While second-order methods are robust, we have already pointed out in section 7.1.1 that Hessians might be expensive to compute. The *OPTIMIZE module therefore provides first-order methods for locating transition states, where approximate rather than exact Hessians are used. The step control method is, however, the same trust-region image optimization.
When locating transition states it is important to have a good description of the mode that should be maximized (i.e. have a negative eigenvalue). It is therefore not recommended to start off with a simple model Hessian, but rather to calculate the initial Hessian analytically. Alternatively it can be calculated using a smaller basis set/cheaper wave function and then be read in. The minimal input for a transition state optimization using *OPTIMIZE is:
**DALTON INPUT .OPTIMIZE *OPTIMIZE .SADDLE **WAVE FUNCTIONS .HF **END OF DALTON INPUTThis will calculate the Hessian at the initial geometry, then update it using Bofill's update [35] (the BFGS update is not suitable since it tends towards a positive definite Hessian). As for minimizations, redundant internal coordinates are used by default for first-order methods.
It is highly recommended that a Hessian calculation/vibrational analysis be performed once a stationary point has been found, to verify that it's actually a first-order transition state. There should be one and only one negative eigenvalue/imaginary frequency.
If no analytical second derivatives (Hessians) are available, it is still possible to attempt a saddle point optimization by starting from a model Hessian indicated by the keyword .INIMOD:
**DALTON INPUT .OPTIMIZE *OPTIMIZE .INIMOD .SADDLE **WAVE FUNCTIONS .HF **END OF DALTON INPUTProvided the starting geometry is reasonably near the transition state, such optimization will usually converge correctly. If not, it is usually a good idea to start from different geometries and also to try to follow different Hessian modes, as described in section 7.1.2 (through the .MODE keyword).