The selective advantage of reaction norms for environmental tolerance

A tolerance curve defines the dependence of a genotype's fitness on the state of an environmental gradient. It can be characterized by a mode (the genotype's optimal environment) and a width (the breadth of adaptation). It seems possible that one or both of these characters can be modified in an adaptive manner, at least partially, during development. Thus, we extend the theory of environmental tolerance to include reaction norms for the mode and the width of the tolerance curve. We demonstrate that the selective value of such reaction norms increases with increasing spatial heterogeneity and between-generation temporal variation in the environment and with decreasing within-generation temporal variation. Assuming that the maintenance of a high breadth of adaptation is costly, reaction, norms are shown to induce correlated selection for a reduction in this character. Nevertheless, regardless of the magnitude of the reaction norm, there is a nearly one to one relationship between the optimal breadth of adaptation and the within-generation temporal variation perceived by the organism. This suggests that empirical estimates of the breadth of adaptation may provide a useful index of this type of environmental variation from the organism's point of view

Quantitative wave function analysis for excited states of transition metal complexes

The character of an electronically excited state is one of the most important descriptors employed to discuss the photophysics and photochemistry of transition metal complexes. In transition metal complexes, the interaction between the metal and the different ligands gives rise to a rich variety of excited states, including metal-centered, intra-ligand, metal-to-ligand charge transfer, ligand-to-metal charge transfer, and ligand-to-ligand charge transfer states. Most often, these excited states are identified by considering the most important wave function excitation coefficients and inspecting visually the involved orbitals. This procedure is tedious, subjective, and imprecise. Instead, automatic and quantitative techniques for excited-state characterization are desirable. In this contribution we review the concept of charge transfer numbers---as implemented in the TheoDORE package---and show its wide applicability to characterize the excited states of transition metal complexes. Charge transfer numbers are a formal way to analyze an excited state in terms of electron transitions between groups of atoms based only on the well-defined transition density matrix. Its advantages are many: it can be fully automatized for many excited states, is objective and reproducible, and provides quantitative data useful for the discussion of trends or patterns. We also introduce a formalism for spin-orbit-mixed states and a method for statistical analysis of charge transfer numbers. The potential of this technique is demonstrated for a number of prototypical transition metal complexes containing Ir, Ru, and Re. Topics discussed include orbital delocalization between metal and carbonyl ligands, nonradiative decay through metal-centered states, effect of spin-orbit couplings on state character, and comparison among results obtained from different electronic structure methods.Comment: 47 pages, 19 figures, including supporting information (7 pages, 1 figure