C 1 1 2 and C 1 1 2_1 are the only two monoclinic settings whose change of
basis from the reference has determinant 1/2, and the reason is physical:
with unique axis c the C-centring vector lies wholly in the oblique a-b
plane and reduces away. Such a group is never a distinct Bravais centring -
it is a primitive lattice written on twice the cell - and it wins the
candidate table only because the table is scored on that doubled cell,
where half the reflection positions are absent by construction.
Refusing to enumerate those settings was measured and is worse: the
volume-preserving alternative keeps the by-construction absences as real
observations and merges no better than P1. So keep the enumeration as it
is and act on the win instead: halve the cell, re-classify in the group's
own system, carry the reflections across (the invented positions map to
non-integral indices and are dropped, which is what the centred candidate
was already doing) and search again there.
Measured on one rotation crystal: C 1 1 2_1 on 68.6 73.0 170.3 90 90 90
becomes P 1 2_1 1 on 50.1 170.3 50.1 90 93.5 90, exactly the deposited
setting, with every merge statistic unchanged (R_meas 0.1209, CC1/2 0.9979,
d_min 1.238) and ISa 18.27 -> 18.31. Stable across +/-0.5 mm of detector
distance. Eight other crystals are bit-identical, and across 112 stored
battery reports exactly one adopts a volume-doubling setting.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EFEJG6WBQv8th4UJFNe53N
leonarski_fandClaude Opus 5
3a30dc8ab5
