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My question is related to the edge between Subatomic Physics and Chemistry, but I decided that here is the best place to discuss it.

As we all know, Theoretical Physics is a well developed field of knowledge, able to describe the very tiny forms of interactions. However, after some researches for some kind of formula to perfectly describe the interactions on the atomic level (not subatomic), more specifically, a way to calculate the strength of chemical bounds, I keep comming across frustrating highschool explanations, such as

ionic > covalent > H-bond > dipole-dipole > van der Waals

The most precise data that I was able to find comes at page number 20 and 21 of this pdf, that apparently shows some experimental results (I'm guessing).

So here is my question: is there really a unified formula? What if I want to simulate chemical interactions (proton-by-proton, electron-by-electron) on a computer, is it that complex to do, even assuming that I want a simple simulation of about 20 atoms?

Edit: When I reffer to calculating chemical bonds strength, I also include predicting many other chemical properties, as electron affinity or reactivity of the elements, which are all related.

Note: I can accept as answer any pdf that clarifies my question, because I wasn't able to find. Maybe I'm looking it with the wrong key-words.

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    $\begingroup$ Welcome to Chemistry.SE! While I don't have the time to give you a full-blown answer at the moment I at least can try point you in the right direction. I think the formula you are looking for is the Schrödinger Equation. It describes the behaviour of particles on an atomic level (in the non-relativistic limit). But it is not directly solvable for systems consisting of more than two particles. For those cases, a lot of methods have been developed to find an approximate solution, e.g. density functional theory (DFT), Hartree-Fock, etc. $\endgroup$ – Philipp Nov 19 '13 at 0:33
  • $\begingroup$ The whole field of theoretical chemistry is devoted to developing better and better approximations to the many-electron wavefunctions that model the bonding between atoms in molecules and the interactions between molecules. $\endgroup$ – Ben Norris Nov 19 '13 at 2:08
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    $\begingroup$ $H | \psi \rangle = E | \psi \rangle$ $\endgroup$ – user26143 Nov 19 '13 at 5:49
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The short answer: no. We do not know how to solve the Schrodinger equation analytically, even for systems as simple as the He atom.

The much longer answer:

The Schrodinger equation is the basis for almost all theoretical chemistry: chemistry that attempts to predict properties of compounds without an actual experiment. The problem is that the Schrodinger equation is unsolvable for any compound with more than two electrons, and so we must make some approximations to solve it. This leads to methods such as Hartree-Fock and Density Functional Theory.

While these approximations are usually pretty good, they are still only approximations, and sometimes stop working correctly. There is an added problem that the Schrodinger equation is only an approximation, and the proper theory to use to describe light-matter interaction is Quantum Electrodynamics, which is incredibly difficult to solve for a single photon reflecting off of a mirror.

Long story short: there may or may not be a "unified theory" for describing exactly how all bonds behave in every situation, but there are currently methods that are good enough to predict a large portion of the behavior that we observe.

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  • $\begingroup$ I have a question. The Schrödinger equation has no analytical solution for most systems, but we use classical computations to achieve a numerical approximation for the answer. However, solving a quantum problem with classical operations creates an exponential slowdown. If quantum computers ever become reality, would molecular modelling suddenly become almost trivial? If so, that will completely reshape the profession of chemistry as we know it; why attempt a synthesis in the lab with expensive reagents, when you can just calculate the result in silico! $\endgroup$ – Nicolau Saker Neto Nov 19 '13 at 11:33
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    $\begingroup$ As far as I know, it is still an open question. arXiv:1007.2648v1 "... there are broad classes of Hamiltonians for which finding the ground state energy (and therefore also a thermal state) is known to be qma-hard, that is, most likely hard even on a quantum computer (see Sec. 2.3) (70,4, 66, 98, 111). Nevertheless, the scaling of the ground- and thermal-state energy problems for chemical systems on a quantum computer is an open question. It is possible that algorithms can be found that are not efficient for all qma-hard Hamiltonians, but nevertheless succeed for chemical problems." $\endgroup$ – user26143 Nov 19 '13 at 12:48
  • $\begingroup$ I don't know about quantum modeling, but some of the other quantum algorithms (Grover search and Shor factorization) are non-deterministic, so you need a classical computer to check them afterward. Don't know if that would apply to this. @user26143 do you know if quantum computer simulations would have to be checked clasically? $\endgroup$ – chipbuster Nov 20 '13 at 8:47
  • $\begingroup$ @chipbuster, I know very little about quantum computing. As far as I know, I haven't awared any necessity of classical check for quantum chemical computing... $\endgroup$ – user26143 Nov 20 '13 at 8:55
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    $\begingroup$ @Nicolau Theory will never be a sufficient substitute for the experiment - however, it will (or is) a very powerful tool for designing chemical reactions. The problem at hand is unfortunately the human brain: We are usually blinded by our own ideas, so that we are not capable of searching further away from them. The calculations tend to only be the tool to put some bone to the idea, but it might never be able to actually go a different way that that, that the user intended. Correct me if I am wrong or too negative... $\endgroup$ – Martin - マーチン May 2 '14 at 3:26
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If you want to have a more comprehensive overview about your question, I would suggest you to read this book The Nobel Prize: The First 100 Years",

In this link The Nobel Prize in Physics 1901-2000 you'll find one of the chapters for free with a reasonable explanation about why we treat our problems using different hierarchies or different approaches (bottom-up or top-bottom).

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formula to perfectly describe the interactions Calculating the bond angle of water, vacuum vs. condensed phase for three small atoms, has a huge literature offering no definitive answer. Something as simple as the pendulum equation (ideal - in vacuo, no friction or other dissipation), is not a closed form,

http://upload.wikimedia.org/math/6/4/c/64cd3db46ef18d401109423e81cdf6ce.png
http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/mechan/Pendulo1.pdf
http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/mechan/Pendulo2.pdf
http://fy.chalmers.se/~f7xiz/TIF080/Period.pdf
http://www.phys.uconn.edu/~hamilton/phys258/N/pend.pdf
http://www.scielo.org.mx/pdf/rmfe/v54n1/v54n1a10.pdf

HyperChem Lite for a very modest price has a lovely MM+ (semi-empirical) calculation engine. I do blocks of 32500 iterations, update screen every 500 iterations, with 1e-020 limit until things look good enough, the method chokes, or the structure is ridiculous (pi bonds in high symmetry environments can go odd places).

http://www.hyper.com/Products/HyperChemLite/FeaturesLite/tabid/375/Default.aspx
ab initio Hartree Fock/6-31G(d) is better if you have two weeks in a cluster.

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    $\begingroup$ HF/6-31G(d) produces sometimes worse results than semi empiric methods or molecular modelling. It will not take two weeks in cluster. A molecule about 20 atoms should not take more than 20 h on a serial core i7 calculation. I am currently doing geo-opt dft with 100 atoms on 4 cores (2.8GHz) in less than a day. $\endgroup$ – Martin - マーチン May 2 '14 at 3:33
  • $\begingroup$ How about CCSD(T)/aug-cc-pVQZ on 8 atoms using 6 cores in just a few hours? :) Hartree-Fock just shouldn't be used... ever... This isn't the 1970s. Correlation energy can be captured with cheap, more rigorous methods on today's computers. Oh, and 6-31G(d)? Great for lab exercises, preliminary starting points, etc. I will try to axe any paper that uses such a small basis for production work without it being extensively calibrated and/or for good reason. $\endgroup$ – LordStryker May 2 '14 at 15:07
  • $\begingroup$ I can send you HyperChem mm+ and HF/6-31G(d) *.hin files for mazepath.com/uncleal/schwartz.png mazepath.com/uncleal/schwart3.png. When things are slow, certainly Christmas, grind it out to observe real world results. If you can unambiguously assign a sense of chirality to the central five atoms of the point group T molecule, I'll send you a very large lollipop or a bottle of Lagavulin 16. It is a Wreave bet that the bottle remains mine - against anybody who tries. "8^>) $\endgroup$ – Uncle Al May 3 '14 at 21:46

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