Multiconfigurational calculations

The emergence of Wigner statistics can be approached from the point of view of ab initio multiconfigurational Dirac-Fock theory. Although a full calculation for the 5p spectrum of Ba presents a formidable challenge and has not yet proved possible, fairly extensive calculations have proved fea- 

We stress that level spacings alone do not suffice to make statements about quantum chaos integrable systems are known which give Wigner distributions [561, 562]. Simple systems are also known whose classical dynamics is chaotic, but whose nearest level spacings differ markedly from the Wigner distribution [563]. For atoms, such systems can have the property that one series is dominant, i.e. has a much higher density of 

The present class of problems should not be confused with the emergence of chaotic behaviour in systems with few degrees of freedom (see next section below). The connection is merely that they happen to possess the same kind of nearest neighbour distribution. 

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The most elaborate systematic study of the structures and of the lA -3fii splitting of the heavier carbene analogs was carried out by Balasubramanian400. He carried out extensive multiconfiguration calculations (CASSCF) followed by configuration interaction calculations, using basis sets that included f-polarization functions, and the results of these calculations are collected in Table 37. 

A fourth Section presents the results of eight-electron multiconfiguration calculations on the electronic ground state A i) of BH3, and discusses their... 

Some time ago, we started HI the development of the Elementary Jacobi Rotation (EJR) algorithms which were known from old times /2, 3, 4/. As a consequence of this development some intermediate work has been published /5,6/. The present paper corresponds, essentially, to the application of our EJR experience to multiconfigurational calculations. 

This spectrum presents an instructive case for the large uncertainties in atomic transition probabilities, obtained even with sophisticated multiconfiguration calculations. For this ion, three extensive and detailed atomic structure calculations have been undertaken in the last ten years [15-17]. 

The two main advantages of these methods compared to the supermolecular approach are that, first, the various contributions are separately know and their physical meaning is apparent, and, second, the results are not affected by BSSE. However, interaction energies computed this way are still rather expensive, either because they require very large basis sets with polarization functions or because they imply multiconfiguration calculations. 

Multiconfiguration calculations have shown that similar values of these effective-operator parameters are to be expected at both ends of the lanthanide... 

In multiconfiguration calculations where off-diagonal two-electron matrix elements are required there are two different wave numbers kx and k2 which can be constructed from the orbital energies. 

In absence of experimental results on these Ions, the 27 energy levels of the three configurations 3s 3p , 3s3p , and 3s 3p3d are studied for all Ions by the Dirac-Fock method. The Breit interaction and Lamb shift are calculated perturbatively and all configurations of the (n = 3) complex are included in this multiconfiguration calculation. Selected results are tabulated below [7] ... 

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