Quantum Chemistry SCF Convergence by Electron Density Region
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Solution Overview
Problem
The high computational cost and extended computation time in quantum chemistry calculations, particularly in density functional theory (DFT), are due to the large number of iterations required for electron density convergence, especially in regions of low electron density where the density fluctuates significantly.
Innovation Solution
A quantum chemistry computation method that reduces the number of SCF iterations by using convergence criteria based on both the difference and difference change rate of electron density, and divides the analysis space into subspaces with tailored criteria for each region, allowing early termination of calculations when either criterion is met.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the self-consistent field method is applied to calculate electron density in quantum chemistry, then the accuracy of the calculation is improved, but the computation time and computational cost increase significantly
Solution Approach 1:
The patent applies local quality by setting different convergence criteria for different spatial regions. High electron density regions use a first convergence criterion while low electron density regions use a second, less stringent criterion. This allows the calculation to maintain accuracy where needed while reducing computation time in regions where high precision is less critical.
Solution Approach 2:
The patent segments the calculation space into multiple regions based on electron density magnitude. By dividing the space and applying different convergence standards to different segments, the overall computation time is reduced without significantly compromising the accuracy of the total electron density calculation.
2Reliability
If the self-consistent field method iteratively calculates electron density until convergence, then the reliability of the result is improved, but the number of iterations increases leading to extended computation time
Solution Approach 1:
The patent implements local quality by applying different convergence criteria to different spatial regions. Regions with high electron density maintain strict convergence standards for reliability, while low electron density regions use relaxed criteria to improve calculation efficiency. This resolves the contradiction between reliability and productivity.
Solution Approach 2:
The patent applies partial action by not requiring full convergence in all regions. Low electron density regions use a second convergence criterion that requires fewer iterations, representing partial convergence that is sufficient for those regions while maintaining overall calculation reliability.
3Stability of the object's composition
If uniform convergence criteria are applied across all space regions, then the consistency of the calculation is maintained, but the computation time increases due to excessive iterations in low electron density regions
Solution Approach 1:
The patent replaces uniform convergence criteria with location-dependent criteria. High electron density regions use a first convergence criterion while low electron density regions use a second criterion. This maintains calculation consistency in critical regions while reducing iteration time in less critical regions.
Solution Approach 2:
The patent segments the calculation domain into high and low electron density regions, each with its own convergence criterion. This segmentation allows the calculation to be consistent where needed while efficient elsewhere, resolving the contradiction between consistency and time consumption.
Data Source
AI summary
An information processing apparatus iteratively calculates, using a self-consistent field method, an electron density at each of a plurality of points in a space where a substance exists. The information processing apparatus determines, for each of the plurality of points, each time the electron density is calculated, whether a plurality of indicator values based on the calculated electron density satisfies respective convergence criteria respectively associated with the plurality of indicator values. Then, the information processing apparatus terminates, for each of the plurality of points, the iteratively calculating of the electron density upon at least one of the plurality of indicator values satisfying the associated convergence criterion.