Overtone Raman spectrum and molecular polarizability surface of CO2

Abstract

The Q branches of the Raman bands associated to the 2 1 :4 2 0 : 1 ϩ2 2 0 Fermi resonance of 12 C 16 O 2 have been observed in the gas phase at 2543, 2671, and 2797 cm Ϫ1 and, in addition, at 2514 cm Ϫ1 , one hot band from their first excited vibrational state is seen. From the analysis of their cross sections, jointly with those of the main Fermi diad, 1 :2 2 0 and its hot bands, an improved description of the molecular polarizability surface has been achieved. The following derivatives of the mean polarizability have been obtained:‫␣ץ‬ ¯/‫ץ‬q 1 ϭ12.43ϫ10 Ϫ42 CV Ϫ1 m 2 ; ‫ץ‬ 2 ␣ ¯/‫ץ‬q 2 2 ϭ2.81ϫ10 Ϫ42 CV Ϫ1 m 2 ͑ϭa,b͒; ‫ץ‬ 2 ␣ ¯/‫ץ‬q 1 2 ϭ0.45ϫ10 Ϫ42 CV Ϫ1 m 2 ; ‫ץ‬ 2 ␣ ¯/‫ץ‬q 3 2 ϭ0.67 or 0.15ϫ10 Ϫ42 CV Ϫ1 m 2 ; ‫ץ‬ 3 ␣ ¯/‫ץ‬q 1 ‫ץ‬q 2 2 ϭϪ0.06ϫ10 Ϫ42 CV Ϫ1 m 2 , in terms of the dimensionless normal coordinates, and, in terms of the symmetry coordinates. The thermal dependence of the mean polarizability is discussed in terms of these quantities.

A study of the Raman spectrum of CO2 using an algebraic approach

“…The wavefunctions (12) obtained with this anharmonic algebraic procedure are close to those given in Table I of Ref. [6].…”

“…(1) are truncated into rectilinear ones and therefore cannot be directly compared to the curvilinear coordinates in Ref. [6]. Hence, the obtained Hamiltonian can be diagonalized in a basis set built as the direct product of harmonic oscillator functions of the symmetry coordinates.…”

“…For the trace scattering of a gas sample at thermal equilibrium, the differential cross section can be expressed in the SI system as follows [6] ∂σ ∂Ω…”

“…This spectrum can be used to test the vibrational wavefunctions as long as a suited description of the dependence of the molecular polarizability tensor on the vibrational motions is available. Tejeda et al expanded the mean polarizability into a Taylor series of the normal coordinates [6] and determined its main derivatives by fitting a set of selected experimental transition moments.…”

Coherent anti-Stokes Raman spectroscopy in the presence of strong resonant signal from background molecules

“…It covers one strong Raman mode of oxygen, corresponding to the Q branch of v = 0 → v = 1 vibrational transition centered at 1555 cm −1 , and one strong Fermi dyad of carbon dioxide at 1285 cm −1 and 1388 cm −1 . The latter is a result of the resonant coupling between the Ramanactive symmetric stretch and the first overtone of the bending mode of CO 2 [22,23]. Shown in the inset is the rotational splitting of the vibrational resonance in O 2 .…”