Atomi polielettronici Flashcards
What is the form of the Slater orbital used in the variational method for a helium atom?
The Slater orbital used in the variational method for a helium atom has the form ϕ(r) = √(ζ^3/πao) * e^(-ζr/ao), where ζ is a variational parameter and ao is the Bohr radius.
What is the effect of the electron-electron interaction on the monoelectronic energies in a helium atom?
The electron-electron interaction affects the monoelectronic energies in a helium atom by reducing the effective nuclear charge seen by each electron.
What is the energy expression obtained using the variational method for a helium atom?
The energy expression obtained using the variational method for a helium atom is E = (ζ^2 - 2Zζ + 5/8ζ) * e^2/ao, where ζ is the variational parameter and Z is the nuclear charge.
What is the purpose of the effective Hamiltonian in treating poly-electronic atoms?
The purpose of the effective Hamiltonian in treating poly-electronic atoms is to simplify the problem by treating each electron as if it were in an effective potential due to the electron-electron interaction.
What is a Slater determinant?
A Slater determinant is a determinant constructed from spin-orbitals that respects the indistinguishability and antisymmetry of electrons and gives the total wave function of a multi-electron system.
What is the difference between the first excited state and the second excited state of helium?
The first excited state has a spin of 1 and corresponds to a triplet state, while the second excited state has a spin of 0 and corresponds to a singlet state.
What is the difference between the first excited state and the ground state of helium in terms of electron configuration?
The first excited state has an electron in a 2s orbital, while the ground state has both electrons in 1s orbitals.stato fondamentale aveva
una parte orbitale simmetrica ed un parte di spin antisimmetrica (= carattere
totale antisimmetrico) le prime due funzioni dello stato eccitato invece hanno
una parte orbitale antisimmetrica ed una parte di spin simmetrica
What is the Eigenvalue of Sz for the last two excited states of helium?
The Eigenvalue of Sz for the last two excited states of helium is 0.
What is the autovalore of Sz for the first two excited states of helium?
The autovalore of Sz for the first two excited states of helium is 1 or -1, corresponding to a triplet state.
Quali sono i valori di Ms per i tre orbitali degeneri
1,-1 e 0
What is the Unsold theorem?
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The Unsold theorem states that in a subshell with a complete set of electrons, the electron density is spherically symmetric, and the potential energy can be approximated as a central potential that depends only on the distance from the nucleus.
What is the effective Hamiltonian in the SCF method?
The effective Hamiltonian in the SCF method is the Hamiltonian that includes the electron-nucleus interaction and the average electron-electron repulsion. It is given by H_eff = -(h^2/2m)∇^2 + V_eff(r), where V_eff(r) is the effective potential energy that depends only on the distance r from the nucleus.
What is the purpose of the SCF method?
The purpose of the SCF method is to calculate the electronic structure of a many-electron system, such as an atom or a molecule, by solving the Schrödinger equation self-consistently.
What is the energy expression for the SCF method?
The total energy of the system in the SCF method is given by E = ∑(i=1 to n) εi - ∑(i=1 to n) ∑(j>i) Jij, where εi is the energy of the i-th electron and Jij is the Coulomb repulsion energy between the i-th and j-th electrons.
What is the Coulomb repulsion energy between two electrons?
The Coulomb repulsion energy between two electrons placed in different orbitals
What is the self-consistent field method?
The self-consistent field method is a method used in the Hartree method to achieve self-consistency by iterating the calculation of the potential and the wave functions until the eigenvalues no longer change.
What is the self-consistent field method?
The self-consistent field method is a method used in the Hartree method to achieve self-consistency by iterating the calculation of the potential and the wave functions until the eigenvalues no longer change.
What is the purpose of the Hartree method?
The purpose of the Hartree method is to solve the Schrödinger equation for a many-electron atom by treating each electron as if it moves in an average field created by all the other electrons.
What is the center field approximation in the Hartree method?
The center field approximation in the Hartree method is when the potential is mediated on the angles so that it depends only on r.
What is the starting defect in the Hartree approach?
The starting defect in the Hartree approach is that it completely overlooked spin.
What is the operator of Fock?
The operator of Fock is an effective monoelectronic Hamiltonian containing kinetic energy, nucleus electron interaction, and potential effective due to all other electrons.
What is the advantage of Roothan’s idea in the Hartree-Fock method?
The advantage of Roothan’s idea in the Hartree-Fock method is that it transforms the problem from the solution of integro-differential equations of Fock to the solution of a system of homogeneous linear equations.
What is the formula for the system energy in the Hartree-Fock method?
The formula for the system energy in the Hartree-Fock method is E = 2∑i hi(1) + ∑ij (2Jij - Kij).
What is the iterative treatment in the Hartree-Fock method?
he iterative treatment in the Hartree-Fock method involves choosing initial (orbital) functions, obtaining new orbitals with which to recalculate a new Fock operator and then new functions, etc., until the functions do not change further in two successive cycles.
What is the third term in the formula for the system energy in the Hartree-Fock method?
The third term in the formula for the system energy in the Hartree-Fock method is the sum of the exchange supplements, which has no simple interpretation from a classical perspective.
What is the significance of the vector model of the atom?
Explain how the vector model of the atom is useful for understanding the angular momentum total of a polyelectron atom.
