Nishioka Hirotaka, Kimura Akihiro, Yamato Takahisa, Kawatsu Tsutomu, Kakitani Toshiaki
Department of Physics, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan.
J Phys Chem B. 2005 Aug 18;109(32):15621-35. doi: 10.1021/jp051606i.
Developing the quantum transition rate theory of Prezhdo and Rossky (J. Chem. Phys. 1997, 107, 5863), we produced a new non-Condon theory of the rate of electron transfer (ET) which happens through a protein medium with conformational fluctuation. The new theory is expressed by a convolution form of the power spectrum for the autocorrelation function of the electronic tunneling matrix element T(DA)(t) with quantum correction and the ordinary Franck-Condon factor. The new theory satisfies the detailed balance condition for the forward and backward ET rates. The ET rate formula is divided into two terms of elastic and inelastic tunneling mechanisms on the mathematical basis. The present theory is applied to the ET from Bph(-) to Q(A) in the reaction center of Rhodobacter sphaeroides. Numerical calculations of T(DA)(t) were made by a combined method of molecular dynamics simulations and quantum chemistry calculations. We showed that the normalized autocorrelation function of T(DA)(t) is almost expressed by exponential forms. The calculated energy gap law of the ET rate is nearly Marcus' parabola in most of the normal region and around the maximum region, but it does not decay substantially in the inverted region, which is called the anomalous inverted region. We also showed that the energy gap law at the high uphill energy gap in the normal region is elevated considerably from the Marcus' parabola, which is called the anomalous normal region. Those anomalous energy gap laws are due to the inelastic tunneling mechanism which works actively at the energy gap far from zero. We presented an empirical formula for easily calculating the non-Condon ET rate, which is usable by many researchers. We provided experimental evidence for the anomalous inverted region which was basically reproduced by the present theory. The present theory was extensively compared with the previous non-Condon theories.
在发展Prezhdo和Rossky的量子跃迁速率理论（《化学物理杂志》，1997年，第107卷，第5863页）的过程中，我们提出了一种新的非康登电子转移（ET）速率理论，该电子转移通过具有构象波动的蛋白质介质发生。新理论由电子隧穿矩阵元T(DA)(t)自相关函数的功率谱与量子校正以及普通弗兰克 - 康登因子的卷积形式表示。新理论满足正向和反向ET速率的细致平衡条件。在数学基础上，ET速率公式分为弹性和非弹性隧穿机制两项。本理论应用于球形红细菌反应中心中从Bph(-)到Q(A)的电子转移。通过分子动力学模拟和量子化学计算相结合的方法对T(DA)(t)进行了数值计算。我们表明T(DA)(t)的归一化自相关函数几乎由指数形式表示。计算得到的ET速率的能隙定律在大多数正常区域和最大值区域附近近似为马库斯抛物线，但在反转区域它不会大幅衰减，这被称为反常反转区域。我们还表明，正常区域中高的上坡能隙处的能隙定律比马库斯抛物线有相当大的提升，这被称为反常正常区域。这些反常能隙定律是由于在远离零的能隙处起作用显著的非弹性隧穿机制。我们提出了一个便于计算非康登ET速率的经验公式，可供许多研究人员使用。我们为反常反转区域提供了实验证据，该区域基本上由本理论再现。本理论与先前的非康登理论进行了广泛比较。
