Importance of vibronic effects on the circular dichroism spectrum of dimethyloxirane

Chiroptical activity of gas-phase propylene oxide predicting the handedness of interstellar circular polarization in the presolar nebula

Propylene oxide, the first chiral molecule recently detected in the interstellar medium, has once again raised the question whether biomolecular chirality might have cosmic origins. However, accurate chiroptical properties of propylene oxide in the ultraviolet spectral range necessary to suggest possible asymmetric synthetic routes in the gas phase are scarce. Here, we report on the first experimental measurements of the anisotropy spectra of gas-phase propylene oxide in the vacuum ultraviolet spectral range. Our experimental results provide novel insights into the handedness of interstellar circular polarization at the dawn of molecular evolution of our star- and planet-forming region. Besides the fundamental importance of this new investigation for understanding the origin and evolution of homochirality on Earth, our high-resolution experimental electronic circular dichroism data will inspire new efforts in quantum computational spectroscopy.

Tailored anharmonic-harmonic vibrational profiles for fluorescent biomarkers

We propose a hybrid anharmonic-harmonic scheme for vibrational broadenings, which embeds a reduced-space vibrational configuration interaction (VCI) anharmonic wave function treatment in the independent-mode displaced harmonic oscillator (IMDHO) model. The resulting systematically-improvable VCI-in-IMDHO model allows including the vibronic effects of all vibrational degrees of freedom, while focusing the effort on the important degrees of freedom with minimal extra computational effort compared to a reduced-space VCI treatment. We show for oligothiophene examples that the VCI-in-IMDHO approach can yield accurate vibrational profiles employing smaller vibrational spaces in the VCI part than the reduced-space VCI approach. By this, the VCI-in-IMDHO model enables accurate calculation of vibrational profiles of common fluorescent dyes with more than 100 vibrational degrees of freedom. We illustrate this for three examples of fluorescent biomarkers of current interest. These are the oligothiophene-based fluorescent dye called HS84, 1,4-diphenylbutadiene, and an anthracene diimide. For all examples, we assess the impact of the anharmonic treatment on the vibrational broadening, which we find to be more pronounced for the intensities than for the peak positions.

Magnetic circular dichroism spectra of transition metal complexes calculated from restricted active space wavefunctions

Multiconfigurational restricted active space (RAS) self-consistent field (SCF) or configuration interaction (CI) approaches, augmented with a treatment of spin–orbit coupling by state interaction, were used to calculate the magnetic circular dichroism , , and/or for closed- and open-shell transition metal complexes.

Time-Dependent Formulation of Resonance Raman Optical Activity Spectroscopy

In this work, we extend the theoretical framework recently developed for the simulation of resonance Raman (RR) spectra of medium-to-large sized systems to its chiral counterpart, namely, resonance Raman optical activity (RROA). The theory is based on a time-dependent (TD) formulation, with the transition tensors obtained as half-Fourier transforms of the appropriate cross-correlation functions. The implementation has been kept as general as possible, supporting adiabatic and vertical models for the PES representation, both in Cartesian and internal coordinates, with the possible inclusion of Herzberg-Teller (HT) effects. Thanks to the integration of this TD-RROA procedure within a general-purpose quantum-chemistry program, both solvation and leading anharmonicity effects can be included in an effective way. The implementation is validated on one of the smallest chiral molecule (methyloxirane). Practical applications are illustrated with three medium-size organic molecules (naproxen-OCD₃, quinidine and 2-Br-hexahelicene), whose simulated spectra are compared to the corresponding experimental data.

Quantitative first principles calculations of protein circular dichroism in the near-ultraviolet

Vibrational structure in the near-UV circular dichroism (CD) spectra of proteins is an important source of information on protein conformation and can be exploited to study structure and folding. A fully quantitative theory of the relationship between protein conformation and optical spectroscopy would facilitate deeper interpretation of and insight into biophysical and simulation studies of protein dynamics and folding. We have developed new models of the aromatic side chain chromophores toluene, p-cresol and 3-methylindole, which incorporate ab initio calculations of the Franck-Condon effect into first principles calculations of CD using an exciton approach. The near-UV CD spectra of 40 proteins are calculated with the new parameter set and the correlation between the computed and the experimental intensity from 270 to 290 nm is much improved. The contribution of individual chromophores to the CD spectra has been calculated for several mutants and in many cases helps rationalize changes in their experimental spectra. Considering conformational flexibility by using families of NMR structures leads to further improvements for some proteins and illustrates an informative level of sensitivity to side chain conformation. In several cases, the near-UV CD calculations can distinguish the native protein structure from a set of computer-generated misfolded decoy structures.

Magnetic circular dichroism of UCl6− in the ligand-to-metal charge-transfer spectral region

We present a combined ab initio theoretical and experimental study of the magnetic circular dichroism (MCD) spectrum of the octahedral UCl₆⁻ complex ion in the UV-Vis spectral region.

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.

Simulation of Vacuum UV Absorption and Electronic Circular Dichroism Spectra of Methyl Oxirane: The Role of Vibrational Effects

Vibrationally resolved one-photon absorption and electronic circular dichroism spectra of (R)-methyl oxirane were calculated with different electronic and vibronic models selecting, through an analysis of the convergence of the results, the best compromise between reliability and computational cost. Linear-response TD-DFT/CAM-B3LYP/SNST electronic computations in conjunction with the simple vertical gradient vibronic model were chosen and employed for systematic comparison with the available experimental data. Remarkable agreement between simulated and experimental spectra was achieved for both one-photon absorption and circular dichroism concerning peak positions, relative intensities, and general spectral shapes considering the computational efficiency of the chosen theoretical approach. The significant improvement of the results with respect to smearing of vertical electronic transitions by phenomenological Gaussian functions and the possible inclusion of solvent effects by polarizable continuum models at a negligible additional cost paves the route toward the simulation and analysis of spectral shapes of complex molecular systems in their natural environment.

The Virtual Multifrequency Spectrometer: a new paradigm for spectroscopy

On going developments of hardware and software are changing computational spectroscopy from a strongly specialized research area to a general tool in the inventory of most researchers. Increased interactions between experimentally-oriented users and theoretically-oriented developers of new methods and models would result in more robust, flexible and reliable tools and studies for the systems of increasing complexity, which are of current scientific and technological interest. This is the philosophy behind this review, which presents the development of a so-called virtual multi-frequency spectrometer (VMS) including state-of-the-art approaches in a user-friendly frame. The current status of the VMS tool will be illustrated by a number of case studies with special reference to infrared and UV-vis regions of the electro-magnetic spectrum including also chiral spectroscopies. Only the basic theoretical background will be provided avoiding explicit equations as far as possible, and pointing out the most recent advancements beyond the standard rigid-rotor harmonic-oscillator model coupled to vertical electronic excitation energies.

Solvation dependence observed in the electronic dissymmetry factor spectra: how much information are we missing by analyzing the circular dichroism spectra alone?

The electronic dissymmetry factor (EDF) spectra reveal that for [1,1′-binaphthalene]-2,2′-diol the experimental EDF spectra show solvent polarity dependent effects that are not apparent in the electronic circular dichroism or absorption spectra.

Toward the design of alkynylimidazole fluorophores: computational and experimental characterization of spectroscopic features in solution and in poly(methyl methacrylate)

The possibilities offered by organic fluorophores in the preparation of advanced plastic materials have been increased by designing novel alkynylimidazole dyes, featuring different push and pull groups. This new family of fluorescent dyes was synthesized by means of a one-pot sequential bromination-alkynylation of the heteroaromatic core, and their optical properties were investigated in tetrahydrofuran and in poly(methyl methacrylate). An efficient in silico pre-screening scheme was devised as consisting of a step-by-step procedure employing computational methodologies by simulation of electronic spectra within simple vertical energy and more sophisticated vibronic approaches. Such an approach was also extended to efficiently simulate one-photon absorption and emission spectra of the dyes in the polymer environment for their potential application in luminescent solar concentrators. Besides the specific applications of this novel material, the integration of computational and experimental techniques reported here provides an efficient protocol that can be applied to make a selection among similar dye candidates, which constitute the essential responsive part of those fluorescent plastic materials.

Vibronic structure in the far-UV electronic circular dichroism spectra of proteins

The Franck–Condon effect is considered and the vibrational structure of the π_nbπ* transition of the peptide backbone is incorporated into matrix method calculations of the electronic circular dichroism (CD) spectra of proteins in the far-ultraviolet. We employ the state-averaged CASPT2 method to calculate the ground and π_nbπ* excited state geometries and frequencies of N-methylacetamide (NMA), which represents the peptide chromophore. The results of these calculations are used to incorporate vibronic levels of the excited states into the matrix method calculation. The CD spectra of a set of 49 proteins, comprising a range of structural types, are calculated to assess the influence of the vibrational structure. The calculated spectra of α-helical proteins are better resolved using the vibronic parameters and correlation between the experimental and the calculated intensity of less regular β structure proteins improves over most wavelengths in the far-UV. No obvious improvement is observed in the calculated spectra of regular β-sheet proteins. Our high-level ab initio calculations of the vibronic structure of the π_nbπ* transition in NMA have provided some further insight into the physical origins of the nature of protein CD spectra in the far-UV.

New developments of a multifrequency virtual spectrometer: stereo-electronic, dynamical, and environmental effects on chiroptical spectra

Computational spectroscopy has recently evolved from a field reserved for specialists toward a general tool allowing interpretations and analyses of experimental results. However, the current practice of providing tables of transitions for rigid geometries, possibly tuned by phenomenological broadening, is by far too naive. In order to improve this situation in the last few years we have been developing a general, robust, and user-friendly virtual spectrometer (VS) able to complement experimental studies for complex systems in condensed phases. The VS is based on flexible graphical pre- and postprocessing tools interfaced with general number-crunching software. This last tool is rooted in several electronic structure methodologies (DFT, TD-DFT, post-Hartree-Fock), powerful discrete/continuum models for describing environmental effects, and general vibrational and vibronic models. These last topics are the main focus of this work, which sketches our latest developments related to effective inclusion of anharmonic contributions, together with time-independent and/or time-dependent descriptions of vibronic transitions including Franck-Condon, Herzberg-Teller, and Duschinsky effects. Some test cases are described in some detail with the aim of showing the role of different effects in ruling vibrational (VCD) and electronic (ECD, CPL) chiral spectroscopies.

Environmental and complexation effects on the structures and spectroscopic signatures of organic pigments relevant to cultural heritage: the case of alizarin and alizarin-Mg(II)/Al(III) complexes

An integrated computational approach allowed an unbiased analysis of optical and structural properties of alizarin-based pigments, which can be directly compared with experimental results. Madder lake pigments have been modeled by Mg(II)- and Al(III)-coordinated alizarin taking into account solvation and metal-linkage effects, responsible for colour modifications. Moreover, different environmental conditions have been analyzed for free alizarin, showing in all cases semi-quantitative agreement with experimental spectroscopic data (UV-VIS). Our results point out the ability of in silico approaches to unravel the subtle interplay of stereo-electronic, dynamic, and environmental effects in tuning the physico-chemical properties of pigments relevant to cultural heritage.

Franck–Condon factors—Computational approaches and recent developments

Algorithms and methodologies for the calculation of Franck–Condon integrals are reviewed. Starting from the standard approach based on the Cartesian representation of the normal modes and the use of Duschinsky's transformation and recursion formulas, methods for treating large displacements of the equilibrium positions and anharmonic and non-Condon effects are considered. Finally, focusing attention on problems arising from the use of recurrence relations, some of the proposed solutions are critically reviewed along with new alternative approaches.

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.

Combining the nuclear-electronic orbital approach with vibronic coupling theory: calculation of the tunneling splitting for malonaldehyde

The nuclear-electronic orbital (NEO) method is combined with vibronic coupling theory to calculate hydrogen tunneling splittings in polyatomic molecules. In this NEO-vibronic coupling approach, the transferring proton and all electrons are treated quantum mechanically at the NEO level, and the other nuclei are treated quantum mechanically using vibronic coupling theory. The dynamics of the molecule are described by a vibronic Hamiltonian in a diabatic basis of two localized nuclear-electronic states for the electrons and transferring proton. This ab initio approach is computationally practical and efficient for relatively large molecules, and the accuracy can be improved systematically. The NEO-vibronic coupling approach is used to calculate the hydrogen tunneling splitting for malonaldehyde. The calculated tunneling splitting of 24.5 cm(-1) is in excellent agreement with the experimental value of 21.6 cm(-1). This approach also enables the identification of the dominant modes coupled to the transferring hydrogen motion and provides insight into their roles in the hydrogen tunneling process.

Circular Dichroism and Conformational Dynamics of Cephams and Their Carba and Oxa Analogues

The biological activity of bicyclic beta-lactam antibiotics depends strongly on the absolute configuration of the bridgehead carbon atom. Frelek and co-workers proposed an empirical helicity rule relating the configuration of the bridgehead carbon atom to the sign of the 220 nm band in the electronic circular dichroism (CD) spectrum of beta-lactams. Here we use synthetic organic chemistry, CD spectroscopy, and time-dependent density functional theory (TDDFT) to investigate the validity of this structure-property relationship for eight model compounds. For conformationally flexible beta-lactams, substantial thermal effects are found which must be included in calculations. To this end, we combine TDDFT calculations of CD with full quantum-mechanical Born-Oppenheimer molecular dynamics (MD) simulations for the first time. The CD spectra are sampled with ground-state density functional trajectories of up to 60 ps. The MD simulations show a surprisingly high sensitivity of the CD to the molecular conformation. On the other hand, the relation between CD and thermally averaged structural parameters is much less complex. While the helicity rule does not seem to hold for individual conformers, it is confirmed by the calculations for seven out of eight systems studied if thermally averaged CD spectra and structures are considered. Since thermal effects on CD can be larger than typical inherent inaccuracies of TDDFT, our results emphasize the need for a systematic treatment of conformational dynamics in CD calculations even for moderately flexible systems. Temperature-dependent CD measurements are very useful for this purpose. Our results also suggest that CD spectroscopy may be used as a sensitive probe of conformational dynamics if combined with electronic structure calculations.

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

There has been a considerable interest in the chiroptical properties of molecules whose chirality is exclusively due to an isotopic substitution and numerous examples for the electronic circular dichroism (CD) spectra of isotopically chiral systems have been reported in literature. Four different explanations have been proposed for the mechanism as to how the isotopic substitution induces a chiral perturbation of the otherwise achiral electronic wave function; however, up to now no conclusive answer has been given about the dominating effect responsible for the experimental observations. In this study we will present, for the first time, fully quantum-mechanical calculations of the CD spectra of three different molecular systems with isotopically engendered chirality. As examples, we consider the spectra of organic molecules with ketone and alpha-diketone carbonyl and diene chromophores. The effect of vibronic couplings for the reorientation of the electric and magnetic transition dipole moments is taken into account within the Herzberg-Teller approximation. The ground and excited state geometries and vibrational normal modes are obtained with (time-dependent) density functional theory [(TD)DFT], while the vibronic coupling effects are calculated at the TDDFT and density functional theory/multireference configuration interaction (DFT/MRCI) levels of theory. Generally, the band shapes of the experimental CD spectra are reproduced very well, and also the absolute CD intensities from the simulations are of the right order of magnitude. The sign and the intensity of the CD band are determined by a delicate balance of the contributions of a large number of individual vibronic transitions, and it is found that the vibrational normal modes with a large displacement are dominant. The separation of the calculated CD spectrum into the different contributions due to the overlap of the in-plane and out-of-plane components (regarding the symmetry plane of the unsubstituted molecule) of the electric and magnetic transition dipole moments yields information about the influence of the vibronic coupling effects for the reorientation of the corresponding transition dipole moments. In conclusion, the calculations clearly show that vibronic effects are responsible or at least dominant for the chiroptical properties of isotopically chiral organic molecules.

A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

We have implemented our new procedure for computing Franck-Condon factors utilizing vibrational configuration interaction based on a vibrational self-consistent field reference. Both Duschinsky rotations and anharmonic three-mode coupling are taken into account. Simulations of the first ionization band of ClO(2) and C(4)H(4)O (furan) using up to quadruple excitations in treating anharmonicity are reported and analyzed. A developer version of the MIDASCPP code was employed to obtain the required anharmonic vibrational integrals and transition frequencies.

Simulation of photoelectron spectra with anharmonicity fully included: Application to the X̃A22←X̃A11 band of furan

Using a new unconventional procedure for calculating Franck-Condon factors with anharmonicity fully included the X 2A2<--X 1A1 band in the photoelectron spectrum of furan (and deuterated furan) was simulated at the second-order perturbation theory level. All 21 vibrational modes were considered but, in the end, only 4 are required to accurately reproduce the spectrum. Except for our own recent work on ethylene such calculations have been previously limited to tri- or tetraatomic molecules. Most of the effect of anharmonicity is accounted for in first order, although second-order corrections to the vibrational frequencies are important. Based on these simulations we were able to improve upon and extend previous assignments as well as suggest further measurements.

Exploring the Ability of Frozen-Density Embedding to Model Induced Circular Dichroism

In this study, we present calculations of the circular dichroism (CD) spectra of complexes between achiral and chiral molecules. Nonzero rotational strengths for transitions of the nonchiral molecule are induced by interactions between the two molecules, which cause electronic and/or structural perturbations of the achiral molecule. We investigate if the chiral molecule (environment) can be represented only in terms of its frozen electron density, which is used to generate an effective embedding potential. The accuracy of these calculations is assessed in comparison to full supermolecular calculations. We can show that electronic effects arising from specific interactions between the two subsystems can reliably be modeled by the frozen-density representation of the chiral molecule. This is demonstrated for complexes of 2-benzoylbenzoic acid with (-)-(R)-amphetamine and for a nonchiral, artificial amino acid receptor system consisting of ferrocenecarboxylic acid bound to a crown ether, for which a complex with l-leucine is studied. Especially in the latter case, where multiple binding sites and interactions between receptor and target molecule exist, the frozen-density results compare very well with the full supermolecular calculation. We also study systems in which a cyclodextrin cavity serves as a chiral host system for a small, achiral molecule. Problems arise in that case because of the importance of excitonic couplings with excitations in the host system. The frozen-density embedding cannot describe such couplings but can only capture the direct effect of the host electron density on the electronic structure of the guest. If couplings play a role, frozen-density embedding can at best only partially describe the induced circular dichroism. To illustrate this problem, we finally construct a case in which excitonic coupling effects are much stronger than direct interactions of the subsystem densities. The frozen density embedding is then completely unsuitable.