Skip to main content
10 votes
Accepted

Are there non-antisymmetric solutions to the electronic Hamiltonian?

So, your question is "are the solutions of the Schrödinger equation guaranteed to be anti-symmetric functions, or is this an ad hoc assumption resulting from knowledge of the anti-symmetry ...
Susi Lehtola's user avatar
  • 19.7k
8 votes
Accepted

Why is chemical bond dissociation difficult to simulate?

Some hints : all methods that attempt to describe the ground state of a many-body electronic system are often reduced to one electron in a mean-field or effective potential that includes the effects ...
M06-2x's user avatar
  • 916
8 votes
Accepted

Acceleration of 8110823001207866000 m/s^2 by using Coulomb's law: did I do it right?

The other answer correctly pointed out that using $F=ma$ and the mass of the hydrogen atom does not give the exact $a$, and even if one uses the correct relativistic formulas and the correct mass, one ...
wzkchem5's user avatar
  • 9,670
7 votes

To what extent can coarse-grained models retain the essential quantum mechanical characteristics of a system?

Generally, in multi-scale modelling, QM characteristics are irrelevant. Most of the processes that we study for these multi-scale modelling are thermodynamics driven. So, I will be very surprised if ...
Roshan Shrestha's user avatar
7 votes

Acceleration of 8110823001207866000 m/s^2 by using Coulomb's law: did I do it right?

"It rises the question, if Columb's law can be useful at such small/atomic scales?" Coulomb's law still plays a role in the Hamiltonian of an atom, but your discussion of "force" ...
Nike Dattani - No Free Time's user avatar
6 votes

Are there non-antisymmetric solutions to the electronic Hamiltonian?

There are several things to notice here. First, the Hamiltonian you wrote is not a completed definition of an operator, since it lacks boundary conditions. This means that there's no eigenproblem yet. ...
Ruslan's user avatar
  • 161
5 votes
Accepted

How do I get the energy, if I have the wavefunction?

"For a known wave function, should I not be able to determine the energy?" The wavefuncton is an eigenfunction of the Hamiltonian, and the energy is a corresponding eigenvalue of the same ...
Nike Dattani - No Free Time's user avatar
5 votes

Is the electron-electron interaction to blame, for the added complexity of using "orbitals" for an N-electron system?

Interpreting the question For a 1-electron system, wavefunctions and orbitals are the same thing. For a 2-electron system, or any N-electron system with N>1, we can use "orbitals" to ...
Nike Dattani - No Free Time's user avatar
5 votes
Accepted

How to check whether spin orbit coupling is strong or weak?

In quantum mechanics, energies associated with coupling, just like energies in other settings, are assessed based on how they compare to other energies. For example, inserting a spin-orbit coupling ...
Nike Dattani - No Free Time's user avatar
4 votes

Are there non-antisymmetric solutions to the electronic Hamiltonian?

It depends on what you mean. If your Hamiltonian is defined on $H_N:=\otimes^N \mathfrak h$, the $N$-fold tensor product of the single-particle Hilbert space $\mathfrak h$, then actually under quite ...
Jakob's user avatar
  • 757
4 votes
Accepted

Is there a minimum inter-defect distance when introducing point defects into a 2D structure, ensuring defects don't exhibit significant interactions?

It depends on the system and the goal. If the goal is to model truly isolated defects (i.e. not clustered together), then you have to use a system large enough that there are no spurious effects of ...
Tyler Sterling's user avatar
4 votes
Accepted

Orthonormality of AOs and MOs in PySCF

Solving the Hartree-Fock equations is equivalent to unitary rotations of the orbitals, but you are missing the key piece: before Hartree-Fock, the basis set is orthonormalized to produce an ...
Susi Lehtola's user avatar
  • 19.7k
4 votes

Script to draw one-dimensional PES comparing harmonic and anharmonic vibrational modes

A script that works for arbitrary potentials My script has produced the following figures for this paper. Simple single-well potential: Double-minimum potential with a small barrier and a "shelf&...
Nike Dattani - No Free Time's user avatar
4 votes
Accepted

Time Evolution of the Hartree-Fock Wave Function

In order to determine the time evolution of a Hartree-Fock state, the Time-Dependent Hartree-Fock (TDHF) method is indeed a suitable approach. TDHF is a mean-field method used to study the dynamics of ...
Sak's user avatar
  • 979
3 votes
Accepted

How to orthonormalize a set of Molecular orbitals?

Since S is created from orthonormal orbitals, it has 1.00 as diagonal elements. If ${\bf S}$ is created from orthonormal orbitals, the overlap matrix is simply the unit matrix, ${\bf S}={\bf 1}$. ...
Susi Lehtola's user avatar
  • 19.7k
3 votes

Why does the C6z operator have 6 eigenvectors in this paper?

The paper appears to have an error. When a $C_6$ operator acts on an atom's (x,y,z) coordinates, the operator's matrix representation is the 3x3 matrix that you correctly provided in your question ...
Nike Dattani - No Free Time's user avatar
3 votes

How do I get the energy, if I have the wavefunction?

UPDATE: I didnt read your post carefully enough. My answer is irrelevant. In your comment above you said I guess what i meant was that if I have an arbitrary state eigenfunction (approximated as the ...
Tyler Sterling's user avatar
2 votes

Are there non-antisymmetric solutions to the electronic Hamiltonian?

Update: I carelessly misunderstood the specific question I replied to as asking about the kinetic energy operator only. My answer isn’t applicable here, but I’m gonna leave it for reference unless ...
Tyler Sterling's user avatar
2 votes

How to use the CI method to compute the order of the molecular orbitals of the nitrogen molecule

The incorrect ordering of molecular orbitals given by Hartree-Fock (Koopmans' defect) can be resolved with methods based on electron propagator/one-electron Green's function theories. Such methods ...
quantumcat's user avatar
2 votes

What is the best program to manipulate plane-wave DFT wavefunctions to calculate custom matrix elements?

In sisl one can do the derivatives if one has access to the Hamiltonian. The sisl code is heavily dependent on the LCAO formalism. So if you can't work with Hamiltonians it might be more difficult (...
nickpapior's user avatar
  • 3,504
2 votes

Symmetric issue about the Gaussian basis Hamiltonian

The simplest way of putting this is to note that the Hamiltonian is an operator corresponding to an observable (the energy) and hence by the postulates of quantum mechanics must be Hermitian. In the ...
Ian Bush's user avatar
  • 774
2 votes

What are the observables when a quantum system is comprised of orthogonal spacetimes?

Preamble After Susi's vote to close this question: "I’m voting to close this question because this belongs in the physics network." I inquired with a Physics.SE diamond moderator to see ...
Nike Dattani - No Free Time's user avatar
1 vote

What is the best program to manipulate plane-wave DFT wavefunctions to calculate custom matrix elements?

You may be interested in DFTK, which is a fully featured plane-wave code like Quantum Espresso but which fits in a mere 7k lines of code. Importantly, DFTK has automatic differentiation, which means ...
Susi Lehtola's user avatar
  • 19.7k

Only top scored, non community-wiki answers of a minimum length are eligible