A theoretical study of the chiroptical properties of molecules with isotopically engendered chirality

Perturb-Then-Diagonalize Vibrational Engine Exploiting Curvilinear Internal Coordinates

The present paper is devoted to the implementation and validation of a second-order perturbative approach to anharmonic vibrations, followed by variational treatment of strong couplings (GVPT2) based on curvilinear internal coordinates. The main difference with respect to the customary Cartesian-based formulation is that the kinetic energy operator is no longer diagonal, and has to be expanded as well, leading to additional terms which have to be taken into proper account. It is, however, possible to recast all the equations as well-defined generalizations of the corresponding Cartesian-based counterparts, thus achieving a remarkable simplification of the new implementation. Particular attention is paid to the treatment of Fermi resonances with significant number of test cases analyzed fully, validating the new implementation. The results obtained in this work confirm that curvilinear coordinates strongly reduce the strength of inter-mode couplings compared to their Cartesian counterparts. This increases the reliability of low-order perturbative treatments for semi-rigid molecules and paves the way toward the reliable representation of more flexible molecules where small- and large-amplitude motions can be safely decoupled and treated at different levels of theory.

General Perturb-Then-Diagonalize Model for the Vibrational Frequencies and Intensities of Molecules Belonging to Abelian and Non-Abelian Symmetry Groups

In this paper, we show that the standard second-order vibrational perturbation theory (VPT2) for Abelian groups can be used also for non-Abelian groups without employing specific equations for two- or threefold degenerate vibrations but rather handling in the proper way all the degeneracy issues and deriving the peculiar spectroscopic signatures of non-Abelian groups (e.g., l -doubling) by a posteriori transformations of the eigenfunctions. Comparison with the results of previous conventional implementations shows a perfect agreement for the vibrational energies of linear and symmetric tops, thus paving the route to the transparent extension of the equations already available for asymmetric tops to the energies of spherical tops and the infrared and Raman intensities of molecules belonging to non-Abelian symmetry groups. The whole procedure has been implemented in our general engine for vibro-rotational computations beyond the rigid rotor/harmonic oscillator model and has been validated on a number of test cases.

Computational Comparison of Chemical and Isotopic Approaches to Control the Photoisomerization Dynamics of Light-Driven Molecular Motors

Synthetic molecular motors driven by E/Z photoisomerization reactions are able to produce unidirectional rotary motion because of a structural asymmetry that makes one direction of rotation more probable than the other. In most such motors, this asymmetry is realized through the incorporation of a chemically asymmetric carbon atom. Here, we present molecular dynamics simulations based on multiconfigurational quantum chemistry to investigate whether the merits of this approach can be equaled by an alternative approach that instead exploits isotopic chirality. By first considering an N-methylpyrrolidine–cyclopentadiene motor design, it is shown that isotopically chiral variants of this design undergo faster photoisomerizations than a chemically chiral counterpart, while maintaining rotary photoisomerization quantum yields of similarly high magnitude. However, by subsequently considering a pyrrolinium–cyclopentene design, it is also found that the introduction of isotopic chirality does not provide any control of the directionality of the photoinduced rotations within this framework. Taken together, the results highlight both the potential usefulness of isotopic rather than chemical chirality for the design of light-driven molecular motors, and the need for further studies to establish the exact structural circumstances under which this asymmetry is best exploited.

SAMPL7: Host-guest binding prediction by molecular dynamics and quantum mechanics

Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) challenges provide routes to compare chemical quantities determined using computational chemistry approaches to experimental measurements that are shared after the competition. For this effort, several computational methods have been used to calculate the binding energies of Octa Acid (OA) and exo-Octa Acid (exoOA) host-guest systems for SAMPL7. The initial poses for molecular dynamics (MD) were generated by molecular docking. Binding free energy calculations were performed using molecular mechanics combined with Poisson-Boltzmann or generalized Born surface area solvation (MMPBSA/MMGBSA) approaches. The factors that affect the utility of the MMPBSA/MMGBSA approaches including solvation, partial charge, and solute entropy models were also analyzed. In addition to MD calculations, quantum mechanics (QM) calculations were performed using several different density functional theory (DFT) approaches. From SAMPL6 results, B3PW91-D3 was found to overestimate binding energies though it was effective for geometry optimizations, so it was considered for the DFT geometry optimizations in the current study, with single-point energy calculations carried out with B2PLYP-D3 with double-, triple-, and quadruple-ζ level basis sets. Accounting for dispersion effects, and solvation models was deemed essential for the predictions. MMGBSA and MMPBSA correlated better to experiment when used in conjunction with an empirical/linear correction.

Unidirectional Rotary Motion in Isotopically Chiral Molecular Motors: A Computational Analysis

Molecular dynamics simulations are performed to explore if isotopic chirality can induce unidirectional rotary motion in molecular motors operated through double-bond photoisomerizations. Using a high-quantum yield motor featuring a chemically asymmetric carbon atom as reference, it is found that isotopically chiral counterparts of this motor sustain such motion almost equally well. Overall, the study reveals a previously unexplored role for isotopic chirality in the design of rotary molecular motors.

A computational study of the vibrationally-resolved electronic circular dichroism spectra of single-chain transoid and cisoid oligothiophenes in chiral conformations

We simulate the vibronic profile of the electronic circular dichroism (ECD) spectra of oligothiophenes in cisoid and transoid chiral arrangements. We consider oligomers of different lengths, from two to fifteen units, and investigate extensively how the ECD spectral shapes depend on the inter-ring torsions. In general, the molecular structures we consider are not stationary points of the ground state potential energy surface. Therefore, in order to perform vibronic calculations, we present a new computational protocol able to define reduced-dimensionality models where the effect of the off-equilibrium modes is removed. This is done adopting a description of the vibrational motions in curvilinear internal coordinates, and vertical harmonic models coupled with an iterative application of projectors to define energy Hessians, and therefore effective normal modes, in the space complementary to the one of the off-equilibrium coordinates. Although we consider both Franck-Condon and Herzberg-Teller contributions, the results show that transoid twisted ribbons always give rise to monosignated ECD spectra, while bi-signated and multi-signated spectra are expected for cisoid helices. These findings are explained on the basis of the different transition strengths of the lowest electronic states imparted by the different spatial arrangement, that is almost linear for transoid structures and more globular for cisoid ones. We predicted the chiroptical response of a large number of possible molecular arrangements. These data are employed to critically discuss the experimental ECD of polythiophenes in different experimental conditions, forming either aggregates or host-guest complexes. The method here proposed to perform vibronic calculations in reduced-dimensionality models is of general applicability and its potential interest goes beyond the practical application presented here.

High-Resolution Absorption and Electronic Circular Dichroism Spectra of (R)-(+)-1-Phenylethanol. Confident Interpretation Based on the Synergy between Experiments and Computations

Using density functional theory and its time-dependent extension for excited states, the S₀ →S₁ high-resolution vibronic absorption and electronic circular dichroism spectra of (R)-(+)-1-phenylethanol are computed and compared to experimental spectra measured in jet-cooled conditions in the region within 1000 cm^-1 of the 0-0 transition. The agreement between theory and computation is satisfactory and allows a confident assignment of several experimental bands in terms of fundamentals of different modes. Cases are documented for which the analysis of optical anisotropy factors, owing to their signed nature, remarkably enhances the possibility of a robust assignment of the experimental absorption bands. Computational analysis shows that the experimental spectra are dominated by Herzberg-Teller contributions and that the electronic circular dichroism spectrum and the anisotropy factors are also strongly modulated by the effect of Duschinsky mixings.

Asymmetric C-Alkylation by the S-Adenosylmethionine-Dependent Methyltransferase SgvM

S-Adenosylmethionine-dependent methyltransferases (MTs) play a decisive role in the biosynthesis of natural products and in epigenetic processes. MTs catalyze the methylation of heteroatoms and even of carbon atoms, which, in many cases, is a challenging reaction in conventional synthesis. However, C-MTs are often highly substrate-specific. Herein, we show that SgvM from Streptomyces griseoviridis features an extended substrate scope with respect to the nucleophile as well as the electrophile. Aside from its physiological substrate 4-methyl-2-oxovalerate, SgvM catalyzes the (di)methylation of pyruvate, 2-oxobutyrate, 2-oxovalerate, and phenylpyruvate at the β-carbon atom. Chiral-phase HPLC analysis revealed that the methylation of 2-oxovalerate occurs with R selectivity while the ethylation of 2-oxobutyrate with S-adenosylethionine results in the S enantiomer of 3-methyl-2-oxovalerate. Thus SgvM could be a valuable tool for asymmetric biocatalytic C-alkylation reactions.

Theoretical study on the photophysical properties of boron-fused double helicenes

Seven boron-fused double helicenes containing different electron-donors or acceptors and their combinations were investigated to shed light on the effective way to enhance the second-order NLO response.

Mass-Selective Chiral Analysis

Three ways of realizing mass-selective chiral analysis are reviewed. The first is based on the formation of diastereomers that are of homo- and hetero- type with respect to the enantiomers of involved chiral molecules. This way is quite well-established with numerous applications. The other two ways are more recent developments, both based on circular dichroism (CD). In one, conventional or nonlinear electronic CD is linked to mass spectrometry (MS) by resonance-enhanced multiphoton ionization. The other is based on CD in the angular distribution of photoelectrons, which is measured in combination with MS via photoion photoelectron coincidence. Among the many important applications of mass-selective chiral analysis, this review focuses on its use as an analytical tool for the development of heterogeneous enantioselective chemical catalysis. There exist other approaches to combine chiral analysis and mass-selective detection, such as chiral chromatography MS, which are not discussed here.

Theoretical study on thiophene-based double helicenes with intrinsic large second-order nonlinear optical response

In view of the intrinsic non-centrosymmetric electronic structures, high transparency, and the large second-order NLO response values, the studied thiophene-based double helicenes are expected to be excellent second-order NLO materials.

Understanding the photophysical properties of chiral dinuclear Re(i) complexes and the role of Re(i) in their complexes

We have investigated the electronic structure, UV-Vis/CD spectra and the second-order NLO properties of chiral dinuclear Re(i) complexes and elucidated structure–property relationships with the aid of DFT calculations.

Anisotropic elliptical dichroism and influence of imperfection of circular polarization upon anisotropic circular dichroism

In spite of the importance of anisotropic circular dichroism, in practice, it is difficult to get rid of the artifacts that arise from the imperfection of the circular polarization. Undesirable linear dichroism, interference of two orthogonal polarization states, and linear birefringence prevent us from making accurate measurements. We propose a theoretical method for evaluating the contributions of the first two, which are thought to be the main artifacts when specimens are not thick enough. Using the time-dependent perturbation theory and taking into account the direction of light propagation toward an orientationally fixed molecule, we formulated the transition probability of systems perturbed by arbitrarily polarized light and the absorption difference associated with two kinds of polarized light. We also formulated, as an extension of the dissymmetry factor of circular dichroism, a newly defined dissymmetry factor associated with two arbitrary polarization states. Furthermore, we considered a mixed-state of photon ensemble in which polarization states distribute at a certain width around a certain average. Although the purity of polarization and ellipticity does not correspond immediately, by considering the mixed state it is possible to treat them consistently. We used quantum statistical mechanics to describe the absorption difference for two kinds of photon ensembles and applied the consequent formula to examine the reported experimental results of single-molecule chiroptical responses under discussion in the recent past. The artifacts are theoretically suggested to be sensitive to the incident direction of elliptically polarized light and to the oriented systems, the ellipticity, and the orientation of ellipse. The mixed state has little, if any, effect when the polarization state distribution is narrow.

Assessment of the tautomeric population of benzimidazole derivatives in solution: a simple and versatile theoretical-experimental approach

Herein, we present a simple and versatile theoretical-experimental approach to assess the tautomeric distribution on 5(6)-aminobenzimidazole (5(6)-ABZ) derivatives in solution via one-photon absorption. The method is based on the optimized weighted sum of the theoretical spectra of the corresponding tautomers. In this article we show how the choice of exchange-correlation functional (XCF) employed in the calculations becomes crucial for the success of the approach. After the systematic analysis of XCFs with different amounts of exact-exchange we found a better performance for B3LYP and PBE0. The direct test of the proposed method on omeprazole, a well-known 5(6)-benzimidazole based pharmacotherapeutic, demonstrate its broader applicability. The proposed approach is expected to find direct applications on the tautomeric analysis of other molecular systems exhibiting similar tautomeric equilibria.

Laser mass spectrometry with circularly polarized light: circular dichroism of cold molecules in a supersonic gas beam

An experiment on chiral molecules that combines circular dichroism (CD) spectroscopy, mass-selective detection by laser mass spectrometry (MS), and cooling of molecules by using a supersonic beam is presented. The combination of the former two techniques (CD-laser-MS) is a new method to investigate chiral molecules and is now used by several research groups. Cooling in a supersonic beam supplies a substantial increase in spectroscopic resolution, a feature that has not yet been used in CD spectroscopy. In the experiments reported herein, a large variation in the electronic CD of carbonyl 3-methylcyclopentanone was observed depending on the excited vibrational modes in the n → π* transition. This finding should be of interest for the detection of chiral molecules and for the theoretical understanding of the CD of vibronic bands. It is expected that this effect will show up in other chiral carbonyls because the n → π* transition is typical for the carbonyl group.

Anisotropic dissymmetry factor, g: theoretical investigation on single molecule chiroptical spectroscopy

A formula for an anisotropic dissymmetry factor g evaluating the chiroptical response of orientationally fixed molecules is derived. Incorporating zeroth- and first-order multipole expansion terms, it is applied to bridged triarylamine helicene molecules to examine the experimental results of single-molecule chiroptical spectroscopy. The ground- and excited-state wave functions and a series of transition moments required for the evaluation of the anisotropic g value are calculated using time-dependent density functional theory (TDDFT). The probability histograms obtained for simulated g values, uniformly sampled in regard to the direction of light propagation toward the fixed molecule, show that even for a given diastereomer, the dissymmetry factors have positive and negative values and can deviate from their averages to a considerable extent when the angle between the electric dipole transition moment and the propagation vector of the incident light is near 0 or 180°.

Theoretical study of two-photon circular dichroism on molecular structures simulating aromatic amino acid residues in proteins with secondary structures

Calculation and comparative analysis of the theoretical two-photon circular dichroism (TPCD) spectra of l-His, l-Phe, and l-Tyr simulating residues in proteins with secondary structures (α-helix, β-strand and random coil), down to the far-UV region (FUV).

General Time Dependent Approach to Vibronic Spectroscopy Including Franck-Condon, Herzberg-Teller, and Duschinsky Effects

An effective time-dependent (TD) approach to compute vibrationally resolved optical spectra from first principles is presented for the computation of one-photon electronic spectra induced by either electric or magnetic transition dipoles or by their mutual interaction, namely absorption, emission, and circular dichroism. Particular care has been devoted to generality, modularity, and numerical stability including all the contributions that play a role at the harmonic level of approximation, namely Franck-Condon, Herzberg-Teller, and Dushinsky (i.e., mode mixing) effects. The implementation shares the same general framework of our previous time-independent (TI) model, thus allowing an effective integration between both approaches with the consequent enhancement of their respective strengths (e.g., spectrum completeness and straightforward account of temperature effects for the TD route versus band resolution and assignment for the TI route) using a single set of starting data. Implementation of both models in the same general computer program allows comprehensive studies using several levels of electronic structure description together with effective account of environmental effects by atomistic and/or continuum models of different sophistication. A few medium-size molecules (furan, phenyl radical, anthracene, dimethyloxirane, coumarin 339) have been studied in order to fully validate the approach.

Cob(I)alamin: insight into the nature of electronically excited states elucidated via quantum chemical computations and analysis of absorption, CD and MCD data

The nature of electronically excited states of the super-reduced form of vitamin B(12) (i.e., cob(I)alamin or B(12s)), a ubiquitous B(12) intermediate, was investigated by performing quantum-chemical calculations within the time-dependent density functional theory (TD-DFT) framework and by establishing their correspondence to experimental data. Using response theory, the electronic absorption (Abs), circular dichroism (CD) and magnetic CD (MCD) spectra of cob(I)alamin were simulated and directly compared with experiment. Several issues have been taken into considerations while performing the TD-DFT calculations, such as strong dependence on the applied exchange-correlation (XC) functional or structural simplification imposed on the cob(I)alamin. In addition, the low-lying transitions were also validated by performing CASSCF/MC-XQDPT2 calculations. By comparing computational results with existing experimental data a new level of understanding of electronic excitations has been established at the molecular level. The present study extends and confirms conclusions reached for other cobalamins. In particular, the better performance of the BP86 functional, rather than hybrid-type, was observed in terms of the excitations associated with both Co d and corrin π localized transitions. In addition, the lowest energy band was associated with multiple metal-to-ligand charge transfer excitations as opposed to the commonly assumed view of a single π → π* transition followed by vibrational progression. Finally, the use of the full cob(I)alamin structure, instead of simplified molecular models, shed new light on the spectral analyses of cobalamin systems and revealed new challenges of this approach related to long-range charge transfer excitations involving side chains.

Empirical correction of nondynamical correlation energy for density functionals

To provide an efficient means to address nondynamical correlation, an empirical correction for single and double hybrid density functionals has been formulated. The correction utilizes the highest doubly occupied, lowest unoccupied, and singly occupied generalized Kohn-Sham orbitals and, for potential energy curves, a few additional strongly correlated orbitals. Utilizing proposed nondynamical correlation corrections, hybrid BLYP predicted potential energy curves that fit well to those obtained by ab initio multireference methods for the torsional rotation of ethylene and the automerization of cyclobutadiene. The empirical nondynamical correlation corrections, calculated at the transition structures, also reduce the overall errors of B2K-PLYP for the DBH24 and BH76 barrier height data sets. The proposed empirical correction can efficiently enhance the utility of both single and double hybrid density functionals for chemical situations with moderate to significant nondynamical correlation.

The Effect of the π-Electron Delocalization Curvature on the Two-Photon Circular Dichroism of Molecules with Axial Chirality

Herein we report on the theoretical-experimental study of the effect of curvature of the π-electron delocalization on the two-photon circular dichroism (TPCD) of a family of optically active biaryl derivatives (S-BINOL, S-VANOL, and S-VAPOL). The comparative analysis of the influence of the different transition moments to their corresponding TPCD rotatory strength reveals an enhanced contribution of the magnetic transition dipole moment on VAPOL. This effect is hereby attributed to the additional twist in the π-electron delocalization on this compound. TPCD measurements were done using the double L-scan technique in the picosecond regime. Theoretical calculations were completed using modern analytical response theory, within a time-dependent density functional theory (TD-DFT) approach, at both, B3LYP and CAM-B3LYP levels, with the aug-cc-pVDZ basis set for S-BINOL and S-VANOL, and 6-31G* for S-VAPOL. Solvent effects were included by means of the polarizable continuum model (PCM) in CH2Cl2.

Vibrationally resolved circular dichroism spectra of a molecule with isotopically engendered chirality

We present a theoretical study of vibrationally resolved circular dichroism spectra, both in the adiabatic and non-adiabatic frameworks, with a full account of Franck-Condon and Herzberg-Teller vibrational contributions for the former. Model calculations have been performed on 2(R)-deuteriocyclopentanone, whose chirality is due solely to isotopic substitution. This molecule has two distinct, nearly isoenergetic, half-chair conformations in equilibrium, and its demanding nature in terms of computational accuracy makes it a perfect candidate for performing a detailed comparison between different vibronic models. Comparisons are made with experimental spectra, and we also consider temperature effects. In order to reproduce the experimental spectrum, it is necessary to consider the geometry relaxation occurring during the n→π* transition.

Dendritic molecular switch: chiral folding and helicity inversion

Appropriately designed chemical architectures can fold to adopt well-defined secondary structures without the need for structural motifs of biological origin. We have designed tris(N-salicylideneaniline)-based hyperbranched molecules that spontaneously collapse to compact three-blade propeller geometry of either (P)- or (M)-handedness. For a homologous series of compounds, a direct correlation was established between the absolute screw sense, either (P)- or (M)-, of this helical folding and the absolute configuration, either (R)- or (S)-, of the chiral alcohol groups introducing local asymmetric bias to the conformationally restricted molecular backbone. 1H NMR and CD spectroscopic studies provided significant insights into structural folding and unfolding of these chiral molecules in solution, which proceed via reversible assembly and disassembly of the C3-symmetric hydrogen-bonding network. Notably, solvents profoundly influenced this dynamic process. A strong correlation between the solvent donor number (DN) or solvent basicity (SB) parameters and the change in the Cotton effects pointed toward specific O-H...solvent interactions that drive structural unfolding and eventual refolding to apparently opposite helicity. This unusual chirality inversion process could also be induced by installation of chemical protecting groups that simulate specific solvent-solute interactions. Removal of this covalent mimic of the solvent shell restored the original screw sense of the parent molecule, thus establishing the feasibility of covalently triggered helicity inversion as a new mode of operation for chiroptical molecular switches.