The Newton-Raphson method works well if the initial geometry is close to a stationary point, but may not work well if it is not.
Also, technically the method
may be difficult to use for some types of problem.
Technical difficulties
arise because of the need to calculate the Hessian, which is a potentially very
large matrix (no. of variables squared)
· calculation of
the second derivatives can be demanding (requiring a lot of computer time)
· storage can be
difficult (a lot of computer memory required)
· Hessian must
be inverted (diagonalized), problem for more than 1000 variables (1000 ´ 1000 matrix),
i.e. approx. 300 atoms
Can avoid calculating the Hessian matrix
at every step by
· using a
guessed matrix (e.g. the identity matrix)
· by using a
Hessian update scheme (constructs an approximate Hessian based on e.g. the
gradient and coordinates at current and new points) - various update schemes
have been developed
Calculating the Hessian at a lower level of theory can also reduce the demands of the calculation:
For example,
can calculate a more approximate Hessian by ‘molecular mechanics’, which could
be used in a geometry optimization with an ‘ab initio’ electronic structure
method. (Calculation of the Hessian
matrix for an ab initio method could be very time-consuming).