Use of Fisher information in quantum chemistry

AbstractThe classical Fisher information concept is generalized to cover the complex probability amplitudes (wave functions) of quantum mechanics. Its contributions due to the probability and probability‐current densities are identified. General properties of this local information measure are examined and the Schrödinger functional for the kinetic energy is interpreted as the average Fisher information. The information current and source densities are introduced in terms of which the relevant continuity equation is formulated, expressing the local balance of the information content. The superposition principles for the particle probabilities, probability currents, and the Fisher information densities are examined. The interference (nonadditive) contributions to these quantities due to the quantum mechanical mixing of individual states are identified. An illustrative application of using the nonadditive Fisher information of the atomic orbital (AO) resolution in indexing the chemical bond within the 2‐AO model is presented. This AO‐phase sensitive index is capable of distinguishing the bonding, nonbonding, and antibonding electronic states, as do the familiar bond‐orders of quantum