用Gaussian03的PBC计算能带结构

1、G03开始，Gaussian就开始支持周期性边界条件了。具体的关键词是tv,也就是translation vector的首字母 缩写。在这里，我们举一个一维的碳链的例子(如上图所示)，来具体手把手的教你如何用Gaussian03计算固体的 能带结构。同样的方法可以用来计算碳纳米管的能带结构等。为了计算能带结构，在G03.C02版本中必须 指定以下的IOP：# IOp(5/33=3)其中5/33=3表示debug，会打印出Fock矩阵。(只对c02版适用，d版以后无需此iop)完整输入文件如下(根据Gaussian手册，在PBC情况下，blyp之类的算法比HF更快)：#p blyp/6-311G

2、*(d) PBC(NKPoint=20) iop(5/33=3)C atom0,1C 0.00 0.00 0.00TV 0.00 0.00 1.44此输入文件说明我们模拟的是一维无穷长的碳链，碳原子之间的距离为1.44A。为了简单起见，我们不考 虑由于派尔斯相变引起的构型变化。用如上的输入文件完成计算后，在输出文件的SCF done和Population Analysis之间会有这样一段输出3 alpha orbitals occupied out of30functions.alpha orb energies kxyz= 00314 0.445 eV00.000 0.000 -10.024

3、 -0.741 -0.344 | -0.344 0.261 0.314 0.alpha orb energies kxyz= 401600 0.736 eV10.000 0.000 -10.023 -0.486 -0.056 | 0.087 0.087 0.600 0.alpha orb energies kxyz= 391609 0.691 eV10.000 0.000 -10.023 -0.491 -0.047 | 0.074 0.074 0.609 0.alpha orb energies kxyz= 381620 0.645 eV10.000 0.000 -10.023 -0.503

4、-0.031 | 0.051 0.051 0.620 0.alpha orb energies kxyz= 371621 0.621 eV10.000 0.000 -10.023 -0.518 -0.007 | 0.021 0.021 0.602 0.alpha orb energies kxyz= 361606 0.606 eV10.000 0.000 -10.024 -0.536 -0.013 | -0.013 0.021 0.563 0.alpha orb energies kxyz= 351579 0.579 eV10.000 0.000 -10.024 -0.555 -0.048 |

5、 -0.048 0.053 0.529 0.alpha orb energies kxyz= 341546 0.546 eV10.000 0.000 -10.024 -0.576 -0.083 | -0.083 0.087 0.501 0.alpha orb energies kxyz= 331512 0.512 eV10.000 0.000 -10.024 -0.596 -0.117 | -0.117 0.122 0.484 0.alpha orb energies kxyz= 321478 0.478 eV10.000 0.000 -10.024 -0.616 -0.150 | -0.15

6、0 0.155 0.477 0.alpha orb energies kxyz=31110.0000.000 -10.024 -0.635-0.181 |-0.1810.1850.4470.447 0.484 eValpha orb energies kxyz=30110.0000.000 -10.024 -0.654-0.210 |-0.2100.2110.4180.418 0.501 eValpha orb energies kxyz=29110.0000.000 -10.024 -0.670-0.236 |-0.2360.2320.3920.392 0.526 eValpha orb e

7、nergies kxyz=28110.0000.000 -10.024 -0.686-0.260 |-0.2600.2480.3690.369 0.542 eValpha orb energies kxyz=27110.0000.000 -10.024 -0.699-0.281 |-0.2810.2580.3490.349 0.518 eValpha orb energies kxyz=26110.0000.000 -10.024 -0.711-0.298 |-0.2980.2630.3330.333 0.497 eValpha orb energies kxyz=25110.0000.000

8、 -10.024 -0.721-0.313 |-0.3130.2640.3210.321 0.480 eValpha orb energies kxyz=24110.0000.000 -10.024 -0.729-0.326 |-0.3260.2640.3130.313 0.466 eValpha orb energies kxyz=23110.0000.000 -10.024 -0.735-0.335 |-0.3350.2640.3100.310 0.456 eValpha orb energies kxyz=22110.0000.000 -10.024 -0.739-0.341 |-0.3

9、410.2620.3120.312 0.449 eValpha orb energies kxyz=21110.0000.000 -10.024 -0.741-0.344 |-0.3440.2620.3140.314 0.445 eVHOCOat k-pointLUCOat k-pointIndirect gap4 kxyz=0 kxyz=3711000 -9.160924-0.200927 eV-9.361851 eV eV以上部分包含的信息是每个K点上，HOMO和LUMO左右的十条轨道的能量。将他们连接起来(按照kxyz =0, 21, 22, 23,.,40的顺序)就是费米面附近的能带图

10、了。注意，以上能量的单位是Hartree(27.2eV)。下图 是用Origin画的能带图，和紧束缚给出的能带相同。当然了，实际情况下，一维的碳链会发生派尔斯畸变，在这里不做进一步讨论。Bandstrqur Csrbon ChinT-T T T f r 、.I在这里不做进一步讨论。Bandstrqur Csrbon ChinT-T T T f r 、.I0 806O.J0.20 0*%用以下的输入文件即可计算(5,5)的碳纳米管的能带结构#p blyp/3-21G PBC IOp(5/33=3) (5,5) CNT0 1C3.390000000000.000000000000.00000000

11、0000C3.0969190000001.378837000000.000000000000C2.7425680000001.9925920000001.229756000000C1.6950000000002.9358260000001.229756000000C1.0475680000003.224082000000.000000000000C-.3543515000003.371429000000.000000000000C-1.0475680000003.2240820000001.229756000000C-2.2683530000002.5192610000001.22975600

12、0000C-2.7425680000001.992592000000.000000000000C-3.315920000000.704820600000.000000000000C-3.390000000000.0000000000001.229756000000C-3.096919000000-1.3788370000001.229756000000C-2.742568000000-1.992592000000.000000000000C-1.695000000000-2.935826000000.000000000000C-1.047568000000-3.2240820000001.229756000000C.354351500000-3.3714290000001.229756000000C1.047568000000-3.22408200