Transition states (index-1 saddle points) play a crucial role in determining
the rates of chemical transformations but their reliable identification
remains challenging in many applications. Deterministic global optimization
methods have previously been employed for the location of transition states
(TSs) by initially finding all stationary points and then identifying the TSs
among the set of solutions. We propose several regional tests, applicable to
general nonlinear, twice continuously differentiable functions, to accelerate the
convergence of such approaches by identifying areas that do not contain any
TS or that may contain a unique TS. The tests are based on the application of
the interval extension of theorems from linear algebra to an interval Hessian
matrix. They can be used within the framework of global optimization methods
with the potential of reducing the computational time for TS location. We
present the theory behind the tests, discuss their algorithmic complexity and
show via a few examples that significant gains in computational time can be
achieved by using these tests.