Unsolved problems or Holy Grails of the HFR-based semiempirics

Unsolved problems or Holy Grails of the HFR-based semiempirics 

rotation barriers and relative stability of conformations of organic molecules  

major part of true chemical transformations involving bond breaking and forming  

The highly specific behavior of transition metal complexes has prompted numerous attempts to access this Holy Grail of the semi-empirical theory - the description of TMCs. From the point of view of the standard HFR-based semiempirical theory, the main obstacle is the number of integrals involving the d- AOs of the metal atoms to be taken into consideration. The attempts to cope with these problems have been documented from the early days of the development of semiempirical quantum chemistry. In the 1970s, Clack and coworkers [78-80] proposed to extend the CNDO and INDO parametrizations by Pople and Beveridge [39] to transition elements. Now this is an extensive sector of semiempirical methods, differing by expedients of parametrizations of the HFR approximation in the valence basis. These are, for example, in methods of ZINDO/1, SAMI, MNDO(d), PM3(tm), PM3 etc. [74,81-86], From the 

Let us consider a two-orbital two-electron model system with the orbitals a and b which can be understood as notation for one-dimensional irreducible representations of the point group of a TMC. In this case, it is easy to see that the corresponding singlet and triplet states 1B and 71 (T . S 0,1) are given respectively by  

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