Complex-coordinate coupled-channel

Complex-Coordinate Coupled-Channel Methods for Predissociating Resonances in van der Waals Molecules... 

Complex-Coordinate Coupled-Channel (CCCC) methods are presented for the accurate and efficient treatment of the resonance energies and widths (lifetimes) of multichannel rotatlonally predissociating van der Waals (vdW) molecule resonances. Algorithms for dealing with the complex scaling of numerical and piecewise analytical potentials are also presented. 

Complex-Coordinate Coupled-Channel Approach to Predissociation of Atom-Diatom Van Per Waals Complexes... 

Hamiltonian and Complex-Coordinate Coupled-Channel Formulation In Space-Fixed Coordinates (18-21). The hamlltonian of a trlatomlc vdW molecule A...BC, after separating out the motion of the centre of mass, may be expressed In the SF frame as... 

We now discuss the complex-coordinate coupled-channel (CCCC) formulation in the SF frame. According to the theory of complex-coordinate transformation, the energy (Ej ) and the width (F) associated with a metastable state of the vdW molecule may be determined by the solutlo of the complex eigenvalue of a non-hermitian ham-11 tonlan H (Re, r), obtained by applying the complex-coordinate... 

Hamiltonian and Complex-Coordinate Coupled-Channel Formulation in Body-Fixed Coordinates (23). In the BF fr jne, the Hamiltonian is identical to equation 3 except that R and r are expressed relative to the unprlmed axes of figure 1 and the angular momentum operator of the rotation of R (i.e. X) is written as X = J-j. The operator (J-J)2 may be expressed as... 

The complex-coordinate coupled-channel (CCCC) formulations described In the last section have been applied to the determination of resonance energies and widths (lifetimes) of several rotatlonally pre-dlssoclatlng vdW molecules, including Ar-H2 (19), Ar-HD (20),... 

The total width of the resonance is directly given by the resonance complex energy. In the case where many channels of autodetachment are open, the question of partial widths for the decay into individual channels arises. This always requires analysis of the wave fimction. The problem of obtaining partial widths from complex coordinate computation has been discussed by Noro and Taylor (39) and Bcicic and Simons (40), and recently by Moiseyev (10). However, these considerations do not seem to have found a practical application. Interchannel coupling for a real, multichannel, multielectron problem has been solved in a practical way within the CESE method by Nicolaides and Mercouris (41). According to this theory the partial widths, 7, and partial shifts to the real energy, Sj, are computed to all orders via the simple formula... 

In the reaction F + C6D6, it appears that the distribution of energy is random when attention is focused on the C6DSF vibrational distribution measured in infrared chemiluminescence experiments [583], but is non-random for the product recoil distribution measured in a molecular-beams experiment [588]. This could be rationalised if certain modes in the complex do not take part in the randomisation or if a few specific modes are coupled to the reaction coordinate at the transition state (the exit channel barrier). 

The hexanuclear complexes of Cu(II) and Ni(II) with polysiloxanolate ligands display different magnetic behavior [20]. The Cu(II) complex shows a ferromagnetic coupling with a ground state of S=3 [113], while in the case of the Ni(II) complex the ground state has S=0 [114]. Analysis of the crystal structures reveals a similar structure of the complex, but in the case of the nickel atom a chloride anion is placed in the center of the channel in order to complete the octahedral coordination whilst the copper atom has square pyramidal coordination (see Fig. 11). 

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