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2
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2answers
67 views
+100

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
16 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
336 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
vote
1answer
62 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
9 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
20 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
72 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
59 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
50 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
72 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
79 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
29 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
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0answers
12 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
288 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
128 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
58 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 ...
0
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0answers
37 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? ...
1
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3answers
151 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
172 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 ...
-1
votes
1answer
103 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
90 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
138 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
vote
5answers
344 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
379 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
150 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 ...
1
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0answers
117 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 ...
1
vote
1answer
125 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 ...
1
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1answer
142 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
84 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 ...
7
votes
3answers
786 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
65 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
67 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
138 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
243 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
91 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
896 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
120 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
553 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 ...
13
votes
3answers
333 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 ...
4
votes
1answer
375 views

Number of unique 2-electron integrals

Consider 2-electron integrals over real basis functions of the form $$(\mu\nu|\lambda\sigma) = \int d\vec{r}_{1}d\vec{r}_{2} \phi_{\mu}(\vec{r}_{1}) \phi_{\nu}(\vec{r}_{1}) r_{12}^{-1} ...
2
votes
2answers
113 views

Driving a solution of optical isomer molecules with the resonant frequency

What happens when we drive a solution of optical isomer molecules (enantiomers) with a microwave radiation in resonance with the tunneling frequency of the molecules (the frequency of the transition ...
3
votes
1answer
280 views

Why do hydrogen atoms attract?

That is, why is the potential energy with the orbitals overlapping less than with the Hydrogen atoms 'independent'. Similarly, why is a noble gas configuration stabler than if an electron were to be ...
7
votes
4answers
4k views

Why do covalent bonds form?

why in a covalent bond are "the bonded electrons are in a lower energy state than if the individual atoms held them at the same proximity"? Also is it correct that " I think when you start pushing ...
2
votes
1answer
332 views

Minimizing the energy of a Slater determinant: why are the Lagrange multiplier elements of a Hermitian matrix?

If I want to minimize the energy of a Slater determinant subject to the constraint that the spin orbitals are orthonormal (as in the Hartree-Fock approximation), I can use Lagrange's method of ...
2
votes
1answer
310 views

Why are do neutral atoms shrink as their valence shells approach 8 electrons?

Why do neutral, unbonded atoms shrink in size as they approach having 8 electrons in their valence shells? A good example is elements 3 through 10 in this table, that is, lithium (1 valence electron) ...
1
vote
1answer
456 views

Density of classical states in quantum theory

Let's first treat electrons as classical objects. I can evaluate the classical energy of each state in a configurational space (3N real numbers and, say, spins) using just Coulomb's law. Then I ...
3
votes
1answer
131 views

Experiment to find structure of water

Who first determined the structure of water (two hydrogen atoms stuck to an oxygen atom at approx 105 degrees), and, more importantly, how was this done?
1
vote
1answer
128 views

Does spin alone have any effect on the physical interactions of particles?

In Hartree-Fock theory the time-independent electronic energy of a single (restricted) determinant electronic wavefunction consists of one electron terms, $h_{ii}$, Coulomb interaction energies, ...
5
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4answers
584 views

Why is quantum physics needed to explain photosynthesis?

Why is quantum physics needed to explain photosynthesis? In what aspect does the corresponding classical theories for photosynthesis fail?
2
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1answer
5k views

Why is oxygen in a triplet state and what are the consequences?

From Wikipedia here and here: ''Almost all molecules encountered in daily life exist in a singlet state, but molecular oxygen is an exception.'' ''The unusual electron configuration prevents ...