I used CASTEP to calculate the modulus of aluminum metal. To do this I followed the tutorial for calculation of Elastic Modulus of BN. However, the calculated shear modulus values are significantly different for Voigt, Reuss predictions. The modulus values are also sensitive to geometry optimisation. (the tutorial says that geometry optimisation is not necessary). The values are given below:

Without Geometry Optimisation:

                              Voigt                    Reuss               Hill

Bulk Modulus          77.48                    77.48               77.48

Shear Modulus        -66.94                   24.37               -21.28

With Geometry Optimisation:

Bulk Modulus          62.9                    62.9                    62.9

Shear Modulus        5.2                      3.8                      4.5

The experimental values for aluminum are Bulk Modulus=76 and  Shear Modulus=26

The bulk modulus is predicted very well without geometry optimisation. However Shear Modulus is good only with Reuss model.

Why is the modulus calculated after geometry optimisation so different from experimental?

Why are  the shear modulus values negative?