The polaron might play an important role in the process of charge migration through duplex DNA stack. In the present work, we investigate properties of hole polarons in DNA molecules containing identical base pairs, such as poly(G)-poly(C) and poly(A)-poly(T), An extended tight-binding model (extended Su-Schrieffer-Heeger model), which involves the effect of an electric field in the direction of DNA stack, will be introduced. The transfer integral and electron-phonon coupling parameters in this model are obtained according to ab initio calculation for different base pair dimers. Calculations reveal that the polaron in poly(A)-poly(T) has a wider shape and a higher mobility under a specific electric field than that in poly(G)-poly(C) DNA stack. SSH model, charge migration, polaron, DNALong-range charge migration in DNA has been attracting more and more attention for its relevance to life science and potential applications in the functional molecule electronic devices [1][2][3][4][5][6][7][8][9] . The overlapping π orbitals of the base pairs in the interior of DNA double helix could provide a channel for migration of an extra charge injected into DNA [10] . The extra hole or electron may spread over a number of base pairs as a polaron, which is induced by the structural distortion of DNA, or by the polarizable medium surrounding the DNA [11,12] . The polaron is the charge carrier in DNA, and plays an important role in explaining the mechanism of long-range charge migration through duplex DNA stack [5] . Lots of experimental results have indeed been interpreted by the mechanisms involving polaron motions [13,14] .The Su-Schrieffer-Heeger (SSH) model Hamiltonian was firstly introduced to study charge carriers in conducting polymers [15,16] , and now is extended to investigate the polaron mechanism of DNA-mediated charge transfer after choosing suited parameters for DNA molecule. The SSH model is a kind of tight-binding Hamiltonian, but includes the electron-phonon coupling to represent the effect of the structure distortion. In this tight-binding model frame, 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 model, and only the electrons in the highest occupied molecular orbital (HOMO) of the single base or base pair are treated in the model. Conwell et al. successfully extended the SSH model to DNA duplex, finding that the polaron in DNA spreads over ~5 sites and is stable at room temperature [11] . The polaron also could drift far in DNA composed of the same base (pairs), or hop in DNA with alternating base (pairs) under the electric field [13] . In our last work, we discussed the reason why polaron could hop or be trapped in DNA molecules with some special sequences [14] . However, the parameters in model Hamiltonian calculation are very simple. The transfer integral between Adenine-Thymine base pairs (AT) or Guanine-Cytosine base pairs (GC) was assumed to be the same for simplifying the calcula-

Proton transfer in DNA has attracted much attention because of its close relationship with charge transfer and DNA base damage. In the present study, the relationship between proton transfer and water polarization at a certain temperature in the radical cation stack of adenine-thymine is investigated by QM/MM molecular dynamics simulations. By analyzing the polarization of aqueous solution, it is found that at low temperature water molecules promote proton transfer by means of displacement polarization and oriented polarization, while at high temperature, water molecules promote proton transfer only by displacement polarization.

One way to improve DNA conductivity is to change the mobility of carriers via functional group modification. Based on molecular dynamics calculations, this paper discusses proton transfer between bases after replacing the nitrogen atoms at the 3 and 7 positions in adenine by carbon and hydrogen. At a high temperature, charge localization is improved, with the charge located on a single base. Additionally, proton transfer and double proton transfer appear at a high temperature. The effects of the aqueous solution, temperature, and functional group on proton transfer are analyzed and discussed. The improved charge localization and reduction in the effect of temperature in the substituted adenine provide great potential for improving charge transport in adenine–thymine base pairs.

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. The bases that span these invariant subspaces are also invariant under the symmetry operations, and they are the symmetry-invariant bases. A standard methodology is available to construct a series of generator functions (GFs) and corresponding symmetry-adapted basis (SAB) functions from these symmetry-invariant bases. Elements of the factorized Hamiltonian and overlap matrix can be expressed in terms of these SAB functions, and their simple representations can be deduced in terms of GFs. The application of this method to the Heisenberg spin Hamiltonian is demonstrated.