Use Sella steppers and sessions

SellaMinSession uses order-zero quasi-Newton steps. SellaSaddleSession partitions a rational function optimization (RFO) step into uphill and downhill subspaces. Both retain a Hessian model and a trust radius, and expose one outer step at a time.

SellaGeom selects a named geometry or an equality Constraints chart. The steppers project onto the tangent space, retract the displacement, and transport vectors. Cartesian sessions use the rigid quotient when internal molecular modes are available. InternalPes maps host-supplied bonds, angles and dihedrals through the Wilson matrix. CellCartesianPes and CellInternalPes include the active cell entries; their energy and gradients are evaluated in the displaced cell.

TrustRegion limits the Euclidean step norm. RestrictedAtomicStep limits the largest atom displacement and uses that same quantity when updating its radius. MaxInternalStep limits weighted internal coordinates. The restricted atomic step (RAS) refuses an internal-coordinate packing.

An order-1 Cartesian search that diagonalizes the Hessian and whose Euclidean radius is above one distance unit takes that atomic step at max(delta, 0.1). The alpha search follows the derivative of the partitioned RFO step, so the uphill and downhill blocks are not a uniform scale of the full step. Rho grows and shrinks the atomic ceiling. The stored Euclidean radius stays where delta * n_free put it. The first finite-difference diagonalization may accept a negative root past the uphill mode once its residual is under gamma and its curvature is below one. A later diagonalization keeps the relative residual. A free block larger than 128 is diagonalized with faer’s self-adjoint eigensolver. A block of 128 or fewer stays on cyclic Jacobi.

update_h_ms applies a simultaneous multi-secant Hessian update. update_hessian_cols applies individual updates in column order. HessUpdate::TsBfgs supports an indefinite Hessian. The retained Sella trajectories are checked by tests/sella_gold.rs.

SamdSession::new uses Euclidean dynamics. on and with_chart retain a geometry for every step; step_on selects a geometry for one step. The velocity-Verlet displacement, transported velocity and stochastic rescaling remain in its tangent space.

force_match_hessian fits pair contributions from Buckingham, Morse, Lennard-Jones and harmonic bond terms. EigenDevice::Dlpk observes the size, disable and allocation-failure policy. The available eigensolver, QR and projection implementations use the host fallback; selecting that policy does not imply GPU acceleration.