Energy curve, diatomic

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... 

Tellinghuisen J A 1974 A fast quadrature method for computing diatomic RKR potential energy curves Comput. Phys. Commun. 6 221-8... 

Figure B3.4.7. Schematic example of potential energy curves for photo-absorption for a ID problem (i.e. for diatomics). On the lower surface the nuclear wavepacket is in the ground state. Once this wavepacket has been excited to the upper surface, which has a different shape, it will propagate. The photoabsorption cross section is obtained by the Fourier transfonn of the correlation function of the initial wavefimction on tlie excited surface with the propagated wavepacket.

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... 

Figure 6.4 Potential energy curve and energy levels for a diatomic molecule behaving as an anharmonic oscillator compared with those for a harmonic oscillator (dashed curve)...

For each excited electronic state of a diatomic molecule there is a potential energy curve and, for most states, the curve appears qualitatively similar to that in Figure 6.4. 

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.)...

At the other end of the spectrum are the ab initio ( from first principles ) methods, such as the calculations already discussed for H2 in Chapter 4. I am not trying to imply that these calculations are correct in any strict sense, although we would hope that the results would bear some relation to reality. An ab initio HF calculation of the potential energy curve for a diatomic Aj will generally give incorrect dissociation products, and so cannot possibly be right in the absolute sense. The phrase ab initio simply means that we have started with a certain Hamiltonian and a set of basis functions, and then done all the intermediate calculations with full rigour and no appeal to experiment. 

FIGURE 7.2 Energy curves for a diatomic molecule. Two possible transitions are shown. When an electron has been excited to the point marked A, the molecule may cleave (p. 312). 

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... 

Considering again the case of a structureless continuum, we have that 8j3 arises from excitation of a superposition of continuum states, hence from coupling within PHmP [69]. The simplest model of this class of problems, depicted schematically in Fig. 5b, is that of dissociation of a diatomic molecule subject to two coupled electronic dissociative potential energy curves. Here the channel phase can be expressed as... 

Hydroxyl radical (OH) is a key reactive intermediate in combustion and atmospheric chemistry, and it also serves as a prototypic open-shell diatomic system for investigating photodissociation involving multiple potential energy curves and nonadiabatic interactions. Previous theoretical and experimental studies have focused on electronic structures and spectroscopy of OH, especially the A2T,+-X2n band system and the predissociation of rovibrational levels of the M2S+ state,84-93 while there was no experimental work on the photodissociation dynamics to characterize the atomic products. The M2S+ state [asymptotically correlating with the excited-state products 0(1 D) + H(2S)] crosses with three repulsive states [4>J, 2E-, and 4n, correlating with the ground-state fragments 0(3Pj) + H(2S)[ in... 

Figure 1.3. Diatomic potential energy curves and intersystem crossing (Si Ti) at point A.

To help visualize this process, let us consider a diatomic molecule with the energy curves shown in Figure 2.5(a). In this example the ground and excited states have the same equilibrium intemuclear distance ra. Since in solution at room temperature almost all the molecules will be in the lowest vibrational level of the ground state vt° (subscripts refer to the electronic... 

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 3.1 Diatomic potential-energy curves for H2, Li2 and their cations. (The one-electron species H2+ is calculated at UHF/6-311++G" level others at B3LYP/6-311++G level.)...

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 3.27 Singlet (solid line) and (if lower) triplet (dotted line) potential-energy curves for first-row homonuclear diatomics B (circles), C (squares), N (triangles),...

Let us also briefly examine the corresponding behavior in second- and third-row homonuclear diatomics. Figures 3.31(a) and (b) display the calculated potential-energy curves for these species (ground-state multiplicities only) and Table 3.16 summarizes the equilibrium bond lengths and bond energies. 

Figure 19.1 Potential energy curve for a diatomic molecule.

Figure 19.2 Two potential energy curves of 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 ... 

The potential energy of a diatomic molecule depends on only the distance between two bonded atoms. The potential energy of a diatomic molecule can be plotted in two dimensions by plotting PE as a function of the bond length. The curve is known as potential energy curve (Fig. 9.9). 

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. 

Use potential energy curves to explain the various types of behaviour when photons interact with diatomic molecules. 

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. 

Differences in the physicochemical properties of isotopes arise as a result of quantum mechanical effects. Figure 1.3 shows schematically the energy of a diatomic molecule, as a function of the distance between the two atoms. According to the quantum theory, the energy of a molecule is restricted to certain discrete energy levels. The lowest level is not at the minimum of the energy curve, but above it by an amount 1/2/tv where h is Planck s constant and v is the frequency with... 

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... 

---