Vibrationally resolved NEXAFS at C and N K-edges of pyridine, 2-fluoropyridine and 2,6-difluoropyridine: A combined experimental and theoretical assessment

In the present work, the near edge X-ray absorption spectroscopy (NEXAFS) spectra at both C and N K-edges of pyridine, 2-fluoropyridine, and 2,6-difluoropyridine have been studied both experimentally and theoretically. From an electronic point of view, both transition potential density functional theory and time-dependent density functional theory approaches lead to reliable results provided that suitable basis sets and density functionals are employed. In this connection, the global hybrid B3LYP functional in conjunction with the EPR-III basis set appears particularly suitable after constant scaling of the band positions. For the N K-edge, vertical energies obtained at these levels and broadened by symmetric Gaussian distributions provide spectra in reasonable agreement with the experiment. Vibronic contributions further modulate the band-shapes leading to a better agreement with the experimental results, but are not strictly necessary for semi-quantitative investigations. On the other hand, vibronic contributions are responsible for strong intensity redistribution in the NEXAFS C K-edge spectra, and their inclusion is thus mandatory for a proper description of experiments. In this connection, the simple vertical gradient model is particularly appealing in view of its sufficient reliability and low computational cost. For more quantitative results, the more refined vertical Hessian approach can be employed, and its effectiveness has been improved thanks to a new least-squares fitting approach

Anharmonicity effects on the structural and vibrational properties of molecular systems in different electronic states

The research work of Marco Mendolicchio involves the inclusion of anharmonicity effects in the calculation of structural and vibrational properties. The thesis is divided into two main parts: the first deals with the development of an algorithmic for the calculation of anharmonic force fields in normal coordinates, that in turn allow anharmonic vibrational frequencies to be derived through the vibrational second-order perturbation theory (VPT2). The second part involves the implementation of a standalone code for the fitting of accurate equilibrium molecular structures by means of the semi-experimental approach.

Development and implementation of theoretical models for the prediction of molecular structures and vibrational spectra

In this thesis, we propose general, effective strategies for the simulation of vibrational spectra and calculation of accurate molecular geometries. Vibrational and rotational spectroscopies are very powerful tools for investigating the physical-chemical properties of molecular systems, since they allow one to obtain a remarkable set of information related to the structure and dynamics. In particular, concurrent use of several spectroscopies is often needed to obtain a full characterization of the complex systems of current fundamental and technological interest. However, experimental spectra are tuned by several intertwined effects which can make the interpretation of experimental data very challenging or even unaffordable without the support of reliable in silico simulations. As a matter of fact, ongoing developments of hardware and software (not to speak of the underlying physical-mathematical models) are allowing the reproduction of experimental outcomes and their interpretation in terms of stereo-electronic, dynamic, and environmental effects. Despite the unquestionable success of static structure-property relationships and of the basic rigid-rotor / harmonic-oscillator model, accurate results, directly comparable with experiment, can be obtained only employing more refined models, and, in particular, including anharmonic effects. The accuracy of theoretical vibrational spectra can be improved either at the electronic level, through highly correlated methods, able to deliver accurate equilibrium structures, energy and properties, and at the nuclear level, including anharmonic effects in the description of the nuclear motions. In this respect, the second-order vibrational perturbation theory (VPT2) has shown to offer a very effective balance between accuracy and computational cost, thus permitting the study of medium-to-large systems. At the VPT2 level, the semi-diagonal cubic force field is required to compute vibration-rotation interaction constants describing the vibrational dependence of rotational constants. These are needed in order to determine accurate molecular structures by the semi-experimental (SE) approach. The extension to the full cubic and semi-diagonal quartic force field allows the calculation of the anharmonic vibrational frequencies and intensities. A current hurdle is that the actual implementation of VPT2 is fragmented between asymmetric tops (no degeneracy) and symmetric/linear rotors (presence of doubly degenerate modes), which means that anywork done on VPT2 needs to be duplicated. Part of this thesis work has been aimed at demonstrating that the standard VPT2 for Abelian groups can be used also for non-Abelian groups without employing specific equations for two- or three-fold 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., -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. In the next part of the research activity, we focused on the development and implementation of a methodology to treat medium-sized molecular systems presenting some flexibility, and thus are unsatisfactory described at the VPT2 level. In fact, while the representation of the nuclear potential energy as a truncated Taylor expansion up to the fourth order in terms of normal coordinates has proven to be very accurate for semi-rigid molecules, it is expected to yield unreliable results for flexible molecules that present one or more LAMs. It is noteworthy that for such systems a pure variational treatment would be prohibitive, and even reaching an accuracy comparable to VPT2 could only be done at several times the cost of the latter. Therefore, the best course of action is the formulation of a strategy based on an interplay between both computational methods, in order to take full advantage of each one. From a practical point of view, this operation can be carried out by separating the normal modes, or more generally a set of coordinates, which are suited for VPT2 from those that are not, and then treat the resulting groups separately. For this purpose, a description of molecular vibrations based on internal coordinates is more suitable, usually leading to a smaller coupling between different degrees of freedom. In this thesis, a theoretical derivation of the VPT2 framework has been carried out starting from the available literature. In this context, the main difference with respect to the Cartesian-based formulation is that the kinetic energy operator is not diagonal anymore, and has to be expanded as well, leading to additional terms which have taken into the proper account. It is worth mentioning that each expression derived in the internal-based framework, can be written as a generalization of the corresponding Cartesian-based counterpart, implying a remarkable simplification at the implementation level. The determination of accurate equilibrium molecular structures plays a fundamental role for understanding many physical-chemical properties of molecules, ranging from the precise evaluation of the electronic structure to the analysis of dynamical and environmental effects in tuning their overall behavior. For this purpose the so-called semi-experimental (SE) approach, based on a nonlinear least-squares fit of the moments of inertia associated with a set of available isotopologues, allows one to obtain very accurate results, without the unfavorable computational cost characterizing high-level quantum chemical methods. In this thesis, the MSR (Molecular Structure Refinement) software for the determination of equilibrium structures by means of the SE approach is presented, and its implementation is discussed in some detail. The software, which is interfaced with a powerful graphical user interface, includes different optimization algorithms, an extended error analysis, and a number of advanced features, the most remarkable ones concerning the choice of internal coordinates and the method of predicate observations. In particular, a newblack-box scheme for defining automatically a suitable set of non-redundant internal coordinates of A1 symmetry in place of the customary Z-matrix has been designed and tested. Moreover, different strategies aimed at handling the cases in which the number of experimental data is not sufficient to characterize all structural parameters have been analyzed. The computational framework developed in this thesis, and implemented in the MSR program, has been employed for the determination of the SE structure for molecular systems of biological and astrochemical interest

Accuracy and Reliability in the Simulation of Vibrational Spectra: A Comprehensive Benchmark of Energies and Intensities Issuing From Generalized Vibrational Perturbation Theory to Second Order (GVPT2)

Vibrational spectroscopy represents an active frontier for the identification and characterization of molecular species in the context of astrochemistry and astrobiology. As new missions will provide more data over broader ranges and at higher resolution, especially in the infrared region, which could be complemented with new spectrometers in the future, support from laboratory experiments and theory is crucial. In particular, computational spectroscopy is playing an increasing role in deepening our understanding of the origin and nature of the observed bands in extreme conditions characterizing the interstellar medium or some planetary atmospheres, not easily reproducible on Earth. In this connection, the best compromise between reliability, feasibility and ease of interpretation is still a matter of concern due to the interplay of several factors in determining the final spectral outcome, with larger molecular systems and non-covalent complexes further exacerbating the dichotomy between accuracy and computational cost. In this context, second-order vibrational perturbation theory (VPT2) together with density functional theory (DFT) has become particularly appealing. The well-known problem of the reliability of exchange-correlation functionals, coupled with the treatment of resonances in VPT2, represents a challenge for the determination of standardized or "black-box" protocols, despite successful examples in the literature. With the aim of getting a clear picture of the achievable accuracy and reliability of DFT-based VPT2 calculations, a multi-step study will be carried out here. Beyond the definition of the functional, the impact of the basis set and the influence of the resonance treatment in VPT2 will be analyzed. For a better understanding of the computational aspects and the results, a short summary of vibrational perturbation theory and the overall treatment of resonances for both energies and intensities will be given. The first part of the benchmark will focus on small molecules, for which very accurate experimental and theoretical data are available, to investigate electronic structure calculation methods. Beyond the reliability of energies, widely used for such systems, the issue of intensities will also be investigated in detail. The best performing electronic structure methods will then be used to treat larger molecular systems, with more complex topologies and resonance patterns

Structural features of the carbon\u2013sulfur chemical bond: a semi-experimental perspective

In this work, semi-experimental (SE) and theoretical equilibrium geometries of 10 sulfur-containing organic molecules, as well as 4 oxygenated ones, are determined by means of a computational protocol based on density functional theory. The results collected in the present paper further enhance our online database of accurate SE equilibrium molecular geometries, adding 13 new molecules containing up to 8 atoms, for 12 of which, to the best of our knowledge, the first SE equilibrium structure is reported. We focus in particular on sulfur-containing compounds, aiming both to provide new accurate data on some rather important chemical moieties, only marginally represented in the literature of the field, and to examine the structural features of carbon-sulfur bonds in the light of the previously presented linear regression approach. The structural changes issuing from substitution of oxygen by sulfur are discussed to get deeper insights on how modifications in electronic structure and nuclear potential can affect equilibrium geometries. With respect to our previous work, we perform nonlinear constrained optimizations of equilibrium SE structures, using a new general and user-friendly software under development in our group with updated definitions of useful statistical indicators

Accurate Geometries of Large Molecules by Integration of the Pisa Composite Scheme and the Templating Synthon Approach

An effective yet reliable computational workflow is proposed, which permits the computation of accurate geometrical structures for large flexible molecules at an affordable cost thanks to the integration of machine learning tools and DFT models together with reduced scaling computations of vibrational averaging effects. After validation of the different components of the overall strategy, a panel of molecules of biological interest have been analyzed. The results confirm that very accurate geometrical parameters can be obtained at reasonable cost for molecules including up to about 50 atoms, which are the largest ones for which comparison with high-resolution rotational spectra is possible. Since the whole computational workflow can be followed employing standard electronic structure codes, accurate results for large-sized molecules can be obtained at DFT cost also by nonspecialists

Development and Implementation of Advanced Fitting Methods for the Calculation of Accurate Molecular Structures

The determination of accurate equilibrium molecular structures plays a fundamental role for understanding many physical-chemical properties of molecules, ranging from the precise evaluation of the electronic structure to the analysis of dynamical and environmental effects in tuning their overall behavior. For this purpose the so-called semiexperimental approach, based on a nonlinear least-squares fit of the moments of inertia associated with a set of available isotopologues, allows one to obtain very accurate results, without the unfavorable computational cost characterizing high-level quantum chemical methods. In the present work the MSR (Molecular Structure Refinement) software for the determination of equilibrium structures by means of the semiexperimental approach is presented, and its implementation is discussed in some detail. The software, which is interfaced with a powerful graphical user interface, includes different optimization algorithms, an extended error analysis, and a number of advanced features, the most remarkable ones concerning the choice of internal coordinates and the method of predicate observations. In particular, a new black-box scheme for defining automatically a suitable set of nonredundant internal coordinates of A₁ symmetry in place of the customary Z-matrix has been designed and tested. Finally, the implementation of the method of the predicate observations is discussed and validated for a set of test molecules. As an original application, the method is employed for the determination of the semiexperimental structure for the most stable conformer of glycine

Systematic Study on the Absorption Features of Interstellar Ices in the Presence of Impurities

Spectroscopic studies play a key role in the identification and analysis of interstellar ices and their structure. Some molecules have been identified within the interstellar ices either as pure, mixed, or even as layered structures. Absorption band features of water ice can significantly change with the presence of different types of impurities (CO, CO2, CH3OH, H2CO, etc.). In this work, we carried out a theoretical investigation to understand the behavior of the water band frequency and strength in the presence of impurities. The computational study has been supported and complemented by some infrared spectroscopy experiments aimed at verifying the effect of HCOOH, NH3, and CH3OH on the band profiles of pure H2O ice. Specifically, we explored the effect on the band strength of libration, bending, bulk stretching, and free OH stretching modes. Computed band strength profiles have been compared with our new and existing experimental results, thus pointing out that vibrational modes of H2O and their intensities can change considerably in the presence of impurities at different concentrations. In most cases, the bulk stretching mode is the most affected vibration, while the bending is the least affected mode. HCOOH was found to have a strong influence on the libration, bending, and bulk stretching band profiles. In the case of NH3, the free OH stretching band disappears when the impurity concentration becomes 50%. This work will ultimately aid a correct interpretation of future detailed spaceborne observations of interstellar ices by means of the upcoming JWST mission