SD/CG Optimization

Overview

The SD/CG optimizer is a hybrid steepest-descent / conjugate-gradient method with optional DIIS (Direct Inversion in the Iterative Subspace) acceleration. It begins with a steepest descent phase to rapidly reduce large forces, then automatically switches to the conjugate gradient algorithm for more efficient convergence near a minimum. DIIS extrapolation can be applied periodically to further accelerate convergence.

This method is invoked with the keyword sdcg. The individual phases (SD, CG, DIIS) can be independently enabled or disabled via parameters, allowing the user to run pure steepest descent (cg_enabled=false, diis_enabled=false), pure conjugate gradient (sd_enabled=false), or any combination.

Parameters

Parameter	Type	Default	Description
`max_step`	float	`0.2`	Maximum step length in Angstrom.
`max_iter`	int	`256`	Maximum number of optimization cycles.
`write_traj`	bool	`False`	Write intermediate geometries to a trajectory file.
`traj_every`	int	`1`	Write trajectory frame every N steps.
`verbose`	int	`1`	Output verbosity level.
`sd_enabled`	bool	`True`	Enable steepest descent phase.
`cg_enabled`	bool	`True`	Enable conjugate gradient phase.
`sd_max_iter`	int	`50`	Max iterations for the initial SD phase.
`cg_switch_fmax`	float	`0.0`	Switch from SD to CG when max force drops below this value.
`cg_restart_threshold`	float	`0.2`	Restart CG directions when gradient change exceeds this ratio.
`cg_beta_method`	str	`"prp+"`	Conjugate gradient beta formula.
`diis_enabled`	bool	`True`	Enable DIIS extrapolation acceleration.
`diis_store_every`	int	`5`	Store DIIS snapshot every N steps.
`diis_min_snapshots`	int	`3`	Minimum snapshots before DIIS extrapolation is attempted.
`diis_memory`	int	`6`	Maximum number of DIIS snapshots stored.

Input Example

A complete input file using the SD/CG optimizer with default parameters:

#model=ani2x
#opt(method=sdcg)
#device=gpu0

O    0.000000    0.000000    0.117300
H    0.000000    0.757200   -0.469200
H    0.000000   -0.757200   -0.469200

When to Use SD/CG

Initial rough optimization: When the starting geometry is far from any minimum and contains large steric clashes or unreasonable bond lengths, the SD phase can quickly reduce the worst forces before the CG phase takes over for efficient convergence.
Very far from the minimum: In the early stages of optimization where the energy surface is steep and nearly linear, the SD phase is just as efficient as higher-order methods and considerably cheaper per step.
When L-BFGS oscillates: If L-BFGS enters a cycle of large oscillating steps, SD/CG can provide a more stable convergence path by combining gradient-only steps with conjugate gradient refinement.
Pure SD or pure CG: Disable one phase to run a single method. Set cg_enabled=false and diis_enabled=false for pure steepest descent, or sd_enabled=false for pure conjugate gradient.

Note

For production-quality geometry optimizations, L-BFGS (the default) is generally preferred due to its superior convergence near minima. SD/CG is most useful as a pre-optimizer for severely distorted structures or when L-BFGS has difficulty converging.