The generalized spin-dependent electronegativity and hardness parameters for the up- and down-spin electrons, defined within the framework of spin-polarized density functional theory are calculated for atomic systems using self-interaction correction along with local spin-density approximation for the exchange correlation. Chemical binding in molecules is formulated in terms of (i) a two-way flow of unpaired electrons of opposite spin between the atoms governed by these parameters and also (ii) the accumulation of electron density at the bond center using the concepts of electronegativity and hardness for the bond region. The associated energy changes obtained by an electronegativity equalization procedure corresponding to these descriptions are shown to provide quite accurate estimates of bond energies for homonuclear as well as simple heteronuclear polyatomic molecules.