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molecular quantum mechanics

molecular quantum mechanics. one electron functions. - electron has cartesian and spin coordinates. - no spin operator in electronic hamiltonian. cartesian and spin coordinates are decoupled. - spinfunction s ( s ) defines the spin state. two spin states possible:. , or.

margaret-walton
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molecular quantum mechanics

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  1. molecular quantum mechanics • one electron functions - electron has cartesian and spin coordinates - no spin operator in electronic hamiltonian cartesian and spin coordinates are decoupled - spinfunction s(s) defines the spin state two spin states possible: , or - spatial part (x,y,z) is a molecular orbital max. two electrons (Pauli principle) , and

  2. molecular quantum mechanics • molecular orbitals - linear combination of atomic orbitals - e.g. H2 ;

  3. molecular quantum mechanics • atomic orbitals - combination of simple spatial functions Slater-type orbitals: gaussian-type orbitals: ai and bi are constants: basisset (sto-3g, 3-21g, 6-31g*, ..) - mimic atomic s,p,d,… orbitals e.g. sto-3g basisset (2D)

  4. molecular quantum mechanics • atomic orbitals - combination of simple spatial functions Slater-type orbitals: gaussian-type orbitals: ai and bi are constants: basisset (sto-3g, 3-21g, 6-31g*, ..) - mimic atomic s,p,d,… orbitals e.g. sto-3g basisset (3D)

  5. molecular quantum mechanics • Hartree-Fock wavefunction - anti-symmetric product of molecular orbitals - molecular orbitals - atomic orbitals with fixed coefficients (basisset) • optimization of MO coefficents cji - variation principle - find cji that minimize the energy

  6. molecular quantum mechanics • Hartree-Fock based methods • Hartree Fock wavefunction as starting point mean field approach: no electron correlation • MCSCF (CI, CASSCF) • perturbation theory (MP2, MP4, CASPT2) • high demand on computational resources • alternative methods • semi-empirical methods • density functional theory methods

  7. excited state quantum chemistry • Hartree-Fock approximation for ground state 2n electrons • all are optimized (self-consistent field) • no static/dynamic correlation

  8. excited state quantum chemistry • Complete Active Space SCF or • and are optimized simultaneously • resolves (part of) static correlation • excited states

  9. excited state quantum chemistry • simple (but incorrect) CAS expansion • ground state S0 • excited state S1 • optimize 2nd root

  10. electronic transitions in QM/MM • diabatic surface hopping - t1: - t2: - t3: - swap electronic states - t3: - t4:

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