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Exhibit 1: Ground state hyperfine splitting of the H atom: 1420405751767(1) mHz (present most accurate experiment) 142045199 mHz (present most accurate theory) The error in the theory is due to the difficulty in treating the nuclear structure (2 up quarks + 1 down). Exhibit 2: Ground state hyperfine splitting of the muonium atom: 4463302780(050) Hz (...

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The 2006 variational calculation by Schwartz is lower (more accurate) than Nakashima & Nakatsuji's 2007 energy: 2006 Schwartz: -2.903724377034119598311159245194404446696925309838 2007 Nakashima & Nakatsuji: -2.90372437703411959831115924519440444669690537 The lowest variational upper bounds ground state energies for the first 6 elements, ...

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First of all, MP2 (for example) is actually guaranteed to converge from above to the basis set limit even though MP2 in one specific basis set can give an energy lower than the FCI energy in that same basis set. So it's variational character in the basis set sense that matters here. Furthermore, variational character is not the most pertinent thing to ...

10

In general, when computing any property with different models (e.g. level of theory, basis set, etc), if you don't have some kind of theoretical bound (like the variational principle) to determine what is a better result, you need a reference value to compare against. One choice for this reference is experimental results. At the end of the day, the goal of ...

10

I wrote an answer to a similar question in the past, but focused in that question only on the state-of-the-art ultra-high precision calculations on atoms and the three most common isotopologues of $\ce{H_2}$. I will first repeat those here: Atomization energy of the H$_2$ molecule: 35999.582834(11) cm^-1 (present most accurate experiment) 35999.582820(26) cm^...

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tldr: This is something of an eternal debate. IMHO very small imaginary frequencies can be okay, but it depends on your system and needs. As you might see from the various comments above, there are often different opinions on whether very small imaginary frequencies matter. The truth is, that it depends a bit on the size of the molecule and what you plan to ...

5

High accuracy energy methods, are they worth it? They are absolutely worth it for many types of studies, but not worth it for other types of studies. It depends on precisely what the aim of your project is. As far as I understand they are used for high-end kinetics calculations of small molecules. They are also used for spectroscopy, benchmarking and for ...

5

Well, Nike already answered the point about the variationality: even though methods like MP2, CCSD, and CCSD(T) are non-variational in that they may over- or underestimate the energy of the ground state (or excited states) of the Schrödinger equation, the energy reproduced by any given method typically does behave variationally with respect to the basis set....

1

Advantage for QMC: While this question is quite open ended due to there being at least 15 different types of QMC, one thing that all 15 of those methods have in common is that as far as I know they can all be restarted when the calculation has to stop for whatever reason. Since you pointed out that ACFDT-RPA calculations cannot be restarted, the ability to ...

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