Refinement: B restraints in proportion to B (Kullback-Leibler form) with contacts, an own ADP weight, overall B into the atoms

- B similarity: E = (B_i - B_j)^2 / (kappa^2 B_i B_j), the symmetric Kullback-Leibler divergence of two
  isotropic Gaussians (Murshudov et al. 2011), so sigma = kappa sqrt(B_i B_j) instead of a fixed 1.5-4.5 A^2.
  kappa 0.1 / 0.133 / 0.2 / 0.3 for main-chain bonded / angle-related and side-chain pairs (REFMAC's logs list
  sigma ~0.1 B for main-chain bonded pairs at B 11-140; the ratios are those of the old sigmas, which these
  equal at B = 15). New class: atoms within 4 A that no bond or angle relates, waters and symmetry mates
  included, kappa 0.5 (BuildBContacts, sharing the neighbour search with BuildRepulsions). CPU and GPU.
- The B factors' X-ray weight is balanced on its own (BalancedADPWeight: B-restraint over X-ray B-gradient on
  the model with B shaken by 20%) instead of being a multiple of the positional weight; the ladder tries B held
  and refined at that weight, the trajectory's B steps divide and multiply it by four, positional steps and the
  final ladder leave it.
- Before each B-refining macro-cycle the overall isotropic B of the scale moves into the atoms and the
  solvent's B (F_model unchanged), so the two do not drift against each other.
Tried and not kept: xyz and B as one L-BFGS vector (the B block scaled by its curvature, the positions by the
median X-ray curvature): no better than alternation with a memory per block on 12 starts (mean R-free 0.265
vs 0.262), worse on 7arr/7d98; a refit before each B step: no gain for +20-40% time.

Refinement battery MD starts, median R-free by the REFMAC 0-cycle scorer, previous commit -> this (REFMAC to
convergence): 5f6m x8 0.167 -> 0.167 (0.168), 8dqb x8 0.291 -> 0.294 (0.284), 7arr x4 0.270 -> 0.278 (0.311),
11if x4 0.245 -> 0.244 (0.251), 5reo x4 0.312 -> 0.258 (0.261: the ladder no longer keeps B held where B is the
model's largest error), 7d98 x4 0.342 -> 0.335 (0.361). Deposited models: unchanged (B stays held there).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_015CeEGgpKdfkCTJb3YNMJcu
(cherry picked from commit ed292f35b482b696d81f71f1d97e0016ca05b144)

image_analysis/structure_refinement/RefinementMath.h

@@ -19,7 +19,7 @@
 // What a restraint is, for the evaluators on either side (RefinementRestraints.h builds them).
 enum class RestraintKind : int { Bond = 0, Angle, Torsion, Chiral, Plane, Repulsion, BSimilarity };
 
-// One restraint. E = ((value - ideal) / sigma)^2, summed over a set.
+// One restraint. E = ((value - ideal) / sigma)^2, summed over a set (BSimilarity: sigma is kappa, BSimilarityTerm).
 struct RestraintRecord {
     int kind = 0;
     int atom[4] = {0, 0, 0, 0};   // Plane: atom[0] the first of its atoms in plane_atoms, atom[1] their number
@@ -199,6 +199,18 @@ REFINE_HD inline T RepulsionTerm(V3<T> a, V3<T> b, T d0, T sigma, V3<T> g[2]) {
     return r * r;
 }
 
+// Two atoms' B alike in proportion to their size: the symmetric Kullback-Leibler divergence of two isotropic
+// Gaussians of variances B_i and B_j over kappa^2 (up to a factor), E = (B_i - B_j)^2 / (kappa^2 B_i B_j) - a
+// difference restraint whose sigma is kappa sqrt(B_i B_j). Sets dE/dB_i and dE/dB_j.
+// Following Murshudov et al. (2011) Acta Cryst. D67, 355-367 (the Kullback-Leibler form of the ADP restraints)
+template <typename T>
+REFINE_HD inline T BSimilarityTerm(T bi, T bj, T kappa, T &gi, T &gj) {
+    const T k2 = kappa * kappa, d = bi - bj;
+    gi = d * (bi + bj) / (k2 * bi * bi * bj);
+    gj = -d * (bi + bj) / (k2 * bi * bj * bj);
+    return d * d / (k2 * bi * bj);
+}
+
 // The unit eigenvector of the smallest eigenvalue of a symmetric 3x3 matrix (a00 a11 a22 a01 a02 a12), by
 // cyclic Jacobi rotations.
 template <typename T>