Cutoff Energy Determination for DFT Convergence
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Solution Overview
Problem
In density functional theory (DFT) calculations, determining the optimal cutoff energy is time-consuming due to the need for multiple iterations, leading to inefficient calculation times and potential overestimation or underestimation of total energy values if not set correctly.
Innovation Solution
A method involving repeat calculations of electron density using a self-consistent field method with progressively reduced cutoff energies until a predetermined condition is met, allowing for the determination of optimal cutoff energy for DFT calculations, thereby reducing calculation time and ensuring accurate total energy convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multiple iterations with different cutoff energies are performed to determine optimal cutoff energy, then accuracy of total energy calculation is improved, but calculation time increases significantly
Solution Approach 1:
The patent applies preliminary action by performing a preliminary calculation with a higher cutoff energy before the main calculation. This preliminary step prepares the electron density and wave functions in advance, allowing the subsequent calculation with lower cutoff energy to converge faster and more accurately, thus reducing the total calculation time while maintaining accuracy.
Solution Approach 2:
The patent uses a composite approach by combining results from two different cutoff energy calculations. The electron density and wave functions obtained from the higher cutoff energy calculation are used to initialize and improve the convergence of the lower cutoff energy calculation, creating a composite solution that leverages the strengths of both approaches.
2Measurement precision
If cutoff energy is set too high, then accuracy of electron density calculation is improved, but calculation complexity and time increase
Solution Approach 1:
The patent applies parameter changes by using a higher cutoff energy for the preliminary calculation to obtain accurate electron density and wave functions, then using these results to initialize a subsequent calculation with lower cutoff energy. This dynamic adjustment of the cutoff energy parameter allows achieving accurate results without the excessive complexity of consistently using high cutoff energy throughout all calculations.
3Productivity
If cutoff energy is set too low, then calculation time is reduced, but total energy values may be overestimated or underestimated
Solution Approach 1:
The patent performs a preliminary calculation with higher cutoff energy to accurately determine the electron density and wave functions before conducting the main calculation with lower cutoff energy. This preliminary action ensures that even though the main calculation uses a lower (more efficient) cutoff energy, the results remain accurate because they are initialized with high-quality data from the preliminary step.
Solution Approach 2:
The patent implements feedback by using the results from the preliminary high-cutoff-energy calculation to initialize and guide the subsequent low-cutoff-energy calculation. The electron density and wave functions obtained from the preliminary calculation serve as feedback that improves the convergence and accuracy of the final results, preventing overestimation or underestimation of total energy values.
Data Source
AI summary
A non-transitory computer-readable recording medium stores a program for causing a computer to execute a process, the process includes in repeat calculation of electron density of a substance by a self-consistent field method that uses a specific number of wave functions according to cutoff energy, executing a second electron density calculation at an (N+1)-th time (N is an integer greater than or equal to 1) by applying second cutoff energy of a value smaller than first cutoff energy applied to an first electron density calculation at an N-th time, determining whether the electron density obtained by the second electron density calculation at the (N+1)-th time satisfies a predetermined condition, and outputting the value of the second cutoff energy in a case where the condition is not satisfied.