Skip to main content

Questions tagged [quantum-mechanics]

Refers to the branch of mechanics that deals with the mathematical description of the motion and interaction of subatomic particles, in particular electrons.

Filter by
Sorted by
Tagged with
12 votes
1 answer
345 views

What are the types of Quantum Molecular Dynamics (QMD)?

In similar spirit to recent questions on Quantum Monte Carlo, ab-initio Molecular Dynamics, types of SCF, and others, I would like to ask: What are the types of Quantum Molecular Dynamics (QMD)? As I ...
epalos's user avatar
  • 4,879
15 votes
3 answers
511 views

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

For pedagogical reasons, I am looking for ways to calculate quantum-mechanical quantities such as $\langle m | \dot{m}\rangle, \langle m | \dot{n}\rangle, \langle m | \ddot{n}\rangle$ using ...
TribalChief's user avatar
  • 2,361
20 votes
3 answers
456 views

How are continued fractions related to quantum materials?

In my spare time, I have been studying and analysing continued fractions. I was having a conversation with someone on Discord in a Mathematics server and he was telling me that continued fractions ...
Mr Pie's user avatar
  • 253
18 votes
1 answer
1k views

Do we know for sure that all atomic and molecular wavefunctions decay exponentially as r goes to infinity?

Slater type orbitals (STO) are considered to be more accurate than gaussian type orbitals (GTO) for atomic and molecular QM calculations because - among other reasons - they decay with $e^{-\alpha r}$ ...
Arc's user avatar
  • 603
16 votes
1 answer
2k views

Does the Schrödinger equation have unique solutions?

I am learning DFT and the Hohenberg Kohn Theorem of Existence. It says that there is a one-to-one correspondence between the external potential and the density. However the proofs that I have seen ...
GalliumBeryllium's user avatar
13 votes
2 answers
1k views

How can we say that the KS equation is describing a noninteracting many-electron system?

Based on HK's two theorems, the density functional theory was built. Because one can't find the universal energy functional $F_{HK}[n(r)]$, Kohn and Sham further proposed the Kohn-Sham ansatz: mapping ...
Jack's user avatar
  • 15.2k
11 votes
2 answers
635 views

How to derive the effective Hamiltonian of two-dimensional TMDCs monolayers?

TMDs are transition metal dichalcogenides and have the chemical formula MX$_2$ where M is the transition metal and X is the chalcogen. An example of a TMD is MoSe$_2$. I would like to demonstrate that ...
Carmen González's user avatar
6 votes
1 answer
73 views

Example of a standard/archetypal/simple 4-band un-gapped condensed matter model with analytic results?

I am looking to study Berry phase-like phenomena in an un-gapped material model. However, I am having trouble finding a widely-used 4-band model with analytic expressions for wavefunctions and ...
TribalChief's user avatar
  • 2,361
5 votes
1 answer
199 views

What is the best algorithm for ERIs of contracted gaussian atomic orbitals

I am currently working on python script that does Hartree-Fock-Calculations. I try to avoid packages as good as possible. I've figured out how to calculate the one electron integrals when it comes to ...
lela2011's user avatar
  • 125
4 votes
2 answers
302 views

How spin-orbit coupling makes spin-forbidden reactions possible?

My question is related to the Wikipedia page of spin-forbidden reactions https://en.wikipedia.org/wiki/Spin-forbidden_reactions When a reaction converts a metal from a singlet to triplet state (or ...
Bottisham's user avatar
2 votes
1 answer
110 views

Understanding the complexity of geminal-based wavefunctions

Cross-posted on Reddit. I have been reading through [1] to get a better understanding of geminal-based methods. Some short passages are included below: The occupation of each orbital in the expansion ...
kevin's user avatar
  • 61
1 vote
1 answer
28 views

Algorithm for finding the v=1 state of an H2O molecule

In the context of simulating the dissociation dynamics of an H₂O molecule on a metal surface, what algorithm is employed for generating the initial state of a tri-atomic non-linear molecule, such as H₂...
Nidhi Tiwari's user avatar