Configuration matrix

The method presented enables expressions to be found for submatrix elements of irreducible tensorial products of second-quantization operators for configurations of any complexity. This method provides a unified approach both to diagonal and non-diagonal (relative to the configuration) matrix elements of operators of physical quantities. 

Thus, the use of wave function in the form (23.67) and operators in the form (23.62)—(23.66) makes it possible to separate the dependence of multi-configuration matrix elements on the total number of electrons using the Wigner-Eckart theorem, and to regard this form of superposition-of-configuration approximation itself as a one-configuration approximation in the space of total quasispin angular momentum. 

V. I. Sivcev, I. S. Kickin and Z. B. Rudzikas. Matrix Elements of Relativistic Energy Operator for Four Subshells of Equivalent Electrons (No 371-76 Dep) Non-Diagonal with Respect to Configurations Matrix Elements of Energy Operator for Four Subshells of Equivalent Electrons (No 2181-Dep76). Allunion Institute of Scientific and Technical Information, Moscow, 1976. 

Scheme 39. A System for Characterization of Total Syntheses o/lOO (en -100) with Blanks to Be Filled to Indicate a) Constitutional Design (sequence of building-block addition) b) Configurational Matrix (to indicate in which order and by what type of stereoselection the stereo-genic centers are introduced for details, see text) c) Numerical Overall Data d) Quick Overview (of building blocks and characteristic intermediates).

Where (xiX2...X3m) = R, the configuration matrix. By an appropriate coordinate transformation, an eigenvalue problem arises... 

Fig. 5. Elements for classification of total syntheses pointing out the constitutional pattern, emphasizing numerical overall data (white field), and using a configurational matrix (orange field) to indicate in which order and by what type of stereoselection the stereogenic centers of the target structure (green field) have been generated.

The configurational matrix reveals that the absolute configuration at C(14) in D, due to an auxiliary s help is responsible for the diastereoselective generation of the stereogenic center C(13) in the Michael adduct AD, whilst the [4+2]-cycloaddition diastereoselectively takes care of stereogenic centers C(8) and C(9). 

The platform consists of a 128 circular sensing sites (8 X 16 element configuration matrix) with a diameter of 10 mm for each sensor and spacing between sensors of 20... 

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