To implement equilibrium hard‐modeling of spectroscopic titration data, the analyst must make a variety of crucial data processing choices that address negative absorbance and molar absorptivity values. The efficacy of three such methodological options is evaluated via high‐throughput Monte Carlo simulations, root‐mean‐square error surface mapping, and two mathematical theorems. Accuracy of the calculated binding constant values constitutes the key figure of merit used to compare different data analysis approaches. First, using singular value decomposition to filter the raw absorbance data prior to modeling often reduces the number of negative values involved but has little effect on the calculated binding constant despite its ability to address spectrometer noise. Second, both truncation of negative molar absorptivity values and the fast nonnegative least squares algorithms are superior to unconstrained regression because they avoid local minima; however, they introduce bias into the calculated binding constants in the presence of negative baseline offsets. Finally, we establish two theorems showing that negative values are best addressed when all the chemical solutions leading to the raw absorbance data are the result of mixing exactly two distinct stock solutions. This allows the raw absorbance data to be shifted up, eliminating negative baseline offsets, without affecting the concentration matrix, residual matrix, or calculated binding constants. Otherwise, the data cannot be safely upshifted. A comprehensive protocol for analyzing experimental absorbance datasets with is included.

中文翻译：

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通过光谱滴定数据的物理化学建模在计算结合常数时正确处理负值

为了实现光谱滴定数据的平衡硬建模，分析人员必须做出各种关键的数据处理选择，以解决负吸光度和摩尔吸光度值。通过高通量蒙特卡罗模拟、均方根误差曲面映射和两个数学定理来评估三种此类方法选项的有效性。计算出的结合常数值的准确性构成了用于比较不同数据分析方法的关键品质因数。首先，在建模之前使用奇异值分解来过滤原始吸光度数据通常会减少所涉及的负值的数量，但对计算出的结合常数几乎没有影响，尽管它能够解决光谱仪噪声问题。第二，负摩尔吸收率值的截断和快速非负最小二乘算法都优于无约束回归，因为它们避免了局部最小值；然而，在存在负基线偏移的情况下，它们会在计算的结合常数中引入偏差。最后，我们建立了两个定理，表明当导致原始吸光度数据的所有化学溶液都是完全混合两种不同储备溶液的结果时，最好解决负值。这允许原始吸光度数据上移，消除负基线偏移，而不影响浓度矩阵、残留矩阵或计算的结合常数。否则，数据无法安全升档。包括用于分析实验吸光度数据集的综合协议。