Modeling of the Chiroptical Response of Chiral Amino Acids in Solution Using Explicit Solvation and Molecular Dynamics

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.

Isolated and solvated chiroptical behavior in conformationally flexible butanamines

The nonresonant optical activity of two highly flexible aliphatic amines, (2R)-3-methyl-2-butanamine (R-MBA) and (2R)-(3,3)-dimethyl-2-butanamine (R-DMBA), has been probed under isolated and solvated conditions to examine the roles of conformational isomerism and to explore the influence of extrinsic perturbations. The optical rotatory dispersion (ORD) measured in six solvents presented uniformly negative rotatory powers over the 320-590 nm region, with the long-wavelength magnitude of chiroptical response growing nearly monotonically as the dielectric constant of the surroundings diminished. The intrinsic specific optical rotation,α λ T (in deg dm-1 [g/mL]-1 ), extracted for ambient vapor-phase samples of R-MBA [-11.031(98) and -2.29 (11)] and R-DMBA [-9.434 (72) and -1.350 (48)] at 355 and 633 nm were best reproduced by counterintuitive solvents of high polarity (yet low polarizability) like acetonitrile and methanol. Attempts to interpret observed spectral signatures quantitatively relied on the linear-response frameworks of density-functional theory (B3LYP, cam-B3LYP, and dispersion-corrected analogs) and coupled-cluster theory (CCSD), with variants of the polarizable continuum model (PCM) deployed to account for the effects of implicit solvation. Building on the identification of several low-lying equilibrium geometries (nine for R-MBA and three for R-DMBA), ensemble-averaged ORD profiles were calculated at T = 300 K by means of the independent-conformer ansatz, which enabled response properties predicted for the optimized structure of each isomer to be combined through Boltzmann-weighted population fractions derived from corresponding relative internal-energy or free-energy values, the latter of which stemmed from composite CBS-APNO and G4 analyses. Although reasonable accord between theory and experiment was realized for the isolated (vapor-phase) species, the solution-phase results were less satisfactory and tended to degrade progressively as the solvent polarity increased. These trends were attributed to solvent-mediated changes in structural parameters and energy metrics for the transition states that separate and putatively isolate the equilibrium conformations supported by the ground electronic potential-energy surface, with the resulting displacement of barrier locations and/or decrease of barrier heights compromising the underlying premise of the independent-conformer ansatz.

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.

Automated Quantum Chemistry-Based Calculation of Optical Rotation for Large Flexible Molecules

The calculation of optical rotation (OR, [α]_D) for nonrigid molecules was limited to small systems due to the challenging problem of generating reliable conformer ensembles, calculating accurate Boltzmann populations and the extreme sensitivity of the OR to the molecules' three-dimensional structure. Herein, we describe and release the crenso workflow for the automated computation of conformer ensembles in solution and corresponding [α]_D values for flexible molecules. A comprehensive set of 28 organic drug molecules (28-144 atoms) with experimentally determined values is used in our assessment. In all cases, the correct OR sign is obtained with an overall mean relative deviation of 72% (mean absolute deviation of 82 °[dm(g/cm³)]^-1 for experimental values in the range -160 to 287 °[dm(g/cm³)]^-1). We show that routine [α]_D computations for very flexible, biologically active molecules are both feasible and reproducible in about a day of computation time on a standard workstation computer. Furthermore, we observed that the effect of energetically higher-lying structures in the ensemble on the OR is often averaged out and that in 23 out of 28 cases, the correct OR sign is obtained by just considering only the lowest free energy conformer. In four example cases, we show that the approach can also describe the OR of pairs of flexible diastereomers properly. In summary, even very sensitive, multifactorial physicochemical properties appear reliably predictable with minimal user input from efficiently automated quantum chemical methods.

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 Critical Appraisal of Dimolybdenum Tetraacetate Application in Stereochemical Studies of vic-Diols by Circular Dichroism

This critical appraisal is intended for users of the dimolybdenum method, well-established in electronic circular dichroism (ECD) to determine the absolute configuration of vic-diols and, in particular, for experimental researchers not being experts in chiroptical methods. The main goal is to demonstrate how to avoid misleading and ambiguous conclusions resulting from the rigorous application of the helicity rule by limiting the analysis to the vic-diol unit alone. We particularly focused on multichromophoric systems, especially those that may interfere with the absorption of an in situ formed dimolybdenum tetraacetate-diol complex. In this context, examples are presented of vic-diols for which stereochemical assignment based solely on the helicity rule is ambiguous and does not necessarily lead to correct results. The motivation for choosing these examples was to demonstrate the impact of the structure of the substrate on the complexation process with the metal core and its selectivity. For each selected case, results obtained are analyzed in detail together with a discussion of existing restrictions and choice of a support method to increase the credibility of the conclusion. Based on seven both educational and challenging examples, it was shown that the dimolybdenum methodology can also be effectively applied to complex chromophoric systems, provided that other chiroptical methods and/or computational support verify obtained results.

Approximate versus Exact Embedding for Chiroptical Properties: Reconsidering Failures in Potential and Response

We investigate the suitability of subsystem time-dependent density-functional theory (sTDDFT) for describing chiroptical properties with a focus on optical rotation parameters. Our starting point is a new implementation of the recently proposed projection-based, coupled frozen-density embedding (FDEc) framework. We adapt the generalized, non-Hermitian formulation of TDDFT and derive corresponding expressions for regular and damped response properties from subsystem TDDFT. We verify that our implementation of this "exact" formulation allows to reproduce supermolecular results of electronic circular dichroism (ECD) spectra, of optical rotatory dispersion, and of polarizabilities. We present a systematic test of the main approximations typically introduced in practical frozen-density embedding (FDE) calculations of response properties: (i) the use of approximate nonadditive kinetic-energy (NAKE) functionals, which can be avoided through projection techniques, (ii) the use of monomer (subsystem) basis sets rather than supersystem basis sets, and (iii) the neglect of intersubsystem response coupling within the so-called uncoupled FDE (or FDEu) approximation. While approximation (i) is known to generally lead to large errors for covalently bound subsystems, we present cases in which either the basis set or the coupling step are similarly or even (much) more important. In particular, we explicitly demonstrate by comparison to a fully coupled calculation that missing intersubsystem response couplings are responsible for the failure of FDE reported in a previous study [ J. Chem. Theory Comput. 2015, 11, 5305-5315]. We show that good agreement with reference results can be obtained in this case even with standard NAKE approximations for the FDE potentials and efficient monomer basis sets, making calculations for larger systems well accessible.

Toward theoretical terahertz spectroscopy of glassy aqueous solutions: partially frozen solute-solvent couplings of glycine in water

The molecular-level understanding of THz spectra of aqueous solutions under ambient conditions has been greatly advanced in recent years. Here, we go beyond previous analyses by performing ab initio molecular dynamics simulations of glycine in water with artificially frozen solute or solvent molecules, respectively, while computing the total THz response as well as its decomposition into mode-specific resonances based on the "supermolecular solvation complex" technique. Clamping the water molecules and keeping glycine moving breaks the coupling of glycine to the structural dynamics of the solvent, however, the polarization and dielectric solvation effects in the static solvation cage are still at work since the full electronic structure of the quenched solvent is taken into account. The complementary approach of fixing glycine reveals both the dynamical and electronic response of the solvation cage at the level of its THz response. Moreover, to quantitatively account for the electronic contribution solely due to solvent embedding, the solute species is "vertically desolvated", thus preserving the fully coupled solute-solvent motion in terms of the solute's structural dynamics in solution, while its electronic structure is no longer subject to solute-solvent polarization and charge transfer effects. When referenced to the free simulation of Gly(aq), this three-fold approach allows us to decompose the THz spectral contributions due to the correlated solute-solvent dynamics into entirely structural and purely electronic effects. Beyond providing hitherto unknown insights, the observed systematic changes of THz spectra in terms of peak shifts and lineshape modulations due to conformational freezing and frozen solvation cages might be useful to investigate the solvation of molecules in highly viscous H-bonding solvents such as ionic liquids and even in cryogenic ices as relevant to polar stratospheric and dark interstellar clouds.

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.

The shape of the electronic circular dichroism spectrum of (2,6-dimethylphenyl)(phenyl)methanol: interplay between conformational equilibria and vibronic effects

Analysis of the interplay between conformational equilibria, solvent effects and vibronic contributions in the ECD spectra.

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.

Concentration Dependent Specific Rotations of Chiral Surfactants: Experimental and Computational Studies

Recent experimental studies have shown unexpected chiroptical response from some chiral surfactant molecules, where the specific rotations changed significantly as a function of concentration. To establish a theoretical understanding of this experimentally observed phenomena, a novel methodology for studying chiral surfactants via combined molecular dynamics (MD) and quantum mechanical (QM) calculations is presented. MD simulations on the +10 000 atom surfactant systems have been performed using MD and QM/molecular mechanics (MM) approaches. QM calculations performed on MD snapshots coupled with extensive analysis on lauryl ester of phenylalanine (LEP) surfactant system indicate that the experimentally observed variation of specific rotation with concentration may be due to the conformational differences of the surfactant monomers in the aggregates. Though traditional MM simulations did not show significant differences in the conformer populations, QM/MM simulations using the forces derived from the PM6 method did predict conformational differences between aggregated and nonaggregated LEP molecules, which is consistent with experimental data. Additionally the electrostatic environment of charged surfactants may also be important, since dramatic changes in the Boltzmann populations of surfactant monomers can be noted in the presence of an electric field generated by the chiral ionic aggregates.

Short-range solvation effects on chiroptical properties: a time-dependent density functional theory and ab initio molecular dynamics computational case study on austdiol

The description of solvation effects on the chiroptical properties of chiral molecules is still a difficult challenge in the field of computational spectroscopy; this issue is critical in stereochemical characterization, since a reliable assessment of absolute configuration requires high accuracy. The present case study reports the huge effect of solvation on the chiroptical properties of austdiol, a fungal metabolite of known stereochemistry. Standard protocols based on time-dependent density functional theory calculations failed to reproduce its experimental chiroptical properties in methanol. When short-range solvation effects are explicitly considered by means of ab initio molecular dynamics, the correlation between calculated and experimental data is greatly improved because of a better description of the chiral environment around the ketone chromophore, showing that the modeling of subtle solvent-induced perturbations may require the most accurate computational methods.

Circular dichroism and optical rotation of lactamide and 2-aminopropanol in aqueous solution

The performance of implicit and explicit solvent models (polarizable continuum model (PCM) and microsolvation with positions of water molecules obtained either from molecular dynamics (MD) simulations or quantum mechanical geometry optimization) for calculations of electronic circular dichroism (CD) and optical rotation (OR) is examined for two polar and flexible molecules: lactamide and 2-aminopropanol. The vibrational structure of the CD spectrum is modeled for lactamide. The results are compared with the newly obtained experimental data. The signs of the bands are correctly reproduced using all three methods under investigation and the CAM-B3LYP functional for the CD spectrum of lactamide, but not for 2-aminopropanol. The sign of the calculated optical rotation is correctly predicted by means of PCM, but its magnitude is somewhat underestimated in comparison with experiment for lactamide and overestimated for 2-aminopropanol. To some extent it is rectified by employing explicit hydration. Overall, microsolvation with geometry optimization seems more cost-effective than classical MD, but this is likely to be a consequence of inadequate classical potential and electronic structure model.

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.

Conformational aspects in the studies of organic compounds by electronic circular dichroism

The electronic circular dichroism (ECD) spectra of flexible molecules include the contributions of all conformers populated at the working temperature. ECD spectra of chiral substrates depend on their stereochemistry in terms of both absolute configuration, as reflected in the sign of the spectrum, and molecular conformation, which dictates the overall spectral shape (possibly including the sign) in a very sensitive manner. The unique high sensitivity of ECD towards conformation, as well as of other chiroptical spectroscopies, renders these techniques a useful alternative or complement to standard spectroscopic tools for conformational investigations, such as NMR. This tutorial review provides first a brief discussion of the main principles of ECD spectroscopy and related methods for interpretation of spectra, with special reference to conformational aspects. The review focuses on the common problems encountered in the application of ECD for assignments of absolute configuration of flexible molecules. These problems can be handled either by taking into account the whole conformational ensemble or by considering rigid derivatives prepared ad hoc. Finally, the review presents the relatively less common but very interesting application of ECD spectroscopy for conformational analyses of organic compounds.

Time-dependent density functional response theory for electronic chiroptical properties of chiral molecules

Methodology to calculate electronic chiroptical properties from time-dependent density functional theory (TDDFT) is outlined. Applications of TDDFT to computations of electronic circular dichroism, optical rotation, and optical rotatory dispersion are reviewed. Emphasis is put on publications from 2005 to 2010, but much of the older literature is also cited and discussed. The determination of the absolute configuration of chiral molecules by combined measurements and computations is an important application of TDDFT chiroptical methods and discussed in some detail. Raman optical activity (ROA) spectra are obtained from normal-mode derivatives of the optical rotation tensor and other linear response tensors. A few selected (ROA) benchmarks are reviewed.