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.

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

I am currently conducting a DFT investigation into the magnetism of 2D materials by introducing defects into the structure. Is there a minimum distance I should maintain between two defects in ...
9 votes
2 answers
2k views

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

I have this very simple function: ...
5 votes
1 answer
170 views

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

In a one-electron system such as the H atom, we are able to say that the orbitals are valid wavefunctions. But for complex systems with N-electrons, I have heard people say that they are just ...
15 votes
3 answers
484 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 ...
3 votes
1 answer
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Orthonormality of AOs and MOs in PySCF

I have a basic question about how to calculate molecular-orbitals from atomic-orbitals in PySCF using the self-consistent field approach. My understanding mathematically is as follows: we start with a ...
1 vote
1 answer
80 views

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

It is well known that the Hartree–Fock (HF) approximation predicts a wrong order for the last two molecular orbitals of N$_{2}$. The calculations indicate that the 1$\pi_{u}$ orbital has higher energy ...
6 votes
2 answers
144 views

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

I recently wrote a simple HF SCF program for my understanding and realized that I do not fully understand such QM calculations. Suppose I have the ground state gaussian wave function of a system, $$ \...
4 votes
1 answer
90 views

How to orthonormalize a set of Molecular orbitals?

I am using PySCF, and checked that the molecular orbitals(MO) from the HF calculation are orthonormal. If S is the Overlap matrix, and V is the matrix of the MO coefficients, It can be seen from the ...
1 vote
1 answer
26 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...
3 votes
1 answer
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Why does the C6z operator have 6 eigenvectors in this paper?

In this paper, I couldn't understand this line in the 3rd section (i.e. III. SYMMETRY ARGUMENTS): In the absence of SOC, the eigenvalues of $C_{6z}$ rotation operator are $e^{i2\pi n/6}$ where $n = 0$...
3 votes
1 answer
106 views

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

We are given a system of three quantum domains A, B, and C with the following properties: (1) domains A and B are independent Hilbert spaces, each with their own space and time dimensions. Both are ...
2 votes
0 answers
160 views

Clarifying local magnetic moment axes in VASP: cartesian vs crystal (for MAGMOM/M_CONSTR)

In VASP, one can set the local magnetic moments of each ion in a non-collinear SOC calculation along a certain direction using the MAGMOM/M_CONSTR tags. The manual linked to states that these local ...
4 votes
1 answer
87 views

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

To what extent can current coarse-grained models, within the context of multiscale modelling, retain essential quantum mechanical characteristics such as electron correlation, polarization, and ...
3 votes
0 answers
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Which is better? Rashba effect or Dresselhaus effect?

My current research focus is on the band splitting observed in 2D perovskite. Existing literature suggests that site inversion asymmetry (SIA) may lead to the Rashba effect, while bulk inversion ...
0 votes
1 answer
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Symmetric issue about the Gaussian basis Hamiltonian

The material system is described by the Hamiltonian and overlap matrice, with the Gaussian basis set. At Gamma point in the reciprocal space, the upper triangle block and the lower triangle block in ...
3 votes
1 answer
152 views

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

This is an extension of a question I asked a little while ago: Software to draw one-dimensional PES including vibrational energy levels. I am asking the followup here based on advice received after ...
10 votes
1 answer
200 views

Time Evolution of the Hartree-Fock Wave Function

The Hartree-Fock Hamiltonian is given by $$ \hat{H} = \sum_i \hat{h}_i + \frac{1}{2}\sum_i\sum_j \left[\hat{J}_{ij} - \hat{K}_{ij}\right] $$ and by choosing a basis, the Hamiltonian can be written in ...
9 votes
1 answer
794 views

Why is chemical bond dissociation difficult to simulate?

I'm a student doing quantum computing research trying to understand better what kinds of chemical systems are difficult to simulate on a classical computer and for which quantum simulation could be ...
4 votes
0 answers
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Why, if the potential is different from the Coulomb one, but has spherical symmetry, the eigenvalues of the system are non-degenerate? [closed]

Question duplicated from here https://mathematica.stackexchange.com/questions/287433/why-if-the-potential-is-different-from-the-coulomb-one-but-has-spherical-symme and here https://physics....
4 votes
1 answer
656 views

Can we download DMol3 for free?

I want to try using DMol3 software for my research studies of doing optimisations and DFT calculations. Anyways I was unable to find a download link. Is it available for free? if so can anyone please ...
5 votes
0 answers
98 views

How can one determine the time-step for imaginary time evolution?

The real-time evolution of a quantum system described by the state $\psi(t)$ is formally given by, $$ \psi(t+\Delta t) = \exp^{- i \hat{H} \Delta t / \hbar} \psi(t)\tag{1}$$ For dynamical simulations ...
6 votes
0 answers
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How To Extrapolate Ground State Energy in Thermodynamic Limit via DMRG [closed]

I am implementing a system of fermions in a trap potential with tensor networks and want to find the ground state energy via DMRG (I'm using SyTen). As usual in quantum chemistry the Hamiltonian has ...
5 votes
1 answer
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Is it possible to model hBN spin defects/plasmons coupling in COMSOL/Lumerical

Hexagonal Boron Nitride (h-BN) is a promising material for Quantum technologies, see [1]. I want to perform a plasmonic simulation in COMSOL to replicate this paper. But I am not able to find any ...
6 votes
2 answers
356 views

Density Functional Perturbation Theory

What is the difference between density functional perturbation theory (DFPT) and many-body perturbation theory (MBPT)? Also, please help me understand why approximations like PBEsol are considered as ...
3 votes
0 answers
66 views

Kohn anomaly and avoided crossing (or anticrossing/level repulsion) [closed]

Kohn Anomaly and Avoided Crossing (Anticrossing/Level Repulsion) are terms that are found to be used when discussing phonon dispersion. The former (see last paragraph, page 198) is related to electron-...
4 votes
1 answer
82 views

How to apply solvent-correction to Gaussian derived Gibbs energies?

I study reaction A + B → C + D in a water using DFT. I think I should apply some kind of correction over RRHO because it is not true in a solvent. I found the given work (https://doi.org/10.1021/...
2 votes
1 answer
106 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 ...
2 votes
0 answers
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How do I get the wavelength of light from a diffraction experiment using Python? [closed]

What is the procedure after using a diffraction grating (device used to see the spectrum) using python? We would see the entire electromagnetic spectrum emitted by an object but what then? how do I ...
5 votes
1 answer
102 views

Cross-post: Matrix elements <n,k|x|n',k'> for Bloch states

Cross posted at Physics.SE I believe this is just elementary QM, but I'm getting awfully confused. The question is drawn from this paper on Wannier-Stark localization (but is self-contained). Let: \...
8 votes
2 answers
298 views

Equation (4) in Hohenberg-Kohn Paper

In their landmark paper of 1964, Inhomogeneous Electron Gas, Hohenberg and Kohn wrote down: We shall be considering a collection of an arbitrary number of electrons, enclosed in a large box and ...
0 votes
1 answer
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How do scalar states with different multiplities make spin-forbidden reactions possible?

This question is related to How spin-orbit coupling makes spin-forbidden reactions possible? - Matter Modeling Stack Exchange Even more importantly, [H,S2]=0 fails for multi-electron systems even ...
4 votes
2 answers
290 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 ...
4 votes
2 answers
156 views

What is a "transient" state?

I was analyzing this source code of the Ising model. I found the term "transient state". I also found the term in this text: There are two absorbing states in this Markov chain because once ...
5 votes
1 answer
183 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 ...
2 votes
1 answer
129 views

What occupation should be used for non metallic energetic materials in Quantum espresso?

I am trying to understand the Quantum espresso input file and I intend to do DFT calculation on an Energetic material (TKX-50) consisting of C, H, O, AND N. I have seen that "smearing" ...
3 votes
0 answers
58 views

Green function KMS boundary condition [closed]

How to obtain the relation between $G_{ab}(\tau,0,0,0)$ and $G_{ab}(\beta-\tau,0,0,0)$ for two-particle fermion Green function $$G_{ab}(\tau_1,\tau_2,\tau_3,\tau_4)=\langle \mathcal{T}a^\dagger(\tau_1)...
15 votes
1 answer
247 views

First order variation of the wave function of conduction states

The first order variation of the wave function $\Delta \psi_n$ is obtained by standard perturbation theory (Eq. 25 of ref 1): \begin{equation} (H_{SCF}-\epsilon_n)|\Delta \psi_n \rangle = -(\Delta V_{...
5 votes
1 answer
157 views

How are the exponents in a STO-nG basis set obtained?

STO-3G has exponent parameters which can be found in a reference book. Can these parameters be calculated using, for instance, a Hartree–Fock equation for one atom? Or using another way?
8 votes
2 answers
1k views

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

Suppose I have the following Hamiltonian to start $$ H_0 = \begin{pmatrix} 0 & 0 & 0 & 0\\ 0 & 0 & 2 & 0\\ 0 & 2 & 0 & 0\\ 0 & 0 & 0 & 0 \end{pmatrix} $$...
18 votes
1 answer
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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 $e^{-\alpha r}$ ...
6 votes
1 answer
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Electric quadrupole operator for periodic systems

Considering one component of the electric quadrupole operator $\hat{r}_x \hat{r}_y$, I'm wondering if the following equalities hold: $$ \langle u_{n\mathbf{k}} | \hat{r}_x \hat{r}_y |u_{m\mathbf{k}} \...
6 votes
1 answer
390 views

How to formulate the second quantization of Dzyaloshinskii-Moriya interaction?

The Dzyaloshinskii-Moriya interaction (DMI) existing in the interface of the ferromagnetic insulator and the metal with strong spin-orbit coupling (SOC) is shown below. Mathematically, it can be ...
8 votes
1 answer
293 views

How to numerically calculate quantum state distance using quantum metric?

In Ran Cheng's review of the quantum geometric tensor, eq. (11) gives the tensor as: $$ Q_{\mu\nu}=\sum_{n\neq 0}\frac{\langle\phi_0|\partial_\mu H|\phi_n\rangle\langle\phi_n|\partial_\nu H|\phi_0\...
7 votes
1 answer
353 views

How to solve time-dependent Schrodinger equation and plot trajectory on Bloch sphere?

Let's say I have a $2 \times 2$ Hamiltonian that I am solving using the time-dependent Schrodinger equation: $$ i \frac{d}{dt} |{\Phi}\rangle=H|{\Phi}\rangle.\tag{1} $$ Consider a generic Hamiltonian $...
8 votes
1 answer
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Help with understanding topologically-protected edge states in domain wall systems

Let's say that I have a simple domain wall system for the following Hamiltonian with added on-site potential $M(x)$: $$\tag{1} H(k,M)=-t \sum_{\delta} [\cos(k\cdot\delta)\sigma_x-\sin(k\cdot\delta)\...
9 votes
2 answers
960 views

Calculating the excited state dipole moment

I am trying to calculate the dipole moment of an excited state, using "Gaussian" software. My input commands were: ...
8 votes
1 answer
82 views

Quantum mechanical antireflection coating; what quantity would be analogous to index of refraction?

Background Quasiparticle interference (QPI) is a technique that can be used to study 2D surface state band structure; carrier reflections at boundaries or impurity sites will interfere producing ...
5 votes
0 answers
389 views

Why does numerical computation of Berry curvature give me a correct Berry phase when it is supposed to diverge? [closed]

I implemented the standard numerical algorithm for calculating the Berry curvature in MATLAB. For a given 2D system, I can visualize the Berry curvature over parameter space. If I sum the Berry ...
5 votes
0 answers
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How to get energy eigenstates using plane wave basis wavefunction .hdf5 output from Quantum ESPRESSO? [closed]

When compiled with the HDF5 flag on, Quantum ESPRESSO (QE) saves wavefunctions in the .save folder. At each k-point, we have an $m\times n$ matrix, where $m$ are the complex number entries of ...
6 votes
1 answer
190 views

Ground State energy trick for many-body electronic structure calculations?

I am an outsider to this field, so I am not sure about the validity of my work below. Let us define the following Hamiltonian from DFT: $$ \tag{1}H_{ij} \psi_{ij} \equiv (-\frac{\hbar^2 \nabla_i^2}{2m}...