Intrinsic-reaction-coordinate calculations

The potential energy profiles along the intrinsic reaction coordinate (IRC) can be computed via the method of Hratchian and Schlegel. The algorithm starts from the transition state and propagates the system via the damped-velocity-Verlet algorithm. The damping is realized via rescaling the velocity vector to a constant value ($v_0$) after each propagation step. At the same time, the time step is adaptively changed so as to ensure that the trajectory generated by the algorithm does not differ from true IRC by more than the predefined tolerance factor $\Delta_0$. As an input, the structure of a well-relaxed transition state and the direction of the unstable vibration mode must be provided. For that purpose, a CONTCAR file from an improved-dimer-method calculation converged with a tight relaxation criterion (e.g., EDIFFG =-0.005) can be used. To obtain a complete energy profile along the IRC connecting two stable states, two independent calculations with positive (IRC_DIRECTION =1) and negative (IRC_DIRECTION =-1) initial displacement along the direction of the unstable mode must be performed.

The following parameters can be modified to affect the performance of the method:

• IRC_DIRECTION direction of the initial displacement (-1|1 – negative|positive)
• IRC_STOP the number of steps the energy must monotonously increase before the algorithm terminates. In order to avoid a premature termination, especially close to transition states., e.g., due to numerical noise, IRC_STOP should always be greater than 1.
• IRC_DELTA0 the tolerance factor $\Delta_0$ in Å
• IRC_MINSTEP specifies the lower limit for the time step in fs
• IRC_MAXSTEP specifies the upper limit for the time step in fs
• IRC_VNORM0 the value of $v_0$ in Å/fs - the smaller the value, the closer the computed trajectory follows the true IRC (but the more ionic steps are required, which might be a limitation if the calculation is performed at a DFT level)

Mind: This method is presently available only for fixed cell shape (i.e., ISIF = 2) simulations.

Mind: The calculation must be initialized from a very well-relaxed transition state (EDIFFG = -0.005 or less in absolute value).

Mind: This type of calculation can be also performed at the MLFF level.

Practical example

As practical example, let us consider the SN2 reaction of CH₃Cl with Cl^- for which we wish to determine potential energy profile along IRC using machine learned forcefield trained to reproduce PBE density functional approximation. We start the calculation from the transition state relaxed using the improved dimer method, whereby the the POSCAR file:

transition state for the SN2 reaction of CH3Cl with Cl-
  1.00000000000000
   12.0000000000000000    0.0000000000000000    0.0000000000000000
    0.0000000000000000   12.0000000000000000    0.0000000000000000
    0.0000000000000000    0.0000000000000000   12.0000000000000000
  C    H    Cl
    1     3     2
Direct
 0.5850650254630181  0.5521044454893749  0.6939500251126378 ! coordinates for atom 1
 0.6199714578785893  0.5165819974397312  0.6189988121747090
 0.5118385673731038  0.5154158337385569  0.7312325135004583
 0.6234250004218902  0.6242616689446465  0.7316356130927977
 0.4726193332894725  0.6677493610140370  0.5868908173955205
 0.6974674608307720  0.4364952304710423  0.8011882402360213 ! coordinates for atom N
! converged unstable direction:
 0.50537765E+00 -0.51655518E+00  0.48200174E+00 ! components for atom 1
-0.26853934E-01  0.27542504E-01 -0.21367401E-01
-0.39750994E-01  0.43340248E-01 -0.39357020E-01
-0.43940173E-01  0.39852778E-01 -0.40927560E-01
-0.20387434E+00  0.20937607E+00 -0.17421377E+00
-0.19095817E+00  0.19644356E+00 -0.20613597E+00 ! components for atom N

Related tags and articles

IRC_DIRECTION, IRC_STOP, IRC_DELTA0, IRC_MINSTEP, IRC_MAXSTEP, IRC_VNORM0