Broken dynamical symmetry condition to control a chemical reaction by the complex coordinate (t, t′) method

Using the (t, t′) formalism [J. Chem. Phys. 99 (1993) 4590] combined with the complex coordinate method, exact (i.e. not perturbative) condition for control of a model chemical reaction is derived regardless of the field intensity and whether the electromagnetic field is time-periodic or not. We prove that upon breaking the dynamical symmetry H(p, x, t) = H(-p, -x, + T/2), the dissociation channel of the A + BA ← ABA → AB + A reaction can be controlled. It is shown that when the molecular/field interaction is given by p ̂_zf(t), where f(t) represents the electromagnetic field, the dissociation channel of the A + BC ← ABC → AB + C reaction can be controlled by breaking the dynamical symmetry property, f(t) = -f(t + T/2). For time-periodic fields T is the time period (i.e. one optical cycle) where for pulsed lasers it is the duration of the pulse. Numerical examples are given for symmetric and asymmetric model Hamiltonians subjected to two cw lasers. These numerical examples illustrate the role of the phase difference between the cw lasers, regardless of the laser intensity, in the coherent control procedure which was first proposed by Brumer and Shapiro [Chem. Phys. Letters 126 (1986) 54].