Chemical Wave functions

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Main Question or Discussion Point

What is the maximum size scale (how many atoms) where the concept of wave function is still useful in chemistry esp. biochemistry? For example. Wave function modelling is easily done in Hydrogen Atom. The interaction Hamiltonian is mostly of the nature E = K + P (Total Energy = Kinetic + Potential Energy) in wave form. So when you add energy to the electron and it rises up an orbital, the kinetic energy component in the wave function is increased. But what happens in the molecules. When you add energy, you only affect the bulk properties or thermal. Does one use the concept of Wave function here? If not, then up to what size scale (how many atoms) is wave function concept still meaningful?

Related to this is, if Hilbert Space formalism is used. Up to what size scale (how many atoms or size of molecules) is Hilbert Space concept still meaningful or useful?

In other words, what advantage do you have in modelling molecules using wave function or Hilbert Space and up to what size is it still accurate and useful??
 

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  • #2
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When it comes to modeling macromolecules like proteins and nucleic acids, Density Functional Theory is a lot more useful than the Schrodinger equation. Unfortunately, that's all I know--can't tell you much about DFT! :)
 
  • #3
Borek
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When you add energy, you only affect the bulk properties or thermal. Does one use the concept of Wave function here?
I am not sure what your question really is. The way you spelled it it looks like if you were thinking electrons in large molecules behave differently than in small molecules, or that large molecules behave classically.

Electrons in large molecules behave exactly the same way as in small molecules, and they are described by exactly the same Schroedinger's equation. If we use different approaches to calculate wave functions/orbitals/energy levels/shapes/electron densities/whatever that's just because some methods are better suited for large molecules and/or give better results with less calculations. But no matter how you approach the problem, in the end you can always find the wave functions. You may not have to, as you may already have answer to the problem you were solving.

When molecules become large enough they start to behave classically, but only when treated as a unit without internal structure, but whatever happens inside and/or during interactions with other molecules (think enzymes catalyzing reactions) still requires quantum approach.

Could be I misread your question, but something just doesn't sound right about what you wrote.
 
  • #4
As far as electrons are concerned, wavefunctions are always important.
If you're modelling the entire system as a wavefunction then I would guess that the point where the physical size of the system (on the order of the distance between the two most distant nucleii) is larger than the wavelength of the molecule (determined by its momentum, estimated from temperature or something).
I seem to recall that someone performed Young's Double Slit experiment with buckminster fullerene and got an interference pattern, so the boundary is pretty illdefined.
 
  • #5
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As far as electrons are concerned, wavefunctions are always important.
If you're modelling the entire system as a wavefunction then I would guess that the point where the physical size of the system (on the order of the distance between the two most distant nucleii) is larger than the wavelength of the molecule (determined by its momentum, estimated from temperature or something).
I seem to recall that someone performed Young's Double Slit experiment with buckminster fullerene and got an interference pattern, so the boundary is pretty illdefined.
How is it related de broglie formula wavelength = h / momentum? I mean if the size of the system is greater than the wavelength. What does it mean?
 
  • #6
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I am not sure what your question really is. The way you spelled it it looks like if you were thinking electrons in large molecules behave differently than in small molecules, or that large molecules behave classically.

Electrons in large molecules behave exactly the same way as in small molecules, and they are described by exactly the same Schroedinger's equation. If we use different approaches to calculate wave functions/orbitals/energy levels/shapes/electron densities/whatever that's just because some methods are better suited for large molecules and/or give better results with less calculations. But no matter how you approach the problem, in the end you can always find the wave functions. You may not have to, as you may already have answer to the problem you were solving.

When molecules become large enough they start to behave classically, but only when treated as a unit without internal structure, but whatever happens inside and/or during interactions with other molecules (think enzymes catalyzing reactions) still requires quantum approach.

Could be I misread your question, but something just doesn't sound right about what you wrote.
While it is true that chemical energy is the energy contained in the chemical bonds of molecules. But if you increase the rotational, translational, vibrations mode. You also increase the energy. Here is it just classical effect or does this thermal degrees of freedom needs to be understood in terms of the Schroedinger Equations too?
 
  • #7
Borek
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Sorry, but I am still not sure what the question is.

Rotational energy makes sense in the case of small gaseous molecule. Large molecule - say hemoglobin - is never gaseous, and in practice never rotates, it is not rigid enough. You can no longer apply the same approach as for small, rigid molecules with just a few degrees of freedom. Does it mean Schroedinger equation doesn't work? No, it means the question about rotational energy has to be reformulated.

In general its is not a problem to treat a large molecule as a rigid rotor and calculate energy levels. But it is moot.
 
  • #8
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Sorry, but I am still not sure what the question is.

Rotational energy makes sense in the case of small gaseous molecule. Large molecule - say hemoglobin - is never gaseous, and in practice never rotates, it is not rigid enough. You can no longer apply the same approach as for small, rigid molecules with just a few degrees of freedom. Does it mean Schroedinger equation doesn't work? No, it means the question about rotational energy has to be reformulated.

In general its is not a problem to treat a large molecule as a rigid rotor and calculate energy levels. But it is moot.
Isn't it that the Schroedinger Equation is used whenever electron is involved? Translational and vibration mode in the molecules don't involve electrons because it is the entire atoms that move and vibrate. So I wonder if the Schroedinger Equation is used. This is my main question.
 
  • #9
Objects which behave classically always have de Broglie wavelength much smaller than their physical dimensions.
 
  • #10
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Objects which behave classically always have de Broglie wavelength much smaller than their physical dimensions.
Wave function is used when there is wave properties. That is why electron and other particles need wave function because they are wave. But macroscopic object like molecules are not or don't have wave behavior. So why still use wave function?
 
  • #11
classical behavior is just the limit of quantum behaviour. The equations should give you the same results.
 
  • #12
cgk
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Isn't it that the Schroedinger Equation is used whenever electron is involved? Translational and vibration mode in the molecules don't involve electrons because it is the entire atoms that move and vibrate. So I wonder if the Schroedinger Equation is used. This is my main question.
1) Electrons cannot be described without quantum mechanics.

2) If you are not interested in the electronic properties, but only in the movement of the entire atoms, you might get away without quantum mechanics. In principle the forces between atoms are determined by the electrons, but often they can be fitted and represented "well enough" by classical mechanical models. For example, biomolecules or solvents are usually treated with classical force fields (look up "molecular mechanics"). The following restrictions apply:

- Classical force fields cannot describe any change in the electronic structure of the molecule. That means: No differnt oxidation states, no chemical reactions, no excited states.

- The accuracy of classical force fields is hard to improve systematically. Usually they are fitted to a rather specific set of molecular degrees of freedom, which is everything they can be applied to. For example, if you have unusual elements, you're out of luck.

- In order to calculate vibrational spectra of molecules, small or large, you need a basis in quantum mechanics. In order to calculate accurate vibrational spectra you might need to calculate wave functions for the nuclei, too (these sit on a potential energy surface generated by the electrons). The corresponding approaches is called vibrational self-consistent field (VSCF), vibrational perturbation theory (VPT2) or vibrational configuration interaction (VCI).

In practice large molecules are often described with a hybrid approach called QM/MM, where a region of interest of a large molecule is described with quantum mechanics (usually some form of Kohn-Sham density functional thery) and the rest with MM force fields.
 
  • #13
alxm
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What is the maximum size scale (how many atoms) where the concept of wave function is still useful in chemistry esp. biochemistry?
Never. We would calculate everything with QM if we could; why wouldn't we?

Electrons always interact quantum mechanically, and you can't separate a molecule into independent parts, since every electron interacts with its neighbors, and they interact with theirs, and so on. It's not the size of the system that determine whether something acts quantum-mechanically, it's the mass of the objects you're studying, and the interactions of your system with the surroundings. Electrons do not get heavier just because you have more of them.

Wave functions are not of use in biochemistry though, because biochemistry is the study of large scale things. How do proteins fold? What things exist in the cell, what do they do, how these things interact, etc.

Biochemistry is not the study of the mechanisms of chemical reactions and other such details that require an explicit quantum mechanical description. There's a difference between a biochemist using the methods of biochemistry to study their subject, and a physical or quantum chemist using their methods to study a molecule that happens to be a biomolecule.

Biochemists don't know much if anything about the Schrödinger equation. And quantum chemists don't know much if anything about what introns and exons are.
 

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