UT theoretical chemistry code forum

Hi, everyone,

the dimer method is a min-mode following method for finding transition state.
but I don't understand why follow the local min curvature mode on PES will
lead to a saddle point? Can anyone give some hints on it?

Min-mode following methods follow the lowest mode up the potential and down all other modes. When the method converges, it is at a maximum along the lowest mode and a minimum in all other directions. This is the definition of a first order saddle point.

well, it makes sense. Thank you.
And if one follows the second lowest mode, when converge, is it a first-order saddle point?

Yes, if you maximize in that direction, minimize in all other directions, and allow the mode you are following to become the lowest mode.

how can a second lowest mode become the lowest mode,
if I keep rotational force normal to the lowest mode during the dimer rotation to find the second lowest mode?

by the way, don't you need some sleep, if you are in US?

You are right, I'm up much too late.

It seems to me that the method you are describing is a bit ill-posed. See, if you always find the lowest two modes and follow the second lowest one uphill, you need to say what you are going to do along the lowest mode. If you maximize along that modes as well, you will converge to a second order saddle.

But, if you want to maximize along the second lowest curvature mode and minimize along the lowest curvature then you are asking for something that can not converge. The problem is that as you minimize along the lowest curvature mode, it will eventually become a minimum so that the mode will be positive. But since you are maximizing along another mode to a maximum, that mode must be negative, and therefor lower than what you were calling the lowest mode. And, if you press on with the method, always following the second lowest mode uphill, I expect that you will not converge.

The point is that if you are maximizing along one mode and minimizing along all others, this will lead to a first order saddle and the mode that you are maximizing along must be a negative mode when you reach a stationary point.

Thank you for your instructive explanation. I understand now.