Gázquez José L, Garza Jorge, Hinojosa Fernando D, Vela Alberto
Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, A. P. 55-534, Mexico, Distrito Federal 09340, Mexico.
J Chem Phys. 2007 Jun 7;126(21):214105. doi: 10.1063/1.2741529.
Chemical hardness, identified as the difference between the vertical first ionization potential I and the vertical electron affinity A, is analyzed in the context of the ionization theorems to derive expressions for its evaluation at different levels of approximation that arise as a direct consequence of the derivative discontinuity of the exchange-correlation potential. The quantities involved in these expressions incorporate indirectly the effects of the discontinuity, but their values may be calculated with any functional of the local density approximation, generalized gradient approximation, or optimized effective potential type, with or without derivative discontinuity, and with or without the correct asymptotic behavior. By comparison with the vertical energy difference values of I and A, which requires the calculation of the N-, (N-1)-, and (N+1)-electron systems, it is found, for a set of 14 closed shell molecules, that the difference between the eigenvalues of the highest occupied molecular orbitals of the N- and (N+1)-electron systems leads to rather accurate values, when the correct asymptotic behavior is incorporated, and that a second-order one-body perturbation approach that only requires information from the N-electron system leads to reasonable values.
化学硬度被定义为垂直第一电离势I与垂直电子亲和能A之间的差值，本文在电离定理的框架下对其进行分析，以推导在不同近似水平下评估化学硬度的表达式，这些近似水平是交换相关势的导数不连续性的直接结果。这些表达式中涉及的量间接包含了不连续性的影响，但其值可以用局域密度近似、广义梯度近似或优化有效势类型的任何泛函来计算，无论是否有导数不连续性，也无论是否有正确的渐近行为。通过与I和A的垂直能量差值进行比较（这需要计算N、(N - 1)和(N + 1)电子体系），对于一组14个闭壳层分子，发现当纳入正确的渐近行为时，N和(N + 1)电子体系的最高占据分子轨道的本征值之差能给出相当准确的值，并且仅需要N电子体系信息的二阶单体微扰方法也能给出合理的值。
