物理化学学报 >> 2007, Vol. 23 >> Issue (09): 1353-1359.doi: 10.1016/S1872-1508(07)60071-0

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Benesi-Hildebrand方程的正确性与可靠性

王睿; 尉志武   

  1. 清华大学化学系, 生命有机磷化学与化学生物学教育部重点实验室, 北京 100084
  • 收稿日期:2007-05-28 修回日期:2007-06-15 发布日期:2007-09-06
  • 通讯作者: 尉志武 E-mail:yuzhw@tsinghua.edu.cn

Validity and Reliability of Benesi-Hildebrand Method

WANG Rui; YU Zhi-Wu   

  1. Key Laboratory of Bioorganic Phosphorous Chemistry &Chemical Biology of the Ministry of Education, Department of Chemistry, Tsinghua University, Beijing 100084, P. R. China
  • Received:2007-05-28 Revised:2007-06-15 Published:2007-09-06
  • Contact: YU Zhi-Wu E-mail:yuzhw@tsinghua.edu.cn

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摘要： Benesi-Hildebrand(B-H)方程现被广泛地应用于各种非键作用体系, 特别是作用比为1:1型和1:2型的体系. 该方程可以用来确定作用体系的平衡常数以及作用比. 通过计算机模拟, 发现在某些情况下, 对于1:2型的作用体系, B-H方程会给出错误的作用比信息. 无论是弱的作用体系还是强的作用体系, 都可能会出现1:1的B-H方程曲线呈现出线性, 同时(或者)1:2的B-H方程曲线呈现出非线性的情况. 此外, 本文还研究了体系中两种作用物质的初态浓度比对于1:1型作用的平衡常数计算的影响, 发现最小的初态浓度比(r0)等于100是可以确保B-H方程近似条件C0B≈CB成立的安全阈值. 当作用很弱的时候, 比如说作用的平衡常数K小于25 L·mol-1 (C0P=4×10-4 mol·L-1)时, 则不需要对最小初态浓度比值r0进行限制, 就可以满足B-H方程的近似条件. 通过计算机模拟还分析了文献中提出的两个边界条件. 研究表明1/(KC0P)≥10可以保证处于平衡状态时的CB/C0B≥0.91. 而另一个条件KC0B>0.1 并不是确保B-H方程近似条件成立的充分条件.

关键词: Benesi-Hildebrand方程, 分子间相互作用, 平衡常数, 作用比

Abstract: Benesi-Hildebrand (B-H) method is a widely used approach for determining the stoichiometry and equilibrium constants of nonbonded interactions, particularly 1:1 and 1:2 interactions. Using computer simulation, it was shown that, under certain conditions, the approach could generate inappropriate stoichiometric conclusions for 1:2 interactions. This problemcould occur in the cases of both weak and strong interactions, where the 1:1 B-H plots showed a linear feature and the 1:2 B-H plots showed a nonlinear feature. In addition, effect of the initial concentrations on the accurate evaluation of equilibrium constants of 1:1 interactions was investigated. It was found that the minimum safe concentration ratio r0 between ligand and central species was 100. However, for weak nonbonding interactions, for example K<25 L·mol-1 (C0P=4×10-4 mol·L-1), the ratio r0 has no limitation. Two conditions proposed in literatures for the safe application of the B-H method were examined. It was found that the inequation, 1/(KC0P)≥10, was a condition to secure CB/C0B≥91%. The other inequation, KC0B≥0.1, was not found to be the safe condition to validate the B-H method.

Key words: Benesi-Hildebrandmethod, Molecular interaction, Equilibriumconstant, Stoichiometry evaluation