Diatomic system

Neuhauser D and Baer M 1989 The application of wavepackets to reactive atom-diatom systems a new approach J. Chem. Phys. 91 4651... 

Including higher-order terms leads to anharmonie correetions to the vibration, sueh effects are typically of the order of a few %. The energy levels obtained from the Schrodinger equation for a one-dimensional harmonie oscillator (diatomic system) are given by... 

In order to relate the formal expression (41) to the experiment of Section III, we now specialize the discussion to the case of one- versus three-photon excitation, limiting attention for simplicity to fragmentation of diatomic systems, relevant to the experiments of Refs. 30, 32, 33, 35, and 39. We note later, however, that our conclusions are general and equally applicable to other excitation schemes and to ionization processes. 

For a homonuclear diatomic system in the Hilrikel approximation the integrals given by Eqs. (128)—(131) take the simple forms Haa = Hyy = or, Hab = Hta = P and 5 = 0. The atomic orbitals involved, Xa and xtb are of coarse the px orbitals of carbon atoms a and b, respectively. The resulting secular determinant is then simply... 

Similar to the diatom-diatom system and Eq. (1), the Hamiltonian for the internal motion of the ABC + D system can be written as45... 

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... 

This time period is too short for a change in geometry to occur (molecular vibrations are much slower). Hence the initially formed excited state must have the same geometry as the ground state. This is illustrated in Figure 1.2 for a simple diatomic molecule. The curves shown in this figure are called Morse curves and represent the relative energy of the diatomic system as a... 

Most catalytic cycles at some point involve a bond activation step, be it of one specific bond in a larger molecule or be it the coordination and activation of a small (e.g. diatomic) system like H2, CO, N2,02 etc. 

Consider a system made up of the atoms A, B, and C. Whereas the configuration of a diatomic system can be represented by a single distance, the internal geometry of a triatomic system requires three independent parameters, such as the three interatomic distances rAB, rBC, and rCA, or rAB, rBC, and the angle 4>abc- These are illustrated in Figure 6.2. 

Lathouwers, L., Van Leuven, P., Deumens, E., and Ohm, Y. (1987), Applications of the Generator Coordinate Approximation to Diatomic Systems. II. Dunham Analysis of Vibration-Rotation Spectra, /. Chem. Phys. 86, 6352. 

As mentioned, most calculations we have done so far have concerned molecular systems. However, prior to development of the non-BO method for the diatomic systems, we performed some very accurate non-BO calculations of the electron affinities of H, D, and T [43]. The difference in the electron affinities of the three systems is a purely nonadiabatic effect resulting from different reduce masses of the pseudoelectron. The pseudoelectrons are the heaviest in the T/T system and the lightest in the H/H system. The calculated results and their comparison with the experimental results of Lineberger and coworkers [44] are shown in Table 1. The calculated results include the relativistic, relativistic recoil. Lamb shift, and finite nuclear size corrections labeled AEcorr calculated by Drake [45]. The agreement with the experiment for H and D is excellent. The 3.7-cm increase of the electron affinity in going from H to D is very well reproduced by the calculations. No experimental EA value is available for T. 

In Ref. 122 we raised the question of whether one can use basis functions (49) in non-BO quantum mechanical calculations of molecular diatomic systems containing positrons and whether those functions are capable of providing a proper representation for the positron-nucleus and positron-electron correlation effects in a diatomic system. e+LiH was chosen as a target system. Along with e+LiH, we also performed the calculations of HPs and Li+ because the total energies of these systems are needed for determining the dissotiation energy. 

In Table 4, finite difference Hartree-Fock energies, Ef p, for the four diatomic systems considered in this work are displayed together with the nuclear separations at which the calculations were performed. 

We now turn our attention to the interaction of an atom with a diatomic molecule. We consider three examples (i) Ar-HF, which is a traditional weakly bound system with a binding energy De(Ar-HF) of just 211 cm- (0.6 kcal/mol) (ii) H-CO", which is also weakly bound, Dg(H-CO ) = 8 kcal/mol, but results in large changes in the CO distance and (Hi) H-CO, a molecule whose bond strength is intermediate between the other atom-diatom systems considered and more traditional, strongly bound molecules (the H-CO bond strength is Just 19 kcal/mol). 

In our discussion we have merely given the expressions for the five integrals that appear in the energy. Those interested in the problem of evaluation are referred to Slater[27]. In practice, these expressions are neither very important nor useful. They are essentially restricted to the discussion of this simplest case of the H2 molecule and a few other diatomic systems. The use of AOs written as sums of Gaussian functions has become universal except for single-atom calculations. We, too, will use the Gaussian scheme for most of this book. The present discussion, included for historical reasons, is an exception. 

An analytical theory for the study of CC of radiationless transitions, and in particular, IC leading to dissociation, in molecules possessing overlapping resonances is developed in Ref. [33]. The method is applied to a model diatomic system. In contrast to previous studies, the control of a molecule that is allowed to decay during and after the preparation process is studied. This theory is used to derive the shape of the laser pulse that creates the specific excited wave packet that best enhances or suppresses the radiationless transitions process. The results in Ref. [33] show the importance of resonance overlap in the molecule in order to achieve efficient CC over radiationless transitions via laser excitation. Specifically, resonance overlap is proven to be crucial in order to alter interference contributions to the controlled observable, and hence to achieve efficient CC by varying the phase of the laser field. 

For example, the permanent dipole components of a diatomic system may thus be written... 

In this expression, the s,s indicate the initial and final states of the supermolecule, Ps is the population probability of the state s, p is the dipole moment induced by intermolecular interactions, cosst = (Es — Es)/h where Es is the energy of the state s). For simplicity, we consider an atom-diatom system, such as H2-He, or a diatom-diatom system like H2-H2, with the absorption coefficient given by Eq. 6.50. Since we... 

A brief comment on the accuracy of current approaches seems in order. For atomic systems in the first or second row of the periodic table, quantitative ( 0.01eV) studies have been carried out. For diatomic systems, constructed from these atoms, an accuracy of 1 kcal in the potential curves can be realized. For polyatomic systems the situation is less clear because of the great increase in computational difficulty. Accuracy of 5 to 10 kcal can probably be achieved for simple potential-energy surfaces, although very few surfaces have been examined in detail. 

---