近年来，石墨二炔（graphdiyne, GDY）材料因其天然均匀的多孔结构、独特的性质和潜在的广泛应用受到了人们的极大关注。本论文使用自洽场晶体轨道法，对一系列以石墨二炔为基础的二维单层和一维纳米带、纳米管体系的结构、电子和输运性质进行了理论研究，并探讨了边缘结构、掺杂、维度、尺寸、发生应变和施加电场等对材料性质的影响。本论文的主要工作如下：

1. 研究了边缘六元环被切割开的扶手椅型和锯齿型γ-GDY纳米带（A′-NR和Z′-NR）的稳定性、能带结构和电子性质。A′-NR是基态为非磁性态的半导体，其电子迁移率高达10⁶ cm²V^-1s^-1。在高速电子器件领域，A′-NR将具有潜在应用。A′-NR的带隔和迁移率随纳米带宽度的变化均与相应的边缘六元环完整的γ-GDY纳米带不同。然而，自旋极化计算表明，Z′-NR是基态为反铁磁性态的窄带隔（0.156-0.245 eV）半导体。非磁性态Z′-NR的两条前线能带在费米能级处形成几乎简并的平坦能带。这主要是由前线晶体轨道相对定域分布在纳米带的边缘（即edge state）造成的。这些均与相应的边缘完整的锯齿型γ-GDY纳米带有很大区别。总的来说，边缘结构的改变会对γ-GDY纳米带的性质产生巨大的影响。

2. 研究了BN单元分别取代掺杂β-GDY中sp²、sp和全部C原子的二维单层（β-GDY_BN1、β-GDY_BN2和β-BNDY）及其一维扶手椅型纳米带的性质。计算发现：无论是二维单层还是一维纳米带，BN单元的比例越高，晶胞膨胀越厉害，材料的面堆积密度和面内刚度越小，结构稳定性越好。这些BN掺杂的β-GDY单层均为半导体，且BN掺杂比例越高，带隔越大。当二维单层受到应力作用时，发生拉伸应变会使单层的带隔减小而压缩应变会使其带隔增大。当二维单层沿着平面两垂直方向发生均匀双轴应变时，其带隔随应变呈线性变化。三种相应的扶手椅型BN掺杂β-GDY纳米带也均为在Γ点存在直接带隔的半导体。随着纳米带宽度的增加，β-GDY_BN1和β-BNDY纳米带的带隔单调递减而β-GDY_BN2纳米带的带隔增大。此外，在电场作用下，这些扶手椅型BN掺杂β-GDY纳米带的最高占据晶体轨道和最低未占据晶体轨道中原本均匀分布在纳米带两侧的原子轨道分别沿着电场方向和电场反方向发生定向移动，并最终分别定域在纳米带低电势和高电势的两侧。随着电场强度的增大，三种扶手椅型BN掺杂β-GDY纳米带的带隔均线性减小，纳米带由半导体变为导体。通过外加电场的作用，带隔最大可由5 eV调至0 eV。

3. 计算了四种石墨二炔（α-、β-、γ-和 6,6,18-GDY）的二维单层以及一维纳米管（graphdiyne nanotube, GDYNT）的几何结构、稳定性、能带结构、电子性质和载流子迁移率，探讨了材料结构、维度、纳米管手性和尺寸等对材料性质的影响。二维α-GDY是导体，而二维β-、γ-和 6,6,18-GDY是半导体。对于二维α-GDY和6,6,18-GDY，电荷载流子迁移率各向异性，有利于空穴和电子输运的方向不同；对于二维β-GDY和γ-GDY，同种电荷载流子迁移率各向同性，且均更有利于电子的输运。扶手椅型α-GDYNT是导体，锯齿型α-GDYNT是带隔随管径呈现周期震荡变化的半导体。所有的β-GDYNT和γ-GDYNT均为半导体。随着管径的增大，β-GDYNT的带隔变化很小（<0.02 eV），而γ-GDYNT的带隔单调减小。扶手椅型6,6,18-GDYNT会随着管径的增大由半导体变为导体，而锯齿型6,6,18-GDYNT始终为半导体。此外，扶手椅型β-GDYNT和γ-GDYNT均更有利于空穴的输运，而锯齿型β-GDYNT和γ-GDYNT更有利于输运电子。β-GDYNT和γ-GDYNT的空穴和电子迁移率均随着纳米管管径的增大而增大。

Graphdiyne-based nanomaterials have attracted broad attention due to their natural uniform porous structures, unique properties and potential applications in recent years. The structural, electronic and transport properties of a series of graphdiyne-based (GDY) nanosheets, one-dimensional nanoribbons and nanotubes are studied by using the self-consistent field crystal orbital method. The effects of structure, dopting, dimension, size, strain and electric field on the properties of these materials are also discussed. The main work is summarized as follows:

1. The stability, band structures and electronic properties of the armchair and zigzag γ-GDY nanoribbons with half of the hexagonal rings at edges being cut off (A′-NR and Z′-NR) are investigated. The ground states of A′-NRs are the nonmagnetic states with the bandgap. The electron mobility of up to 10⁶ cm²V^-1s^-1 may enable the A′-NRs to be potential candidates for high-speed electronic devices. The variations in the bandgap and the mobility are both very different from those of the corresponding γ-GDY nanoribbons with intact hexagonal rings at edges. However, spin-polarization calculations indicate that the antiferromagnetic states with small bandgaps (0.156-0.245 eV) are the ground states of Z′-NRs. The two frontier bands of Z′-NRs form nearly degenerate flat-bands at the Fermi level in the nonmagnetic state due to the localized distribution of the frontier crystal orbitals at the edge sites. The flat-band states are known as edge states. These are quite different from the cases in the zigzag γ-GDY nanoribbons with intact hexagonal rings at edges. In general, the change of edge structures can make a great impact on the electronic properties of graphdiyne nanoribbons.

2. Three kinds of β-GDY with sp², sp and all carbon atoms substituted by BN units are denoted as β-GDY_BN1, β-GDY_BN2 and β-BNDY, respectively. The properties of these BN co-doped β-GDY nanosheets and the corresponding 1D nanoribbons with armchair edges are investigated theoretically. The calculations show that with the increasing co-doping ratio of BN units in all nanosheets and nanoribbons studied here, the expansion degree of unit cells and the structural stability increase, while the in-plane stiffness and the planar packing density decrease. β-GDY_BN1, β-GDY_BN2 and β-BNDY nanosheets are semiconductors and their bandgaps increase with the increasing co-doping ratio. When the 2D nanosheets are subjected to stress, their bandgaps decrease and increase in the case of stretching and compression strain, respectively. The bandgaps change linearly with the uniform biaxial strain. All of these corresponding armchair nanoribbons are semiconductors with direct bandgaps at the Γ point. With the increasing nanoribbon width, the bandgaps of the β-GDY_BN1 and β-BNDY nanoribbons decrease, while the bandgaps of the β-GDY_BN2 nanoribbons increases monotonically. In addition, the atomic orbitals in the highest occupied crystal orbital (HOCO) and the lowest unoccupied crystal orbital (LUCO) are evenly distributed on both sides of the nanoribbons. When an electric field is applied, the atomic orbitals in the HOCO move along the same direction of the electric field and are finally localized on the side with low potential, while the LUCO move along the opposite direction and are localized on the high potential side. With the increasing electric field intensity, the bandgaps of these nanoribbons decrease linearly and these nanoribbons transfer from semiconductors to conductors. The bandgaps can be tuned even from 5 eV to 0 eV by the electric field.

3. The geometric structures, stability, band structures, electronic properties and charge carrier mobilities of four kinds of graphdiyne nanosheets (α-, β-, γ- and 6,6,18-GDY) and their corresponding nanotubes (GDYNTs) are investigated systematically. The effects of structure, dimension, chirality and size on the properties of these materials are discussed. α-GDY is a conductor, but β-, γ- and 6,6,18-GDY are semiconductors. α-GDY and 6,6,18-GDY nanosheets have anisotropic mobilities, which are different along different directions. However, the carrier mobilities of β-GDY and γ-GDY nanosheets in different directions are almost the same, indicating the isotropic transport characteristics, and they prefer transporting electrons. Armchair α-GDYNTs are conductors, but zigzag α-GDYNTs are semiconductors and their bandgaps have oscillatory behaviour. All of β-GDYNTs and γ-GDYNTs are semiconductors. With the increasing tube diameter, the bandgaps of β-GDYNTs change slightly (<0.02 eV), while the bandgaps of γ-GDYNTs decrease monotonically. Armchair 6,6,18-GDYNTs change from semiconductors into conductors as the tube diameter increases and zigzag 6,6,18-GDYNTs are always semiconductors. Moreover, armchair β-GDYNTs and γ-GDYNTs are more favourable to transport holes, while the zigzag tubes prefer to transport electrons. The charge carrier mobilities of β-GDYNTs and γ-GDYNTs increase with the increasing tube diameter.