23 votes
Accepted

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

I'll answer this question from the theoretical side. The exponential behavior follows simply from the Schrödinger equation. Consider the one-electron Schrödinger equation: $$ (-\frac{1}{2}\nabla^2 + V(...
  • 7,463
18 votes

What are the situations/problems where Born-Oppenheimer approximation is invalid?

Adding to the answer given by Cody Aldaz, there are many situations in chemistry when the Born-Oppenheimer approximation (BOA) breaks down, conical intersection is just one of them! In fact, the ...
18 votes

What are the situations/problems where Born-Oppenheimer approximation is invalid?

TL;DR conical intersections, and polarons. Or any other case when the velocity of the nuclei is faster than the electrons can respond nearly instantaneous The long answer requires a lot of ...
  • 7,794
15 votes

Which method gives the most accurate electron density, and how can it be verified experimentally?

The coupled-cluster hierarchy is a systematic approach to the exact many-body solution to the electronic Schrödinger equation, which yields size extensive energies and often converges extremely ...
  • 15.1k
15 votes
Accepted

Does the Schrödinger equation have unique solutions?

The solutions to the Schrödinger equation are not unique in general, and uniqueness depends on several things such as the form of the potential and boundary conditions. Many papers have discussed ...
  • 29.1k
15 votes
Accepted

How are continued fractions related to quantum materials?

In the paper "A Continued-Fraction Representation of the Time-Correlation Functions", generalized susceptibilities and transport coefficients for materials are obtained using a continued-...
  • 29.1k
14 votes

How is Poier and Jensen's Bond Capacity Model Parameterized and Optimized?

The specific questions: Only $l = 0$ overlaps are (currently) considered, in the spirit of atoms being represented by (only) a spherical charge distribution (point charges). The overlap/attenuation ...
  • 1,021
13 votes

How are continued fractions related to quantum materials?

You may take a look at the Method of Continued Fractions used in quantum scattering theory—this was only formed in 19831 so is rather recent. Related is the PhD thesis by Kónya (2000)2; §3.3 ...
12 votes
Accepted

How do I figure out how many monomer configurations I need for my simulation?

tldr; it depends on flexibility / number of rotatable bonds A while ago, I answered a related question - in general, molecules with fewer "rotatable bonds" need fewer conformers geometries ...
12 votes

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

First of all, let me emphasize that it is more appropriate to speak of KS equations (plural), which you correctly denoted by an index $i$ in your post. This index goes over all KS orbitals (i.e. ...
12 votes
Accepted

How to determine which levels correspond to each other in LS coupling and jj-coupling?

In the jj-representation, each electron from $i$ to $N$ will have: $\vec{l}_i$ (orbital angular momentum), $\vec{s}_i$ (spin angular momentum), and $\vec{j}_i=\vec{l}_i + \vec{s}_i$ (total angular ...
  • 29.1k
11 votes

Derivation of Slater-Koster equations

Spherical harmonics are not themselves full atomic orbitals. Consider the Hydrogen wave function, which separates into a radial part and an angular part. The latter is a spherical harmonic, but the ...
  • 4,238
11 votes
Accepted

How exact is DFT, really?

I'll try to give a short but reasonably rigorous way of thinking about the exactness of density functional theory (DFT). Consider $N$ electrons under the influence of a fixed external potential $v(\...
  • 1,853
11 votes

What does “strongly correlated” mean?

Here I assume that we are focus on the condensed matter system which is composed of nuclei and electrons with the fundamental force: Coulomb Force. Furthermore, I ...
  • 14k
11 votes
Accepted

What does it mean when the first order correction energy is 0?

The first-order correction $\langle \psi_0|H|\psi_0\rangle$ vanishes since $H|\psi_0 \rangle$ is orthogonal to $|\psi_0\rangle$. You need to go higher in perturbation theory to get a correction that ...
  • 15.1k
10 votes
Accepted

Anomalous Quantum Hall Effect

What is the quantum anomalous Hall effect? Figure from C-X. Liu, S-C. Zhang, and X-L. Qi. "The Quantum Anomalous Hall Effect: Theory and Experiment," Annual Review of Condensed Matter ...
  • 4,238
10 votes

What are the situations/problems where Born-Oppenheimer approximation is invalid?

The Born-Oppenheimer approximation comprises two different approximations: Adiabatic separation of electron and nuclear coordinates Semi-classical approximation for nuclei Previous answers have ...
  • 4,382
9 votes
Accepted

Dynamic phase in an adiabatic system

The exponential comes from solving a linear differential equation: \begin{align} \frac{\textrm{d}|\psi(t)\rangle}{\textrm{d}t} &= -\frac{\textrm{i}}{\hbar}H|\psi(t)\rangle\tag{1}\\ |\psi(t)\rangle ...
  • 29.1k
9 votes

What are the situations/problems where Born-Oppenheimer approximation is invalid?

In addition to the classic examples of where non-adiabatic effects are important, the Born-Oppenheimer approximation cannot be taken for granted in the electronic structure computations of small ...
  • 1,053
9 votes
Accepted

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

As you note, the interacting electrons and the Kohn-Sham non-interacting electrons have the same density. How is this possible when the Hamiltonians for the two systems are so different? The answer is ...
  • 1,853
9 votes

What does “strongly correlated” mean?

Here is my summary of definition of strong correlated systems in different context. For ab initio electronic structure Hamiltonian The eigen value of the system can not be well approximated by single ...
  • 3,609
8 votes

What are the situations/problems where Born-Oppenheimer approximation is invalid?

The first answer is most relevant to materials modeling, but I also want to chip in that Born-Oppenheimer is more than just a kinetic assumption, it also assumes nuclei are point charges. This is ...
8 votes

Can Machine Learning lead to the more accurate theories and methods for matter modeling?

It is certainly possible to develop ML models that yield more accurate results than would be possible without ML. One route to do this is through so-called "Δ-learning" where you use ML to ...
  • 6,941
8 votes

What will break the time-reversal symmetry?

I will first take a generic view-point and then quote some examples in condensed matter & materials modeling. Time-reversal symmetry is one of two discrete symmetries usually discussed in the ...
  • 2,212
8 votes

What will break the time-reversal symmetry?

Another way to explicitly break time-reversal symmetry is by applying circularly polarized light. Under time reversal, left circularly polarized light transforms to right circularly polarized light, ...
  • 4,238
8 votes

What does “strongly correlated” mean?

You got it completely correct when you said: "it seems that the definition of it is ambiguous and sometimes inconsistent in different field of study." As the other answers show, it's a bit ...
  • 29.1k
8 votes

Help with translating Hamiltonian into matrix

For this type of calculation, I find MATLAB/Octave to be easier, at least for demonstrating what to do. You can add the np. everywhere afterwards if you want to use ...
  • 29.1k
7 votes
Accepted

Property related with Berry curvature: $\Omega_{n,\mu\nu}=-\Omega_{n,\nu\mu}$

You can just exchange the $\mu,\nu$ indices to verify the antisymmetry: $$ \Omega_{n,\mu\nu}(\mathbf{k})=\partial_{\mu}A_{n\nu}(\mathbf{k})-\partial_{\nu}A_{n\mu}(\mathbf{k})\\ \Rightarrow \Omega_{n,\...
  • 4,238
7 votes

How to understand the formation of covalent bond from the viewpoint of wavefunction interaction?

There is more than one way to answer this question well. I'll give one answer here. Let's treat the two atoms (that will form a covalent bond) as two localized election states (orbitals). The detailed ...
7 votes

Dynamic phase in an adiabatic system

Here are some basic comments: I don't think you should call Eq(1) as the Schrödinger equation. It's just defining the energy eigen states/values, or in other words, establishing the relation of those ...

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