【作者】 高绪团；

【导师】 解士杰；

【作者基本信息】 山东大学 ， 凝聚态物理， 2007， 博士

【摘要】 脱氧核糖核酸（DNA）是复杂的生物大分子，是生命遗传信息的载体。DNA是生物界最重要的大分子体系，在生物进化中起着非常重要的作用，其结构中蕴藏着决定遗传、细胞分裂、分化、生长和蛋白质生物合成等生命过程的信息。DNA分子具有双螺旋结构，其螺旋的骨架是由磷酸根和糖基通过共价键连接而成，连接在糖基上的四种碱基腺嘌呤（A—Adenine），鸟嘌呤（G—Guanine），胸腺嘧啶（T-Thymine），胞嘧啶（C-Cytosine）按互补配对规则（G-C，A-T）通过氢键结合。近年来由于生命科学中的基因损伤与修复等原因以及分子纳米器件的应用与发展，DNA的电荷输运性质成为当前生命科学、物理、化学、材料科学等多个交叉学科的研究热点。研究已初步发现，电荷转移反应产物能导致细胞突变，光诱导电荷转移氧化损伤DNA分子或光诱导电荷转移修复DNA分子可治疗肿瘤等。例如，当DNA分子受到电离辐射或紫外线照射时会产生电子，这个电子被别的原子捕获前可能沿着DNA分子链运动，所以有人认为DNA分子有可能是快速的、不依赖于距离的电子转移通道。同时，DNA分子具有两个独特的性质，即自识别和自组装功能。另一方面，近几十年来，电子信息技术迅猛发展，芯片上的晶体管越来越密集，速度也越来越快。按照半导体工业著名的摩尔定律，每18个月左右，芯片的运算速度就增加一倍、尺寸减小一半。但由于热耗散和不同组件间电容耦合的存在，其发展速度将受到传统印刷电路制版技术的限制，预计到2010年，就会达到其物理的极限。因为按照微电子技术器件越来越小的发展思路，将会面对无法逾越的量子效应。传统的以硅、锗等半导体材料为基础的电子器件，其信息的传输原理是根据半导体的能带输运理论，但是，当体系的尺度达到纳米量级时，能带就变成了分立的能级，体系呈现出量子效应，能带论不再适用。为了使电路小型化，进一步提高电路的集成度和运算速度，突破电路小型化的物理极限，40年前，诺贝尔奖获得者、量子物理学家费曼提出了一种新的电路设计理念，即从底到顶的设计思想。费曼在题为《底部还有很大空间》的演讲中提出：为什么我们不可以从另一个角度出发，从单个分子甚至单个原子开始组装，以达到我们的要求——“至少依我看来，物理学的规律不排除一个原子一个原子地制进行精确的工程加工，把一个原子放到另一个原子上，制造出最小的人工机器来。步，2001年12月21日，Science杂志将分子电子学所取得的一系列成就评为现阶段，分子电子学的主要任务是寻找和研究性能优异的分子器件材料，如有机小分子、生物大分子和碳纳米管等都是被广泛研究的材料。DNA分子具有自识别和自组织两个独特性质，如果再具有导电性，将是纳米导线及分子器件的理想材料。但其电荷输运机制目前尚不清楚，甚至存在很大争议。DNA分子的电荷输运实验显示DNA分子呈现出导体、半导体、绝缘体等丰富的电学性质。所以如何从理论上解释这一现象，弄清电荷在DNA中的传输机理，为利用DNA分子设计分子器件提供理论基础，同时为DNA的突变和修复规律提供理论解释，阐明DNA结构中蕴藏的生命过程的各种信息，具有重要的科学意义。DNA分子是复杂的生物大分子，具有软性。其电荷输运行为易受来自内部和外部的多种因素的影响，例如：分子构形、碱基序列、温度、湿度、溶液、杂质等。目前，科学家提出了单步隧穿，多步隧穿，热跃迁及极化子传输等几种输运机制来解释DNA分子中的电荷输运现象。另一方面，由于DNA自身结构的复杂性，科学家一直在寻找一个最为恰当的模型来对它进行研究，到目前为止，科学家已建立了一维紧束缚模型、鱼骨模型、梯子模型、三维紧束缚模型等几个模型从不同的侧重点来研究DNA分子中的电荷输运现象。同时，各种因素对DNA分子的电子结构及其电荷输运特性的影响也被广泛研究。以上理论工作部分地解释了DNA分子所呈现出的丰富的电学性质。通过广泛调研，我们发现DNA分子中巡游电子数密度是可变的。从理论上讲其巡游电子主要来源于未成对的π—电子，而未成对的π—电子则是分子成键时SP、SP²轨道杂化产生的，DNA分子中的糖基和四种碱基都是由碳、氧、氮等组成的杂环结构，其轨道杂化情况较为复杂。另一方面DNA分子具有双螺旋结构，其对称性较低，分子中存在大量的悬挂键，这些悬挂键上的未成对电子也会进入π—电子系统。所以DNA分子中的巡游电子数密度易受内部组分、结构和外部环境的影响，其巡游电子数密度是可变的。同时，实验也证明其巡游电子数密度与DNA分子的组分、结构有关，受实验条件的影响。例如，Yao等人的实验证明Poly（dG）-Poly（dC）是P型半导体，而Poly（dA）-Poly（dT）是N型半导体，说明Poly（dG）-Poly（dC）中的多子是空穴，Poly（dA）-Poly（dT）中的多子是电子，即巡游电子数密度与碱基对序列有关。基于以上原因，我们提出DNA分子中巡游电子数密度是可变的思想。在本文中，我们分别采用一维紧束缚模型和三维紧束缚模型，系统地研究了巡游电子数密度对DNA分子的电子结构及其电荷输运性质的影响。其次，由于DNA分子是柔软的生物大分子，其晶格位置易受环境因素的影响而发生涨落，因此，我们又研究了晶格位置涨落对DNA分子的电子结构及其电荷输运性质的影响。具体内容和主要结果如下：1、一维紧束缚模型下，巡游电子数密度对DNA分子的电子结构和输运特性的影响。1．1 DNA是柔软的生物大分子，其中存在强的电子—晶格相互作用，巡游电子数密度的变化必定引起其电子结构的变化，反之亦然。电子结构则直接决定其电荷输运性质。我们采用包含了电子—晶格相互作用的一维紧束缚模型研究了巡游电子数密度对DNA分子的电子结构及其电荷输运性质的影响。发现：随着巡游电子数密度的变化，DNA分子能带结构中费米能级附近的能隙（最低空轨道（LUMO）与最高电子占据轨道（HOMO）之间的能量差）随之改变，体系的电阻率亦随之改变，使得体系呈现不同的导电性质，分别倾向于导体，半导体或绝缘体。1．2 DNA分子链上的碱基对序列对其电荷输运有重要影响，我们分别研究了单一基对周期序列DNA分子Poly（dG）-Poly（dC），按Fibonacci序列构造的准周期序列和取自λ—DNA分子的非周期序列等三种不同周期序列DNA分子的电子结构和输运性质。计算结果表明不同序列的DNA分子导电性有很大的差异。随巡游电子数密度的变化，周期序列Poly（dG）-Poly（dC）分子的能隙和电阻率以半满占据为中心对称，半满占据时，Poly（dG）-Poly（dC）分子链发生二聚化，能带劈裂为导带和价带，其电阻率约为10^-2（Ωcm）量级；当巡游电子数密度偏离半满占据小于20％时，禁带中出现定域能级，其电阻率增大；当巡游电子数密度偏离半满占据大于20％时，禁带中的定域能级扩展成准连续的能带，其电阻率减小。当巡游电子数密度相同时，周期序列DNA分子链的导电性好于非周期序列DNA分子链，准周期序列DNA分子的电阻率介于二者之间。1．3周期序列DNA分子的电阻率随分子链长度增加而减小，并趋于定值，准周期序列DNA分子链具有自相似性，其电阻率随分子链长度增加起伏变化，呈现出长度关联效应，非周期序列DNA分子链的电阻率分子链长度增加而增大，趋于绝缘体。2、一维紧束缚模型下，晶格位置涨落对DNA分子的电子结构和电荷输运性质的影响。考虑到DNA分子是软分子，温度、湿度、分子中的杂质离子、基因变异等因素都会引起DNA分子晶格结构和电子结构的变化，进而影响其电荷输运行为。鉴于DNA分子的复杂性，不可能对以上因素逐一进行研究，为使问题简化，我们采用模型化的方法，将各种因素的影响归结为碱基对相对其平衡位置的涨落。采用方形随机分布模拟碱基对的位置涨落，在一维紧束缚模型的框架下，研究了位置涨落对DNA分子的电子态及其电荷输运行为的影响。发现：2．1随涨落的增强，周期序列半满占据的DNA分子链的带隙变小，同时其电子态倾向于局域化。综合考虑，带隙变小将有利于载流子的输运，但电子态局域化又不利于载流子的输运，二因素相互制约、相互竞争，决定了DNA分子的电荷输运行为。较弱的涨落使带隙变小，电子态仍具有较好的扩展性，有利于载流子的输运。这是因为位置涨落可削弱或抵消了DNA分子中的晶格二聚化，同时使载流子获得能量，容易摆脱格点的束缚。较强的涨落虽然使带隙进一步变小，但电子态呈现出强的局域行为，带输运机制不再适用。室温下DNA分子的导带底的电子态将呈现出较强的局域行为，这对DNA的室温导电行为有重要影响。2．2计算周期序列DNA分子的电阻率随涨落强度的变化。发现随涨落增强，其电阻率先减小后增大，与定性的分析相一致。3、三维紧束缚模型下，巡游电子数密度对DNA分子的电子结构及其电荷输运性质的影响。3．1 DNA分子的一维紧束缚模型把DNA分子简化为一维分子链，忽略了其双螺旋结构，而实验证实DNA分子的空间构形对其电荷输运性质有重要影响。我们借鉴D. Hennig等人提出的三维紧束缚模型，建立了一个描述DNA分子的三维紧束缚模型，并利用该模型研究了巡游电子数密度对DNA分子的电子结构和输运性质的影响。与一维紧束缚模型相比，在一维紧束缚模型中晶格运动仅通过电子—晶格相互作用影响电子跃迁积分，进而影响其电子结构和电荷输运性质；而在三维紧束缚模型中晶格运动通过电子—晶格相互作用一方面影响电子跃迁积分，另一方面影响格点在位能。计算发现：晶格运动对电子跃迁积分的影响较小，对格点在位能的影响较大，即在三维紧束缚模型中，晶格运动主要通过改变格点在位能，影响其电子结构和电荷输运性质。3．2与一维紧束缚模型不同，在三维紧束缚模型下，Poly（dG）-Poly（dC）的导电性质随巡游电子数密度的变化发生奇偶相变。即当HOMO为奇数能级时，Poly（dG）-Poly（dC）的电子结构和电阻率与金属导体类似，呈现金属相；当HOMO为偶数能级时，Poly（dG）-Poly（dC）的电子结构和电阻率与半导体类似，呈现半导体相。4、温度对DNA分子Poly（dG）-Poly（dC）的电荷输运性质的影响。考虑DNA分子的空间双螺旋结构，在三维紧束缚模型下，研究了温度引起的氢键键长热涨落和螺旋角热涨落对Poly（dG）-Poly（dC）的透射率、电子定域长度、伏安特性和电导率的影响。发现：4．1螺旋角热涨落对Poly（dG）-Poly（dC）的电荷输运性质影响较小，氢键键长热涨落引起格点在位能的变化是影响Poly（dG）-Poly（dC）电荷输运性质的重要因素。4．2 Poly（dG）-Poly（dC）的电导率随温度升高减小，低温区电导率减小较快，高温区电导率缓慢减小。我们认为这是由于随温度升高，Poly（dG）-Poly（dC）的电荷输运机制发生了从能带输运机制到跃迁输运机制的转变。更多还原

【Abstract】 Desoxyribo-Nucleic-Acid （DNA） is a complicated biomolecule, which encodes the fundamental nature of living species. DNA has a double helix structure, and the backboned of the double helix is composed of phosphates and sugars joined by covalent bond, on which four type bases （Adenine-A, Guanine-G, Cytosine-C, and Thymine-T） paired together through hydrogen bonds according to complementary pairs law （A with T, and G with C）.DNA is the most important molecule of bioorganic system. Its structure contains information that determines heredity, cell division, growth and biosynthesis of protein. Interference with gene function and prevention of transcription and translation can kill invading microorganisms or tumor cells. In recent years, the charge migration along the duplex DNA stack is attracting considerable interest for the biochemical reasons in life science, as well as for the possible applications in molecular electronics. A number of experiments have showed that, the product of electron transfer will lead to DNA mutation; light-induced electron transfer will damage DNA, or repair it to cure tumors. For example, under the irradiation of the ionization or ultraviolet radiation, an electron in DNA will move along DNA before being trapped by other atoms. So it is thought that DNA may be a quick channel for electron transfer which is independent of distance. Meanwhile DNA has two special characters: recognition, structuring and self-assembly properties.On the other hand, the progress of the electronic industry in the past few decades was based on the delivery of smaller and smaller devices and denser integrated circuits, which ensured the attainment of more and more powerful computers. However, such a fast growth is compromised by the intrinsic limitations of the conventional technology. Electronic circuits are currently fabricated with complementary metal-oxide-semiconductor （CMOS） transistors. Higher transistor density on a single chip means faster circuit performance. The trend towards higher integration is restricted by the limitations of the current lithography technologies, by heat dissipation and by capacitive coupling between different components. Moreover, the down-scaling of individual devices to the nanometer range collides with fundamental physical laws. In fact, in conventional silicon-based electronic devices the information is carried by mobile electrons within a band of allowed energies according to the semiconductor band structure. However, when the dimensions shrink to the nanometer scale, and bands turn into discrete energy levels, then quantum correlation effects induce localization. It is presupposed that the conventional electronic industry will go to its physical limitation in 2010. In order to pursue the miniaturization of integrated circuits further, a novel technology, which would exploit the pure quantum mechanical effects that rule at the nanometer scale, is therefore demanded. 40 years ago, quantum physicist, and Nobelist Feynman put forward a new idea to design circuit, under which the circuit is designed from bottom to top. This physical idea is regarded as the origin of molecular electronics and nanotechnology. The basic idea of molecular electronics is to use individual molecules as wires, switches, rectifiers and memories. Another conceptual idea that is advanced by molecular electronics is the switch from a top-bottom approach, where the devices are extracted from a single large-scale building block, to a bottom-up approach in which the whole system is composed of small basic building blocks with recognition, structuring and self-assembly properties. The great advantage of molecular electronics in the frame of the continued device miniaturization is the intrinsic nanoscale size of the molecular building blocks that are used in the bottom-up approach, as well as the fact that they may be synthesized in parallel in huge quantities and at low cost. In the past 20 years, molecular electronics has procured much material advancement, and the advancement made by molecular electronics is appraised as the first of ten technology advancements by Science in 2001.Different candidates for molecular devices are currently the subject of highly interdisciplinary investigation efforts, including small organic polymers, large bio-molecules, nanotubes and fullerenes. DNA has two special characters: recognition, structuring and self-assembly properties. If the charge can transport in DNA molecule, it should be a well prospective candidates for molecular electronic devices. However, at present the mechanism of charge transport in DNA molecule is controversial. The experiments of charge transport in DNA molecule have shown that DNA molecule may be conductor, semiconductor or insulator. So how to interpret these controversial experiment phenomena and ravel the mechanism of charge transport in DNA molecule has important significance for using DNA as a molecular device and understanding the mechanism of DNA mutation and repairing of the damaged DNA.DNA is a soft biomolecule. The charge transport in DNA is affected by many factors, such as the molecular configuration, the sequence of base pairs, temperature, humidity, solution and impurity in the molecule. The effect of these factors on the electronic structure of DNA and the charge transport of DNA has been extensively studied. These theory works partly represent the diversity of charge transport in DNA. However, at present there is currently no unanimous understanding of its electrical behavior and of the mechanisms that might control charge mobility through its structure. There are more works to understand the electrical behavior and the mechanisms of charge transport in DNA.Through widely investigations we found that the density of itinerant electrons is variable, not fixed. In theory the itinerant electrons of DNA is the unpairedπ-electrons which come from SP and SP² orbit hybridization as atoms combine with bond. The sugar and four type bases in DNA are all heterocyclic structures made of C, O, N, and H atoms, and the condition of these orbit hybridization is complex, then the number of itinerant electrons is difficult to determine. On the other hand, the double helix DNA molecule with low symmetry has a lot of hanging bonds, and the unpaired electrons of these hanging bonds may come into theπ-electrons system. Then the density of itinerant electrons in DNA molecule is not fixed, but depends upon the component and structure of DNA molecule, the environment condition also has an important effect on the density of itinerant electrons. This viewpoint is proved by experiment also. For example, Yoo et al. have found that poly（dA）-poly（dT） behaves as an n-type semiconductor, whereas poly（dG）-poly（dC） behaves as a p-type semiconductor by the gate-voltage dependent transport measurements. This suggests that the density of itinerant electrons is different in poly（dA）-poly（dT） from that in poly（dG）-poly（dC）. Based on above reasons we put forward the idea that the density of itinerant electrons in DNA molecule is variable.The structure of DNA is complex. Several models have been suggested to describe DNA molecule, such as, the simple one dimensional tight binding model, the fish bone model, the ladder model, and three dimensionals tight binding model.In this paper, the effects of the density of itinerant electrons on the electronic structure of DNA and the charge transport in DNA are studied with one dimensional tight binding model and three dimensionals tight binding model respectively. The effect of structural fluctuations on the electronic structure of DNA and the charge transport in DNA are studied with one dimensional tight binding model and three dimensionals tight binding model respectively also. The differences between two models are compared. The primary contents and results are given as follows:1. Effect of the density of itinerant electrons on the electronic structure of DNA and the charge transport in DNA with one dimensional tight binding model1.1 DNA is a soft biomolecule with strong electron-latttice interaction. The electronic structure of DNA depends on the density of itinerant electrons, vice versa. The electronic structure directly affects the behavior of charge transport in DNA. One dimensional tight binding model with electron-lattice interaction is adopted to study the effect of the density of itinerant electrons on the electronic structure of DNA and the charge transport in DNA. It is found that the energy gap （the difference between the lowest unoccupied molecular orbit （LUMO） and the highest occupied molecular orbit （HOMO）） changes with the density of itinerant electrons, and the resistivity of DNA changes with the density of itinerant electrons too. DNA may show the behavior of conductor, semiconductor, or insulator with different density of itinerant electrons.1.2 The sequence of base pairs has an important effect on the charge transport in DNA. The electronic structure and the charge transport of three different periodic sequences DNA molecule （periodic sequence, quasiperiodic sequence, and aperiodic sequence） are studied. The calculations show that the dependences of electronic structure and the behaviors of charge transport on the density of itinerant electrons are different for three different periodic sequences DNA molecule. The energy gap and the resistivity of the periodic sequence DNA （Poly （dG）-Poly （dC）） are symmetrical about the half-filling state. At the half-filling state, due to the instability of Peierls, the energy band of Poly（dG）-Poly（dC） is split into two sub-bands: the occupied valence band and the unoccupied conduction band, with a band gap of about 1 eV, and theresistivity of Poly（dG）-Poly（dC） is on the order of 10^-2Ωcm. Departing from thehalf-filling state, a few localized energy levels appear in the energy band gap. These states will have important effects on the conductivity of Poly（dG）-Poly（dC）. Since these states are localized and not favorable for charge transport, the resistivities of Poly（dG）-Poly（dC） are large in this region. When the density of itinerantπ-electrons departs over 20% from the half-filling state, many energy levels appear in the energy band gap. The electronic states of these levels become delocalized and have large transmission coefficients, and the resistivity decreased. The aperiodic sequence DNA molecule has no symmetry, and the resistivity is larger than Poly（dG）-Poly（dC）. The resistivity of quasiperiodic sequence DNA molecule is between the periodic sequence and the aperiodic sequence.1.3 The dependences of the resistivity on the length of DNA molecule chain are different for three different periodic sequences DNA molecule. The resistivity of periodic sequence decreases with the length increasing, and tends towards a steady value when the length is long enough. The resistivity of quasiperiodic sequence fluctuates with the length increasing, and shows a long range correlation effect. The resistivity of aperiodic sequence increases with the length increasing.2. Effect of lattice site fluctuations on the electronic structure of DNA and the charge transport in DNA with one dimensional tight binding modelDue to the softness of DNA, many environment factors, such as temperature, humidity, solution and impurity in the molecule may cause the changes of molecular structure and electronic structure, and then affect its behavior of charge transport. In order to simplify the problem, the effect of all these factors on the charge transport is treated as the lattice site fluctuations and a uniform distribution is adopted to simulate the lattice site fluctuations. The effect of lattice site fluctuations on the electronic structure and charge transport of DNA are studied with one dimensional tight binding model.2.1 It was found that at half filling state of itinerant electrons the energy band gap of a periodic sequence DNA molecule decreases with increasing of the lattice site fluctuations, meanwhile the electronic states of DNA tend to localizing. One hand the decreasing of band gap is favor of charge transport in DNA, on the other hand the localizing of electronic states goes against charge transport in DNA. When the fluctuations are small, the band gap of periodic sequence DNA decreases, and the electron states is still extended, the DNA molecule has good conductance. The reason is that small lattice site fluctuations can counteract the dimerizing of the lattices, and the electrons may gain energy from the lattice fluctuations, and easily get rid of the fetters of lattice sites. When the fluctuations are large, although the band gap decreases, but the electronic states become localized heavily, and the resistivity becomes large.2.2 The resistivity of periodic sequence DNA first decreases and then increases with increasing of lattice site fluctuations. This is consistent with the qualitative analysis.3. The effect of the density of itinerant electrons on the electronic structure of DNA and the charge transport in DNA with three dimensionals tight binding model3.1 One dimensional tight binding model ignores the double helix structure of DNA, however, experiments have proved that the helix structure of DNA has important effects on the charge transport in DNA. Referencing D.Hennig’s work, we suggest a three dimensionals tight binding model to describe DNA molecule. Comparing with one dimensional tight binding model, in the frame work of three dimensionals model, one hand the movement of lattice sites affects the electron transition integral by the electron-lattice interaction, on the other hand affects the on-site energy; in the frame work of one dimensional model, the movement of lattice sites only affects the electron transition integral by the electron-lattice interaction. It was found that in the frame work of three dimensionals model the effect of the movement of lattice sites on the electron transition integral is small, and the movement of lattice sites mainly changes the on-site energy, and then affects the electronic structure and charge transport in DNA.3.2 Differing from one dimensional tight binding model, in the frame work of three dimensionals tight binding model, the conductivity of PoIy（dG）-Poly（dC） takes place parity phase-transition with the varying of the density of itinerant electrons as the density of itinerant electrons departure from the half filling state over 20%. Namely, when HOMO is odd number energy level, the electronic structure and the resistivity of Poly（dG）-Poly（dC） are analogous with metal conductor; when HOMO is even number energy level, the electronic structure and the resistivity of Poly（dG）-Poly（dC） are analogous with semiconductor.4. The effect of temperature on the charge transport in Poly（dG）-Poly（dC） withthree dimensionals tight binding modelIn the frame of three dimensionals tight binding model, considering the effect of temperature on the charge transport in periodic sequence DNA, the effect of hydrogen bond length fluctuations and helix angle fluctuations on the charge transport in Poly（dG）-Poly（dC） are studied, the transmission coefficient, the localization length of electronic states, direct measured quantity current-voltage character （I-V） and the conductivity of Poly（dG）-Poly（dC） are calculated.4.1 The helix angle fluctuations have small effect on the charge transport in PoIy（dG）-Poly（dC）, the hydrogen bond length fluctuations have important effect on the charge transport in Poly（dG）-Poly（dC）. Namely, temperature mainly through the hydrogen bond length fluctuations to affect the charge transport in DNA.4.2 The conductivity of Poly（dG）-Poly（dC） decreases with temperature increasing. At low temperature range, the conductivity decreases rapidly, at high temperature range, the resistivity decreases slowly. We conjecture that the mechanism of charge transport in Poly（dG）-Poly（dC） transits from band resonant transport mechanism to more hopping transport mechanism with temperature increasing.更多还原