The joint probability density functions of the normalized structure amplitudes of the structure and the model (i.e.,y_N andy_p^c) are derived for triclinic crystals containing heavy atoms (1, 2 and many) by taking the model to consist of the heavy atoms and a part of the light atoms in the unit cell. These functions are derived for the two cases where the model is completely correct (i.e., the related case) and where the model is completely wrong (i.e., the unrelated case) in terms of the fractional contributions to the local mean intensity from the heavy atoms and all known atoms (i.e., σ_1h^/2 and σ₁²) as parameters. These functions are then used to obtain the theoretical local values of 〈y_N〉 and 〈|y_Nⁿ − σ₁ⁿ(y_P^c)ⁿ|〉,n=1, 2. A method of using these results to compute the theoretical overall values ofR(F) andR(I) for the related and unrelated cases is briefly described. A comparison of the observed values of these indices with their theoretical values for the related and unrelated cases would help in determining the correctness of the proposed trial structure.

Theoretical expressions of 〈y_N〉, 〈|y_N − σ₁y_P^c |〉 and 〈|y_N² −σ₁² (y_P^c)²|〉 (wherey_N andy_P^c are the normalized structure amplitudes of the structure and the model respectively) are derived in terms of the heavy atom contributionσ₁² for monoclinic and orthorhombic crystals containing a few (i.e., 1 or 2) heavy atoms of the same kind per asymmetric unit by taking the heavy atom part alone as the model. Results are obtained for both the related and unrelated cases. The local values of 〈y_N〉 and 〈|y_Nⁿ − σ₁ⁿ (y_P^c)ⁿ|〉, (n=1, 2) calculated from these expressions can be used to calculate the overall values of the conventionalR-indicesR(F) andR(I) for the related and unrelated cases. These overall values could be used to check the correctness of heavy atoms located in the structure.

Theoretical expressions for the overall values of the conventional discrepancy indicesR(F) andR(I) are derived for a non-centrosymmetric crystal with a centrosymmetric group by taking the centrosymmetric group and a part of the other atoms in the unit cell as the trial structure. These results are used to obtain tables of values of these indices in terms of the parameter σ_1c² and σ₁² which define the fractional contribution to the local mean intensity from the centrosymmetric group and all the known atoms respectively.