18
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How Does Our Current Understanding of QFT Affect Chemistry and Biology?
It doesn't.
Chemistry (or slightly more generally molecular physics) is sufficiently complicated on its own that it relies on separate phenomenological recipes and approximations to produce results. ...
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16
votes
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Why does Hartree-Fock work so well?
I don't know why (or if) people originally expected Hartree-Fock to work as well as it does, but after thinking about it for a while, I'm personally a little less surprised by it. It seems surprising ...
- 54.7k
10
votes
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Is there a limit of electrons a single hydrogen atom can have?
By definition, "hydrogen atom" refers to the neutral system with one proton and one electron, so it cannot hold any extra electrons.
However, protons can hold more than one electron, in ...
- 134k
10
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Does the hydrogen anion have bound excited states?
A reasonable answer is given in
A.R.P. Rau, "The negative ion of hydrogen". J. Astroph. Astron. 17, 113 (1996)
where Rau explains as follows:
Of particular interest among the $Ν = 2$ ...
- 134k
10
votes
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Creation and annihilation operators in the hydrogen atom
Yes, there is set of ladder operators for the discrete spectrum of the Hydrogen atom, too. Following Fitts, we can set the variables of the radial equation so that this is exactly as:
$$\left(\rho^2 \...
- 4,391
9
votes
Are there exact analytical solutions to the electronic states of the hydrogen molecular ion $\mathrm H_2^+$?
To avoid re-treading old ground, this answer contains some previous literature that has been mentioned on this thread, as well as the surface layer obtainable via naive google searches:
A. H. Wilson. ...
- 134k
9
votes
What *really* happens to atoms in chemical reactions?
Your intuition is spot on. If we have two atoms approaching each other with a large kinetic energy then they will have too much energy to form a stable molecule. Their electrons will interact as they ...
- 359k
9
votes
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Why does Hartree-Fock (HF) theory even work?
I think the confusion here is about the number of orbitals vs. the number of electrons in the Slater determinant. In the first equation the indices of $x_i$ enumerate the electrons, but the indices of ...
- 61.8k
9
votes
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Density functional theory: logical steps from Hohenberg-Kohn theorems to Kohn-Sham equations
1. The Hohenberg-Kohn Theorems:
I think the first part of your question does indeed summarize well the Hohenberg-Kohn theorems. Apart from some minor details (such as that $V$ is unique up to an ...
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8
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A simple example for the application of the Hartree-Fock method?
I would suggest that you try to write a small code that can perform a Hartree-Fock calculation.
Specify molecule and basis set.
Get the integrals. The integrals can be hard to calculate on your own ...
8
votes
Are all waves periodic?
Introductory texts often restrict themselves (for simplicity) to scenarios where waves have a constant uniform velocity and are periodic, so it is easy to get the impression that these conditions ...
- 57.5k
7
votes
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Why does a neutral atom have no external electric field?
Why does a neutral atom have no external electric field?
Why do you think this is true? How do you think the bonding of atoms into solids happen?
Take the van der waals forces
Van der Waals forces ...
- 235k
6
votes
How does one obtain observables from a wave function?
$\hat{O}$ will have a set of eigenvectors $\phi_i$ and eigenvalues $o_i$.
You can expand your wave-function $\psi$ in terms of the basis set $\phi_i$, i.e. $\psi=\sum_i c_i\phi_i$.
If you make a ...
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6
votes
Would an $H_2O$ Molecule actually look like this 3D representation if we could see it?
As part of an undergraduate project I calculated the electron density for various small molecules such as water and ammonia, and the disappointing result is that they are all basically formless blobs ...
- 359k
6
votes
Other than approximating the total energy of the system, what other information does the Hartree-Fock method provide?
In addition to energy, Hartree-Fock gives you the optimal wave function of the many-electron system (within the limits of the theory) as well. Any physical observable can be obtained from the wave ...
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5
votes
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Does the Dirac equation ever get used in Physical Chemistry?
Graphene is a material that needs the Dirac equation for example. The electron band structure of this material has a closed gap some electrons have "mass=0", that can only we treated with the dirac ...
- 458
5
votes
DFT: When would one use a LDA over a GGA method?
In earlier DFT studies of ferroelectric materials, GGAs such as PBE were avoided as they tended to exaggerate the ferroelectric distortion. Instead, LDA calculations were performed and an artificial (...
- 231
5
votes
How can the mechanism of electrons in an atom be explained?
A basic difference between quantum mechanics and classical mechanics is that the potentials do not act on masses in quantum mechanics. Instead they are part of the differential equation that has to be ...
- 235k
5
votes
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Atom orbitals physics vs. chemistry
If an operator has a degenerate eigenvalue
$$
A|a_1\rangle = a|a_1\rangle \qquad A|a_2\rangle = a|a_2\rangle
$$
Then for any linear combination of the degenerate eigenvectors we have
\begin{align}
A(\...
- 9,261
5
votes
How Does Our Current Understanding of QFT Affect Chemistry and Biology?
Given these limitations, could our current ignorance in non-perturbative QFT hinder our understanding of chemistry or cell biology? Or are the effective theories we currently use sufficient for a ...
- 65k
4
votes
Formalism of quantum mechanics
Well this is what I can think of.
If $H$ is a matrix and $\psi$ is a vector of length $n$,
$$H \psi = E \psi$$
is an eigenvalue problem.
Let's say you got as many solutions (pairs of $\psi, E$) to ...
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4
votes
Why does the conjugated $\pi$ bond not violate the Pauli Exclusion Principle?
Just a chemist, but maybe there would've been less confusion in that forum. It's because this is not how the model works. Orbitals are something you get from Hartree-Fock theory (let's leave it at ...
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4
votes
Non-relativistic chemical bond models
The best answer I can give is that there are plenty of models of chemical bonds that don't include relativity. In fact, many of the commonly used models ignore relativity or treat it as a 2nd or 3rd ...
- 1,085
4
votes
Does the $p^+p^-e^-$ system have bound states?
I have worked previously on high accuracy three-particle atomic and molecular calculations using a series solution method first developed by C. L. Pekeris back in 1958. Myself and others developed a ...
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4
votes
What exactly are the approximations in Hartree-Fock?
Is an approximation to consider only one determinant? In a word, yes. Hartree-Fock methods require that the wavefunction be as separable as possible, and this means that they are unable to describe ...
- 134k
4
votes
Why are high electronegativity atoms found in the periodic table's upper right corner?
Mendeleev's periodic table of elements is based on the number of protons in an atom. Also, in an electrically neutral atom,
$$no. \ of\ electrons=no. \ of \ protons$$
So for stability, octet ...
- 169
4
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Corrections from violation of P-symmetry for chemistry, biochemistry, life?
If P-symmetry is not violated, different enantiomers ($R$ and $S$) of molecules would have the same energy, and the standard reaction enthalpy of interconversion is zero.
$$R \rightleftharpoons S, \...
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4
votes
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Why is the distinction between Mott Insulators and Charge Transfer Insulators important?
The issue is discussed in some detail in [1] , referring to perovskites as an example , applying second-order perturbation to the Hamiltonian
$$\mathcal{H}=\epsilon_d\sum_{i,\sigma}d^\dagger_{i,\...
- 1,113
4
votes
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Shape of Hydrogen atom in excited state with nonzeros angular momentum
Just to be clear, even without a magnetic field, the eigenstates of the hydrogen atom are simply not all spherically symmetric. The space of eigenstates of a given energy is spherically symmetric. ...
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