Matsika_ExcStMCC - Electronic Structure for Electronic...

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Electronic Structure for Electronic Structure for Excited States Excited States ( ( multiconfigurational multiconfigurational methods) methods) Spiridoula Matsika Spiridoula Matsika
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Excited Electronic States Excited Electronic States • Theoretical treatment of excited states is needed for: – UV/Vis electronic spectroscopy – Photochemistry – Photophysics • Electronic structure methods for excited states are more challenging and not at the same stage of advancement as ground state methods – Need balanced treatment of more than one states that may be very different in character – The problem becomes even more complicated when moving away from the ground state equilibrium geometry
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Excited states configurations Excited states configurations Singly excited conf. Doubly excited conf. Ground state
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- + Singlet CSF Triplet CSF Configurations can be expressed as Slater determinants in terms of molecular orbitals. Since in the nonrelativistic case the eigenfunctions of the Hamiltoian are simultaneous eigenfunctions of the spin operator it is useful to use configuration state functions ( CSFs )- spin adapted linear combinations of Slater determinants, which are eigenfunctiosn of S 2
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Excited states can have very different Excited states can have very different character and this makes their balanced character and this makes their balanced description even more difficult. For example description even more difficult. For example excited states can be: excited states can be: • Valence states • Rydberg states • Charge transfer states
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Rydberg Rydberg states states • Highly excited states where the electron is excited to a diffuse hydrogen-like orbital • Low lying Rydberg states may be close to valence states • Diffuse basis functions are needed for a proper treatment of Rydberg states, otherwise the states are shifted to much higher energies • Diffuse orbitals need to be included in the active space or in a restricted active space (RAS)
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Potential Energy Surfaces and Potential Energy Surfaces and Excited States Excited States Vert. Abs. Vert. Emis . Adiabatic exc.en. Energy coordinate For absorption spectra one is interested in the Franck Condon (FC) region. In the simplest case a single point calculation is used to give vertical excitation energies
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When one is interested in the photochemistry and photophysics of molecular systems the PES has to be explored not only in the FC region but also along distorted geometries. Minima, transition states, and conical intersections need to be found (gradients for excited states are needed) Energy Reaction coordinate TS TS CI CI
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Electronic structure methods for Electronic structure methods for excited states excited states • Single reference methods Δ SCF, Δ (DFT), Δ (CI),… – TDDFT – EOM-CCSD • Multi-reference methods – MCSCF – CASPT2, MR-MP2 – MRCI
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• In the simplest case one can calculate excited state energies as energy differences of single-reference calculations.
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This note was uploaded on 12/07/2011 for the course CHEM 350 taught by Professor Duanejohnson during the Summer '06 term at University of Illinois, Urbana Champaign.

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Matsika_ExcStMCC - Electronic Structure for Electronic...

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