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Updated: Jun 5, 2025

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密度的断片线性要求如何影响Kohn-Sham系统中的数量.

Eli Kraisler1

  • 1Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, 9190401 Jerusalem, Israel.

Journal of chemical theory and computation
|December 16, 2024
PubMed
概括

科恩-沙姆密度函数理论 (KS-DFT) 的计算通过了解电子密度如何与电子数线性变化而得到改善. 这项研究揭示了KS数量的限制,有助于减少开放系统中的错误.

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Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Linear Circuits01:17

Linear Circuits

A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise...
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Linear time-invariant Systems

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
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