Density functional electronic structure calculations have been carried out on Sc, Y

and RE orthophosphates and oxides, and h- and o’-P2O5 polymorphs to calculate the

electronic heats of formation 'Ee

f

ox(0). Calculated heats of formation are systematically

approximately 40 kJ/mol less exothermic than measured 'H

f

ox(298.15). The systematic

error is not uniform with large deviations for Gd(m) (-64.7 kJ/mol) and Ce(m) (-27.6

kJ/mol). For systems where low-temperature heat capacity data are available, H(298.15)-

H(0) corrections are estimated to be less than 1 kJ/mol. Empirical estimates for ZPE of

orthophosphate and oxide phases are nearly independent of atomic number, and give a 0-

+12 kJ/mol correction to the 'Ee

f

ox(0). Ab initio calculation of the zero-point correction

for formation of YPO4, based on the computed vibrational spectrum of YPO4 and Y2O3,

gives 'ZPE and '[H(298.15)-H(0)] close to zero. Thus the origin of the 40 kJ/mol

discrepancy between the measured values of 'H

f

ox(298.15) and calculated values of

'Ee

f

ox(0) appears to be electronic in origin. DFT+U calculations for Ce2O3 and CePO4

make only a 3 kJ/mol correction, indicating that the systematic difference cannot be

corrected by including electron correlation at the DFT+U level. The observed correlation

between atomic number and heat of formation results from the lanthanide contraction and

the localized charge on the oxide anion relative to the phosphate anion and can be

reproduced from the simplest ionic model.

This is probably no longer relevant to the original poster, but for the benefit of future readers:

To compute the formation energy of a material (or chemical) you need to know first what you are going to form the material from. In the example in the question, we wish to form Pd_x Zr_y from pure Pd and pure Zr. The equation is:

E_f(Pd_x Zr_y) = E(Pd_x Zr_y) - x.E(Pd) - y.E(Zr)

so you need to perform three CASTEP calculations:

1. Compute the ground state energy per atom of bulk Pd metal; this is E(Pd)

2. Compute the ground state energy per atom of bulk Zr metal; this is E(Zr)

3. Compute the ground state energy per formula unit of Pd_x Zr_y; this is E(Pd_x Zr_y)

Once you have those three quantities, you can use the equation to compute the formation energy. (Note that we've neglected entropy etc. for simplicity.)

The cohesive energy is exactly the same calculation, except that your reference for Pd and Zr is the isolated atom, rather than the elemental solid.

Of course, you might be interested in the formation energy with respect to a different alloy composition Pd_a Zr_b, in which case you'd need to do something like either:

(a) E_f(Pd_x Zr_y) = E_f(Pd_x Zr_y) - (x/a).E(Pd_a Zr_b) - (y-(xb)/a).E(Zr)

or

(b) E_f(Pd_x Zr_y) = E_f(Pd_x Zr_y) - (y/b).E(Pd_a Zr_b) - (x-(ya)/b).E(Pd)

depending on whether the new alloy composition has a greater fraction of Zr or Pd.