Magnitude of zero-point vibrational corrections to optical rotation in rigid organic molecules: a time-dependent density functional study

Theoretical Study of the Isotope Effect in Optical Rotation

In this work, the isotope effect in optical rotation (OR) is examined by exploring structure-property relationships for H → D substitutions in chiral molecules. While electronic effects serve as the dominant source of optical activity, there is a non-negligible contribution from nuclear vibrations, which changes with isotopic substitution. We employ a test set of 50 small organic molecules: three-membered rings with varying heteroatoms (PCl, PH, S, NCl, NH, O, and NBr) and functional groups (Me, F), and simulations were run at the B3LYP/aug-cc-pVDZ level of theory. The objectives of this work are to determine locations of isotopic substitution that result in significant changes in the vibrational correction to the OR and to evaluate which vibrational modes and electronic response are the major contributors to the isotope effect. Molecules with more polarizable heteroatoms in the ring (e.g., S and P) have the largest change in the vibrational correction compared to the unsubstituted parent molecules. In many cases, isotopic substitution made to the hydrogens on the opposite side of the ring from the functional group provides the largest change in the OR. H/D wagging modes and C vibrations (for D-C centers) are the largest contributors to the isotope effect. This is explained with a molecular orbital decomposition analysis of the OR. The relevant vibrational modes affect the orbital transitions that are already significant at the equilibrium geometry. However, this effect is only large when polarizable heteroatoms are involved because the electron density surrounding them is diffuse enough to feel the subtle effect of change in mass due to isotopic substitution on the relevant vibrational modes.

First Principles Simulations of Optical Rotation of Chiral Molecular Crystals

In this work, we present simulations of the optical rotation (OR) for five molecular crystals at density functional theory level with periodic boundary conditions (DFT-PBC). Calculations are compared with experimental measurements and show semi-quantitative agreement with experimental data for three of the crystals: tartatic acid, benzil, and pentaerythritol. For the other two crystals, aspartic acid and glutamic acid, the calculated data are in qualitative agreement with, but two orders of magnitude smaller than, the experimental data. We provide some arguments that support the theoretical predictions and suggest that the experiments should be revisited. We also find that the position of H centers provided in experimental X-ray data is not sufficiently reliable for simulating OR, and better results are obtained when H atoms are allowed to relax while keeping heavier elements fixed at the experimental positions. Comparison with molecular cluster calculations with a better functional and a larger basis set indicate that the role of intermolecular interactions (reproduced with the PBC technique) is as or more important than the choice of model chemistry. Despite the current limitations in the level of theory that can be employed, these simulations provide a promising avenue to investigate the effect of intermolecular interactions on this sensitive electronic property of molecules and materials.

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.

Natural Optical Activity from Density-Functional Perturbation Theory

We present an accurate and computationally efficient first-principles methodology to calculate natural optical activity. Our approach is based on the long-wave density-functional perturbation theory and includes self-consistent field terms naturally in the formalism, which are found to be of crucial importance. The final result is expressed exclusively in terms of response functions to uniform field perturbations and avoids troublesome summations over empty states. Our strategy is validated by computing the natural optical activity tensor in representative chiral crystals (trigonal Se, α-HgS, and α-SiO_{2}) and molecules (C_{4}H_{4}O_{2}), finding excellent agreement with experiment and previous theoretical 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.

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.

Performance of the DLPNO-CCSD and recent DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals

In the present study, the performance of a set of density functionals: BP86, PBE, OLYP, BEEF, PBEpow, TPSS, SCAN, PBEGXPBE, M06L, MN15L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, mPW1PW, B98, TPSS0, PBE1KCIS, SCAN0, M06, M06-2X, MN15, CAM-B3LYP, ωB97x, B2PLYP, and the B3LYP/N07D and PBE/N07D schemes in the calculation of the ¹⁴N anisotropic hyperfine coupling (HFC) constants of a set of 23 nitroxide radicals is evaluated. The results are compared with those obtained with the DLPNO-CCSD method and experimental HFC values. Harmonic contribution to the ¹⁴N HFC vibrational correction was calculated at the revPBE0/def2-TZVPP level and included in the evaluation. With the vibrational correction, the DLPNO-CCSD method yielded HFC values in good agreement with the experiment (mean absolute deviation (MAD) = 0.3 G for the dipole-dipole contribution and MAD = 0.8 G for the contact coupling contribution). The best DFT results are obtained using the M06 functional with MAD = 0.2 G for the dipole-dipole contribution and MAD = 0.7 G for the contact coupling contribution. In general, vibrational correction significantly improved most DFT functionals' performance but did not change its overall ranking.

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.

Validation of microscopic magnetochiral dichroism theory

Magnetochiral dichroism (MChD), a fascinating manifestation of the light-matter interaction characteristic for chiral systems under magnetic fields, has become a well-established optical phenomenon reported for many different materials. However, its interpretation remains essentially phenomenological and qualitative, because the existing microscopic theory has not been quantitatively confirmed by confronting calculations based on this theory with experimental data. Here, we report the experimental low-temperature MChD spectra of two archetypal chiral paramagnetic crystals taken as model systems, tris(1,2-diaminoethane)nickel(II) and cobalt(II) nitrate, for light propagating parallel or perpendicular to the c axis of the crystals, and the calculation of the MChD spectra for the Ni(II) derivative by state-of-the-art quantum chemical calculations. By incorporating vibronic coupling, we find good agreement between experiment and theory, which opens the way for MChD to develop into a powerful chiral spectroscopic tool and provide fundamental insights for the chemical design of new magnetochiral materials for technological applications.

Absolute Configurations of Naturally Occurring [5]- and [3]-Ladderanoic Acids: Isolation, Chiroptical Spectroscopy, and Crystallography

We have isolated mixtures of [5]- and [3]-ladderanoic acids 1a and 2a from the biomass of an anammox bioreactor and have separated the acids and their phenacyl esters for the first time by HPLC. The absolute configurations of the naturally occurring acids and their phenacyl esters are assigned as R at the site of side-chain attachment by comparison of experimental specific rotations with corresponding values predicted using quantum chemical (QC) methods. The absolute configurations for 1a and 2a were independently verified by comparison of experimental Raman optical activity spectra with corresponding spectra predicted using QC methods. The configurational assignments of 1a and 2a and of the phenacyl ester of 1a were also confirmed by X-ray crystallography.

Calculation of Dipole-Forbidden 5f Absorption Spectra of Uranium(V) Hexa-Halide Complexes

Restricted-active-space wave function calculations including spin-orbit coupling, in combination with Kohn-Sham density functional calculations of vibrational modes, were used to determine the vibronic and electronic absorption intensities of the near-infrared electric dipole-forbidden 5f-5f transitions of representative uranium(V) hexa-halide complex ions. The agreement with experimentally assigned vibronic and electronic transitions measured for powder or solution samples of salts of the complex ions is reasonable overall and excellent for the experimentally best-resolved E_5/2u → E_5/2u^' bands. The intensity of the vibronic transitions may be borrowed from ligand-to-metal charge-transfer excitations as well as 5f-to-6d metal-centered transitions. Magnetically allowed electronic transitions contribute to the two lower-frequency bands of the ligand-field spectrum.

Comparison of measured and predicted specific optical rotation in gas and solution phases: A test for the polarizable continuum model of solvation

A comparative theoretical and experimental study of dispersive optical activity is presented for a set of small, rigid organic molecules in gas and solution phases. Target species were chosen to facilitate wavelength-resolved measurements of specific rotation in rarefied vapors and in organic solvents having different polarities, while avoiding complications due to conformational flexibility. Calculations were performed with two density functionals (B3LYP and CAM-B3LYP) and with the coupled-cluster singles and doubles (CCSD) ansatz, and solvent effects were included through use of the polarizable continuum model (PCM). Across the various theoretical methods surveyed, CCSD with the modified velocity gauge provided the best overall performance for both isolated and solvated conditions. Zero-point vibrational corrections to equilibrium calculations of chiroptical response tended to improve agreement with gas-phase experiments, but the quality of performance realized for solutions varied markedly. Direct comparison of measured and predicted specific-rotation suggests that PCM, in general, is not able to reproduce attendant solvent shifts (neither between gas and solution phases nor among solvents) and fares better in estimating actual medium-dependent values of this property (although the error is rather system dependent). Thus, more elaborate solvation models seem necessary for a proper theoretical description of solvation in dispersive optical activity.

Circularly Polarized Luminescence from Axially Chiral BODIPY DYEmers: An Experimental and Computational Study

With our new home-built circularly polarized luminescence (CPL) instrument, we measured fluorescence and CPL spectra of the enantiomeric pairs of two quasi-isomeric BODIPY DYEmers 1 and 2, endowed with axial chirality. The electronic circular dichroism (ECD) and CPL spectra of these atropisomeric dimers are dominated by the exciton coupling between the main π-π* transitions (550-560 nm) of the two BODIPY rings. Compound 1 has strong ECD and CPL spectra (g_lum =4×10^-3 ) well reproduced by TD-DFT and SCS-CC2 (spin-component scaled second-order approximate coupled-cluster) calculations using DFT-optimized ground- and excited-state structures. Compound 2 has weaker ECD and CPL spectra (g_lum =4×10^-4 ), partly due to the mutual cancellation of electric-electric and electric-magnetic exciton couplings, and partly to its conformational freedom. This compound is computationally very challenging. Starting from the optimized excited-state geometries, we predicted the wrong sign for the CPL band of 2 using TD-DFT with the most recommended hybrid and range-separated functionals, whereas SCS-CC2 or a DFT functional with full exact exchange provided the correct sign.

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.

Good Computational Practice in the Assignment of Absolute Configurations by TDDFT Calculations of ECD Spectra

Quantum-mechanical calculations of chiroptical properties have rapidly become the most popular method for assigning absolute configurations (AC) of organic compounds, including natural products. Black-box time-dependent Density Functional Theory (TDDFT) calculations of electronic circular dichroism (ECD) spectra are nowadays readily accessible to nonexperts. However, an uncritical attitude may easily deliver a wrong answer. We present to the Chirality Forum a discussion on what can be called good computational practice in running TDDFT ECD calculations, highlighting the most crucial points with several examples from the recent literature. Chirality 28:466-474, 2016. © 2016 Wiley Periodicals, Inc.

Temperature Dependence of NMR Parameters Calculated from Path Integral Molecular Dynamics Simulations

The influence of temperature on NMR chemical shifts and quadrupolar couplings in model molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory (DFT) calculations of shielding and electric field gradient (EFG) tensors. An approach based on convoluting calculated shielding or EFG tensor components with probability distributions of selected bond distances and valence angles obtained from DFT-PIMD simulations at several temperatures is used to calculate the temperature effects. The probability distributions obtained from the quantum PIMD simulations, which includes nuclear quantum effects, are significantly broader and less temperature dependent than those obtained with conventional DFT molecular dynamics or with 1D scans through the potential energy surface. Predicted NMR observables for the model systems were in excellent agreement with experimental data.

Microsolvation of 2-thiouracil: molecular structure and spectroscopic parameters of the thiouracil-water complex

State-of-the-art quantum-chemical computations have been employed to accurately determine the equilibrium structure and interaction energy of the 2-thiouracil-water complex, thus extending available reference data for biomolecule solvation patterns. The coupled-cluster level of theory in conjunction with a triple-ζ basis set has been considered together with extrapolation to the basis set limit, performed by employing second-order Møller-Plesset perturbation theory, and inclusion of core-correlation and diffuse-function corrections. On the basis of the comparison of experiment and theory for 2-thiouracil [ Puzzarini et al. Phys. Chem. Chem. Phys. 2013 , 15 , 16965 - 16975 ], structural changes due to water complexation have been pointed out. Molecular and spectroscopic properties of the 2-thiouracil-water complex have then been studied by means of the composite computational approach introduced for the molecular structure evaluation. Among the results achieved, we mention the accurate determination of the molecular dipole moment and of the spectroscopic parameters required for predicting the rotational spectrum.

Molecular structure and spectroscopic signatures of acrolein: theory meets experiment

A comprehensive study of the molecular structure and IR spectrum of cis and trans acrolein has been performed by an integrated computational approach coupling methods rooted in the coupled-cluster ansatz and the density functional theory. From the one side, DFT anharmonic force fields allow us to determine very reliable semiexperimental structures for both isomers, which are in remarkable agreement with the geometries issuing from CCSD(T) computations accounting for the extrapolation to the complete basis set and core correlation. The same kind of coupled-cluster computations provide dipole moment, relative energies, and interconversion barrier in remarkable agreement with experiments. Finally, harmonic CCSD(T) results coupled to DFT evaluation of mechanical and electrical anharmonicity allow us, in the framework of second-order perturbative vibrational theory, to confirm most of the experimental assignments of IR spectra, and to suggest some additional interpretations for congested regions including fundamental bands together with overtones and combination bands.

Development of a virtual spectrometer for chiroptical spectroscopies: the case of nicotine

The impressive advances of computational spectroscopy in most recent years are providing robust and user-friendly multifrequency virtual spectrometers, which can also be used by nonspecialists to complement experimental studies. At the heart of these developments there are latest-generation models based on Density Functional Theory for the proper treatment of stereo-electronic effects, coupled to the polarizable continuum model to deal with bulk solvent effects, and low-order perturbative treatments of anharmonic effects. Continuing our efforts to increase the range of application of virtual spectrometers, we report here about chiroptical spectroscopies with special reference to optical rotation and vibrational circular dichroism. The capabilities and possible limitations of our latest tool will be analyzed for the specific case of (S)-nicotine in vacuo and in different solvents.

Accurate structure, thermodynamics, and spectroscopy of medium-sized radicals by hybrid coupled cluster/density functional theory approaches: the case of phenyl radical

The coupled-cluster singles doubles model with perturbative treatment of triples (CCSD(T)) coupled with extrapolation to the complete basis-set limit and additive approaches represent the "golden standard" for the structural and spectroscopic characterization of building blocks of biomolecules and nanosystems. However, when open-shell systems are considered, additional problems related to both specific computational difficulties and the need of obtaining spin-dependent properties appear. In this contribution, we present a comprehensive study of the molecular structure and spectroscopic (IR, Raman, EPR) properties of the phenyl radical with the aim of validating an accurate computational protocol able to deal with conjugated open-shell species. We succeeded in obtaining reliable and accurate results, thus confirming and, partly, extending the available experimental data. The main issue to be pointed out is the need of going beyond the CCSD(T) level by including a full treatment of triple excitations in order to fulfil the accuracy requirements. On the other hand, the reliability of density functional theory in properly treating open-shell systems has been further confirmed.

Molecular structure determination using chiroptical spectroscopy: where we may go wrong?

Chiroptical spectroscopy is being widely used for determining the three-dimensional molecular structures (i.e., absolute configurations and conformations) of chiral molecules. The general procedure used with any of the chiroptical spectroscopic methods is to analyze the experimental data using corresponding quantum chemical predictions. Such analysis involves multiple steps, including consideration of conformations, solvent effects, electronic transitions, stereoisomers, and experimental artifacts, each of which possesses certain limitations. These limitations, when not recognized or properly taken into account, may lead to incorrect conclusions. This review emphasizes on selected examples that illustrate the potential limitations in utilizing the chiroptical spectroscopic methods. The examples used include hibiscus acid dimethylester, hibiscus acid disodium salt, 3,3'-diphenyl-[2,2'-binaphthalene]-1,1'-diol, tartaric acid esters, and 6,6'-dibromo-[1,1'-binaphthalene]-2,2'-diol.

Vibrational averaging of the chemical shift in crystalline α-glycine

Averaging of the chemical shift over the molecular motion improves the simulated data and provides additional information about the temperature dependence and system dynamics. However, crystal modeling is difficult due to the limited precision of the plane-wave density functional theory (DFT) methods and approximate vibrational schemes. On the glycine example, we investigate how the averaging can be achieved within the periodic boundary conditions at the DFT level. The nuclear motion is modeled with the vibrational configuration interaction, with other simplified quantum anharmonic schemes, and the classical Born-Oppenheimer molecular dynamics (BOMD). The results confirm a large vibrational contribution to the isotropic shielding values. Both the first and second derivatives of the shielding were found important for the quantum averaging. The first derivatives influence the shielding mostly due to the anharmonic character of the CH and NH stretching modes, whereas second derivatives produce most vibrational corrections associated with the lower-frequency vibrational modes. Temperature excitations of the lowest-frequency vibrational states and the expansion of the crystal cell both determine the temperature dependence of nuclear magnetic resonance parameters. The vibrational quantum approach as well as classical BOMD schemes provided temperature dependencies of the chemical shifts that are consistent with the previous experimental data.