A symmetric orthogonal transformation applied to molecular geometry optimizations constrained on a hypersphere

In a recent paper Celani et al. (Chem. Phys. Lett. 243 (1995) 1) presented a method to perform constrained geometry optimization of stationary points on the surface of a hypersphere which uses the parameterization of a unitary matrix. Employing a rank-1 symmetric orthogonal transformation we present an algorithm that has some analogy with the algorithm of Celani et al. The method is applied to the calculation of the intrinsic reaction coordinate reaction path of an elementary reaction.