Breaking covalent bonds in the context of the many-body expansion (MBE). I. The purported "first row anomaly" in XH n (X = C, Si, Ge, Sn; n = 1-4).

We present a new, novel implementation of the Many-Body Expansion (MBE) to account for the breaking of covalent bonds, thus extending the range of applications from its previous popular usage in the breaking of hydrogen bonds in clusters to molecules. A central concept of the new implementation is the in situ atomic electronic state of an atom in a molecule that casts the one-body term as the energy required to promote it to that state from its ground state. The rest of the terms correspond to the individual diatomic, triatomic, etc., fragments. Its application to the atomization energies of the XH _n series, X = C, Si, Ge, Sn and n = 1-4, suggests that the (negative, stabilizing) 2-B is by far the largest term in the MBE with the higher order terms oscillating between positive and negative values and decreasing dramatically in size with increasing rank of the expansion. The analysis offers an alternative explanation for the purported "first row anomaly" in the incremental H _n-1 X-H bond energies seen when these energies are evaluated with respect to the lowest energy among the states of the XH _n molecules. Due to the "flipping" of the ground/first excited state between CH ₂ ( ³ B ₁ ground state, ¹ A ₁ first excited state) and XH ₂ , X = Si, Ge, Sn ( ¹ A ₁ ground state, ³ B ₁ first excited state), the overall picture does not exhibit a "first row anomaly" when the incremental bond energies are evaluated with respect to the molecular states having the same in situ atomic states.