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.