The location of transition states and the calculation of their properties is the central question in studying reaction mechanisms using quantum mechanical procedures. When a reasonable guess at the location of a transition state is known, standard gradient minimizers (such as LTRD and TRUSTG) can be very effective at refining the geometry. Even when a reasonable guess is given, gradient minimizers may still fail. Also, gradient minimizers are not selective and may locate any nearby critical point including local minima or other nearby critical points (inflection points) without regard to their relationship to the reaction path. Reaction coordinate methods (IRC and PATH) can sometimes prove useful for finding transition states, however, these methods generate a series of relatively inexpensive intermediate optimizations and so can fail to locate a saddle point when a non-continuous reaction path is followed. Transition states corresponding to the crossing of electronic states (an avoided crossing) are often responsible for such discontinuities in the reaction path. The CHN methods were developed to overcome many of these difficulties.

CHN (and its predecessor CHAIN) was developed to locate the transition state(s) between a given pair of minima (respectively the reactants and the products of the chemical reaction under study). CHN does not require a guess at the transition state, so avoids the major limitation of local gradient minimizers. Non-local search strategies, such as simulated annealing (MANNEAL, GANNEAL and TSANNEAL), can also find transition states without requiring a guess for the transition state, however, it is impossible to focus the search on just the transition state(s) of interest.

CHN takes as input two or more geometries. Each of the geometries must have the same composition and atom ordering. The first geometry is taken as the reactant (starting point) and the last geometry is taken as the product (ending point). If more than 2 geometries are specified, then they are taken as intermediates on the path between the reactants and the products. (CHAIN is an exception to this rule and expects exactly 3 geometries, which are given in the order: approximate transition state, reactant, and then product.) If OPTIL is specified then the reactant geometry is optimized to a minimum by TRUSTE and if OPTIR is specified then the product geometry is optimized to a minimum. OPTILR or OPTIRL causes both geometries to be optimized.

The first stage of CHN is to generate a series of geometries that form a smooth continuous path between the reactants and products. If more than 2 geometries were supplied by the user, then the generated path will pass through those additional geometries. The generated geometries are approximately evenly spaced, like pearls on a chain (hence the name CHAIN/CHN). Energies and a tentative categorization (type of extrema) of each geometry in the chain is given in the output file. If CHECKCHN is used instead of CHN or FULLCHN, then the program halts at this point. (This can be useful for quickly trying out various options without having to do a full calculation.)

This initial chain (iteration 0) is represented as a series of geometries C(0)=(R,...,p(i),...,P) running from reactants, R, to products, P. Starting with C(n) (the chain at iteration n), the geometries are relaxed in directions perpendicular to the chain path giving rise to a new chain C(n+1) at iteration n+1. During each chain iteration, the geometries are relaxed in directions perpendicular to the chain path. The highest energy point along the path is relaxed by a dedicated trust region method. As the chain evolves, it must regularized so that the distance between successive nodes is neither too small or too large. So, if the distance between nodes becomes too large, a new geometry may be inserted and similarly if the distance between nodes becomes too small, a node may be removed. (The threshold for determining when two nodes are too far apart varies but is printed in the output file.) Next, a new highest energy point along the path is selected and is characterized by using HESSEI. If this geometry contains spurious negative eigenvalues, the geometry is displaced along the eigenvectors corresponding to the spurious eigenvalues. This chain iteration process is then repeated until the chain is converged. If FULLCHN is used, then refinement will take place over the entire chain to isolate all extrema along the path. This is more expensive than just CHN or CHAIN but is particularly useful for multi-step reaction mechanisms.

FORCE or LFORCE may be used along with CHAIN, CHN, or FULLCHN to properly characterize the resulting extrema and to compute their IR frequencies. In the case of FORCE, thermodynamic properties are also computed at each of the extrema. The output file (jobname.out) will contain the limitant (highest energy) transition state along CHN path. Both the archive file (jobname.arc) and the visualization file (jobname.vis) will contain all of the geometries along the path and are useful for visualizing the entire path.

This section contains an alphabetical list of all keywords used with the CHN and CHAIN methods.