Transition elements, diatomic molecules

A recent EH-type calculation by Hare et al. (34) and Cooper et al. 35) has been applied to diatomic transition metal molecules. Input data were chosen from previously explained procedures to determine which input data sets give the best fit to experimental data. The off-diagonal Hamiltonian elements were calculated using Eq. (8). A comparison of calculated and experimental data for transition element diatomics is shown in Table II. Although some discrepancies are apparent, the procedure seems qualitatively correct for these molecules. 

Electronic transitions in diatomic molecules are determined by matrix elements of the dipole operator,... 

For molecular transitions the matrix elements Dim and Dmf are composed of three factors the electronic transition dipole element, the Franck-Condon factor, and the Honl-London factor (Sect. 1.7). Within the two-photon dipole approximation a co) becomes zero if one of these factors is zero. The calculation of linestrengths for two- or three-photon transitions in diatomic molecules can be found in [243, 244]. 

For a determination of the permanent multipole moments, Eq. 2.42 must be averaged over the ground state nuclear vibrational wavefunction transition elements are also often of interest which are matrix elements between initial and final rotovibrational states. For example, for a diatomic molecule with rotovibrational states vJM), the transition matrix elements (v J M Q(m vJM) will be of interest a prime designates final states. 

Consideration of the matrix elements m a n of the polarizability shows that the selection rule for a pure-rotational Raman transition of a l2 diatomic molecule is (see Wilson, Decius, and Cross)... 

As it has already been pointed out,10 the spectra of these complex molecules can be interpreted as arising from diatomic molecules. The probability, k, for the radiationless transition Si G is proportional to the square of the matrix element which mixes the two states.6,7... 

Equation (18) may be derived in a manner similar to that described above for vibration-vibration energy transfer, with the difference that the product of the squared matrix elements of the two vibrations concerned, appears in the expression for transition probability. Since both molecules require suitable orientation for vibrational exchange, for two diatomic molecules the steric factor is usually taken to be ( )2. If AE - 0 (exact resonance), eqn. (18) is no longer valid and the following equation may be employed... 

For concrete estimates of the parameters of a reaction (3.1) let us turn to diatomic molecules, such as Na2, K2, Te2, which have been studied most in experiments on optical pumping of molecules via depopulation. A number of data characterizing the states and transitions in these objects under conditions typical for such experiments are given in Table 3.7. These parameters are, to a certain extent, characteristic of diatomic molecules in thermal vapors of the first, sixth and seventh group of the periodic system of elements, such as alkali diatomics, S2, Se2,12, etc. These molecules may... 

For diatomic molecules some of the transition dipole matrix elements will be parallei% to the molecular axis and some will be perpendicular to it. Hence / ... 

The relationships between bond enthalpy, bond length and bond order which appear relatively simple in the case of a main group element such as carbon and its compounds, are more difficult to establish when the d-transition metal elements and their compounds are considered. Progress in establishing these relationships for metals is severely hindered by a lack of relevant thermochemical data. This paper reviews some of the more useful information that is available for diatomic molecules, for polynuclear binary carbonyls and for binuclear complexes of the d-transition elements. 

The saturated vapors of many elements contain moderately high concentrations of dimer molecules some vapors or gases even consist only of dimer molecules. The longest known and widely used lasers involving diatomic molecules are obviously the hydrogen and nitrogen lasers (20,21), which can be excited by short pulsed discharges. The laser transitions in dimer molecules are transitions between rotational-vibrational levels of different electronic states. 

The electron affinities of the main group homonuclear diatomic anions have been measured by PES. A few experimental values for the transition metal dimers are also available. The electron affinities of all the 3d homonuclear diatomic molecules have been calculated using density functional methods [1-4], Only the AEa of I2, 2.524 eV C2, 3.27 Si2, 2.2o S2, 1.67 F2, 3.0g Cl2, 2.4s Br2, 2.5, and 02, 1.07 have been measured by more than one method [1-3]. CURES-EC calculations confirm these to within 0.1 eV. Positive excited states Ea have been measured for 02, C2, and I2 and are inferred for other X2 [5-8]. Just as in the case of the atomic Ea, the trends in the Periodic Table can support the assignments of AEa for the other elements. 

In this example the master equation formalism is appliedto the process of vibrational relaxation of a diatomic molecule represented by a quantum harmonic oscillator In a reduced approach we focus on the dynamics of just this oscillator, and in fact only on its energy. The relaxation described on this level is therefore a particular kind of random walk in the space of the energy levels of this oscillator. It should again be emphasized that this description is constructed in a phenomenological way, and should be regarded as a model. In the construction of such models one tries to build in all available information. In the present case the model relies on quantum mechanics in the weak interaction limit that yields the relevant transition matrix elements between harmonic oscillator levels, and on input from statistical mechanics that imposes a certain condition (detailed balance) on the transition rates. 

In a collision system such as an atom A colliding with a diatomic molecule BC, one is interested in the transition amplitudes, or S-matrix elements, which describe transitions between specific quantum states of the molecule BC. From the S-matrix elements one can construct scattering amplitudes for any collision process resulting from A + BC, the square modulus of the amplitudes being the cross sections. 

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