Potential energy curve For diatomic molecule

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... 

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

W.-D. Sepp, D. Kolb, W. Sengjer, H. Har-tung, B. Fricke. Relativistic Dirac-Fock-Slater program to calculate potential-energy curves for diatomic molecules. Phys. Rev. A, 33(6) (1986) 3679-3687. 

CORRELATED MULTEDETERMINANTAL POTENTIAL ENERGY CURVES FOR DIATOMIC MOLECULES WITH ONE VALENCE-BOND PAIR... 

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]. 

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

In summary then, the structure and energetics of a diatomic molecule are defined by the parameters R D, and Dq on the effective potential energy curve for the molecule, all of which can be calculated within the Bom-Oppenheimer approximation (see the figure above). In Chapter 20 we show how and Dq can be determined experimentally by molecular spectroscopy. 

The relationship between vibrational and rotational energy levels is illustrated for a diatomic molecule in Figure 2.4, which shows a potential-energy curve for a molecule... 

Figure 6.34 shows potential energy curves for a hypothetical diatomic molecule X2, which approaches a surface, coming from the right-hand side of the diagram. First... 

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 ... 

The first-row homonuclear diatomic molecules A2 of main-group elements (A = B, C, N, O, F) exhibit a well-known diversity of ground-state multiplicities, bond lengths, and bond energies. Calculated potential-energy curves for low-lying singlet and triplet states of these species are pictured in Fig. 3.27 and summarized in Table 3.13 (with comparison experimental values). Because these homonuclear... 

Figure 19.1 Potential energy curve for a diatomic molecule.

In the general case R denotes a set of coordinates, and Ui(R) and Uf (R) are potential energy surfaces with a high dimension. However, the essential features can be understood from the simplest case, which is that of a diatomic molecule that loses one electron. Then Ui(R) is the potential energy curve for the ground state of the molecule, and Uf(R) that of the ion (see Fig. 19.2). If the ion is stable, which will be true for outer-sphere electron-transfer reactions, Uf(R) has a stable minimum, and its general shape will be similar to that of Ui(R). We can then apply the harmonic approximation to both states, so that the nuclear Hamiltonians Hi and Hf that correspond to Ui and Uf are sums of harmonic oscillator terms. To simplify the mathematics further, we make two additional assumptions ... 

Figure 2.3 shows the potential energy curve for a diatomic molecule, often referred to as a Morse curve, which models the way in which the potential energy of the molecule changes with its bond length. 

Figure 3.6 shows the Morse potential energy curves for two hypothetical electronic states of a diatomic molecule, the vibrational energy levels for each, and the shape of the vibrational wavefunctions (i//) within... 

FIGURE 3.6 Potential energy curves for the ground state and an electronically excited state of a hypothetical diatomic molecule. Right-hand side shows relative intensities expected for absorption bands (from Calvert and Pitts, 1966). 

FIGURE 3.7 Potential energy curves for a hypothetical diatomic molecule showing electronic transitions to two repulsive excited states having no minima. A is an electronically excited atom. 

FIGURE 3.8 Potential energy curves for the ground state and two electronically excited states in a hypothetical diatomic molecule. Predissociation may occur when the molecule is excited into higher vibrational levels of the state E and crosses over to repulsive state R at the point C (from Okabe, 1978). 

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. 

Figure 2.9 Potential energy curve for a diatomic molecule, (a) Attractive curve—bonding interaction (b) repulsive curve—antibonding interaction.

The shapes of the absorption band associated with the intensities of vibrational transitions, are sensitive functions of the equilibrium bond length, about which approximately harmonic vibrational oscillations occur. Potential energy curves for a diatomic molecule (Figure 4.2), are commonly represented by Morse equation,... 

Figure 1-6 Potential energy curve for a diatomic molecule. Solid line indicates a Morse potential that approximates the actual potential. Broken line is a parabolic potential for a harmonic oscillator. De and D0 are the theoretical and spectroscopic dissociation energies, respectively.

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