A critical geometry searcher

critics can search for:

• minimum
• saddle point
• minimum energy crossing

For now saddle point search is only a local search by minimizing the norm of gradient

cmake -DCMAKE_C_COMPILER=icc -DCMAKE_CXX_COMPILER=icpc -DCMAKE_PREFIX_PATH=~/Software/Mine/diabatz/tools/v0/critics/libadiabatz ~/Software/Mine/critics/

We minimize the total energy of the crossed states

E = E1 + E2

subject to

C = (E2 - E1)^2

This definition of E and C avoids the discontinuity arisen from the interchange between 1 and 2

We carry out this constrained optimization by augmented Lagrangian method

We minimize the augmented Lagrangian by a line search method, e.g. the BFGS quasi-Newton method in our implementation

Once we reach the degenerate seam, we may should remove the projections of the search direction on g and h