1 / 10

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
Télécharger la présentation

molecular quantum mechanics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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:

More Related