Electronic, vibrational and rotational energies

Electronic structure theory describes the motions of the electrons and produces energy surfaces and wavefiinctions. The shapes and geometries of molecules, their electronic, vibrational and rotational energy levels, as well as the interactions of these states with electromagnetic fields lie within the realm of quantum stnicture theory. 

Electronic, vibrational and rotational energy levels, not to scale (only the first two electronic levels are shown). 

We shall approximate the molecular energy as the sum of electronic, vibrational, and rotational energies the wave function will be approximated as the product of wave functions for these three kinds of motion. The (equilibrium) electronic energy of a given electronic state is defined as... 

Ue in (6.7), the value at the equilibrium geometry of the potential energy for nuclear motion. The convention is to denote quantities of the upper electronic state of a transition by single primes, and quantities of the lower electronic state by double primes. The symbols Te, G, and F are used for the electronic, vibrational, and rotational energies in cm-1 ... 

Figure 9-17 Schematic representation of electronic, vibrational, and rotational energy levels. The vertical scale is greatly distorted rotational energy levels are normally 10 4-10-2 kcal mole-1 apart, vibrational energy levels are 1-10 kcal mole-1 apart, while electronic transitions involve 10-1000 kcal mole-1.

G. M. Burnett and A. M. North, Transfer and Storage of Energy by Molecules, Vols. 1-3, Electronic, Vibrational, and Rotational Energy, Wiley-Interscience, New York, 1970. 

FIGURE 2. The relative ordering of electronic, vibrational, and rotational energy levels. (Modified from Ref. 1.)... 

Fig. 7.10 Schematic diagram of the electronic, vibrational and rotational energy level of...

Molecular orbital computations are currently used extensively for calculation of a range of molecular properties. The energy minimization process can provide detailed information about the most stable stmcture of the molecule. The total binding energy can be related to thermodynamic definitions of molecular energy. The calculations also provide the total electron density distribution, and properties that depend on electron distribution, such as dipole moments, can be obtained. The spatial distribution of orbitals, especially the HOMO and LUMO, provides the basis for reactivity assessment. We illustrate some of these applications below. In Chapter 3 we show how MO calculations can be applied to intermediates and transitions structures and thus help define reaction mechanisms. Numerical calculation of spectroscopic features including electronic, vibrational, and rotational energy levels, as well as NMR spectra is also possible. 

Figure 7.3 Radiative (absorption, stimulated emission, fluorescence) and non-radiative (quenching, collisional energy transfer, elastic scattering) processes in a molecular system with electronic, vibrational and rotational energy levels...

The quantities lit, and represent the electronic, vibrational, and rotational energy levels of each species, and Ui represents translational energy. The connection between the rate of reaction (17) and the rate of an elementary reaction between A and B can be made if the rate of the state-to-state process can be written conventionally. If A, is taken to represent the energy state of A in equation (17) and By the state of B, then the rate of the state-to-state reaction is... 

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