DOI: 10.66106/fzsxbi.20250101 ISSN: 3105-7462

基于改进最小二乘法的分子结构参数拟合与误差分析（Fitting and Error Analysis of Molecular Structure Parameters via Improved Least Squares Method）

聂佳磊 Jialei Nie
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Abstract：Traditional least squares suffer from weak robustness, sensitivity to spectral outliers, low multi-parameter fitting precision and accumulated residuals in molecular parameter fitting. This paper proposes an improved least squares algorithm with adaptive weights and iterative residual correction. It dynamically updates sample weights by fitting residuals to weaken noise interference, and adopts closed-loop iteration to curb error accumulation. Comparative experiments on FTIR data of organic small molecules show that the proposed method has higher correlation coefficient and lower root mean square/mean absolute error. It can accurately calibrate bond lengths, bond angles and vibrational frequencies under noisy measurements. The algorithm overcomes the defects of traditional fitting approaches and offers a robust, high-precision fitting tool for quantum chemistry, spectral analysis and molecular design.

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