- #1
Derivator
- 149
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Hi folks,
Hartree Fock theory tells us, that the energy functional [itex]<\Psi|H|\Psi>[/itex] where [itex]\Psi[/itex] is a single Slater determinant is minimized by using spin orbitals [itex]\phi_i[/itex] that fulfill the Hartree Fock equations [itex]f_i \phi_i = \epsilon_i \phi_i[/itex].
Since the Fock operator [itex]f_i[/itex] depends on the solution, the hartree fock equations are solved in a self consistent iteration. That is, for an N-particle Slater determinant, one starts with N guessed spin-orbitals, uses these guessed spin orbitals to calculate the fock operator, then one solves the eigenvalue problem given by this guessed fock operator, obtains new spin orbitals, calculates a new fock operator and so on... until there is no difference between input and output spin orbitals.
My question:
Suppose, you have guessed N spin-orbitals and have obtained an initial fock operator [itex]\tilde f_i[/itex]. Then you want to solve the eigen-problem [itex]\tilde f_i \phi_i = \epsilon_i \phi_i[/itex] to obtain N new spin orbitals [itex]\phi_i[/itex]. However solving [itex]\tilde f_i \phi_i = \epsilon_i \phi_i[/itex] will give you an infinite number of spin orbitals. Which of them will you use to construct your new fock matrix?
best,
derivator
Hartree Fock theory tells us, that the energy functional [itex]<\Psi|H|\Psi>[/itex] where [itex]\Psi[/itex] is a single Slater determinant is minimized by using spin orbitals [itex]\phi_i[/itex] that fulfill the Hartree Fock equations [itex]f_i \phi_i = \epsilon_i \phi_i[/itex].
Since the Fock operator [itex]f_i[/itex] depends on the solution, the hartree fock equations are solved in a self consistent iteration. That is, for an N-particle Slater determinant, one starts with N guessed spin-orbitals, uses these guessed spin orbitals to calculate the fock operator, then one solves the eigenvalue problem given by this guessed fock operator, obtains new spin orbitals, calculates a new fock operator and so on... until there is no difference between input and output spin orbitals.
My question:
Suppose, you have guessed N spin-orbitals and have obtained an initial fock operator [itex]\tilde f_i[/itex]. Then you want to solve the eigen-problem [itex]\tilde f_i \phi_i = \epsilon_i \phi_i[/itex] to obtain N new spin orbitals [itex]\phi_i[/itex]. However solving [itex]\tilde f_i \phi_i = \epsilon_i \phi_i[/itex] will give you an infinite number of spin orbitals. Which of them will you use to construct your new fock matrix?
best,
derivator