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Multiconfiguration second‐order perturbation theory approach to strong electron correlation in chemistry and photochemistry

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Rooted in the very fundamental aspects of many chemical phenomena, and for the majority of photochemistry, is the onset of strongly interacting electronic configurations. To describe this challenging regime of strong electron correlation, an extraordinary effort has been put forward by a young generation of scientists in the development of theories ‘beyond’ standard wave function and density functional models. Despite their encouraging results, a twenty‐and‐more‐year old approach still stands as the gold standard for these problems: multiconfiguration second‐order perturbation theory based on complete active space reference wave function (CASSCF/CASPT2). We will present here a brief overview of the CASSCF/CASPT2 computational protocol, and of its role in our understanding of chemical and photochemical processes. © 2011 John Wiley & Sons, Ltd.

Figure 1.

Division of the orbital space into three subspaces: inactive, active, and virtual orbitals. The inactive orbitals are fully occupied and the virtual orbitals are unoccupied. Within the active orbitals, a full list of so‐called configuration state functions, with the required space and spin symmetry, is constructed.

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Figure 2.

Statistical evaluation of CASPT2 studies published in the last five years (in %). Different aspects were analyzed: the chemical nature of the molecules (a), the fields of application (b), the techniques employed to simulate the environment (c), and the type of work (d) (216 papers considered).39

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Figure 3.

Scheme of the main photophysical and photochemical molecular processes occurring after the Absorption (Abs) of nonionizing radiation, and ionization phenomena. Transition states (TS) connect different points of the potential energy surfaces. Reactions can occur along the excited state surface (photoadiabatic reactions) or jumping between surfaces in regions of near degeneracy (nonadiabatic reactions), such as conical intersections (CI), singlet triplet crossings (STC), and singlet doublet crossings (SDC). Radiative deactivation in the photophysical and photochemical processes can take place by fluorescence (F) or phosphorescence (P), whereas nonradiative relaxations are associated to internal conversion (IC) and intersystem crossing (ISC) phenomena. Electron attachments (I) and detachments (I+) are processes involving the formation of anion and cation species, respectively.

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Figure 4.

Scheme of different photophysical and photochemical processes taking place in a pair of π‐stacked canonical pyrimidine nucleobases after UV irradiation: the formation of excimers (Bioexc), the photoproduction of cyclobutane pyrimidine dimers (CBP) via the conical intersection of the dimer (CIdim), the photoreversibility of the photodimers, and the energy deactivation through the conical intersection located in the monomers (CImon). Energies (in eV) correspond to the vertical absorption of single nucleobases (red) and CBPs (green). CC (top) and TT (bottom) structures shown as an illustration. Detailed information can be found in Refs 60–62.

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Figure 5.

Schematic reaction paths for three small models of the firefly‐luciferin molecule: 1,2‐dioxetane, 1,2‐dioxetanone, and thiazole‐substituted dioxetanone. (Reprinted with permission from Refs 75–77. Copyright 2011 American Chemical Society.)

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Figure 6.

Chemical structure of the meso‐triphenyl corrole Cu(TCP) molecule. This transition‐metal complex is an example of a large molecular structure studied at the CASPT2 level of theory (see Ref 89).

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Figure 7.

Active molecular orbitals contributing to the quintuple bond in the molecule of diuranium. The occupation numbers are given in the figure (see Ref 92).

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Figure 8.

Two examples of biological systems studied at the CASPT2/MM level of theory: the cytosine dimer in a dG18·dC18 double strand in water (left) and the oxyluciferin molecule in the luciferase protein (right). Both nucleobases in the highlighted dinucleotide (left) are treated at the CASPT2 level, while the remaining nucleic acid and water molecules are included in the MM part. In the case of the oxyluciferin‐luciferase system, the MM atoms allowed to move during the CASPT2/MM geometry optimizations are shown: the surrounding residues (green) to the QM subsystem (oxyluciferin) and the closest water molecules (red and white).

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