The current version of the EF optimization routine is a combination of the original EF algorithm of Simons et al. (J. Phys. Chem. 89, 52) as implemented by Baker (J. Comp. Chem. 7, 385) and the QA algorithm of Culot et al. (Theo. Chim. Acta 82, 189), with some added features for improving stability.
The geometry optimization is based on a second order Taylor expansion of the energy around the current point. At this point the energy, the gradient and some estimate of the Hessian are available. There are three fundamental steps in determining the next geometry based on this information:
The acceptance criteria used is that the actual/predicted ratio should be larger than RMIN, which for the default value of RMIN=0 is equivalent to a lower energy. If the ratio is below RMIN, the step is rejected, the trust radius reduced by a factor of two and a new step is predicted. The RMIN, RMAX and OMIN features has been introduced in the current version of EF to improve the stability of TS optimizations. Setting RMIN and RMAX close to one will give a very stable, but also very slow, optimization. Wide limits on RMIN and RMAX may in some cases give a faster convergence, but there is always the risk that very poor steps are accepted, causing the optimization to diverge. The default values of 0 and 4 rarely rejects steps which would lead to faster convergence, but may occasionally accept poor steps. If TS searches are found to cause problems, the first try should be to lower the limits to 0.5 and 2. Tighter limits like 0.8 and 1.2, or even 0.9 and 1.1, will almost always slow the optimization down significantly but may be necessary in some cases.
In minimum searches it is usually desirable that the energy decreases in each iteration. In certain very rigid systems, however, the initial diagonal Hessian may be so poor that the algorithm cannot find an acceptable step larger than DDMIN, and the optimization terminates after only a few cycles with the "TRUST RADIUS BELOW DDMIN" warning long before the stationary point is reached. In such cases the user can add DDMIN=0.0 and RMIN set to some negative value, say -10, thereby allowing steps which allow the energy to increase. An alternative is to use LET DDMIN=0.0.
The algorithm has the capability of following Hessian eigenvectors other than the one with the lowest eigenvalue toward a TS. Such higher mode following are always much more difficult to make converge. Ideally, as the optimization progresses, the TS mode should at some point become the lowest eigenvector. Care must be taken during the optimization, however, that the nature of the mode does not change all of a sudden, leading to optimization to a different TS than the one desired. OMIN has been designed for ensuring that the nature of the TS mode only changes gradually, specifically the overlap between to successive TS modes should be higher than OMIN. While this concept at first appears very promising, it is not without problems when the Hessian is updated.
As the updated Hessian in each step is only approximately correct, there is a upper limit on how large the TS mode overlap between steps can be. To understand this, consider a series of steps made from the same geometry (e.g. at some point in the optimization), but with steadily smaller step-sizes. The update adds corrections to the Hessian to make it a better approximation to the exact Hessian. As the step-size become small, the updated Hessian converges toward the exact Hessian, at least in the direction of the step. The old Hessian is constant, thus the overlap between TS modes thus does not converge toward 1, but rather to a constant value which indicate how well the old approximate Hessian resembles the exact Hessian. Test calculations suggest a typical upper limit around 0.9, although cases have been seen where the limit is more like 0.7. It appears that an updated Hessian in general is not of sufficient accuracy for reliably rejecting steps with TS overlaps much greater than 0.80. The default OMIN of 0.80 reflects the typical use of an updated Hessian. If the Hessian is recalculated in each step, however, the TS mode overlap does converge toward 1 as the step-size goes toward zero, and in this cases there is no problems following high lying modes.
Unfortunately setting RECALC=1 is very expensive in terms of computer time, but used in conjecture with OMIN=0.90 (or possibly higher), and maybe also tighter limits on RMIN and RMAX, it represents an option of locating transitions structures that otherwise might not be possible. If problems are encountered with many step rejections due to small TS mode overlaps, try reducing OMIN, maybe all the way down to 0. This most likely will work if the TS mode is the lowest Hessian eigenvector, but it is doubtful that it will produce any useful results if a high lying mode is followed. Finally, following modes other than the lowest toward a TS indicates that the starting geometry is not "close" to the desired TS. In most cases it is thus much better to further refined the starting geometry, than to try following high lying modes. There are cases, however, where it is very difficult to locate a starting geometry which has the correct Hessian, and mode following may be of some use here.