Localized Bonds in Hydrides Revisited

In the ground-state the chemical interaction between two (singly occupied) orthonormal AOs / = (fl ) originating from atoms A and B, respectively, gives rise to the doubly occupied, bonding MO and the unoccupied antibonding MO (p a., 

Their shapes are determined by the complementary (conditional) probabilities P(a Wd.)=P(%anti.)=P and P(%bond.)=P(tf Panti.) = Q, which COn-trol the bond polarization, covering the symmetrical bond combination for P = Q = 1/2 and the limiting lone-pair (nonbonding) configurations for P = (0,1). The associated model CBO matrix, 

Both components yield the conserved overall bond index Af P) = 1 in the whole range of bond polarizations P e [0,1]. Therefore, this model properly accounts for the competition between the bond covalency and ionicity, while 

In the xa = (ha,cra) representation, the corresponding CBO matrix ya for a single a bond X-Ha ya,p then includes the following nonvanishing elements  

The corresponding conditional probabilities (see Eq. [4]), which determine the nonvanishing communication connections, then read  

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