Abstract
In the previous chapter, we first learned about a series of operations, assuming that the “specifications given to the input file” were “prepared and given by the teacher” in order for you to grasp the “sequence of operations”. Now, the main subject of this chapter is to learn how those specifications should be determined in the first place. First, we will explain why it is important to determine the conditions for calculations in the prediction of physical properties. Next, we describe how to determine the parameters those are relatively easy to understand, namely those to define the resolution of the calculation, and give an explanation so that the reader can imagine the physical meaning of the parameters. In the latter part of the lecture, we will understand how much of a difference in prediction is caused by the selection of pseudo-potential and exchange-correlation potential through practical use. The explanation of the reasons for the differences is given in the next chapter (Chap. 5). As an important technical matter, we will explain how to use a script to perform a loop process to automatically submit calculations with different calculation conditions one after another.
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Notes
- 1.
The readers might include those mainly using Gaussian basis set for isolated systems like molecules. For isolated systems, there is no such concept like k-mesh, basically, but we can regard it as a calculation with 1\(\times \)1\(\times \)1-mesh (sometimes referred as “\(\Gamma \)-point calculation”). What is corresponding to \(E_\textrm{cut}\) is the basis set quality specification such as “6-31G”, “6-311G++”, etc. [2], for which we will explain more in detail in the next chapter.
- 2.
It is the convention in ab intio calculations to take \(m_e\) \(=\) 1 and \(\hbar \) \(=\) 1, called natural unit system.
- 3.
When calculating physical quantities, it is necessary to count up all the electronic states occupying the band, which is performed as the integration over the region of the structure in k-space assembled from the occupied states.
- 4.
In order to be able to handle the practical level, one needs to be familiar with several correction schemes related to the overlap** integral error between bases (BSSE), the complete basis limit (CBS) etc.
- 5.
This is the mnemonic based of “\(E_\textrm{cut}\) of wavefunction’.
- 6.
The unit for ecutwfc is “Ry” (Rydberg).
- 7.
To avoid typos, the input files used in this course are included as text files in the downloaded materials as introduced in Sect. 2.4.2. You can copy them, or “cut and paste”, or for comparing to find mistakes using “diff” or “sdiff” command. These files are stored with the same file name under “\(\sim \)/work/setupMaezono/inputFiles/”.
- 8.
This is the mnemonic of “‘ecut’ of rho (= \(\rho \); charge density).
- 9.
This is a typical example of an input parameters that are “too advanced for beginners for the time being and can be left for later understanding” as described in Sect. 5.2.1. It is best to use the recommended values, leaving it to the methodological experts to decide what settings are best. However, the recommended values are often updated as time goes by, so you need to pay attention to such updating.
- 10.
The backslash “\(\backslash {}\)” is used to show a too long string to fit on a line (see Acronym).
- 11.
To avoid typos, the input files used in this course are included as text files in the downloaded materials as introduced in Sect. 2.4.2. You can copy them, or ‘cut and paste’, or for comparing to find mistakes using ‘diff’ or ‘sdiff’ command. These files are stored with the same file name under ‘\(\sim \)/work/setupMaezono/inputFiles/’.
- 12.
The backslash ‘\(\backslash {}\)’ is used to show a too long string to fit on a line (see Acronym).
- 13.
In general, it can be different, so we have confirmed this point first.
- 14.
We strongly recommend to use any of ‘text editor’ instead of ‘MS-Word’. Most of beginners (including the author in past!) tend to write everything in Word files (as recognized as ‘files’), but since Word is originally a multifunctional word processing software for creating beautiful ‘final documents’ including figures, variations of fonts etc., it is heavy in operation and capacity. If you are handling only the text information, no need to use such a heavy operation tools at all. You will find how lighter and handy operations are realized by the text editors. You can find any of your appropriate text editors working on your OS (usually free, long-life, and world-wide users) by search on web as ‘text editor windows’ etc. Note for the beginners that it is possible to save and keep files even for text editors, as a matter of course. It is never ‘(Document files) = (Word files)’.
- 15.
It is also called exchange-correlation functionals depending on contexts.
- 16.
In this wording, we note again that the meaning of the ‘model’ here is a slightly different from that used for the model theories. It will be explained in detail in the next chapter (Sect. 5.3.3).
- 17.
From experimental facts, the correct answer is known to be \(\alpha \)-quartz (‘qa’) [9].
- 18.
In practical projects, there are also the cases to evaluate and compare the ground state energies for a fixed geometry, typically the experimental one [7].
- 19.
Exactly saying, ‘HF’ and ‘DMC’ are actually not the exchange-correlation potentials, but the name of other methods than DFT which handles the exchange and correlation in other framework.
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Maezono, R. (2023). Determining Computational Conditions. In: Ab initio Calculation Tutorial. Springer, Singapore. https://doi.org/10.1007/978-981-99-0919-3_4
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