electronic structure theory Flashcards
wavefunction depends on coordiantes of all
electrons and all nuclei
wlwctrons are very light compared to nuclie which means they
move much faster
born-oppenheimer approximaiton
nuclei as fixed in space and electrons can then be viewed as moving within the fixed nuclear framework
withon the born-oppenheimer approximation the nuclei can be regarded as moving on the
potenial energy surface
nuclear wavefunction depends on ell the
nucleir and describes nuclear motion
electronic wavefunction depends on all the
electrons and E_e is the elcetronic energu
as nuclear coordinates vary the …. and … will change
electronic wavefunction and electronic energy
total wavefunction is
nuclear wavefunciton times electronic wavefunction
spin orbital is a combination of
spatial orbitals and spin functions
spin orbital tells us the
postion and spin of an electron
electronic wavefunction depends on the
space-spin coordinates of all electrons
From the pauli principle it must be
antisymmetric with respect to exchange of electrons
the electronic wavefunction must change sign if we interchange the
space-spin coordinates of any two electrons
antisymmetric wavefunctions can be easily represented using
determinants
restriced hartree-fock theory
approximating electronic wavefunction by a single slater determinant and restrict spatial orbitals occupied by alpha electrons to be the same as the spatial orbitals occupied by the beta electrons
total electronic energy is the expectation value of the
lectronic hamiltonian
V_nn is the
nuclear - nuclear repulsion energy
exchange energy is an energy
lowering that arises from the Pauli requirment that the electronic wavefunction be antisymmetric
2 electrons of like spin cannot be at the same point in space so there is a
reduction in electron repulsion and energy lowering is the exchange energy
the exchange energy is an energy lowering (reduction in repulsion) that arises from the
Pauli requirement that the electronic wavefunction by antisymmetric
exclusion principle 2 electrons of same spin
cannot be at same point in space
like-spin electrons avoid one another which means there is a reduction in
electron repulsion
variartion principle state the best orbitals are ones that
minimise energy
sum of orbital energies does not equal the
total electronic energy
the ionisation potential to remove an electron from orbital whilst leaving all other orbitals unchanged is the negative of the
ith Hartree-Fock orbital energy
Kartree fock analysis ignores
relaxation of the orbitlas
in reality orbital will adjust and the energy of the cation will
reduce
The true Hart-ree - fock ionsiation potential tend to be too small due to
neglect of electron correlation