An Introduction to First-Principles Calculations

The term "first-principles calculations" in the title may be unfamiliar to you. "First principles" refers to the most fundamental laws within a given scope of consideration. First-principles calculations are a method for determining various physical quantities based solely on theoretical calculations from these fundamental laws. With the exception of phenomena involving nuclear forces, such as radioactivity, and gravitational phenomena, the events that occur around us are governed by the fundamental laws of electromagnetism and quantum mechanics. While "first-principles calculations" exist in several fields, each with different assumed fundamental laws and calculation targets, here we are considering those that investigate the properties of matter based solely on calculations from fundamental equations such as those of electromagnetism and quantum mechanics.

Personally, I believe the most fascinating aspect of first-principles calculations is explaining real-world phenomena through theoretical calculations alone. Of course, there are many other advantages. For example, because these are simulations run on a computer, we can obtain information at the atomic and electronic levels that cannot be observed in experiments, thereby deepening our understanding of phenomena. Furthermore, first-principles calculations have a predictive accuracy comparable to that of experiments, so they are often used as a substitute for them. Recently, they have also been used for screening, where calculations are performed instead of experiments to select promising materials from a large pool of candidates in the search for useful substances.

In my laboratory, we conduct high-precision calculations of X-ray photoelectron spectroscopy spectra from core electrons to investigate the configuration of impurity atoms in semiconductors. X-ray photoelectron spectroscopy is a technique that involves irradiating a sample with X-rays, measuring the kinetic energy of the ejected electrons, and thereby examining the state of the atom from which the electron originated. The figure shows the electronic state of two adjacent arsenic (As) atoms in a silicon (Si) semiconductor. A photoelectron is emitted from the core 3d orbital of an As atom. The left (right) side shows the state before (after) electron emission. In the final state, the absence of the electron has the same effect as the presence of a positive charge, and you can see that the surrounding electrons are attracted to this positive charge (bottom right figure). Thus, the state of the electron's surroundings changes significantly before and after its emission. What is interesting is that although it may seem that the state after the electron is ejected has no bearing on the ejected electron itself, in many cases, the results do not align well with experiments unless this final state is included in the calculations. This is thought to be due to a quantum mechanical effect.