M. Sánchez-Castellanos

Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra

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.

A systematic polyad breaking approach to anharmonic systems

A general systematic polyad breaking approach based on Van Vleck perturbation theory is proposed for anharmonic systems where interacting Morse and/or Poschl–Teller (PT) potentials are considered to describe molecular vibrational excitations in the framework of local mode models. Our approach is based on the algebraic representation of the Hamiltonian via the realization of the coordinates and momenta as an expansion in terms of creation and annihilation operators of Morse and/or PT functions. This algebraic representation permits to establish a perturbation expansion of the Hamiltonian suitable to apply Van Vleck perturbation theory. As an example to assess our approach a Hamiltonian of two interacting Morse oscillators with a coupling potential bilinear in the Morse coordinates is analysed in detail. Successive corrections to energies as well as to wavefunctions are presented.

An algebraic approach applied to the determination of the polarizability in CO2

A local algebraic approach to describe vibrational excitations of molecules presenting both local and normal mode behaviors is presented. This approach allows the connection with configuration space to be established. The model consists in expanding the kinetic energy as well as the potential in terms of coordinates and momenta. An algebraic representation is obtained by introducing creation and destruction bosonic operators associated with the harmonic oscillators. From the resulting Hamiltonian a local algebraic representation is obtained through a canonical transformation to local bosonic operators. Finally an anharmonization is carried out by changing the local bosonic operators to ladder operators associated with the Morse or Poschl-Teller functions. Since the model is connected with configuration space, non linear curvilinear coordinates are contemplated. Our model is applied to the vibrational spectroscopic description of the 12C16O2 molecule. The eigenstates are tested by calculating the derivatives for the polarizability for this molecule.