Position Operator in Trigonal lattice

For a trigonal lattice Wannier90 will choose different shells depending on the lattice angle. For certain angles there are two plausible choices, eg

 +----------------------------------------------------------------------------+
 |                    Distance to Nearest-Neighbour Shells                    |
 |                    ------------------------------------                    |
 |          Shell             Distance (Ang^-1)          Multiplicity         |
 |          -----             -----------------          ------------         |
 |             1                   0.694489                      6            |
 |             2                   0.834672                      2            |
 |             3                   0.845305                      6            |
 |             4                   1.102143                      6            |
 |             5                   1.281969                      6            |
 |             6                   1.302703                      6            |

We could choose shells 1 and 2 (8 b-vectors), or shells 1 and 3 (12 b-vectors). By default Wannier90 chooses the inner most shells, (ie 1 and 2). Below we compare the two choices. As expected, by using the inner most shells the position operator is closer to the true position operator (smaller b-vectors) but the position operator is less spherically symmetric (fewer b-vectors). But the differences are small and I would conclude that either choice is ok (using the inner shells requires 4/12 fewer operations).

(c) 2006 Jonathan Yates