I got really confused at the algorithm of self-consistent loop in ELK. Anyone can help me to understand why the energy at each step keeps increasing to the fully relaxed ground-state? e.g., in a case of two Al atoms in a large box, the TOTENERGY.OUT is like,
-485.514183787
-485.501237409
-485.479853108
-485.452378201
-485.424358805
-485.401402902
-485.386124799
-485.377643940
-485.373334063
-485.370978895
-485.369443677
-485.368355484
-485.367649304
-485.367268902
-485.367090200
-485.367015601
-485.366986485
-485.366977491
According to the variational principle, starting from a random wavefunction or charge density, going through the sc loops, the energy will slowly reduce to find its minimum, which is the ground state.I want to use this first step energy and expect it is a higher energy than ground-state. But why ELK goes the opposite way? If the first step energy is lower than ground-state energy, it means it is even more stable than ground-state. Did I miss something here?
Thanks.
Best,
Fei
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Summing up: total energy is variational, you just have to look at the correct properties. You looked at the total energy of a density which get's closer in each iteration to be the solution of the Kohn-Sham equation, but the process of solving the Kohn-Sham equation does not provide variational energies (Why? You try to solve an equation by solving it over and over again feeding back the output as input with the hope to find its solution -> self-consistent field (scf) method). However, the scf solution itself is variational with respect to a change of the initial conditions, e.g. the atomic position. If you displace one atom from its equilibrium position then the total energy will be higher.
Best,
Marc
p.s. your argument would be true, if the starting density would have been a solution of the specific Kohn Sham equation. But in fact, it is not.
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Dear Users of ELK,
I got really confused at the algorithm of self-consistent loop in ELK. Anyone can help me to understand why the energy at each step keeps increasing to the fully relaxed ground-state? e.g., in a case of two Al atoms in a large box, the TOTENERGY.OUT is like,
-485.514183787
-485.501237409
-485.479853108
-485.452378201
-485.424358805
-485.401402902
-485.386124799
-485.377643940
-485.373334063
-485.370978895
-485.369443677
-485.368355484
-485.367649304
-485.367268902
-485.367090200
-485.367015601
-485.366986485
-485.366977491
According to the variational principle, starting from a random wavefunction or charge density, going through the sc loops, the energy will slowly reduce to find its minimum, which is the ground state.I want to use this first step energy and expect it is a higher energy than ground-state. But why ELK goes the opposite way? If the first step energy is lower than ground-state energy, it means it is even more stable than ground-state. Did I miss something here?
Thanks.
Best,
Fei
Hi Fei,
this issue has already been discussed in the forum:
https://sourceforge.net/p/elk/discussion/897820/thread/ae2fd149/
Summing up: total energy is variational, you just have to look at the correct properties. You looked at the total energy of a density which get's closer in each iteration to be the solution of the Kohn-Sham equation, but the process of solving the Kohn-Sham equation does not provide variational energies (Why? You try to solve an equation by solving it over and over again feeding back the output as input with the hope to find its solution -> self-consistent field (scf) method). However, the scf solution itself is variational with respect to a change of the initial conditions, e.g. the atomic position. If you displace one atom from its equilibrium position then the total energy will be higher.
Best,
Marc
p.s. your argument would be true, if the starting density would have been a solution of the specific Kohn Sham equation. But in fact, it is not.