What is the importance of cut-off energy in Plane Wave Density Functional Theory
Hi Wasseem,
The cutoff energy tells us about the cutoff on the number of plane wave functions being utilized as basis functions to represent the wavefunction. Theoretically, an infinite number of basis functions is required to produce an exact answer. However, this is not computationally feasible and a cutoff must be introduced. I hope this helps.
Thanks Adib ...
Adib as you are an expert in DFT, could you please suggest me any literature .. that covers basics of DFT modeling .... may be a book or video lecture... or anything .. As I am new to this field ...
Hi Waseem,
A very nice book in my opinion is "Electronic Structure: Basic Theory and Practical Methods" by R.M.Martin. Its well written and gives you an intuitive feel for the subject. Extending upon Abid's answer, the planewaves are your basis set - the set of functions you combine to describe your wavefunction. The more you include, the better your representation will become. Eventually, the high frequency (high energy) planewaves will only give very minor improvements. This is in much the same way as you may calculate sin(x) using a Taylor expansion for example - the first few terms give you a useful sensible answer, you can keep adding higher order terms to improve the precision but you don't need to go to the 100th term if you only need an answer to the 1st decimal place!
This becomes more important once you consider how these codes are implemented. These functions are discretised on numerical grids. Adding high frequency (small wavelength) planewaves will therefore require increasingly finer grid points to be described which will quickly increase computational cost.
This is why you add a cut off energy. An important note to consider, you won't know what a sensible cut-off energy is a priori, so any calculation must begin by convergence testing. Repeat some basic calculations for your system increasing the cut-off energy and check for property convergence.
Hope this helps,
Jacob
Thanks jacob .. quite helpful ... could you please suggest me a software .. as there are lot of option such as vasp, quantum expresso, quantumwise etc
Hi Waseem,
Vasp and Quantumwise are paid codes while QE is free. So for your learning period, you can go with QE.
i liked this video for a basic understanding of basis sets using for wave function. In fact i could easily understand the answer of Jacob Chapman , as i have seen this video earlier. Else i might not have understood what Jacob has written above.
watch
https://www.youtube.com/watch?v=vjtgxySnYJw
https://www.youtube.com/watch?v=e40CsK7kgS0&t=328s
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