Theory for Vibrationally Resolved Two-Photon Circular Dichroism Spectra. Application to (R)-(+)-3-Methylcyclopentanone

FCclasses3: Vibrationally-resolved spectra simulated at the edge of the harmonic approximation

We introduce FCclasses3, a code to carry out vibronic simulations of electronic spectra and nonradiative rates, based on the harmonic approximation. Key new features are: implementation of the full family of vertical and adiabatic harmonic models, vibrational analysis in curvilinear coordinates, extension to several electronic spectroscopies and implementation of time-dependent approaches. The use of curvilinear valence internal coordinates allows the adoption of quadratic model potential energy surfaces (PES) of the initial and final states expanded at arbitrary configurations. Moreover, the implementation of suitable projectors provides a robust framework for defining reduced-dimensionality models by sorting flexible coordinates out of the harmonic subset, so that they can then be treated at anharmonic level, or with mixed quantum classical approaches. A set of tools to facilitate input preparation and output analysis is also provided. We show the program at work in the simulation of different spectra (one and two-photon absorption, emission and resonance Raman) and internal conversion rate of a typical rigid molecule, anthracene. Then, we focus on absorption and emission spectra of a series of flexible polyphenyl molecules, highlighting the relevance of some of the newly implemented features. The code is freely available at http://www.iccom.cnr.it/en/fcclasses/.

Accurate Computation of the Absorption Spectrum of Chlorophyll a with Pair Natural Orbital Coupled Cluster Methods

The ability to accurately compute low-energy excited states of chlorophylls is critically important for understanding the vital roles they play in light harvesting, energy transfer, and photosynthetic charge separation. The challenge for quantum chemical methods arises both from the intrinsic complexity of the electronic structure problem and, in the case of biological models, from the need to account for protein–pigment interactions. In this work, we report electronic structure calculations of unprecedented accuracy for the low-energy excited states in the Q and B bands of chlorophyll a. This is achieved by using the newly developed domain-based local pair natural orbital (DLPNO) implementation of the similarity transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD) in combination with sufficiently large and flexible basis sets. The results of our DLPNO–STEOM-CCSD calculations are compared with more approximate approaches. The results demonstrate that, in contrast to time-dependent density functional theory, the DLPNO–STEOM-CCSD method provides a balanced performance for both absorption bands. In addition to vertical excitation energies, we have calculated the vibronic spectrum for the Q and B bands through a combination of DLPNO–STEOM-CCSD and ground-state density functional theory frequency calculations. These results serve as a basis for comparison with gas-phase experiments.

Theoretical Investigation of the Circularly Polarized Luminescence of a Chiral Boron Dipyrromethene (BODIPY) Dye

Over the last decade, molecules capable of emitting circularly polarized light have attracted growing attention for potential technological and biological applications. The efficiency of such devices depend on multiple parameters, in particular the magnitude and wavelength of the peak of emitted light, and also on the dissymmetry factor for chiral applications. In light of these considerations, molecular systems with tunable optical properties, preferably in the visible spectral region, are particularly appealing. This is the case of boron dipyrromethene (BODIPY) dyes, which exhibit large molecular absorption coefficients, have high fluorescence yields, are very stable, both thermally and photochemically, and can be easily functionalized. The latter property has been extensively exploited in the literature to produce chromophores with a wide range of optical properties. Nevertheless, only a few chiral BODIPYs have been synthetized and investigated so far. Using a recently reported axially chiral BODIPY derivative where an axially chiral BINOL unit has been attached to the chromophore unit, we present a comprehensive computational protocol to predict and interpret the one-photon absorption and emission spectra, together with their chiroptical counterparts. From the physico-chemical properties of this molecule, it will be possible to understand the origin of the circularly polarized luminescence better, thus helping to fine-tune the properties of interest. The sensitivity of such processes require accurate results, which can be achieved through a proper account of the vibrational structure in optical spectra. Methodologies to compute vibrationally-resolved electronic spectra can now be applied on relatively large chromophores, such as BODIPYs, but require more extensive computational protocols. For this reason, particular attention is paid in the description of the different steps of the protocol, and the potential pitfalls. Finally, we show how, by means of appropriate tools and approaches, data from intermediate steps of the simulation of the final spectra can be used to obtain further insights into the properties of the molecular system under investigation and the origin of the visible bands.

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.

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.

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.

Two-photon absorption and two-photon circular dichroism of hexahelicene derivatives: a study of the effect of the nature of intramolecular charge transfer

Effect of the strength and nature of the extension of the π-electronic delocalization on TPA and TPCD of helicenes derivatives.

Ab initio study of the circular intensity difference in electric-field-induced second harmonic generation of chiral natural amino acids

We present a systematic computational study of circular intensity difference (CID) in electric-field-induced second harmonic generation (EFISHG) of some representative chiral natural amino acids (Alanine, Arginine, Aspartic Acid, Cysteine and Tryptophan), taking into account the electric-dipole, electric-quadrupole and magnetic-dipole interactions. The calculations are performed by applying cubic response theory at both Hartree-Fock and Density Functional theory levels, the latter with the popular Becke-three parameters, Lee, Yang and Parr (B3LYP) functional. Special focus is given to the basis set, electron correlation and origin dependence of the properties. The full set of molecular parameters defined by Lam and Thirunamachandran in their reference theoretical paper published in 1982 [J. Chem. Phys., 1982, 77, 3810] is obtained and discussed. This permits the prediction of the CID observable for different possible experimental setups.

Comparison of vertical and adiabatic harmonic approaches for the calculation of the vibrational structure of electronic spectra

The calculation of the vibrational structure associated to electronic spectra in large molecules requires a Taylor expansion of the initial and final state potential energy surface (PES) around some reference nuclear structure. Vertical (V) and adiabatic (A) approaches expand the final state PES around the initial-state (V) or final-state (A) equilibrium structure. Simplest models only take into account displacements of initial- and final-state minima, intermediate ones also allow for difference in frequencies and more accurate models introduce the Dushinsky effect through the computation of the Hessians of both the initial and final state. In this contribution we summarize and compare the mathematical expressions of the complete hierarchy of V and A harmonic models and we implement them in a numerical code, presenting a detailed comparison of their performance on a number of prototypical systems. We also address non-Condon effects through linear expansions of the transition dipole as a function of nuclear coordinates (Herzberg-Teller effect) and compare the results of expansions around initial and final state equilibrium geometries. By a throughout analysis of our results we highlight a number of general trends in the relative performance of the models that can provide hints for their proper choice. Moreover we show that A and V models including final state PES Hessian outperform the simpler ones and that discrepancies in their predictions are diagnostic for failure of harmonic approximation and/or of Born-Oppenheimer approximation (existence of remarkable geometry-dependent mixing of electronic states).

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.

Two-photon polarization dependent spectroscopy in chirality: a novel experimental-theoretical approach to study optically active systems

Many phenomena, including life itself and its biochemical foundations are fundamentally rooted in chirality. Combinatorial methodologies for catalyst discovery and optimization remain an invaluable tool for gaining access to enantiomerically pure compounds in the development of pharmaceuticals, agrochemicals, and flavors. Some exotic metamaterials exhibiting negative refractive index at optical frequencies are based on chiral structures. Chiroptical activity is commonly quantified in terms of circular dichroism (CD) and optical rotatory dispersion (ORD). However, the linear nature of these effects limits their application in the far and near-UV region in highly absorbing and scattering biological systems. In order to surmount this barrier, in recent years we made important advancements on a novel non linear, low-scatter, long-wavelength CD approach called two-photon absorption circular dichroism (TPACD). Herein we present a descriptive analysis of the optics principles behind the experimental measurement of TPACD, i.e., the double L-scan technique, and its significance using pulsed lasers. We also make an instructive examination and discuss the reliability of our theoretical-computational approach, which uses modern analytical response theory, within a Time-Dependent Density Functional Theory (TD-DFT) approach. In order to illustrate the potential of this novel spectroscopic tool, we first present the experimental and theoretical results obtained in C(2)-symmetric, axially chiral R-(+)-1,1'-bi(2-naphthol), R-BINOL, a molecule studied at the beginning of our investigation in this field. Next, we reveal some preliminary results obtained for (R)-3,3'-diphenyl-2,2'-bi-1-naphthol, R-VANOL, and (R)-2,2'-diphenyl-3,3'-(4-biphenanthrol), R-VAPOL. This family of optically active compounds has been proven to be a suitable model for the structure-property relationship study of TPACD, because its members are highly conjugated yet photo-stable, and easily derivatized at the 5- and 6-positions. With the publication of these outcomes we hope to motivate more members of the scientist community to engage in state-of-the-art TPACD spectroscopy.

Excitation and circular dichroism spectra of (+)-(S,S)-bis(2-methylbutyl)chalcogenides

Theoretical electronic spectra and natural circular dichroism (CD) spectra of (+)-(S,S)-bis(2-methylbutyl)chalcogenides, Ch[CH₂CH(CH₃)C₂H₅]₂ (Ch = S, Se, and Te), were calculated by the symmetry adapted cluster (SAC) and SAC-configuration interaction (SAC-CI) methods. Whereas the calculated CD spectrum for each stable conformation itself did not reproduce the corresponding experimental one, their Boltzmann-averaged spectra showed good agreement with the experimental results. We provided the assignment for each spectral band according to our calculation results. For the telluride compound, temperature dependence of the CD spectra was experimentally observed due to variation in the Boltzmann factor, and our calculations reproduced it qualitatively. The spectral features that we could not reproduce can be attributed to triplet transitions through the spin-orbit interaction effects as well as accuracy incompleteness on the calculation conditions.