Timeline for Was Walter Kohn wrong about this?
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22 events
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| Nov 7, 2020 at 1:19 | comment | added | Matt Horton | @Nike Dattani, that's an important distinction, my apologies! | |
| Nov 5, 2020 at 22:24 | comment | added | Nike Dattani - No Free Time | @MattHorton I wrote "one of my favorite humans of all time", not "favorite human of all time" :D | |
| Nov 5, 2020 at 20:51 | comment | added | Matt Horton | Kohn being your favorite human of all time sounds like strong praise :-) Do you have any references on him as an individual? | |
| Jul 6, 2020 at 12:50 | vote | accept | ProfM | ||
| Jun 29, 2020 at 20:15 | history | edited | Nike Dattani - No Free Time | CC BY-SA 4.0 |
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| Jun 27, 2020 at 20:42 | comment | added | Nike Dattani - No Free Time | @Tyberius, Greg: I agree. The last section of my answer says that what matters is not the number of electrons but the specific situation. You give a specific example of M non-interacting He atoms, or some systems with identical geometries where tiny changes of SCF give huge changes in wfn... in those situations getting an accurate wfn represented in classical storage (bits) is extremely hard. 50 electrons would be extremely hard. However what about a single-reference system where a single determinant gives a very accurate description of the system? 10000 electrons is now easy. | |
| Jun 27, 2020 at 18:41 | comment | added | Greg | @NikeDattani Consider a situation when you have nearly identical or identical geometries, and even small changes of SCF process leads to very different looking wave functions. The density, the energy, etc can be accurate, but there is something inherently ad hoc about the wfn representation. | |
| Jun 27, 2020 at 17:09 | comment | added | Tyberius♦ | @NikeDattani I think Greg's answer gets at the point that Kohn made in regards to overlap of the true and approximate wavefunction. He gives an example of N identical non-interacting n electron systems. If you are even slightly inaccurate in determining the wavefunction of one of these systems, the overlap for the N system wavefunction will quickly decay to zero with increasing n. We can often get some accurate properties like the energy and density which trace over most of the underlying dimensions, but it's not guaranteed and we lack a direct way of to distinguish a good/bad wavefunction | |
| Jun 27, 2020 at 16:16 | comment | added | Nike Dattani - No Free Time | @Greg In my answer I included "A good energy doesn't necessarily mean an accurate wavefunction, but coupled cluster wavefunctions are not bad at all (otherwise you wouldn't be able to calculate accurate properties like polarizabilities)" so I agree that energy is irrelevant. But if you can get good energies and polarizabilities, and other properties, I imagine the wfn must be quite decent (?). Surely the wfn becomes hard to calculate accurately (even with coupled cluster or any method), when N becomes too big, but isn't that also true of the density? | |
| Jun 27, 2020 at 16:03 | comment | added | Greg | I do not think Kohn was talking about accuracy in energy. I think it is much more about how the error propagates in the calculations, and how the orbital coefficients become extremely correlated. I often see very different looking wavefunctions as the results of calculations on the same systems, which has very different orbital coefficients when compared to each other but produce similar energies and properties. In that sense, one can say these wavefunctions are not a very insightful representation of the system. | |
| Jun 27, 2020 at 14:17 | history | edited | Nike Dattani - No Free Time | CC BY-SA 4.0 |
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| Jun 26, 2020 at 22:36 | history | edited | Nike Dattani - No Free Time | CC BY-SA 4.0 |
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| S Jun 26, 2020 at 19:56 | history | suggested | Glorfindel | CC BY-SA 4.0 |
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| Jun 26, 2020 at 19:44 | review | Suggested edits | |||
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| Jun 26, 2020 at 19:24 | history | edited | Nike Dattani - No Free Time | CC BY-SA 4.0 |
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| Jun 26, 2020 at 19:19 | history | edited | Nike Dattani - No Free Time | CC BY-SA 4.0 |
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| Jun 26, 2020 at 17:40 | history | edited | Nike Dattani - No Free Time | CC BY-SA 4.0 |
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| Jun 26, 2020 at 17:37 | comment | added | ProfM | +10 Thank you so much for this comprehensive answer! | |
| Jun 26, 2020 at 17:31 | comment | added | Nike Dattani - No Free Time | Interesting that my sections always grow longer and longer, when in fact I intend for them to get shorter and shorter. | |
| Jun 26, 2020 at 17:30 | history | edited | Nike Dattani - No Free Time | CC BY-SA 4.0 |
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| Jun 26, 2020 at 17:24 | comment | added | Nike Dattani - No Free Time | By the way, how do you calculate the density using first principles? I'm not familiar enough with density-based quantum chemistry, but it seems another argument is that the density can't be calculated accurately (if you want to argue that the wavefunction can't). | |
| Jun 26, 2020 at 17:23 | history | answered | Nike Dattani - No Free Time | CC BY-SA 4.0 |