A connection between an algebraic approach to the dynamics of triatomic molecules based on the U (2) × U (3) × U (2) Lie algebra and the traditional description in configuration space is presented. The connection is established in four steps. First, the molecular Hamiltonian is expanded in symmetrized local coordinates. Second, the Hamiltonian is transformed into an algebraic representation by introducing the realization of coordinates and momenta in terms of bosonic creation and annihilation operators of normal character. The third step is to perform a canonical transformation applied to the bosons associated with the stretching degrees of freedom in order to obtain a unified representation in a local scheme. Finally, an anharmonization procedure is applied to identify the U (2) × U (3) × U (2) dynamical algebra. The main advantage of the proposed approach is that it provides relations between the spectroscopic parameters and the molecular structure and force constants. As an application, the analysis of the vibrational excitations of CO 2 in its ground electronic state is considered. In this scheme, each stretching degree of freedom is identified as an interacting Morse oscillator, with an associated U (2) dynamical algebra, and the doubly degenerate bending degree of freedom is modelled with a U (3) dynamical algebra, obtaining as a final result a reasonable set of force constants.

The potential energy surface for the ground state of the 12 C 16 O 2 molecule is estimated through an algebraic approach based on unitary groups. It is shown that a purely algebraic approach may lead to a unphysical surface even when the fit turns out to be of a remarkable high quality. The vibrational description is obtained in the framework of the U (2) × U (3) × U (2) model, where the U (2) algebras are associated with the CO bond stretching and the U (3) algebra with the OCO bending. The algebraic representation of the Hamiltonian is obtained through the connection between the coordinates and momenta and the generators of the dynamical algebra. It is shown that through this connection is possible to choose the appropriate set of spectroscopic parameters leading to the right Potential Energy Surface (PES). The fit from which the PES is estimated involves 101 energy levels with an standard deviation of rms = 0.53 cm −1 .

The carbon dioxide Raman spectrum is simulated within an algebraic approach based on curvilinear coordinates in a local representation. The two main advantages of the present algebraic approach are a possible connection with configuration space and the correct description of systems with either local or normal mode character. The system Hamiltonian and polarizability tensor are expanded in terms of curvilinear coordinates. The curvilinear coordinates are in turn expanded into normal coordinates, obtaining an algebraic representation in terms of normal bosonic operators. A canonical transformation maps the operators into a local algebraic representation. The final step is an anharmonization procedure to local operators. The Raman spectrum of CO2 has been simulated, obtaining results close to experimental accuracy, and polarizability transition moments for the Raman spectral lines between 1150 cm(-1) and 1500 cm(-1) are reported. The comparison between experimental and simulated spectra has provided six new CO2 experimental vibrational terms.

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An electrochemical analysis strategy based on the Marcus–Hush approximation is presented to analyze the kinetic component of organic redox flow battery (RFB) electrolytes. The procedure was applied to aqueous solutions of methyl viologen (MV) and 2,2′-bipyridyl (diquat, DQ) derivatives as model redox-active electrolytes; although these systems are promising negolyte candidates in organic RFBs, their electrode kinetics continues to be unclear. For compound MV, the voltammetric analysis revealed an adsorption process of electrogenerated species to the glassy carbon electrode surface, so its electron transfer rate constant k s should not be estimated by applying outer sphere electron transfer formulations. For the remaining compounds studied, experimental k s values were obtained and they range from 0.22 to 0.62 cm s–1. Quantum chemical modeling was applied not only to decipher properties of the adsorption process of the MV structure but also to rationalize the kinetic differences in compounds studied through their total and inner reorganization energies. This experimental and theoretical approach allowed elucidation of the kinetic component of compounds studied, revealing that k s values for MV and DQ compound derivatives should not exhibit the reported differences of at least one order of magnitude. Finally, the experimental k s value (0.62 cm s–1) obtained for compound 5,5′-DMDQ is the largest value reported to date in the literature of aqueous organic RFBs, which makes it a strong anolyte candidate.