# Compute minimum energy paths from arbitrary positions on the potential energy surface

The minimum energy path is a useful concept in understanding chemical reaction paths. As I understand it, such MEP's are most often computed to verify that a transition state structure connects two minima of interest. Several algorithms exist for computing MEP's, but I suppose all have in common that they are able to follow the gradient.

I am in a situation where I think it would be useful to follow the gradient, but not from a TS structure. Can this be done? I think the IRC functionality of software expects to follow the gradient in two directions, and demand the reaction vector.

Is there a simple and common way of computing MEP's from arbitrary positions on the PES? (I will use Molcas). What would happen if I just do a geometry optimization from the arbitrary position? It is my understanding that geometry optimization algorithms displace the atoms in the direction of the force, and in that way a lower energy is guaranteed for each successive step. But will this actually follow the gradient?

• theory.cm.utexas.edu/vtsttools/neb.html – permeakra Apr 27 '16 at 12:30
• >What would happen if I just do a geometry optimization from the arbitrary position? || More or less. Usually some extrapolation techniques are used to improve convergence speed. – permeakra Apr 27 '16 at 12:31
• I am not sure, but have a look at technique like metadynamics? You can map entire potential energy surface on it. But I am not sure about MOLCAS – ipcamit Apr 27 '16 at 16:31
• Not all optimization follows the gradient! Actually you should be able to do this with IRC. – Greg Feb 17 '17 at 16:09

There are some possibilities here:

1. The negative of the gradient of a function always points to the direction of optimal descent (for a discussion, see here). A method that simply follows the gradient is called first order. As permeakra pointed out, extrapolation techniques are commonly used for optimizations. This is because we take finite steps in the PES and this introduces the risk of "jumping" over the minima. Better approximations are either second order in nature (e.g., the Hessian matrix is calculated in each step) or quasi-second order (the Hessian matrix is approximated or approximately updated).

In order to simply follow the gradient you want the steepest descent-like, first order method with probably a very small maximum step and this can be accomplished by setting the Hessian or the Hessian approximation equal to the identity matrix. In ORCA (I have never used Molcas, sorry) for example you may use (source):

! Opt
%geom
inhess unit
update noupdate
step qn
end

2. permeakra also cited the Nudged Elastic Band, which is used for finding minimum energy paths connecting two structures. This might be very useful and is available for instance in VASP and in NWChem (free).

3. You may also want to take a direction from one Hessian eigenvector. This is commonly associated with a molecular vibrational degree of freedom. This may be accomplished with NWChem.

If you just want to go down the PES from an arbitrary geometry without any jumping, solution 1. is probably the one you want.