Complex Absorbing Potentials with Voronoi Isosurfaces Wrapping Perfectly around Molecules

Complex absorbing potentials (CAPs) are imaginary potentials that are added to a Hamiltonian to change the boundary conditions of the problem from scattering to square-integrable. In other words, with a CAP, standard bound-state methods can be used in problems involving unbound states such as identifying resonance states and predicting their energies and lifetimes. Although in wave packet dynamics, many CAP forms are used, in electronic structure theory, the so-called box-CAP is used almost exclusively, because of the ease of evaluating its integrals in a Gaussian basis set. However, the box-CAP does has certain disadvantages. First, it will, e.g., break the symmetry of C-nv, molecules if n is odd and the main axis is placed along the z-axis by the standard orientation of the electronic structure code. Second, it provides a CAP starting at the smallest box around the entire molecular system. For larger molecules or clusters, which do not fill the space efficiently, that implies that much dead space within the molecule will be left, where there is neither a CAP nor a sufficient description with basis functions. Here, two new CAP forms are introduced and systematically explored: first, a Voronoi-CAP (that is, a CAP defined in each atom's Voronoi cell), and second, a smooth Voronoi-CAP (which is similar to the Voronoi-CAP; however, the noncontinuously differentiable behavior at the surfaces between the Voronoi cells is smoothed out). Both have isosurfaces that are similar to the cavities used in solvation modeling. An obvious disadvantage of these two CAPs is that the integrals cannot be obtained analytically, but must be computed numerically. However, Voronoi-CAPs share the advantage of having the same symmetry as the molecular system, and, more importantly, considerably facilitate the treatment of larger molecules with asymmetric side chains and of molecular clusters.