Last Updated: 2025-12-18

1. Mode-Following RS-I-RFO (MF-RS-I-RFO)#

Overview#

This is an algorithm for Saddle Point Optimization that proceeds by tracking a specific Hessian mode. Based on the conventional RS-I-RFO method, it incorporates tracking logic to prevent mode swapping between steps.

Implementation Details#

• Mode Tracking Strategy: Uses the ModeFollowing class to calculate the overlap with the Hessian eigenvectors of the previous step.
• Mass-Weighted Overlap (MWO): If an atom list is provided, the projection is performed in the mass-weighted coordinate system rather than Cartesian coordinates, achieving physically valid tracking.
• Adaptive Update (EMA): Uses Exponential Moving Average (EMA) to dynamically update the reference vector, allowing the method to follow mode rotation.
• Gradient Bias: Adds the overlap in the direction of the current force (gradient) to the score, prioritizing the selection of energetically significant modes.

Command Line Arguments (-opt)#

Detailed parameters are specified using colons : within the -opt argument string.

• Basic Format: -opt mf_rsirfo:<target_index>:<ema_val>:<grad_val>
• Parameters:
  • target_index: The index of the eigenvalue to track (starting from 0).
  • ema<val>: Update rate (0.0 to 1.0). 1.0 for full replacement (adaptive), 0.0 for fixed.
  • grad<val>: Weighting for the gradient direction.

Usage Example:#

# Execute transition state geometry optimization tracking mass-weighted mode 1, 
# with an adaptive update rate of 0.5 and a gradient bias of 0.3.
python optmain.py input.xyz -opt mwmf_rsirfo_fsb:1:ema0.5:grad0.3 -fc 5 -order 1 -freq -tcc

2. Constrained RS-I-RFO (C-RS-I-RFO)#

Overview#

A method for performing saddle point searches using RS-I-RFO while imposing geometric constraints (bond distances, angles, etc.).

Implementation Details#

• Subspace Projection: Uses Singular Value Decomposition (SVD) to construct a “null space basis” orthogonal to the imposed constraints.
• Constrained Optimization: Projects the full-space gradient and Hessian onto this subspace and calculates the RFO step within it. This calculates the movement vector to the saddle point while maintaining the constraints.
• SHAKE-like Correction: Includes geometric adjustment logic to correct deviations in constraints due to numerical errors.

Command Line Arguments (-opt, -pc)#

Specify crsirfo family methods with -opt and define constraints with -pc.

Usage Example:#

# Geometry optimization while fixing the distance between atoms 1 and 2, and the angle of atoms 2-3-4.
python optmain.py input.xyz -opt crsirfo_block_fsb -pc bond 1,2 bend 2,3,4

3. Integration of Multiple PES Information and Model Function Optimization (BITSS, etc.)#

Overview#

A feature to perform geometry optimization on an “effective potential” constructed by combining energies or gradients from multiple electronic states (PES). Specifically, version 1.20.3 implements the Binary-Image Transition State Search (BITSS) method.

Implementation Details#

• Independent Calculator Instances: ModelFunctionHandler creates independent directories and calculators for State1 and State2 to prevent interference between states.
• BITSS Implementation:
  • 6N-Dimensional Expansion: Concatenates two structures (Image 1 & 2) and treats them as a $6N \times 6N$ Hessian and a $2N$ atom system.
  • Second Derivative (Hessian): Mathematically derives the second derivatives for distance and energy equality constraint terms and implements them as the calc_hess method.

Command Line Arguments (-mf)#

Use the -mf argument to specify the type of model function and accompanying parameters (the file path of the reference structure in the case of BITSS).

Usage Example:#

# Search for a pathway connecting two points using the BITSS method, with target.xyz as the target structure.
python optmain.py start.xyz -mf bitss target.xyz

# Minimum energy seam of crossing (MESX) using Seam Model Function (between charge 0, multiplicity 1 and 3 states)
python optmain.py input.xyz -mf opt_meci 0 3 -elec 0 -spin 3

Note: Internal Data Structure Changes#

• OptimizationState: In BITSS mode, element_list and geometry are automatically expanded to double size (2N).
• Hessian Integration: Model_hess (derived from PES) and bias_hessian (derived from constraint/penalty terms) are managed separately and summed just before being passed to the optimizer.

References#

• J. Chem. Phys. 157, 124107 (2022)
• J. Am. Chem. Soc. 2015, 137, 10, 3433–3445