Even though I'm in my late early thirties there are days I feel like I'm teenager again, and I'm not talking about raging hormones and acne, though those are both problems I have. I thought the acne was supposed to clear up once you got passed a certain age? I feel like the teenager stomping up and down saying, "Quit trying to tell me what I am/what to be!" in a nasally whiny voice (so my normal way of speaking). I tend to consider myself a reasonable person, reasonably intelligent anyway, which is not always a valid assumption.
In quantum chemistry there is this interesting phenomena where people like to use relatively inexpensive, computationally speaking, methods to solve the many-fermion Schrodinger equation. More specifically, they like second order many-body perturbation theory (MP2) and density functional theory (DFT). They both have some benefits, but if you want an accurate description of the problem, at the electronic structure level, they are not very reliable without some major work which can often muddle if not entirely obfuscate the physical interpretation of the results, more particularly with DFT. So not only do you end up with results that may or may not be accurate (maybe this is a lengthy and cruel joke playing off of Schrodinger's cat) and which may not even have a straightforward or even real physical meaning. For DFT you can imagine it as you have a giant machine with lots of knobs, switches, buttons, and even a henchman to do the work of twisting, flipping, switching, and manipulating all of the controls for you. This machine has the potential to provide you with very accurate answers, but only when the toggles, knobs, switches and dials are placed in the correct configuration, even then it's not always clear what they do exactly or what they mean. The problem is that no one knows what this correct configuration should be and even worse, from the stand point of trying to find that correct configuration, people like to add more adjustable doo-hickies to get a "better" answer, whatever that means.
One of the benefits and why some people like to use DFT is it has this nice property that it's variational. This means that the answer you get will always be greater than, or equal to the exact answer. This leads many people to say, "Wow! That's amazing! I'll never get answer lower than the real one!" But let's think about his for a second. We need to introduce the idea of a model space (I'm not going to be mathematically rigorous here because I don't want to be too over bearing, I just want to get the idea across. So if by some chance a person mathematically inclined reads this and says "That's not really true..." you can comment on it and I'll likely agree with you. It's called heuristic for a reason). Take earth, for example, and say we want to model the ocean. We need a good representation of the earth and so we shouldn't use a model space like mars, jupiter, saturn, pluto, or the sun as they will not give us a proper space/description of what we wish to model. When we first start with the Schrodinger equation we have a proper model space, we know we are not only on a planet, but on the correct planet. As we start to add knobs, dials, toggles and switches to manipulate things we start to change the landscape of the planet we are. Oceans might become deserts; the size, gravity, temperature, etc. might be changed too and we don't know how because there it not a specific physical meaning assigned to these adjustable parts. All we have to compare against is some numbers of what we know the answer should be for various situations. So we adjust all the different variables, which before we made any adjustments we were in the correct model space, or on the correct planet, and by the time we're done we have answers that come out close to the 'correct' ones, but we don't know anymore if we're still on an earth-like planet or if we've morphed into a rocky, barren desert, or even a giant ball of gas without any solid surface, or something else entirely (maybe a black hole?). This is a real problem because we're using these approaches to model reality but which reality does it belong to? Am I sitting comfortably on a beach watching the oceans rise slowly? Or am I stranded on the surface of venus scrambling to get inside before the sulfuric acid eat through my space suit and then my face? The numbers may come out being similar, but that's where it ends.
I would rather spend a longer amount of time using computer resources to compute an answer that has a physically meaningful and relevant interpretation. But this is definitely in the minority and many of the people that use DFT have most likely never even thought about this. Science is indeed in sad shape in some areas. A little more understanding, and math background, would go a long way to help advance many fields, as this is not a unique problem to my field.
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