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2 Lasers
Published in Peter K. Cheo, Handbook of Molecular Lasers, 2018
The symmetric triatomic molecule CO2 has three fundamental normal vibrational modes. Each of these vibrational modes is further subdivided into a rotational manifold of sublevels. The energy-level diagram of the CO2 molecule is graphically depicted in Fig. 4.1. The upper laser level is the 001 asymmetric stretch mode of vibration. The lower laser levels are the 100 symmetric stretch mode (producing radiation in the 10.4-μm band) and the 020 bending mode (producing radiation in the 9.4-μm band). Excitation of the upper laser level can be achieved by direct inelastic electron collisions, optical pumping, or resonant transfer from other excited diatomic molecules. The most efficient excitation schemes for large-aperture devices have used a combination of inelastic electron-molecule collisions and resonant transfer. When gases mixtures containing CO2 and N2 buffered by He are used, it is possible to obtain an efficient transfer of electrical energy from the primary energy source to the N2 molecule followed by a resonant vibrational energy transfer to the asymmetric stretch mode of the CO2 molecule as shown in Fig. 4.1. In practice this technique has proved to be very efficient, with pumping efficiencies in excess of 80% obtained in large-aperture devices. Later in this section we describe specific pumping systems based on both electron-beam-controlled discharges and self-sustained (Townsend avalanche) discharges.
Infrared Radiative Energy Transfer in Gases
Published in E. M. Sparrow, R. D. Cess, Radiation Heat Transfer, 2018
The picture is much the same for polyatomic molecules, except that these have more vibrational degrees of freedom. Carbon dioxide, for example, is a linear triatomic molecule and thus possesses four vibrational degrees of freedom. The two bending frequencies, however, are identical, while one of the stretching modes is symmetric and thus has no permanent dipole moment. Consequently, carbon dioxide has two fundamental bands. In addition to fundamental and overtone bands, the infrared spectrum of polyatomic molecules also includes combination and difference bands, which occur at linear combinations or differences of the fundamental frequencies. Again choosing carbon dioxide as an example, the important infrared bands are the 15 μ, and 4.3 μ fundamental bands and the 2.7 μ and 1.9 μ combination bands (see Table 1-3 and Fig. 1-12).
2 Structure, Thermodynamics, and Kinetics
Published in Yun Zheng, Bo Yu, Jianchen Wang, Jiujun Zhang, Carbon Dioxide Reduction through Advanced Conversion and Utilization Technologies, 2019
Yun Zheng, Bo Yu, Jianchen Wang, Jiujun Zhang
CO2 is a linear triatomic molecule with a molecular weight of 44 Dalton, as shown in Figure 2.1. In the molecule, carbon (C) and oxygen (O) atoms are held together through bonds formed by sharing electrons, and these bonds possess strong electrical affinities. They possess a circular axial symmetry, a center of symmetry, and a horizontal plane of symmetry.1 O atoms are better in grabbing the electron pair than that of C atoms and therefore the electrons are pulled partially away from the C atom, resulting in the C atom being in a relatively low energy state.2
Field-free alignment of triatomic molecules controlled by a slow turn-on and rapid turn-off shaped laser pulse
Published in Molecular Physics, 2021
Qi-Yuan Cheng, Yu-Zhi Song, Qing-Tian Meng
Consider a linear triatomic molecule placed to a shaped nonresonant laser pulse given by where E0, N, ω, σr and σf are the electric field amplitude, shape parameter, central frequency, rising time and falling time, respectively. With the rigid rotor approximation, the total Hamiltonian of the molecule exposed to the external field can be expressed as with Be being the rotational constant of the molecule, the angular momentum operator. In the right-hand side of above equation, the first term is the molecular rotation energy and the second, third and last terms are the interaction potentials of the shaped laser pulse with the permanent dipole moment, polarizability and hyperpolarizability of the molecule, respectively. Here,
Investigation of non-adiabatic effects for the ro-vibrational spectrum of H3+: the use of a single potential energy surface with geometry-dependent nuclear masses
Published in Molecular Physics, 2018
Ralph Jaquet, Mykhaylo V. Khoma
Introducing the functions Dλ(X1) the energy contribution from Tmix(X1) results from an additional kinetic energy operator for the adiabatic electronic state λ acts only on the nuclear wavefunction . The final total kinetic energy operator for nucleus 1 and coordinate X1 for the adiabatic electronic state λ is with mX11 = m1 + Δm1, where Δm1 is an effective mass correction which is position and orientation dependent. Now mX11 can be calculated for every isotope, where only the constant mass m1 has to be exchanged. Because the mass contributions are calculated in Cartesian coordinates for every atom, contributions for the relative motion of a triatomic molecule are easily to be calculated for any internal coordinates. We use nine Cartesian derivatives to calculate six different effective masses for the relative motion.
Connection between the su(3) algebraic and configuration spaces: bending modes of linear molecules
Published in Molecular Physics, 2018
M. M. Estévez-Fregoso, R. Lemus
In this section we present the main ingredients of the model to describe the bending degrees of freedom of a triatomic molecule. The goal is to establish the expansion of the coordinates and momenta in terms of generators of the group, and provide the physical insight associated with the different subgroup chains. Although simple we need to start with the 2D-harmonic oscillator.