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0answers
32 views

Geometric measure of entanglement for fermions or bosons?

For a system consisting of multiple components, say, a spin chain consisting of $N\geq 3 $ spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner ...
1
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1answer
86 views

Does O$^{2-}$ really exist?

In chemistry it is common sense that we have O$^{2-}$. But from a physical point of view, does O$^{2-}$ really exist as a negative ion? I mean, as an isolated ion. It is not apparent that a neutral ...
0
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0answers
22 views

Valence bond wavefunction of nitrogen

Could someone explain to me how one finds the valence bond wavefunction of an atom? Take nitrogen for example, I know both nitrogen molecules have a valence-electron configuration of 2s22p1x2p1y2p1z ...
1
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2answers
58 views

How to use Hartree-Fock for helium?

I am thinking of using Hartree-Fock approximation to calculate the ground state energy of helium. The ground state wave function must have a symmetric orbital wave function. But in HF we need a Slater ...
2
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6answers
178 views

Rutherford's gold foil experiment: can alphas be deflected by electrons vs. nucleus?

In this experiment, is it possible that some of the alpha particles are deflected by the electrons? Gold, after all, usually also has ~79 of them in each atom. Since the alpha particles want ...
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0answers
37 views

Partial diagonalization of the Fock matrix

I'm currently writing my dissertation on the application of SCF semi-empirical methods to large systems, in particular proteins, and I'm stuck with a problem: I don't understand why, given the fact ...
0
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1answer
107 views

Kinetic energy (KE) in atomic orbital

Within an atomic orbital, electrons must obviously have relative differences between points in space due to potential gradient. But there is kinetic energy as well. If we choose a particular point as ...
1
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2answers
33 views

Bond Formation during reaction

My Chemistry textbook says that on approaching each other, atomic orbitals of atoms interact. This interaction, it says, can be additive and subtractive, and lead to formation of bonding and ...
3
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0answers
83 views

Quantum Mechanical Thinking

I've just been wondering about how atoms and molecules can be quantum mechanically thought about, and I have a question. It is often said that intermolecular bonding is purely "electrostatic". I hope ...
1
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1answer
47 views

How to find bond length from potential?

A bonding potential like the Morse potential or a Lennard-Jones potential is characterized by a distance at which the potential is minimal, referred to as e.g. 'equilibrium bond distance'. Is this ...
0
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1answer
31 views

Applying the time evolution operator as a form of molecular dynamics

I had a kind of weird idea. In molecular dynamics, long timescale simulations (like protein folding) are a really hard problem because you can't "skip steps" of the simulation without huge ...
2
votes
2answers
95 views

Wavefunction of isomers

In quantum chemistry, the wavefunction for a molecule can be viewed as the output of a function $\xi(m, n_1,..., n_k)$ with $m, n_i \in \mathbb{Z}^+$ that returns a $|\psi\rangle$ that satisfies a ...
0
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0answers
19 views

Conical intersections - phase

Can anyone explain why at a conical intersection the wavefunction changes sign? My understanding is that it is a test to see if the crossing IS indeed a conical intersection or just a coincidence of ...
2
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4answers
376 views

Two soft questions about spin and the particle nature of electrons

How can we define spin as the spin of an electron around it's own axis if an electron is described by a probability cloud of finding an electron in a point in space? How does that probability cloud ...
1
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1answer
94 views

How many wavefunctions are in a minimal basis set for benzene?

I am reading Modern Quantum Chemistry by Szabo and Ostlund and on page 62 he says "A minimal basis set for benzene consists of 72 spin orbitals." I tried to understand this number but failed. ...
0
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0answers
41 views

Difference between non-adiabatic coupling and diagonal Born Oppenheimer correction?

I think my question is quite well formulated in the title! I'm trying to understand collision process involving crossing between different electronic states in the potential energy surface, which ...
2
votes
0answers
28 views

Coefficients and Parameters for contracted Gaussian basis sets

This is a repost from Chemistry.stackexchange in the hopes that someone here will be able to help me. Any help at all would be greatly appreciated. As far as I understand, an STO-NG contracted ...
3
votes
1answer
150 views

The Physics Behind Chemical Bonding

Ok so here's the problem: say I'm a sodium atom. It is 'charged' at +1e. A partner Chlorine atom is flying about, also 'charged' at -1e. According to chemistry (or rather the measurement of the ...
0
votes
1answer
87 views

Jahn-Teller effect is based on the Born-Oppenheimer approximation?

I am now reading the quantum mechanics textbook by Landau and Lifshitz. In section 102, they discuss the Jahn-Teller effect. It seems that they assume the Born-Oppenheimer approximation. There is ...
0
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1answer
79 views

Fock matrix elements for RHF formalism

Here I refer to a particular book Molecular Quantum Mechanics by Peter W. Atkins and Ronald S. Friedman, but similar derivation could be found in many other texts. So, when obtaining the explicit ...
1
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1answer
85 views

Darboux theorem and the canonical decomposition of a two-fermion wave function

It is a classical theorem in quantum mechanics or quantum chemistry or quantum information that a two-fermion wave function has a beautiful canonical expansion: $$f(x_1, x_2) = \sum_{j=1}^N ...
3
votes
1answer
118 views

Proving that the electronic Schrödinger equation has no closed analytic solutions for >1 electron

It is stated in many books that analytic closed solutions to the time-independent electronic Schrödinger equation, $$\hat{H}\Psi = E\Psi, $$ exist for the one-electron problem (e.g. hydrogen atom, ...
1
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0answers
31 views

Most atoms have a nonzero magnetic moment, right?

This is my feeling. But more is different. If atoms form a solid, it is hard to say whether the solid will be ferromagnetic or not.
0
votes
0answers
13 views

Modelling of nuclear motions (Classification) after invoking the BO approximation

I know that after invoking the Born-Oppenheimer approximation, the nuclei will move on the adiabatic potential provided by the electronic energy (also called potential energy surface (PES)). Such ...
3
votes
3answers
1k views

1D Infinite Square Well: Box Suddenly Increases in Size. How treat this?

I am currently working my way through John S. Townsend book "A Fundamental Approach to Modern Physics" (ISBN: 978-1-891389-62-7). Exercise 3.12 (p.111) is about the 1D infinite square well. The box ...
0
votes
1answer
176 views

Aufbau principle in modern quantum theory

What is the rigorous definition of the Aufbau principle and the mathematical model used for its description? From Wikipedia, we have that the principle postulates a hypothetical process in which an ...
0
votes
1answer
87 views

What happens to the electrons that escape an atom when matter is converted to a plasma state?

Lets say we have a device that generates plasma fields; if this device creates plasma by heating a gas, where do the electrons that escaped the "orbits" of the atom go? Would the electron physically ...
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0answers
38 views

Flammability and statistical mechanics

I am wondering to what extent the flammability can be predicted from the statistical properties of an ensemble. Given the partition function of an ensemble, can we in principle predict this property? ...
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3answers
227 views

Electron in a covalent bond: what happens when it moves out?

Let's look at a covalent bond in, say, a water molecule: H : O : H H is bonded to O by a pair of electrons. But electrons are in constant motion. What happens when the electron leaves? Why does ...
2
votes
1answer
276 views

Why do electrons couple in atoms?

In describing electron states in hydrogen, we have a very "simple" picture, at least in intro-quantum. But this only has one electron! As we permit more electrons, we also have things like the ...
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1answer
107 views

How are atomic bonds created?

From what I have learned in my chemistry course, Electrons with similar quantum numbers but with opposite spin are attracted to each other. What does this mean when there is a covalent bond being ...
0
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2answers
131 views

Number of 2-electron integrals

Consider 2-electron integrals over real basis functions of the form $$ (μν|λσ)=∫dr⃗_1dr⃗_2ϕ_μ(r⃗_1)ϕ_ν(r⃗_1)r^{−1}_{12}ϕ_λ(r⃗_2)ϕ_σ(r⃗_2) $$ I am told that for a basis set of size $K=100$, there are ...
0
votes
1answer
224 views

Dopant Charge Transfer and Fermi Level shift

When a system has a dopant, how much does the Fermi level shift? For example, say a finite concentration of substitutional dopants replace some bulk atoms, and each has one extra electron. Ignore any ...
1
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5answers
397 views

What laws (formulas) govern forces between atoms?

What laws (formulas) govern the fundamental forces of nature? For example, gravity is governed by the inverse-square law. I am thinking about how particles attract each other, but also repel. All ...
4
votes
1answer
553 views

Can we model Chemical Reactions using Quantum Mechanics? If so, what is the most complex reaction we can model?

Not a physicist or Chemist, just interested in QM and it's applications. I've been reading lately about Quantum Chemistry and it occurred to me that since we can model electron orbitals in QM and ...
3
votes
1answer
181 views

What determines the form of the intensity curves in Laser-Induced Fluorescence (LIF) measurements?

What determines the form of the intensity spectra of different particle species in Laser-Induced Fluorescence (LIF) measurements? See e.g. I figure that bigger particles have more ways to get ...
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0answers
185 views

Derivation of the Hartree-Fock equations. Functional varitation

I asked this question at chemistry.stackexchange.com, but the attendance of that source is a little bit lower than here. I would like to ask a question about mathematical derivation of the HF ...
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1answer
145 views

Chemistry from a physical perspective [duplicate]

I'm currently learning chemistry for the first time, and loving it. I have a reasonably good physics and maths background and it's great to see things like spherical harmonics in quantum mechanics ...
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1answer
151 views

Meaning of $C$ in wavefunction equation ($\Psi_{MO} = C_1\phi_A(1s) + C_2\phi_B(1s)$, where $C_1=\pm C_2$)

I've just cracked open a biophysics textbook and it's all fine up until the introduction of the letter C in a wavefunction equation, and declaring C1= ±C2 I've had lectures on eigenfunctions etc. ...
2
votes
1answer
86 views

Why does bringing N 1-orbital atoms together yield N levels?

A common example of this is that when bringing N hydrogen atoms together into a ring. Far apart, assume each electron exists in the 1s state. As we bring them together, instead of each electron ...
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3answers
2k views

What is the quantum mechanical explanation of the octet rule?

What is the quantum mechanical explanation of the octet rule? In other words, what makes the octet rule be true from a quantum mechanical view? How we explain what makes some atoms don't follow the ...
0
votes
0answers
71 views

Quantum chemistry: Localized Molecular Orbitals

Very basic question.... I know that GAMESS can be used to compute localized molecular orbitals, using for example Boys equation; how does one use the program to get the resulting coefficients used to ...
1
vote
1answer
71 views

The Molecular Hamiltonian and the avoidance of Overcounting

Whenever I see the total non-relativistic molecular Hamiltonian, $\hat{H}_{molecular} = \hat{T}_{e} + \hat{T}_{n} + \hat{V}_{ee} + \hat{V}_{nn} + \hat{V}_{en}$ I always notice that the sums ...
1
vote
1answer
167 views

Coulomb interaction and conservation laws

In many-body solid-state physics, the Coulomb interaction term in the Hamiltonian usually implies the momentum conservation law in indicies: $$H_c=\frac{1}{2} \sum_{\mathbf{k},\mathbf{k}',\mathbf{q} ...
2
votes
1answer
302 views

Ground state energy of hydrogen molecule ion

In this paper, it is mentioned: Furthermore, since the energy of $H_2^+$in the ground state must be lower than that of an H atom in the ground state,the negative (attractive) forces in the ...
0
votes
1answer
92 views

What is the $Q_y$ transition in a bacteriochlorophyll?

Bacteriochlorophyll (BChl) are pigments that occur in the photosynthetic mechanisms of bacteria. I am studying some papers on the excitonic properties of BChl's, and the term $Q_y$ transition comes up ...
2
votes
2answers
1k views

Changes in Water Bonding Angle

I heard something recently in a casual discussion, but have yet to be able to confirm it: is there any evidence that the bonding angle for a water molecule, currently defined as 104.5, has been either ...
1
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1answer
133 views

How does the specific frequency of EM Radiation relate to displacing electrons from their orbits?

I've only a general grasp on how all this works, so it could be I'm asking this poorly or misunderstanding what happens. With that said: The energy of EM radiation is a function of its frequency. ...
2
votes
1answer
624 views

Theoretical treatment of Hydrogen bond?

I would like to understand how the Hydrogen bond can be described through the Schroedinger equation. I don't need numerical methods that one uses them to simulate it, rather I need its treatment from ...
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votes
3answers
367 views

Chemical reaction as state transition?

When considering diffusion of chemicals, the reaction part is business of chemical kinetics, where the relevant characteristics of different substances come from collision theory together with some ...