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

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

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

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

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

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

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

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

9. excited state quantum chemistry simple (but incorrect) CAS expansion simple (but incorrect) CAS expansion ground state S 0 ground state S 0 excited state S 1 excited state S 1 optimize 2 nd root optimize 2 nd root

10. electronic transitions in QM/MM diabatic surface hopping diabatic surface hopping - t 1 : - t 2 : - t 3 : - t 4 : - swap electronic states