=A simple formalism of real irreducible tensorial sets of real bases is proposed. The definition of the real bases, the coupling of the real bases, and the transformation of the real bases in a group chain including the three-dimensional rotation group and the molecular point groups are studied. The double coset technique is used to derive the close formulas for generating the coupling coefficients and the transformation coefficients. . Introductionhe irreducible tensor method (or Wigner-T Racah algebra) is a powerful group theoretical tool in physics and chemistry [l-141. The irreducible tensorial sets are almost built on the complex bases [15][16][17][18][19][20][21][22][23][24][25][26][27]. However, since the atomic and molecular orbitals can be chosen to be real functions, it is desirable to build the real irreducible tensorial sets of the real bases. Griffith calculated the coupling coefficients of the real trigonal basis and the real tetragonal basis of the octahedral group 0 [6]. The coefficients of the other point groups still need to be generated. Alt-* To whom correspondence should be addressed.

The molecular orbitals obtained from conventional quantum chemistry calculations, are expressed in terms of symmetrized valence bond functions of fragment, and a direct picture of chemical bonding can be drawn easily. This method is utilized, together with extended Huckel calculations, to interpret the bonding properties of a centipede‐like chain structure for novel laser‐producing boranes B3k+pH−5k+p+3 which is constructed from the repeated unit B3H5 halted to each other by three B—H—B bonds.

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