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2
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1answer
71 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, ...
1
vote
1answer
519 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 ...
0
votes
1answer
26 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
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0answers
62 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
1answer
137 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 ...
0
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2answers
43 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
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0answers
36 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
74 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
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0answers
8 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
42 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
91 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
47 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 ...
2
votes
1answer
367 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
2answers
84 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
279 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
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0answers
45 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 ...
6
votes
2answers
1k views

Is Palladium an exception?

I have been taught in school that atoms cannot have more than 8 electrons in the outer shell. Palladium atom's electron configuration is 2,8,18,18. Why isn't it 2,8,18,17,1 like the case of Platinum ...
9
votes
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 ...
6
votes
1answer
243 views

The Born-Oppenheimer approximation and muonic molecules

Does the Born-Oppenheimer approximation fail for muonic molecules (i.e. molecules where one or more electrons are replaced with muons)?
3
votes
0answers
90 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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2answers
36 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 ...
12
votes
4answers
3k views

Does there exist a free good molecule / atom simulation software?

I'm looking for a software or software package (for example C/C++) that can simulate a lot (say thousands at least) of molecules in action (ie. in movement or attached to say static walls). I have ...
1
vote
1answer
50 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
35 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
99 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
391 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 ...
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 ...
1
vote
1answer
124 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
50 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
32 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 ...
0
votes
1answer
102 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 ...
3
votes
1answer
172 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
99 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
130 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
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.
5
votes
4answers
660 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?
1
vote
1answer
158 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. ...
0
votes
1answer
194 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
98 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 ...
2
votes
1answer
307 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 ...
2
votes
1answer
334 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
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
242 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 ...
8
votes
4answers
6k 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 ...
0
votes
2answers
146 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 ...
1
vote
5answers
431 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 ...
-1
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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 ...
4
votes
1answer
523 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} ...