We let compounds between a 3d transition metal (M) and a nonmetal X (X=C,N,O,S) be characterized by three parameters: the average number of valence electrons per atom (

n_{e}

), the average volume per atom (Ω), and the logarithmically averaged atomic mass (

M_{eff)}

. Three quantities with the dimension of energy are then considered: the cohesive energy

E_{coh}

of the compound, its enthalpy of formation

Δ^{0}

H, and $FTHETA sub S— is a Debye temperature, properly defined to give the vibrational entropy at high temperatures. Remarkably accurate empirical relations are found between

n_{e}

on one hand and

E_{coh}

, Δ

{}^{0}H

, and

E_{S}

. For compounds MX of the NaCl crystal structure one can understand the correlation from the electron band structure of (p-d)-bonded systems. We then extend the correlation to carbides and nitrides of more complex structure, for which not much is known about the electron states. The relation between

E_{S}

and

n_{e}

is of particular importance, since it allows an estimate of cohesive properties and the vibrational entropy in systems where there is no, or uncertain, experimental information. The correlations are applied to e.g., a study of the phase stability of the NaCl structure for large

n_{e}

and to the estimation of the standard entropies

{}^{0}S

and enthalpies of formation Δ

{}^{0}H

of various nitrides, carbides, and oxides. We also demonstrate how our method can be coupled with the so-called CALPHAD (‘‘calculation of phase diagrams’’) work.

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