Configuration interaction , open-shell

Configuration interaction, which is necessary in treatments of excited states and desirable in calculations of spin densities, is more complex with open-shell systems. This is because more types of configurations are formed by one-electron promotions. These configurations (Figure 5) are designated as A, B, Cq, C(3 G is the symbol for a ground state. Configurations C and Cp have the same orbital part but differ in the spin functions. 

As far as the molecular calculation is concerned, the use of an ab initio method is necessary for an adequate representation of the open-shell metastable N (ls2s) + He system with four outer electrons. The CIPSI configuration interaction method used in this calculations leads to the same rate of accuracy as the spin-coupled valence bond method (cf. the work on by Cooper et al. [19] or on NH" + by Zygelman et al. [37]). 

Fig. 12.1 An ultra-fast heating of a cluster containing both N2 and 02 molecules upon impact at a surface. [9] Shown is the instantaneous configuration of 14 N atoms (dark) and 14 O atoms (light) 50 fsec after a cluster of 7 N2 and 7 02 molecules embedded in 97 Ne atoms impacts a surface at a velocity of 20 Mach. The potential used allows for alii 25 atoms of the cluster to interact with one another and with the atoms of the surface. In addition, each atom-atom chemical interaction is influenced by the presence or absence of other open-shell atoms nearby.

I. Selection of parameters and the basis of configuration interaction in closed shell and restricted open shell semiempirical methods. J. Phys. Chem. 77, 107 (1973). 

In the present work we present the generalisation of the theory to the case of K interacting fragments one of which may be described by an open shell configuration. This extension implies a drastic modification of the procedure which is here reported in full detail. 

In (22.37) ip is the wave function of an atom with motionless nucleus. The one-electronic submatrix element of the gradient operator (n/ V ni/i) is non-zero only for h = / 1. Therefore, the matrix element of operator (22.38) inside a shell of equivalent electrons vanishes and one has to account for this interaction only between shells. For the configuration, consisting of j closed and two open shells, it is defined by the following formula [156] ... 

Such general expressions for matrix elements of electrostatic interactions, covering the cases of three and four open shells, may be found in Chapter 25 of [14]. However, they are rather cumbersome and, therefore of little use for practical applications. Quite often sets of simpler formulas, adopted for particular cases of configurations, are employed. Below we shall present such expressions only for the simplest interconfigurational matrix elements occurring while improving the description of a shell of equivalent electrons (the appropriate formulas for the more complex cases may be found in [14]) ... 

Auger spectra, involving electrons of outer open shells. Specific for Auger spectra is the interaction of the electronic configuration with two vacancies in final state of an ion, first of all, with quasidegenerated configurations, particularly if they are energetically close. 

In order to calculate the spin-angular parts of matrix elements of the two-particle operator (1) with an arbitrary number of open shells, it is necessary to consider all possible distributions of shells upon which the second quantization operators are acting. In [2] they are found to be grouped into 42 different distributions, subdivided into 4 different classes. This also explains why operator (1) is written as the sum of four complex terms. The first term represents the case when all second-quantization operators act upon the same shell (distribution 1 in [2]), the second describes the situation when these operators act upon the two different shells (distributions 2-10), third and fourth are in charge of the interactions upon three and four shells respectively (distributions 11-18 and 19-42). Such expression is particularly convenient to take into account correlation effects, because it describes all possible superpositions of configurations for the case of two-electron operator. 

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