Energy curves of diatomic molecules

A. J. Thakkar, J. Chem. Phys., 62, 1693 (1975). A New Generalized Expansion for the Potential Energy Curves of Diatomic Molecules. 

Figure S-1. Form of a potential energy curve for diatomic molecule AB. VfrAa) is the potential energy, Tab is the intemuclear distance, is the equilibrium intemuclear distance, and D is the bond dissociation energy. (The zero point energy is neglected in the figure.)...

Fig. 3.5). For example, the ideal bond distance r0 (minimum of the curve) and rcfp (center of the zeroth vibrational level) are not identical because of the anharmoni-city of the potential energy curve. For diatomic molecules there are acknowledged though complicated procedures for obtaining the theoretical values rQ, D0 and k0 from experiment, but for larger molecules this is largely impossible. 

The Frank-Condon principle is based on the fact that the time of an electronic transition (of the order of 10 s) is shorter than that of a vibration (of the order of 10 s). This means that during an electronic transition the nuclei do not change their positions. This phenomenon can be illustrated using the Morse potential energy curves for diatomic molecules (Figure 2.17). The series of horizontal lines... 

As the opposite to the examples given above, we note now processes that involve a fission of electron-pair bonds. Here the change in correlation energy is extremely large and the Hartree-Fock approximation is inherently incapable of giving a reasonable account of heats of reaction, A very illustrative example is provided by potential curves of diatomic molecules. From Fig, 4,2 it is seen that for larger depar ... 

Construct qualitative potential energy curves for diatomic molecules and relate trends in well depth (bond dissociation energies) and location of the... 

The direct irradiation of molecule sets up the molecule in vibrationally excited state. When the energy of photon is sufticient to overcome bond dissociation energy, the fragmentation will occur at the excited bond. The photodissociative mechanisms are best represented with the help of potential energy curves for diatomic molecules [likeCl2 and HI]. 

To compare the relative populations of vibrational levels, the intensities of vibrational transitions out of these levels are compared. Figure B2.3.10 displays typical potential energy curves of the ground and an excited electronic state of a diatomic molecule. The intensity of a (v, v ) vibrational transition can be written as... 

The fact that the separated-atom and united-atom limits involve several crossings in the OCD can be used to explain barriers in the potential energy curves of such diatomic molecules which occur at short intemuclear distances. It should be noted that the Silicon... 

The relationships between bond length, stretching force constant, and bond dissociation energy are made clear by the potential energy curve for a diatomic molecule, the plot of the change in the internal energy AU of the molecule A2 as the internuclear separation is increased until the molecule dissociates into two A atoms ... 

Figure 19.2 Two potential energy curves of a diatomic molecule.

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

This striking result can be qualitatively understood as related to CB DOS-influenced changes in the 02 anion lifetime [118]. For a diatomic molecule with R as the internuclear coordinate, a transient anion state is described in the fixed nuclei limit [123,124] by an energy and i -dependent complex potential Vo i R,E ) = Fd(2 ) + A( i)—l/2 T( i), where Va R) = a R) + is the potential energy curve of the discrete state, Vg(R) is the... 

Historically the first application of symmetry to potential energy surfaces was to prove the so-called non-crossing rule. In its simplest form this may be stated as potential energy curves for states of diatomic molecules of the same symmetry do not cross . We have already seen in section 2 that this should be qualified to apply to adiabatic curves, as in some situations it may be convenient to define diabatic curves wdiich do cross. 

The analysis of spectroscopic data for bound states of diatomic molecules gives accurate potential curves if one follows the semi-classical Rydberg-Klein-Rees method. For a review of this see Ref. 126). It is sufficient to note that this gives the two values of r as a function of potential energy by considering the dependence of the total spectroscopic energy on the vibrational and rotational quantum numbers n and J. A somewhat simpler procedure, and the only one plicable to polyatomic molecule, is to use the Dunham expansion of the potential 127). 

The pump-probe scheme that we use is as follows the molecule is initially excited by a pump laser photon (htOj) to the first excited neutral state. The dynamics is then followed with a probe laser by one-photon ionization (hooa). Compared to a free diatomic, solvation by CH3CN brings two new factors come into play. Firstly, the potential energy curves of the diatomic are modified by the presence of the neighboring molecule. Secondly, the fragmentation dynamics of the diatomic is changed as there may be collisions with, and a transfer of energy to, the acetonitrile. 

Fig. VII-1.—A curve representing the electronic energy of a diatomic molecule as a function of the distance between the nuclei. The zero for energy is the energy of the separated atoms. The minimum of the curve corresponds to the equilibrium value of the internuclear distance. The curve shown, which approximates closely the observed electronic energy curves for many states of diatomic molecules, corresponds to the Morse function.

A. simple function that gives a close approximation to the electronic energy curve for many states of diatomic molecules is the Morse function. This function is... 

The Vibration and Rotation of Molecules.—The nature of the vibrational motion and the values of the vibrational energy levels of a molecule are determined by the electronic energy function, such as that shown in Figure VII-1. The simplest discussion of the vibrational motion of a diatomic molecule is based upon the approximation of the energy curve in the neighborhood of its minimum by a parabola that is, it is assumed that the force between the atoms of the molecule is proportional to the displacement of the internuclear distance from its equilibrium value r.. This corresponds to the approximate potential function... 

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