Quasi-degenerate

Electron correlation was treated by the CIPSI multi-reference perturbation algorithm ([24,25] and refs, therein). The Quasi Degenerate Perturbation Theory (QDPT) version of the method was employed, with symmetrisation of the effective hamiltonian [26], and the Maller-Plesset baricentric (MPB) partition of the C.I. hamiltonian. 

According to most theoretical analyses of the present neutrino experiment results, next-generation DBD experiments with mass sensitivities of the order of lOmeV may find the Majorana neutrino with a non-zero effective electron neutrino mass, if the neutrino is self-conjugate and the neutrino mass spectrum is of the quasi-degenerate type or it has inverted hierarchy [83], Majorana massive neutrinos are common predictions in most theoretical models, and the value of a few 10 2cV predicted for its effective mass, if reached experimentally, will test its Majorana nature. 

To make the ideas sharper consider the case of two quasi degenerate quantum states of the active precursor and successor complexes. The discussion made around equation (57) holds true here too. The activated complex will be the place of a coherent electro-nuclear fluctuation that will go on forever, unless there are quantum states belonging to the relaxation channels of Hc(i) and Hc(j). Note that the mechanisms of excitation to get into the quantum activated complex and those required to relax therefrom are related to the actual rate, while the mechanism of interconversion is closely connected with an... 

The second situation corresponds to an indirect coupling of the APC states with the ASC ones via the quantum states of the interconversion states (if). The largest contribution comes again from those state being quasi degenerate in the energy scale. Thus, to second order in TDPT one gets... 

Thus, all those quantum states of the interconversion complex (QIC) that are quasi degenerate with the APC would contribute to the population rate of the ASC. Note that there is no first order contributionsin the present theory since the matrix elements of the dipole transition between quantum states belonging to APC and ASC are zero. 

M. G. Sheppard and K. F. Freed, Effective valence shell Hamiltonian calculations using third-order quasi-degenerate many-body perturbation theory. J. Chem. Phys. 75, 4507 (1981). 

The difference between Es and ET is about constant for the helicenes with five to nine rings (Table 22), while the kisc increase by a factor of about 3 I25). This may suggest the participation of a quasi degenerate triplet state in the intersystem crossing. This most likely will be the 3Lb state since a direct spin-orbit coupling between Lb and 3Lb is allowed in the helicenes because of their C2-symmetry. It is proposed 125) that the increase in kisc reflects the departure from coplanarity when the amount of benzene rings increases. 

Fig. 9. Comparison between the second-order perturbation theory and quasi-degenerate perturbation theory for the D value of ( 20) +.

Fig. 20. A schematic representation of the emission of an isolated large molecule following internal conversion from the second to the first singlet, a" and 6J1 denote the amplitudes of the second singlet and quasi-degenerate vibrational levels of the first singlet, respectively, in the excited molecular state >/in. /v, and m are the corresponding electronic dipole transition matrix elements coupling < >n and as indicated.

Let us consider a pair of the electronic wave functions, >i) and 2), tending to crossover at the nuclear coordinate Qo (Fig. 114). A proper electronic wave function A) should be considered as a (quasi) degenerate, and then a linear combination of the respective pair is appropriate ... 

As a parametrization scheme this model is a typical intermediate between the crude spherical parametrization of the B and C parameters and the complete (and therefore impractical) set of the tetragonal repulsion integrals [31]. A similar strategy was used before by Koide and Pryce [32] in their treatment of octahedral d5-complexes they showed that quasi-degenerate terms of the half-filled d-shell configuration could be splitted by introducing a covalency difference between the t2g and eg orbitals. 

S. Wilson, K. Jankowski, and J. Paldus, Int.]. Quantum Chem., 28,525 (1985). Applicability of Non-Degenerate Many-Body Perturbation Theory to Quasi-Degenerate Electronic States. II. A Two-State Model. 

Here we will skip the notation details, as the relation established to the Coupled Perturbed frame allow us the shortcut of passing the references to the comprehensive works devoted to the analytic derivatives of molecular energy [9]. The recent advances in the analytic derivatives and Coupled Perturbed equations into multiconfigurational second order quasi-degenerate perturbation theory is the premise of further development in the ab initio approach of vibronic constants of JT effects [10]. 

We discuss here two examples of vibronic effects in polynuclear highly symmetrical transition metal clusters. The existence of degenerate and quasi-degenerate molecular orbitals in their energy spectra results in the Jahn-Teller effect or in the vibronic mixing of different electronic states. We show that both quantum-chemical methods and model approaches can provide valuable information about these vibronic effects. In the case of the hexanuclear rhenium tri-anion, the Jahn-Teller effect is responsible for the experimentally observed tetragonal distortion of the cluster. The vibronic model of mixed-valence compounds allows to explain the nature of a transient in the photo-catalytic reaction of the decatungstate cluster. 

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