What is the difference between ab initio calculations and molecular orbital theory?

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    $\begingroup$ What is the difference between sunrise an chair? $\endgroup$ – Mithoron Jun 13 '19 at 17:32
  • $\begingroup$ "ab initio" literally means "from first principles" or "from the beginning" in latin. It therefore (literally) depends what you consider the most fundamental theory (what mirhoron calls high level theory). en.wikipedia.org/wiki/Ab_initio_quantum_chemistry_methods $\endgroup$ – Buck Thorn Jun 13 '19 at 18:45

Ab initio means calculations that are strictly from the principles of quantum mechanics. This contrasts with a non ab initio method which can involve parameters that do not arise directly from principles (i.e. results from experiment and/or 'better' calculations). One typical example of something that is not ab initio is a functional for Density Functional Theory. Because the exact functional is unknown, different functionals are generated using large datasets of high level calculations. These are often good at reproducing experimental data in many situations however you cannot derive them directly from the postulates quantum mechanics.

Molecular Orbital Theory (which can be implemented with the Hartree-Fock method) is an example of an ab initio method. One can (very roughly) come up with MO theory by approximating each electron as only feeling the effect of the average positions of the other electrons. So, if an orbital has an electron in it all the other electrons will feel a repulsion from the space occupied by that orbital. This results in a set of coupled one particle problems the solutions (eigenfunctions) which can be solved to find the Molecular Orbitals for the system.

More generally, ab initio calculations also refer to the more accurate post Hartree-Fock methods such as Configuration Interaction (CI), and Coupled Cluster (CC).

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    $\begingroup$ Ab initio can mean pretty much whatever people consider relatively high level of theory. $\endgroup$ – Mithoron Jun 13 '19 at 17:35
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    $\begingroup$ This is misleading at the very least. Regarding DFT: chemistry.stackexchange.com/q/33764/4945 It is paramount to understand, that DFT is exact in principle. HF is not the same as MO theory; it is one attempt at mathematically formalising MO theory. $\endgroup$ – Martin - マーチン Jun 14 '19 at 5:29
  • $\begingroup$ DFT is of course exact in principle, but also the perfect example of a method that needs parameters from another source for its practical usage. This is why I referred to specific functionals. For this question, I think directing towards HF is the most helpful direction for future inquiry. $\endgroup$ – PJ R Jun 14 '19 at 22:34
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    $\begingroup$ The way you wrote this is a bit misleading; at least I obviously misunderstood what you meant. Sure, there are density functional approximations which contain empirically fitted parameters, but there are also some that do not. The usage of this terminology may lead to confusion, and judging from the question, there is not a solid foundation to clear these up. I am not sure how helpful it is to direct someone to HF, when MO theory is not a solid foundation. $\endgroup$ – Martin - マーチン Jun 17 '19 at 7:59
  • $\begingroup$ Thank you for those comments Martin, I have incorporated them into the answer to (hopefully) improve clarity. $\endgroup$ – PJ R Jun 18 '19 at 21:31

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