I should do this before I unconsciously turn this blog into photography-themed website..as I ‘ve promised, here I am to explain what I have got in Monte Carlo’s CASINO winter-school, or perhaps I should change the title into “How to gamble in CASINO properly”. Be careful, the rest of this article contains things behind human’s comprehension and in inhuman language.

Things that should be noted before I start explaining is the keywords to understand the method better: “DFT” (Density Functional Theory or to be more general; ab initio/ first principle, because we are working on Quantum Monte Carlo), “random walk” (random numbers ‘thrown’ into certain area of integration, a mathematical algorithm), Jastrow Factor (how can I not remember this thing), and the last is CASINO itself. I’ve had opportunity to meet and talk to the developers of this amazing computational program and was taught what was behind-the-program last month. Many of the courses filled with mathematics and algorithm rather than physical properties of a matter, and I honestly don’t want to include all things mathematical here or it’ll turn into one-lengthy-page-of-QMC-lecture. So be glad.

Quantum Monte Carlo was a very powerful method to compute a system, and has become quite a worldwide trend beside molecular dynamics. If QMC people are allowed to boast, it is more precise than DFT and 2-5% statistically closer to experimental. This ‘gambling’ method doesn’t need exchange correlation (as DFT’s basic and the source of the drift on Platinum to Gold system) and works in different way to solve Schrodinger Equation. In short, QMC excels DFT in term of accuracy and precision, because DFT isn’t that reliable.

That is the summary of the course and the reason why we need to learn about QMC. But unfortunately, my engineering-mind works in quite different way from my fellow scientists (alas, I’m the youngest, the only person who is still in undergrads, and in engineering field while people attending the course were mainly from Chemistry, Physics, or IT). I question what engineers usually ask:

“Is the method financially effective and efficient?”

Unfortunately the answer is “not quite”.
As QMC is better than DFT in term of accuracy, it still can’t generate geometrical structure of the said system and it still has to give DFT the job. It is worse because unless you have HPC (High Performance Computing) facility with you, you can’t do the method well, since it divides load into many processors, and Monte Carlo itself requires high spec computer to generate random walks. More so with bigger and complex system. Plus we need other (paid) software to generate our dear wave function…

My professor said that some of researcher dislike QMC because of this, plus because our lab doesn’t really have good computer facility (only 108 cores スパーちゃん, unlike K-Comp or other country’s super HPC facilities), and he said although DFT isn’t really reliable with LDA and GGA exchange correlation, PBE exchange correlation has good term with QMC’s computational result. “So, why bother?” he said. It is true that DFT’s exchange correlations have limit and scientists over the globe are working and submitting new exchange correlations each day, but -well- people still use existing (popular) exchange correlations for their researches. “We are working on our research to give us bigger picture and understanding of a system and oversee our newly designed nanomaterial, not really working for high precision. DFT can do the job quite well with PBE exc-corr. So, we’ll do that still.”

I agree with him, it is back to our research’s goal. Both of these methods are still incomplete, and both still have problem with pseudopotentials. It is not like who will win between DFT or QMC, but they complement each other. When DFT fails especially for some complex unusual matter and Titanium Dioxide, let’s use QMC instead. If we can manage the system with DFT well, just leave it to that method.

How about comparing QMC with molecular dynamics, my specialty? Unfortunately QMC only compute state statically. Just in one condition per time, and certainly not dynamics… well, I think you can make it “dynamics” by moving the temperature over time but it’ll become quantum molecular dynamics other than pure QMC (ha!). MD, as its name said, has different approach than the other two, as it gives you understanding mainly about dynamics, not quite in ground-state condition, and for bigger thousands of atoms involved, which QMC and DFT fail. Back to last paragraph’s conclusion, these three complement each other and give you different physical properties to be analyzed for you to understand and oversee the matter/system you’ve designed. Like I’ve quoted my professor for the tenth thousand times (read: four times in winter-school), you need to learn DFT, MC, MD, (and tight-binding?!**) to understand material completely.

…and don’t tell me you fell into first paragraph’s joke.

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