Perhaps the most significant difficulty in locating transition states is to obtain a good initial guess of the geometry to feed into a surface walking algorithm. This difficulty becomes especially relevant for large systems, where the search space dimensionality is high. Interpolation algorithms are promising methods for locating good guesses of the minimum energy pathway connecting reactant and product states, as well as approximate saddle point geometries. For example, the nudged elastic band method [426, 427] and the string method [428] start from a certain initial reaction pathway connecting the reactant and the product state, and then optimize in discretized path space towards the minimum energy pathway. The highest energy point on the approximate minimum energy pathway becomes a good initial guess for the saddle point configuration that can subsequently be used with any local surface walking algorithm.

Inevitably, the performance of an interpolation method heavily relies on the choice of the initial reaction pathway, and a poorly chosen initial pathway can cause slow convergence, or convergence to an incorrect pathway. The freezing string [429, 430] and growing string methods [431] offer elegant solutions to this problem, in which two string fragments (one from the reactant and the other from the product state) are grown until the two fragments join. The freezing string method offers a choice between Cartesian and Linear Synchronous Transit (LST) interpolation methods. It also allows users to choose between conjugate gradient and quasi-Newton optimization techniques. It can be invoked by (JOBTYPE = FSM) using the following *$rem* keyword:

FSM_NNODE

Specifies the number of nodes along the string

TYPE:

INTEGER

DEFAULT:

Undefined

OPTIONS:

N

number of nodes in FSM calculation

RECOMMENDATION:

15. Use 10 to 20 nodes for a typical calculation. Reaction paths that connect multiple elementary steps should be separated into individual elementary steps, and one FSM job run for each pair of intermediates. Use a higher number when the FSM is followed by an approximate-Hessian based transition state search (Section 9.7).

FSM_NGRAD

Specifies the number of perpendicular gradient steps used to optimize each node

TYPE:

INTEGER

DEFAULT:

Undefined

OPTIONS:

N

number of perpendicular gradients per node

RECOMMENDATION:

4. Anything between 2 and 6 should work, where increasing the number is only needed for difficult reaction paths.

FSM_MODE

Specifies the method of interpolation

TYPE:

INTEGER

DEFAULT:

2

OPTIONS:

1

Cartesian

2

LST

RECOMMENDATION:

2. In most cases, LST is superior to Cartesian interpolation.

FSM_OPT_MODE

Specifies the method of optimization

TYPE:

INTEGER

DEFAULT:

Undefined

OPTIONS:

1

Conjugate gradients

2

Quasi-Newton method with BFGS Hessian update

RECOMMENDATION:

2. The quasi-Newton method is more efficient when the number of nodes is high.

References [429] and [430] provide a guide to a typical use of this method. The following example input will be helpful for setting up the job:

**Example 9.198**

$molecule 0 1 Si 1.028032 -0.131573 -0.779689 H 0.923921 -1.301934 0.201724 H 1.294874 0.900609 0.318888 H -1.713989 0.300876 -0.226231 H -1.532839 0.232021 0.485307 **** Si 0.000228 -0.000484 -0.000023 H 0.644754 -1.336958 -0.064865 H 1.047648 1.052717 0.062991 H -0.837028 0.205648 -1.211126 H -0.8556026 0.079077 1.213023 $end $rem jobtype fsm fsm_ngrad 3 fsm_nnode 12 fsm_mode 2 fsm_opt_mode 2 method b3lyp basis 6-31G $end

The *$molecule* section should include geometries for two optimized intermediates separated by **** symbols. The order of the atoms is important, as Q-Chem will assume atom X in the reaction complex moves to atom X in the product complex. The FSM string is printed out in the file ‘stringfile.txt’, which is an XYZ file containing the structures connecting reactant to product. Each node along the path is labeled with its energy. The highest energy node can be taken from this file and used to run a TS search, as detailed in section 9.1. If the string returns a pathway that is unreasonable, double check whether the atoms in the two input geometries are in the correct order.