An Effective and Automated Processing of Resonances in Vibrational Perturbation Theory Applied to Spectroscopy

The broader availability of cost-effective methodologies like second-order vibrational perturbational theory (VPT2), also in general-purpose quantum chemical programs, has made the inclusion of anharmonic effects in vibrational calculations easier, paving the way to more accurate simulations. Combined with modern computing hardware, VPT2 can be used on relatively complex molecular systems with dozen of atoms. However, the problem of resonances and their corrections remains a critical pitfall of perturbative methods. Recent works have highlighted the sensitivity of band intensities to even subtle resonance effects, underlying the importance of a correct treatment to predict accurate spectral bandshapes. This aspect is even more critical with chiroptical spectroscopies whose signal is weak. This has motivated the present work in exploring robust methods and criteria to identify resonances not only in energy calculations but also on the transition moments. To study their performance, three molecules of representative sizes ranging from ten to several dozens of atoms were chosen. The impact of resonances, as well as the accuracy achievable once they are properly treated, is illustrated by the changes in spectral bandshapes, including chiroptical spectroscopies

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

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

A general time-dependent route to Resonance-Raman spectroscopy including Franck-Condon, Herzberg-Teller and Duschinsky effects

We present a new formulation of the time-dependent theory of Resonance-Raman spectroscopy (TD-RR). Particular attention has been devoted to the generality of the framework and to the possibility of including different effects (Duschinsky mixing, Herzberg-Teller contributions). Furthermore, the effects of different harmonic models for the intermediate electronic state are also investigated. Thanks to the implementation of the TD-RR procedure within a general-purpose quantum-chemistry program, both solvation and leading anharmonicity effects have been included in an effective way. The reliability and stability of our TD-RR implementation are validated against our previously proposed and well-tested time-independent procedure. Practical applications are illustrated with some closed- and open-shell medium-size molecules (anthracene, phenoxyl radical, benzyl radical) and the simulated spectra are compared to the experimental results. More complex and larger systems, not limited to organic compounds, can be also studied, as shown for the case of Tris(bipyridine)ruthenium(II) chloride

Anharmonic Effects on Vibrational Spectra Intensities: Infrared, Raman, Vibrational Circular Dichroism, and Raman Optical Activity

The aim of this paper is 2-fold. First, we want to report the extension of our virtual multifrequency spectrometer (VMS) to anharmonic intensities for Raman optical activity (ROA) with the full inclusion of first- and second-order resonances for both frequencies and intensities in the framework of the generalized second-order vibrational perturbation theory (GVPT2) for all kinds of vibrational spectroscopies. Then, from a more general point of view, we want to present and validate the performance of VMS for the parallel analysis of different vibrational spectra for medium-sized molecules (IR, Raman, VCD, ROA) including both mechanical and electric/magnetic anharmonicity. For the well-known methyloxirane benchmark, careful selection of density functional, basis set, and resonance thresholds permitted us to reach qualitative and quantitative agreement between experimental and computed band positions and shapes. Next, the whole series of halogenated azetidinones is analyzed, showing that it is now possible to interpret different spectra in terms of mass, electronegativity, polarizability, and hindrance variation between closely related substituents, chiral spectroscopies being particular effective in this connection

Generalized vibrational perturbation theory for rotovibrational energies of linear, symmetric and asymmetric tops: Theory, approximations, and automated approaches to deal with medium-to-large molecular systems

Models going beyond the rigid\u2010rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium\u2010to\u2010large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first\u2010order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods

Accurate Quantum Chemical Spectroscopic Characterization of Glycolic Acid: A Route Toward its Astrophysical Detection

The first step to shed light on the abiotic synthesis of biochemical building blocks, and their further evolution toward biological systems, is the detection of the relevant species in astronomical environments, including earthlike planets. To this end, the species of interest need to be accurately characterized from structural, energetic, and spectroscopic viewpoints. This task is particularly challenging when dealing with flexible systems, whose spectroscopic signature is ruled by the interplay of small- and large-amplitude motions (SAMs and LAMs, respectively) and is further tuned by the conformational equilibrium. In such instances, quantum chemical (QC) calculations represent an invaluable tool for assisting the interpretation of laboratory measurements or even observations. In the present work, the role of QC results is illustrated with reference to glycolic acid (CH2OHCOOH), a molecule involved in photosynthesis and plant respiration and a precursor of oxalate in humans, which has been detected in the Murchison meteorite but not yet in the interstellar medium or in planetary atmospheres. In particular, the equilibrium structure of the lowest-energy conformer is derived by employing the so-called semiexperimental approach. Then, accurate yet cost-effective QC calculations relying on composite post-Hartree–Fock schemes and hybrid coupled-cluster/density functional theory approaches are used to predict the structural and ro-vibrational spectroscopic properties of the different conformers within the framework of the second-order vibrational perturbation theory. A purposely tailored discrete variable representation anharmonic approach is used to treat the LAMs related to internal rotations. The computed spectroscopic data, particularly those in the infrared region, complement the available experimental investigations, thus enhancing the possibility of an astronomical detection of this molecule

Ultraviolet resonance Raman spectroscopy of anthracene: Experiment and theory

AbstractUltraviolet resonance Raman (UVRR) scattering is a highly sensitive and selective vibrational spectroscopic technique with a broad range of applications from polyaromatic hydrocarbons (PAHs) to biomolecular systems (peptides/proteins and nucleic acids) and catalysts. The interpretation of experimental UVRR spectra is not as straightforward as in purely vibrational Raman scattering (Placzek approximation) due to the involvement of higher lying electronic states and vibronic coupling. This necessitates the comparison with theoretical UVRR spectra computed by electronic structure calculations. Anthracene is an ideal model system for such a comparison between experiment and theory because it is rigid, symmetric, and of moderate size. By taking into account Herzberg–Teller contributions including Duschinsky effects, bulk solvent effects, and anharmonic contributions, a good qualitative agreement close to the resonance condition is achieved. The present study shows that within the framework of time‐dependent density functional theory (TD‐DFT), a general and robust approach for the analysis and interpretation of resonance Raman spectra of medium‐ to large‐size molecules is available

Scaling-up VPT2: A feasible route to include anharmonic correction on large molecules

Vibrational analysis plays a crucial role in the investigation of molecular systems. Though methodologies like second-order vibrational perturbation theory (VPT2) have paved the way to more accurate simulations, the computational cost remains a difficult barrier to overcome when the molecular size increases. Building upon recent advances in the identification of resonances, we propose an approach making anharmonic simulations possible for large-size systems, typically unreachable by standard means. This relies on the fact that, often, only portions of the whole spectra are of actual interest. Therefore, the anharmonic corrections can be included selectively on subsets of normal modes directly related to the regions of interest. Starting from the VPT2 equations, we evaluate rigorously and systematically the impact of the truncated anharmonic treatment onto simulations. The limit and feasibility of the reduced-dimensionality approach are detailed, starting on a smaller model system. The methodology is then challenged on the IR absorption and vibrational circular dichroism spectra of an organometallic complex in three different spectral ranges