Thanks for this great channel, you already supported many hundreds of chemical students at technical university of Graz to properly understand this topic. I really try to understand, can you again point out: The hamiltonian operator is the theoretical solution for the energy of the wave functions (but unsolvable). But for the Hartree Fock Theory to become solved we use a fock-operator which distinguishes between 1e- operator and 2e- operator, whereof the latter is solvable only approximately and we can devide it into coulomb and exchange integral and these depend on the specific molecule, since there are different interactions possible. The strategy to solve the 2e- part is to do this shady mean field thing, which again is a approximation like "the root mean square of the forces acting on the electrons". Please correct me, if it seems as I did not understand. Thanks in advance for responding!
Awesome, but I didn’t quite get the meaning of the exchange operator... I understand it comes from indistinguishability but what effect does it have on the energy eigenvalues, put into words?
Hi Luis. The exchange operator is quite complicated to visualize, as it does not have a direct classical analog. Roughly speaking, the effect of exchange is that in order to avoid occupying the same physical state, electrons are repelled even more strongly than predicted by the Coulomb force, and the net effect is to slightly push apart the electron density clouds, thus slightly decreasing their repulsion energy because they are farther apart. Notice that there is a negative sign, though exchange integrals are typically smaller in magnitude than Coulomb integrals (due to weak overlap within the complex conjugate and orbital within each electron). This means that exchange can only serve to lower the amount of electron repulsion energy in the system.
okay I got it's due to mean field but J need 2 wave functions on the right to operator right? your green equation on right has only 1 electrons wave fucntion
how to understand this mean field experienced by other electrons? Is this mean field for classical point particles like in electrostatics? But here We represent electrons by wavefunctions (probability density). Is the average of potential of the form (V12+V23+V13)/3 for 3-electron system with each electron fixed at each point?
The electrostatics experienced between pairs of electrons can be viewed in the same way as the electrostatics between classical electric charge distributions. Whether a single point particle or a field of charge density, the operator is the same. The potential energy is q1 * q2 / r12 for a pair of point particles. It's density1 * density2 / r12 integrated over all xyz1 and xyz2 for a pair of charge densities. Electrostatics is a pairwise force, so there is no potential energy for anything beyond 2-body interactions. The only time we need to concern ourselves with more than 2 particles in electronic structure theory is because we are using *approximate* methods for the 2 body interactions, and overcoming some of those shortcomings with higher-order terms.
Hi Zineb. Electronic correlation is the difference between the exact electron repulsion energy and the Hartre--Fock electron repulsion energy. Hartree-Fock approximates electrons as not repelling each other based on their explicit locations, but based on their average charge density spread over all space. In reality, the location of electron 1 affects the charge density of electron 2, electron 3, ..., electron N, and this approximation is not exact. The electrons "correlate" their motions to more effectively avoid each other, and reduce their overall repulsion energy based on their explicit positions.
Your explanation remembers me to London-interaction (induced dipole - induced dipole interaction) from the chapter of intermolecular forces within a gerneral chemistry course.
Thanks for this great channel, you already supported many hundreds of chemical students at technical university of Graz to properly understand this topic.
I really try to understand, can you again point out:
The hamiltonian operator is the theoretical solution for the energy of the wave functions (but unsolvable).
But for the Hartree Fock Theory to become solved we use a fock-operator which distinguishes between 1e- operator and 2e- operator, whereof the latter is solvable only approximately and we can devide it into coulomb and exchange integral and these depend on the specific molecule, since there are different interactions possible.
The strategy to solve the 2e- part is to do this shady mean field thing, which again is a approximation like "the root mean square of the forces acting on the electrons".
Please correct me, if it seems as I did not understand.
Thanks in advance for responding!
Awesome, but I didn’t quite get the meaning of the exchange operator... I understand it comes from indistinguishability but what effect does it have on the energy eigenvalues, put into words?
Hi Luis. The exchange operator is quite complicated to visualize, as it does not have a direct classical analog. Roughly speaking, the effect of exchange is that in order to avoid occupying the same physical state, electrons are repelled even more strongly than predicted by the Coulomb force, and the net effect is to slightly push apart the electron density clouds, thus slightly decreasing their repulsion energy because they are farther apart. Notice that there is a negative sign, though exchange integrals are typically smaller in magnitude than Coulomb integrals (due to weak overlap within the complex conjugate and orbital within each electron). This means that exchange can only serve to lower the amount of electron repulsion energy in the system.
Thanks!!
I know I am pretty off topic but does anyone know of a good site to watch newly released movies online ?
in the previous video, J, K were having 2 indices now why it's only one here?
okay I got it's due to mean field but J need 2 wave functions on the right to operator right? your green equation on right has only 1 electrons wave fucntion
how to understand this mean field experienced by other electrons? Is this mean field for classical point particles like in electrostatics? But here We represent electrons by wavefunctions (probability density). Is the average of potential of the form (V12+V23+V13)/3 for 3-electron system with each electron fixed at each point?
The electrostatics experienced between pairs of electrons can be viewed in the same way as the electrostatics between classical electric charge distributions. Whether a single point particle or a field of charge density, the operator is the same. The potential energy is q1 * q2 / r12 for a pair of point particles. It's density1 * density2 / r12 integrated over all xyz1 and xyz2 for a pair of charge densities. Electrostatics is a pairwise force, so there is no potential energy for anything beyond 2-body interactions. The only time we need to concern ourselves with more than 2 particles in electronic structure theory is because we are using *approximate* methods for the 2 body interactions, and overcoming some of those shortcomings with higher-order terms.
@@TMPChem Thanks..
Plz what is an electronic correlation ?
Hi Zineb. Electronic correlation is the difference between the exact electron repulsion energy and the Hartre--Fock electron repulsion energy. Hartree-Fock approximates electrons as not repelling each other based on their explicit locations, but based on their average charge density spread over all space. In reality, the location of electron 1 affects the charge density of electron 2, electron 3, ..., electron N, and this approximation is not exact. The electrons "correlate" their motions to more effectively avoid each other, and reduce their overall repulsion energy based on their explicit positions.
@@TMPChem oh thank u so much
Your explanation remembers me to London-interaction (induced dipole - induced dipole interaction) from the chapter of intermolecular forces within a gerneral chemistry course.
@@jw3983 London dispersion is indeed a part of the correlation energy!