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
