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1. The valence and Rydberg states of dienes

   https://doi.org/10.1039/c9cp06952f  

   Ning, Jiaxin; Truhlar, Donald G. (March 2020, Physical Chemistry Chemical Physics)

   The molecules 1,4-cyclohexadiene (unconjugated 1,4-CHD) and 1,3-cyclohexadiene (conjugated 1,3-CHD) both have two double bonds, but these bonds interact in different ways. These molecules have long served as examples of through-bond and through-space interactions, respectively, and their electronic structures have been studied in detail both experimentally and theoretically, with the experimental assignments being especially complete. The existence of Rydberg states interspersed with the valence states makes the quantum mechanical calculation of their spectra a challenging task. In this work, we explore the electronic excitation energies of 1,4-CHD and 1,3-CHD for both valence and Rydberg states by means of complete active space second-order perturbation theory (CASPT2), extended multi-state CASPT2 (XMS-CASPT2), and multiconfiguration pair-density functional theory (MC-PDFT); it is shown by comparison to experiment that MC-PDFT yields the most accurate results. We found that the inclusion of Rydberg orbitals in the active space not only enables the calculation of Rydberg excitation energies but also improves the accuracy of the valence ones. A special characteristic of the present analysis is the calculation of the second moments of the excited-state orbitals. Because we find that the CASPT2 densities agree well with the CASSCF ones and since the MC-PDFT methods gets accurate excitation energies based on the CASSCF densities, we believe that we can trust these moments as far as giving a more accurate picture of the diffuseness of the excited-state orbitals in these prototype molecules than has previously been available. 

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2. Mixed-Valence Superstructure Assembled from a Mixed-Valence Host–Guest Complex

   https://doi.org/10.1021/jacs.8b05322  

   Liu, Zhichang; Frasconi, Marco; Liu, Wei-Guang; Zhang, Yu; Dyar, Scott M.; Shen, Dengke; Sarjeant, Amy A.; Goddard, William A.; Wasielewski, Michael R.; Stoddart, J. Fraser (July 2018, Journal of the American Chemical Society)
3. Mixed-valence halide perovskites

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   Deschene, Christina R; Zwanziger, Clara; Matheu, Roc; Karunadasa, Hemamala I (September 2025, Coordination Chemistry Reviews)
4. Valence Photoionization and Autoionization of the Formyl Radical

   https://doi.org/10.1021/acs.jpca.1c01775  

   Savee, John D.; Sztáray, Bálint; Welz, Oliver; Taatjes, Craig A.; Osborn, David L. (May 2021, The Journal of Physical Chemistry A)

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5. Behavioral plasticity and the valence of indirect interactions

   https://doi.org/10.1002/ecy.70157  

   Fahimipour, Ashkaan_K; Gil, Michael_A; Hein, Andrew_M (July 2025, Ecology)

   Abstract Behavioral plasticity in animals influences direct species interactions, but its effects can also spread unpredictably through ecological networks, creating indirect interactions that are difficult to anticipate. We use coarse‐grained models to investigate how changes in species behavior shape indirect interactions and influence ecological network dynamics. As an illustrative example, we examine predators that feed on two types of prey, each of which temporarily reduces activity after evading an attack, thereby lowering vulnerability at the expense of growth. We demonstrate that this routine behavior shifts the indirect interaction between prey species from apparent competition to mutualism or parasitism. These shifts occur when predator capture efficiency drops below a critical threshold, causing frequent hunting failures. As a result, one prey species indirectly promotes the growth of the other by relaxing its density dependence through a cascade of network effects, paradoxically increasing predator biomass despite decreased hunting success. Empirical capture probabilities often fall within the range where such dynamics are predicted. We characterize such shifts in the qualitative nature of species interactions as changes ininteraction valence, highlighting how routine animal behaviors reshape community structure through cascading changes within ecological networks. 

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