Tight-Binding Model Method For Charge Transport In DNA Molecules

Deoxyribonucleic acid (DNA) is a kind of important biomacromolecule that contains the genetic information used in the development and functioning of most known living organisms. Because of the key role in many of basic life processes such as gene damage and repair, as well as the promising application in molecular electronics, charge transport in DNA molecules has caught considerable attention of chemists, physicists and biologists in recent years. Charge-transfer reactions and conductivity measurements show a large variety of possible electronic behavior, ranging from Anderson and band-gap insulators to semiconductors, conductors, and even induced superconductors. After ten years of research, although the specific mechanism still remains controversial, the basic ability of charge migration through the DNA has been universally recognized. However the conductivity of DNA is greatly affected by many factors, such as the base sequence, the integrity of base stacking, the fluctuations of conformation, solvent environment, the electrode (or the charge donor and acceptor) and so on. These factors, some of which give a subversive influence on the conductivity of DNA, are found directly related to the microstructure of DNA. Due to the difficulties in experiment to control this, theoretical efforts should be made to understand the electronic properties of DNA and to look for common mechanism to elucidate charge transport in DNA.The electronic structure calculation of complicated biomacromolecule such as DNA has been a challenging task for routine quantum computation methods, because these molecules are very large in size, and without periodic conditions. The tight-binding model has been extensively adopted to investigate electronic structure of DNA because of its advantages, for example, simplicity. In this tight-binding model approach, the backbone of DNA is generally ignored because it makes little contribution to the charge transfer. Each base or base pair is set to be one lattice site in the model, and each site provide only one site orbital for electron locate at this site. Electrons can hop between the adjacent site orbitals, and the electronic structure can be described by two parameters:the on-site energy and the transfer integral between two adjacent sites.Although this tight-binding model approach has been extensively used, researches on this methods itself are seldom reported, resulting in lack of standard values of the two parameters. Parameters used in various literatures are inconsistent, seriously affecting the accuracy of this method. In view of this problem, we derived the parameter formula from the first principles with gradual approximation and put forward systematic scheme for calculating the two parameters. The detailed scheme is given as follows:1. Quantum chemical calculations are carried out for all the isolated lattice system, and the site orbitals are obtained.2. Quantum chemical self-consistent field calculations are carried out for the subsystem which contains the isolated lattice and its adjacent lattices. Then the single-electron Hamiltonian for this subsystem, which is an effective Hamiltonian for calculating the parameters, is obtained. The other atoms in the total system can be taken as point charges or be ignored.3. The matrix elements of the effective Hamiltonian based on the site orbital are calculated. Then the on-site energy and the transfer integral can be calculated from these matrix elements using the corresponding formula.According to the proposed parameter calculation scheme, our researches on the tight-binding model method of DNA are as follows:By calculating the hole and the electron tight binding parameters of various base sequences, the influence of primary structure (base sequence) on the parameters are investigated. The results show that the on-site energy depends mainly on the base type. The order of the hole-on-site energy among the four type bases is G< A< T< C, while the order of electron-on-site energy is opposite. The on-site energy level splits because of the polarization of the adjacent lattices. As for the hole, this polarization leads to a lower energy and the 3'end gives a stronger polarization than the 5'end. The on site energy of guanine base shows the most obvious polarization effect among the four bases. The value of transfer integral of ideal B-form DNA ranges from 0.02 to 0.12eV, which depends on the bases type too. These parameters can be used to construct the tight-binding model Hamiltonian of arbitrary sequences of DNA molecules, calculate the hole or the electron states, and study the influence of the base sequence of the DNA on its charge-transport behavior.Dependence of the two tight binding model parameters on the secondary structure (double-helical conformation) of DNA such as rise and twist was also investigated. The results show that the transfer integral between adjacent sites critically depends on the double-helical conformation, especially the twist between the two adjacent base pairs. When the distance between the two adjacent sites takes the standard value (3.38A), the transfer integral of AA and GG with the twist angle of 0°is nearly 0.8eV, but with the twist angle 36°, both types of transfer integral is under 0.1 ev. When the value of twist angle is fixed, the transfer integral decays exponentially with the increase of distance between the two adjacent sites. The influence of the polarization of the adjacent site on the transfer integral was discussed. The result show that, when two-site subsystem used to construct the effective DNA Hamiltonian is obviously asymmetric, the polarization of the site is different from each other, which result in the disuse of the frontier orbital splitting to calculate the transfer integral. In addition, we also compared the on site energy and the transfer integral differences between the average A-DNA and the B-DNA crystal structure.With the parameters obtained, we investigated properties of polarons in different quantum well-barrier potential structures of DNA using the tight-binding SSH model. In the case of single-well potential structures, the hole localizes at the GC base pair, forming a polaron, and the polaron is most stable when the quantum well contains three GC base pairs. In the other case, namely periodic well-barrier potential structure, the width of the quantum wells and the quantum barriers both show a significant effect on the polaron. The electron-phonon coupling factor in SSH model is obtained by calculating the relationship between the transfer integral and distance in poly(G)-poly(C) and poly(A)-poly(T) DNA molecules. Properties of hole polarons in these two molecules are investigated using SSH model. The results of model calculation illustrate that polaron in poly(A)-poly(T) has a larger width and is more delocalized than that in poly(G)-poly(C) DNA molecule. Polarons in both the two kind of DNA molecules move in the form of drifting when a electric field is applied in the direction of the DNA chain, and polaron in poly (A)-poly (T) has a higher drifting mobility.In addition to the investigations on the tight binding model method of DNA, we also do some study on the generator method to simplify the calculation of elements of the Hamiltonian matrix. When a system under consideration has some symmetry, usually its Hamiltonian space can be parallel partitioned into a set of subspaces, which is invariant under symmetry operations. A general algorithm to construct the generator functions is proposed, and is extended to deal with system having high-dimensional irreducible representations. Furthermore, two model Hamiltonians is used to show how the generator method simplifies the calculation of Hamiltonian matrix elements.The original contributions in this doctoral dissertation are as follows:1. Computing formula for the parameters of tight binding model was obtained from the most fundamental equation of quantum mechanics with the gradual approximation, and a systematic parameter calculation scheme has been proposed.2. With the obtained parameter calculation scheme, the influences of primary structure and secondary structure on the parameters are investigated. The result illustrate that the on site energy depends on the base type of the lattice, and can be affected by the sequence of DNA molecule. While the transfer integral depends mainly on the conformation of DNA molecule, and the influence of the sequence of DNA molecule can be ignored.3. Two types of special quantum well-barrier potential structures of the DNA chains are constructed based on the calculated on site energy, properties of hole polaron in them are investigated using the SSH model. Furthermore, with the electron-phonon coupling factor obtained by fitting dependence of transfer integral on distance, static and dynamic properties of hole polarons in poly(G)-poly(C) and poly(A)-poly(T) DNA molecules are investigated.4. With the concept that symmetry-invariant subspace, the previously proposed generator method is proved through group representation theory and properties of projection operator, and then generalized to the circumstance of high-dimension irreducible representations of point group.