced by time-dependent DFT calculations using the polarizable continuum model (PCM), except for the benzene for which explicit solvent model should be necessary. Finally, VCD and ROA spectra were perfectly reproduced by the DFT/PCM calculations for the Boltzmann-averaged G₊ and G_- conformers.

Optical Rotation Calculations for a Set of Pyrrole Compounds

Optical rotation of 14 molecules containing the pyrrole group is calculated by employing both time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the second-order approximate coupled-cluster singles and doubles (CC2) method. All optical rotations have been provided using the aug-cc-pVDZ basis set at λ = 589 nm. The two methods predict similar results for both sign and magnitude for the optical rotation of all molecules. The obtained signs are consistent with experiments as well, although several conformers for four molecules needed to be studied to reproduce the experimental sign. We have also calculated excitation energies and rotatory strengths for the six lowest lying electronic transitions for several conformers of the two smallest molecules and found that each rotatory strength has various contributions for each conformer which can cause different optical rotations for different conformers of a molecule. Our results illustrate that both methods are able to reproduce the experimental optical rotations, and that the CAM-B3LYP functional, the least computationally expensive method used here, is an applicable and reliable method to predict the optical rotation for these molecules in line with previous studies.