Vibronic parameters

The TIP contributions as functions of v/ho) are shown in Figs 5 and 6. The main common feature of TIP and TIP is the presence of the plateau for relatively small values of vibronic parameter. However, for A < 0 contrary to the g-factors the TlPy values decrease with the growth of 141. In the limit of strong fields TlPy vanishes. At the same time in the range of small v-values TIP remains practically constant. Thus TIP demonstrates a strong anisotropy just like the g-factors. This anisotropy comes... 

Fig. 5. Energy gaps (a) between the ground and excited minima of the lower adiabatic potential sheet Ui(q,Q) and angles ft (b) characterizing the configuration of the Fe-(NO) fragment in these minima as functions of the vibronic parameter V with t = 5.5hcoBl, v2 = 6.2ho)Bl, Vi = 1.5h(oBl, Deltas = 15850 cm-1, A2 = 21185 cm-1 coBi = 340 cm-1 coAl = 400 cm"1.

Here g-j)presents the /ill -component in the /th well and A, is the temperature dependent Boltzmann population of the /th well. Analysis of the spectra shows that the tetragonal deformation appears abruptly at Tc= 191 K corresponding to the separation energy 8 li2(3) 130 cm-1. 8 1 2(3) gradually increases to 150 cm-1 as the temperature decreases to T 60 K. The corresponding adiabatic potential calculated for the vibronic parameters of cubic symmetry to which the Ae cos cp component (Ae = 8 1 2(3)) is added, is shown in Ref. [20]. The energy difference between the deepest and the two higher wells is equal to 140 cm-1 and the potential barrier between the wells is about 400 cm-1. 

He represent parameters describing the electron transfer from the Fe +-ion to the 7t level of the NO ligand. At the first step these parameters were put equal to A2 He Al) = B2 He Al) = t. In the model under consideration three vibronic parameters are involved. The parameter V = A2 Vb B2) character-... 

Fig. 11.14. Temperature variation of the effective magnetic moment for the S = S2 = S3 = 1/2 system in a geometry of the isosceles triangle left—J/k = +10 K, individual curves correspond to the vibronic parameter X/k = 0 (solid), 30 K (long dashed), 40 K (medium dashed), 50 K (short dashed) and 100 K (dotted) right—J/k = —10 K, X/k = 0 (solid), 50 K (long dashed) and 100 K (medium dashed).

The calculation and the correlative understanding of harmonic and anharmonic force constants in molecules has been a very active field in the last 25 years. The vibrational assignment of innumerable molecules and their isotopic derivatives, the study of ro-vibronic parameters, the application of group theory and chemical correlations have allowed to introduce, into grand least-squares fitting procedures [2,13,14] by computers, many experimental data, from which seemingly reliable sets of vibrational force constants have been derived. This statement is certainly true for molecules which contain covalent a bonds, or... 

Table 4a. Spectroscopic and vibronic parameters obtained from intensity distributions in the progressions. a-coupling cases...

Figure 3. Low-energy vibronic spectrum in a. 11 electronic state of a linear triatomic molecule, computed for various values of the Renner parameter e and spin-orbit constant Aso (in cm ). The spectrum shown in the center of figure (e = —0.17, A o = —37cm ) corresponds to the A TT state of NCN [28,29]. The zero on the energy scale represents the minimum of the potential energy surface. Solid lines A = 0 vibronic levels dashed lines K = levels dash-dotted lines K = 1 levels dotted lines = 3 levels. Spin-vibronic levels are denoted by the value of the corresponding quantum number P P = Af - - E note that E is in this case spin quantum number),...

Figure 5, Low-eriergy vibronic spectrum in a electronic state of a linear triatomic molecule. The parameter c determines the magnitude of splitting of adiabatic bending potential curves, is the spin-orbit coupling constant, which is assumed to be positive. The zero on the...

Another group of approaches for handling the R-T effect are those that employ various forms of effective Hamiltonians. By applying pertuibation theory, it is possible to absorb all relevant interactions into an effective Hamiltonian, which for a particular (e.g., vibronic) molecular level depends on several parameters whose values are determined by fitting available experimental data. These Hamiltonians are widely used to extract from high-resolution [e.g.. 

The illustration of various types of vibronic transitions in Figure 7.18 suggests that we can use the method of combination differences to obtain the separations of vibrational levels from observed transition wavenumbers. This method was introduced in Section 6.1.4.1 and was applied to obtaining rotational constants for two combining vibrational states. The method works on the simple principle that, if two transitions have an upper level in common, their wavenumber difference is a function of lower state parameters only, and vice versa if they have a lower level in common. 

In using the combination difference method to obtain vibrational parameters, cOg, etc., for two electronic states between which vibronic transitions are observed, the first step is to organize all the vibronic transition wavenumbers into a Deslandres table. An example is shown in Table 7.7 for the system of carbon monoxide. The electronic... 

For the d5, 2A (a2 53) system an identical approach is adopted (68). In the adiabatic situation the distortion parameter is given by /A = 2 cs/(c2 - s2), again withe2 + s2 = 1, and carrying through the vibronic treatment as before yields... 

V 0.48), Ammeter and Swalen also calculated the adiabatic distortion parameter for the Co(Cp)2/Fe(Cp)2 system, finding A = 528 cm 1. In both cases however calculations were carried out to determine the value of the purely static distortion which would reproduce, via the vibronic coupling mechanism, the results for c and 45- For the Ru(Cp)2 host the corrected value of A proved to be 200 cm 1 and for the Fe(Cp)2 host 840 cm-1. Thus in the Ru(Cp)2 host, with a rather long metal to carbon distance, the vibronic effect... 

In the past decade, vibronic coupling models have been used extensively and successfully to explain the short-time excited-state dynamics of small to medium-sized molecules [200-202]. In many cases, these models were used in conjunction with the MCTDH method [203-207] and the comparison to experimental data (typically electronic absorption spectra) validated both the MCTDH method and the model potentials, which were obtained by fitting high-level quantum chemistry calculations. In certain cases the ab initio-determined parameters were modified to agree with experimental results (e.g., excitation energies). The MCTDH method assumes the existence of factorizable parameterized PESs and is thus very different from AIMS. However, it does scale more favorably with system size than other numerically exact quantum... 

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