A second-order perturbation theory route to vibrational averages and transition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies

CC/DFT Route toward Accurate Structures and Spectroscopic Features for Observed and Elusive Conformers of Flexible Molecules: Pyruvic Acid as a Case Study

The structures and relative stabilities as well as the rotational and vibrational spectra of the three low-energy conformers of pyruvic acid (PA) have been characterized using a state-of-the-art quantum-mechanical approach designed for flexible molecules. By making use of the available experimental rotational constants for several isotopologues of the most stable PA conformer, Tc-PA, the semiexperimental equilibrium structure has been derived. The latter provides a reference for the pure theoretical determination of the equilibrium geometries for all conformers, thus confirming for these structures an accuracy of 0.001 Å and 0.1 deg for bond lengths and angles, respectively. Highly accurate relative energies of all conformers (Tc-, Tt-, and Ct-PA) and of the transition states connecting them are provided along with the thermodynamic properties at low and high temperatures, thus leading to conformational enthalpies accurate to 1 kJ mol(-1). Concerning microwave spectroscopy, rotational constants accurate to about 20 MHz are provided for the Tt- and Ct-PA conformers, together with the computed centrifugal-distortion constants and dipole moments required to simulate their rotational spectra. For Ct-PA, vibrational frequencies in the mid-infrared region accurate to 10 cm(-1) are reported along with theoretical estimates for the transitions in the near-infrared range, and the corresponding infrared spectrum including fundamental transitions, overtones, and combination bands has been simulated. In addition to the new data described above, theoretical results for the Tc- and Tt-PA conformers are compared with all available experimental data to further confirm the accuracy of the hybrid coupled-cluster/density functional theory (CC/DFT) protocol applied in the present study. Finally, we discuss in detail the accuracy of computational models fully based on double-hybrid DFT functionals (mainly at the B2PLYP/aug-cc-pVTZ level) that avoid the use of very expensive CC calculations.

Accurate Infrared (IR) Spectra for Molecules Containing the C≡N Moiety by Anharmonic Computations with the Double Hybrid B2PLYP Density Functional

Herein, we report a comprehensive benchmark of C≡N stretching vibrations computed at harmonic and anharmonic levels with the aim of proposing and validating a reliable computational strategy to get accurate results for this puzzling vibrational mode without any ad hoc scaling factor. Anharmonic calculations employing second-order vibrational perturbation theory provide very good results when performed using the B2PLYP double-hybrid functional, in conjunction with an extended basis set and supplemented by semiempirical dispersion contributions. For larger systems, B2PLYP harmonic frequencies, together with B3LYP anharmonic corrections, offer a very good compromise between accuracy and computational cost without the need of any empirical scaling factor.

Identification of Serine Conformers by Matrix-Isolation IR Spectroscopy Aided by Near-Infrared Laser-Induced Conformational Change, 2D Correlation Analysis, and Quantum Mechanical Anharmonic Computations

The conformers of α-serine were investigated by matrix-isolation IR spectroscopy combined with NIR laser irradiation. This method, aided by 2D correlation analysis, enabled unambiguously grouping the spectral lines to individual conformers. On the basis of comparison of at least nine experimentally observed vibrational transitions of each conformer with empirically scaled (SQM) and anharmonic (GVPT2) computed IR spectra, six conformers were identified. In addition, the presence of at least one more conformer in Ar matrix was proved, and a short-lived conformer with a half-life of (3.7 ± 0.5) × 10(3) s in N2 matrix was generated by NIR irradiation. The analysis of the NIR laser-induced conversions revealed that the excitation of the stretching overtone of both the side chain and the carboxylic OH groups can effectively promote conformational changes, but remarkably different paths were observed for the two kinds of excitations.

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-rotor 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-to-large 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-order 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.

Quantum Chemistry Meets Spectroscopy for Astrochemistry: Increasing Complexity toward Prebiotic Molecules

For many years, scientists suspected that the interstellar medium was too hostile for organic species and that only a few simple molecules could be formed under such extreme conditions. However, the detection of approximately 180 molecules in interstellar or circumstellar environments in recent decades has changed this view dramatically. A rich chemistry has emerged, and relatively complex molecules such as C60 and C70 are formed. Recently, researchers have also detected complex organic and potentially prebiotic molecules, such as amino acids, in meteorites and in other space environments. Those discoveries have further stimulated the debate on the origin of the building blocks of life in the universe. Many efforts continue to focus on the physical, chemical, and astrophysical processes by which prebiotic molecules can be formed in the interstellar dust and dispersed to Earth or to other planets.Spectroscopic techniques, which are widely used to infer information about molecular structure and dynamics, play a crucial role in the investigation of planetary atmosphere and the interstellar medium. Increasingly these astrochemical investigations are assisted by quantum-mechanical calculations of structures as well as spectroscopic and thermodynamic properties, such as transition frequencies and reaction enthalpies, to guide and support observations, line assignments, and data analysis in these new and chemically complicated situations. However, it has proved challenging to extend accurate quantum-chemical computational approaches to larger systems because of the unfavorable scaling with the number of degrees of freedom (both electronic and nuclear).In this Account, we show that it is now possible to compute physicochemical properties of building blocks of biomolecules with an accuracy rivaling that of the most sophisticated experimental techniques, and we summarize specific contributions from our groups. As a test case, we present the underlying computational machinery through the investigation of oxirane. We describe how we determine the molecular structure and then how we characterize the rotational and IR spectra, the most important issues for a correct theoretical description and a proper comparison with experiment. Next, we analyze the spectroscopic properties of representative building blocks of DNA bases (uracil and pyrimidine) and of proteins (glycine and glycine dipeptide analogue).Solvation, surface chemistry (dust fraction, adsorption, desorption), and inter- and intramolecular interactions, such as self-organization and self-interaction, are important molecular processes for understanding astrochemistry. Using the specific cases of uracil dimers and glycine adsorbed on silicon grains, we also illustrate approaches in which we treat different regions, interactions, or effects at different levels of sophistication.

Criteria for first- and second-order vibrational resonances and correct evaluation of the Darling-Dennison resonance coefficients using the canonical Van Vleck perturbation theory

The second-order vibrational Hamiltonian of a semi-rigid polyatomic molecule when resonances are present can be reduced to a quasi-diagonal form using second-order vibrational perturbation theory. Obtaining exact vibrational energy levels requires subsequent numerical diagonalization of the Hamiltonian matrix including the first- and second-order resonance coupling coefficients. While the first-order Fermi resonance constants can be easily calculated, the evaluation of the second-order Darling-Dennison constants requires more complicated algebra for seven individual cases with different numbers of creation-annihilation vibrational quanta. The difficulty in precise evaluation of the Darling-Dennison coefficients is associated with the previously unrecognized interference with simultaneously present Fermi resonances that affect the form of the canonically transformed Hamiltonian. For the first time, we have presented the correct form of the general expression for the evaluation of the Darling-Dennison constants that accounts for the underlying effect of Fermi resonances. The physically meaningful criteria for selecting both Fermi and Darling-Dennison resonances are discussed and illustrated using numerical examples.

Reassessment of the Thermodynamic, Kinetic, and Spectroscopic Features of Cyanomethanimine Derivatives: A Full Anharmonic Perturbative Treatment

Herein we report a full thermodynamic and vibrational investigation of C-cyanomethanimine isomers rooted into the Density Functional Theory (DFT) and the second-order vibrational perturbation theory (VPT2). We show that an anharmonic treatment affects dramatically the vibrational behavior of the molecules, especially thanks to the inclusion of interaction terms between the various modes. Furthermore, the equilibrium constant between the isomers, as well as the rate constant, have been obtained at both harmonic and anharmonic levels showing, as expected, slight but non-negligible differences. To support our investigation, dispersion effects have been employed.

To π or not to π – how does methanol dock onto anisole?

Supersonic jet spectroscopy reveals that methanol opts against aromatic docking onto anisole despite a very close competition.

Microsolvation of 2-thiouracil: molecular structure and spectroscopic parameters of the thiouracil-water complex

State-of-the-art quantum-chemical computations have been employed to accurately determine the equilibrium structure and interaction energy of the 2-thiouracil-water complex, thus extending available reference data for biomolecule solvation patterns. The coupled-cluster level of theory in conjunction with a triple-ζ basis set has been considered together with extrapolation to the basis set limit, performed by employing second-order Møller-Plesset perturbation theory, and inclusion of core-correlation and diffuse-function corrections. On the basis of the comparison of experiment and theory for 2-thiouracil [ Puzzarini et al. Phys. Chem. Chem. Phys. 2013 , 15 , 16965 - 16975 ], structural changes due to water complexation have been pointed out. Molecular and spectroscopic properties of the 2-thiouracil-water complex have then been studied by means of the composite computational approach introduced for the molecular structure evaluation. Among the results achieved, we mention the accurate determination of the molecular dipole moment and of the spectroscopic parameters required for predicting the rotational spectrum.

Nonempirical anharmonic vibrational perturbation theory applied to biomolecules: free-base porphin

Anharmonic vibrational frequencies and intensities (infrared and Raman) of an isolated free-base porphin molecule are predicted from the quantum mechanical (QM) geometry, the "semi-diagonal" quartic force field, and dipole moment and polarizability surfaces. The second-order vibrational perturbation theory plus the numerical diagonalization of the Hamiltonian matrix containing off-diagonal Fermi and Darling-Dennison resonance couplings (VPT2+WK) was used. The QM calculations were carried out with the Becke-Lee-Yang-Parr composite exchange-correlation functional (B3LYP) and with the 6-31+G(d,p) basis set. The harmonic force field for the equilibrium configuration was transformed into nonredundant local symmetry internal coordinates, and normal coordinates were defined. The semi-diagonal quartic rectilinear normal coordinate potential energy surface (PES), as well as the cubic surfaces of dipole moment (p) and polarizability (α) components, needed for the VPT2+WK calculation, were constructed by a five-point finite differentiation of Hessians (for PES) and of the values and first derivatives of p and α. They were obtained at the point of equilibrium and for 432 displaced configurations. This theoretical approach provides very good agreement between the predicted and experimental frequencies and intensities. However, the favorable result can be partly attributed to error cancellation within the B3LYP/6-31+G(d,p) QM model, as observed in earlier studies. Reassignments of some observed bands are proposed.

Conformational switching in pyruvic acid isolated in Ar and N₂ matrixes: spectroscopic analysis, anharmonic simulation, and tunneling

Monomers of pyruvic acid (PA) isolated in cryogenic argon and nitrogen matrixes were characterized by mid- and near-infrared spectroscopy. Interpretation of the experiments was aided by fully anharmonic calculations of the fundamental modes, overtones, and combinations up to two quanta, including their infrared intensities. The initially dominating PA conformer (Tc) has a cis CCOH arrangement and is stabilized by a strong intramolecular H-bond. Selective near-infrared excitation of Tc at the first OH overtone (6630 cm(-1) in Ar, 6643 cm(-1) in N2) induced a large scale conformational conversion to the higher-energy conformer (Tt) with trans CCOH arrangement. Tt was then converted back to Tc by selective NIR irradiation at the first Tt OH overtone (6940 cm(-1) in Ar, 6894 cm(-1) in N2). In N2 matrix, the Tt form was stabilized due to interaction between the OH group and the matrix molecules. This stabilization manifested itself in the absence of Tt → Tc relaxation and in a considerable change of the vibrational Tt signature upon going from argon to nitrogen matrix. In argon, the Tt form spontaneously decayed back to Tc in the dark (characteristic lifetime +16 h). In the presence of broad-band near-infrared light, the Tt → Tc relaxation speed considerably increased. The decay mechanisms are discussed.

ACCURATE SPECTROSCOPIC CHARACTERIZATION OF PROTONATED OXIRANE: A POTENTIAL PREBIOTIC SPECIES IN TITAN'S ATMOSPHERE

An accurate spectroscopic characterization of protonated oxirane has been carried out by means of state-of-the-art computational methods and approaches. The calculated spectroscopic parameters from our recent computational investigation of oxirane together with the corresponding experimental data available were used to assess the accuracy of our predicted rotational and IR spectra of protonated oxirane. We found an accuracy of about 10 cm-1 for vibrational transitions (fundamentals as well as overtones and combination bands) and, in relative terms, of 0.1% for rotational transitions. We are therefore confident that the spectroscopic data provided herein are a valuable support for the detection of protonated oxirane not only in Titan's atmosphere but also in the interstellar medium.

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.

Accurate molecular structures and infrared spectra of trans-2,3-dideuterooxirane, methyloxirane, and trans-2,3-dimethyloxirane

Oxirane derivatives are the most used benchmarks for chiroptical spectroscopies in view of their small size and relative rigidity. The molecular structure, vibrational harmonic and anharmonic frequencies, and infrared intensities of the ground electronic states are analyzed in this paper. Equilibrium structure and harmonic force fields have been evaluated by means of high-level quantum-chemical calculations at the coupled-cluster level including single and double excitations together with a perturbative treatment of triples (CCSD(T)). Extrapolation to the complete basis-set limit as well as core-correlation effects have also been taken into account. Anharmonic contributions have been computed at the CCSD(T)/cc-pVTZ level for trans-2,3-dideuterooxirane. These data can serve as references to evaluate the accuracy of less expensive computational approaches rooted in the density functional theory (DFT). The latter have been used within hybrid CC/DFT approaches, which have been applied to simulate fully anharmonic infrared (IR) spectra. Finally, the best theoretical estimates of the equilibrium structures and vibrational wavenumbers are compared to the most accurate experimental data and show in all cases very good agreement, i.e., within 0.001 Å, 0.1 deg, 10 cm(-1), and 0.5 km mol(-1), for bond lengths, angles, wavenumbers, and IR intensities, respectively.

Molecular structure and spectroscopic signatures of acrolein: theory meets experiment

A comprehensive study of the molecular structure and IR spectrum of cis and trans acrolein has been performed by an integrated computational approach coupling methods rooted in the coupled-cluster ansatz and the density functional theory. From the one side, DFT anharmonic force fields allow us to determine very reliable semiexperimental structures for both isomers, which are in remarkable agreement with the geometries issuing from CCSD(T) computations accounting for the extrapolation to the complete basis set and core correlation. The same kind of coupled-cluster computations provide dipole moment, relative energies, and interconversion barrier in remarkable agreement with experiments. Finally, harmonic CCSD(T) results coupled to DFT evaluation of mechanical and electrical anharmonicity allow us, in the framework of second-order perturbative vibrational theory, to confirm most of the experimental assignments of IR spectra, and to suggest some additional interpretations for congested regions including fundamental bands together with overtones and combination bands.

Dispersion corrected DFT approaches for anharmonic vibrational frequency calculations: nucleobases and their dimers

Computational spectroscopy techniques have become in the last few years an effective means to analyze and assign infrared (IR) spectra of molecular systems of increasing dimensions and in different environments. However, transition from compilation of harmonic data to fully anharmonic simulations of spectra is still underway. The most promising results for large systems have been obtained, in our opinion, by perturbative vibrational approaches based on potential energy surfaces computed by hybrid (especially B3LYP) density functionals and medium size (e.g. SNSD) basis sets. In this framework, we are actively developing a comprehensive and robust computational protocol aimed at quantitative reproduction of the spectra of nucleic acid base complexes and their adsorption on solid supports (organic/inorganic). In this contribution we report the essential results of the first step devoted to isolated monomers and dimers. It is well known that in order to model the vibrational spectra of weakly bound molecular complexes dispersion interactions should be taken into proper account. In this work we have chosen two popular and inexpensive approaches to model dispersion interactions, namely the semi-empirical dispersion correction (D3) and pseudopotential based (DCP) methodologies both in conjunction with the B3LYP functional. These have been used for simulating fully anharmonic IR spectra of nucleobases and their dimers through generalized second order vibrational perturbation theory (GVPT2). We have studied, in particular, isolated adenine, hypoxanthine, uracil, thymine and cytosine, the hydrogen-bonded and stacked adenine and uracil dimers, and the stacked adenine-naphthalene heterodimer. Anharmonic frequencies are compared with standard B3LYP results and experimental findings, while the computed interaction energies and structures of complexes are compared to the best available theoretical estimates.

Stereo-electronic, vibrational, and environmental contributions to polarizabilities of large molecular systems: a feasible anharmonic protocol

Reliable computations of linear and non-linear optical properties of molecular systems in condensed phases require a proper account of stereo-electronic, vibrational, and environmental effects. In the framework of density functional theory, these effects can be accurately introduced using second-order vibrational perturbation theory in conjunction with polarizable continuum models. We illustrate the combination of an anharmonic description of the ground-state potential energy surface with solvation effects treated with the polarizable continuum model (PCM) in the calculation of the electronic, zero-point, and pure vibrational polarizabilities of selected systems. The description of the solvation environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions through the inclusion of both electronic and vibrational non-equilbrium effects, as well as the direct effect of the solvent on the electric field that generates the molecular response (local field effect). This treatment yields accurate results which can be directly compared with experimental findings without the need of empirical corrections.

ACCURATE SPECTROSCOPIC CHARACTERIZATION OF OXIRANE: A VALUABLE ROUTE TO ITS IDENTIFICATION IN TITAN'S ATMOSPHERE AND THE ASSIGNMENT OF UNIDENTIFIED INFRARED BANDS

In an effort to provide an accurate spectroscopic characterization of oxirane, state-of-the-art computational methods and approaches have been employed to determine highly accurate fundamental vibrational frequencies and rotational parameters. Available experimental data were used to assess the reliability of our computations, and an accuracy on average of 10 cm-1 for fundamental transitions as well as overtones and combination bands has been pointed out. Moving to rotational spectroscopy, relative discrepancies of 0.1%, 2%-3%, and 3%-4% were observed for rotational, quartic, and sextic centrifugal-distortion constants, respectively. We are therefore confident that the highly accurate spectroscopic data provided herein can be useful for identification of oxirane in Titan's atmosphere and the assignment of unidentified infrared bands. Since oxirane was already observed in the interstellar medium and some astronomical objects are characterized by very high D/H ratios, we also considered the accurate determination of the spectroscopic parameters for the mono-deuterated species, oxirane-d1. For the latter, an empirical scaling procedure allowed us to improve our computed data and to provide predictions for rotational transitions with a relative accuracy of about 0.02% (i.e., an uncertainty of about 40 MHz for a transition lying at 200 GHz).

Fully anharmonic IR and Raman spectra of medium-size molecular systems: accuracy and interpretation

Computation of full infrared (IR) and Raman spectra (including absolute intensities and transition energies) for medium- and large-sized molecular systems beyond the harmonic approximation is one of the most interesting challenges of contemporary computational chemistry. Contrary to common beliefs, low-order perturbation theory is able to deliver results of high accuracy (actually often better than those issuing from current direct dynamics approaches) provided that anharmonic resonances are properly managed. This perspective sketches the recent developments in our research group toward the development of a robust and user-friendly virtual spectrometer rooted in second-order vibrational perturbation theory (VPT2) and usable also by non-specialists essentially as a black-box procedure. Several examples are explicitly worked out in order to illustrate the features of our computational tool together with the most important ongoing developments.

Accurate Characterization of the Peptide Linkage in the Gas Phase: A Joint Quantum-Chemical and Rotational Spectroscopy Study of the Glycine Dipeptide Analogue

Accurate structures of aminoacids in the gas phase have been obtained by joint microwave and quantum-chemical investigations. However, the structure and conformational behavior of α-aminoacids once incorporated into peptide chains are completely different and have not yet been characterized with the same accuracy. To fill this gap, we present here an accurate characterization of the simplest dipeptide analogue (N-acetyl-glycinamide) involving peptidic bonds. State-of-the-art quantum-chemical computations are complemented by a comprehensive study of the rotational spectrum using a combination of Fourier transform microwave spectroscopy with laser ablation. The coexistence of the C7 and C5 conformers has been proved and energetically as well as spectroscopically characterized. This joint theoretical-experimental investigation demonstrated the feasibility of obtaining accurate structures for flexible small biomolecules, thus paving the route to the elucidation of the inherent behavior of peptides.

Alcohol dimers – how much diagonal OH anharmonicity?

The massive infrared attenuation and increased anharmonicity of OH stretching overtones in alcohol dimers is experimentally quantified.

A robust and effective time-independent route to the calculation of Resonance Raman spectra of large molecules in condensed phases with the inclusion of Duschinsky, Herzberg-Teller, anharmonic, and environmental effects

We present an effective time-independent implementation to model vibrational resonance Raman (RR) spectra of medium-large molecular systems with the inclusion of Franck-Condon (FC) and Herzberg-Teller (HT) effects and a full account of the possible differences between the harmonic potential energy surfaces of the ground and resonant electronic states. Thanks to a number of algorithmic improvements and very effective parallelization, the full computations of fundamentals, overtones, and combination bands can be routinely performed for large systems possibly involving more than two electronic states. In order to improve the accuracy of the results, an effective inclusion of the leading anharmonic effects is also possible, together with environmental contributions under different solvation regimes. Reduced-dimensionality approaches can further enlarge the range of applications of this new tool. Applications to imidazole, pyrene, and chlorophyll a1 in solution are reported, as well as comparisons with available experimental data.