The tag has no usage guidance.

learn more… | top users | synonyms

2
votes
0answers
36 views

Why is the activation energy of combustion so large compared with regular bonding?

I wanted to know why combustion requires an activation energy and I found this article (see this too). It says that molecular oxygen ground state is a triplet state (according to Hund's rules), and ...
0
votes
1answer
29 views

One-electron reduced density matrix: Argument for positive semidefiniteness

I cannot follow an argument for positive-semidefiniteness of the one-electron density matrix given in "Molecular Electronic-Structure Theory" by Helgaker/Jorgensen/Olsen. First some definitions: ...
11
votes
2answers
846 views

Is there experimental verification of the s, p, d, f orbital shapes?

Have there been any experiments performed (or proposed) to prove that the shapes of the s,p,d,f orbitals correspond to our spatial reality as opposed to just being a figment of the mathematics that ...
0
votes
0answers
31 views

How can I guess/draw the shape and phase of the molecular orbitals of C4H4? [closed]

I used Huckel's method along with a Linear Combination of Atomic Orbitals (LCAO) to calculate an estimate for the orbital energies of cyclobutadiene (C4H4) and butadiene (C4H6). For butadiene, you end ...
2
votes
1answer
106 views

What is the difference between real orbital & complex orbital?

While reading Atomic orbitals, I came before these two terms. The 'real orbital' is given here: Real orbitals An atom that is embedded in a crystalline solid feels multiple preferred axes, ...
0
votes
1answer
34 views

Software to calculate electron binding energy of molecules?

I need to calculate the binding energies for the various electrons in a few different molecules (to determine an appropriate wavelength to selectively ionize them). Are there any software packages to ...
1
vote
0answers
67 views

Finding Electronic Energy Levels by Representation Theory

Let $$u=\left( \begin{array}{cccc} c_1&c_2&c_3&c_4 \end{array} \right)^T$$ for $$\psi = c_1\psi_1 + c_2\psi_2 + c_3\psi_3+ c_4\psi_4$$ We assume that $<\psi_i|\psi_j> = \delta_{ij}$ ...
0
votes
2answers
74 views

Correlation energy - is it the difference between the Hartree-Fock energy and exact energy, or Hartree-Fock PE and exact PE?

For some reason I can't find anything stating it either way explicitly. What I'm talking about is this. Is this difference referring to potential energies or just energies in general? I assume it's ...
1
vote
0answers
39 views

Why don't wavefunctions for electrons in neighbouring molecules overlap?

I've come across this picture of two linked molecules. The intramolecular distances look similar to the intermolecular distances and it seems like that will be the case however you draw it because of ...
1
vote
2answers
87 views

Atomic orbitals

I just studied atomic orbitals in a theoretical QM class, and I'm left with several questions, that are probably more questions in quantum chemistry: Many orbitals seem to have a preferred axis - ...
2
votes
0answers
9 views

What would be the Slater's determinant of an excited state? [duplicate]

Setup Introducing this spinorbital notation: \begin{align} \Psi_1=\chi_{(r1)}\alpha_{(\omega1)} &= 1 \\ \Psi_1=\chi_{(r1)}\beta_{(\omega1)} &= \bar{1} \end{align} and the Slater's ...
2
votes
0answers
50 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
vote
1answer
97 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
votes
0answers
53 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
vote
2answers
94 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
votes
6answers
393 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 ...
0
votes
0answers
49 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
votes
1answer
172 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
vote
2answers
40 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
votes
0answers
93 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
vote
1answer
52 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
votes
1answer
36 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
101 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
votes
0answers
21 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
votes
4answers
406 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
136 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
votes
0answers
55 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
34 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
187 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
114 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
votes
1answer
107 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
vote
1answer
93 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
148 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
vote
0answers
34 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.
3
votes
3answers
2k 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
212 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
106 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
votes
0answers
40 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
vote
3answers
259 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
327 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
110 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
votes
2answers
160 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
286 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
451 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
677 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
199 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
vote
0answers
264 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
168 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
vote
1answer
159 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
88 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 ...