CeO nanorods are functional mimics of natural haloperoxidases. They catalyze the oxidative bromination of phenol red to bromophenol blue and of natural signaling molecules involved in bacterial quorum sensing. Laboratory and field tests with paint formulations containing 2 wt% of CeO nanorods show a reduction in biofouling comparable to Cu O, the most typical biocidal pigment.
Traditional methods for characterizing an optimized molecular structure as a minimum or as a saddle point on the nuclear potential energy surface require the full Hessian. However, if f denotes the number of nuclear degrees of freedom, a full Hessian calculation is more expensive than a single point geometry optimization step by the order of magnitude of f. Here we present a method which allows to determine the lowest vibrational frequencies of a molecule at significantly lower cost. Our approach takes advantage of the fact that only a few perturbed first-order wave functions need to be computed in an iterative diagonalization scheme instead of f ones in a full Hessian calculation. We outline an implementation for Hartree–Fock and density functional methods. Applications indicate a scaling similar to that of a single point energy or gradient calculation, but with a larger prefactor. Depending on the number of soft vibrational modes, the iterative method becomes effective for systems with more than 30–50 atoms.
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