Periodic Boundary Conditions (PBC)
5-1 Start a new file by selecting the option from the menu in the main window.
5-2 Make the Carbon Tetrahedral fragment the “current fragment” by double-clicking on the tool button and then clicking on Carbon and then Carbon Tetrahedral in the Element Fragment palette.
5-3 Click anywhere in the empty View window to create a methane molecule.
5-4 Center the molecule in the View window by clicking on the toolbar button and then position the molecule so all atoms are visible.
5-5 Turn on atom labels for the View window by checking from the menu of the main window.
5-6 Show the Point Group dialog for the molecule by selecting from the menu of the main window. In the Point Group dialog, check the box, and then select from the drop-down list.
5-7 Change the CH bond lengths to match the experimental values for the diamond CC bond length. Click on the toolbar button, and then click on atoms 1 and 2 in the the View window. In the corresponding Semichem Smartslide dialog, change the bond length value from 1.07 to 1.54 in the input field, and then click on the button. Note that all of the CH bond lengths have increased to 1.54 to preserve the Td symmetry. In the Point Group dialog, uncheck the box, and then click the button.
5-8 Show the PBC dialog for the molecule by selecting from the menu of the main window.
5-9 In the Symmetry tab of the PBC dialog, select from the drop-down list.
5-10 In the Cell tab of the PBC dialog, push down the button to enable placement of the cell origin (O (0,0,0)) vertex at any atom selected in the View window using the mouse. In the drop-down list, select instead of so that the whole cell will be translated rather than just the cell origin vertex. In the View window, click on atom 3.
5-11 In the Cell tab of the PBC dialog, select instead of to enable placement of the head of the “a” lattice vector at any atom selected in the View window using the mouse. In the drop-down list, select instead of so that just the “a” vertex will be translated rather than the whole cell. In the View window, click on atom 5.
5-12 In the Cell tab of the PBC dialog, select instead of to enable placement of the head of the “b” lattice vector at any atom selected in the View window using the mouse. In the View window, click on atom 4.
5-13 In the Cell tab of the PBC dialog, select instead of to enable placement of the head of the “c” lattice vector at any atom selected in the View window using the mouse. In the View window, click on atom 2.
5-14 In the Contents tab of the PBC dialog, select the item from the menu of the editor.
5-15 In the Contents tab of the PBC dialog, change the hydrogen atom to a carbon atom atom by editing the second row of the column in the editor.
5-16 In the Contents tab of the PBC dialog, select from the popup menu.
5-17 The bonds between reference unit cell atoms and replicate cell atoms are shown in the replicate format, which is by default. In the View tab of the PBC dialog, select from the drop-down list in order to better see the bonds in this case.
5-18 At this point, we have defined a primitive unit cell for a PBC/3D model of a diamond crystal.
5-19 Show the PBC dialog for the molecule by selecting from the menu of the main window.
5-20 In the View tab of the PBC dialog, select from the drop-down list.
5-21 In the View tab of the PBC dialog, check the checkbox.
5-22 In the View tab of the PBC dialog, show one replicate cell along the “-c” axis, using the corresponding spin boxes ( ) in the Cell Replication section.
5-23 In the Cell tab of the PBC dialog, select from the drop-down list, and check the atoms checkbox. Then, push down the button, and select instead of to enable placement of the head of the “a” lattice vector at any atom selected in the View window, using the mouse. In the View window, click on the atom at position (1, 1,-1).
5-24 In the View tab of the PBC dialog, show zero replicate cells along the “-c” axis again, one along the “-a” axis, and two along the “+b” axis, using the corresponding spin boxes ( ) in the Cell Replication section.
5-25 In the Cell tab of the PBC dialog, select instead of to enable placement of the head of the “b” lattice vector at any atom selected in the View window, using the mouse. In the View window, click on the atom at position (-1, 2, 0).
5-26 In the View tab of the PBC dialog, show one replicate cell along the “+a” axis again, one along the “-b” axis, and two along the “+c” axis, using the corresponding spin boxes ( ) in the Cell Replication section.
5-27 In the Cell tab of the PBC dialog, select instead of to enable placement of the head of the “c” lattice vector at any atom selected in the View window, using the mouse. In the View window, click on the atom at position (0, -1, 2).
5-28 In the View tab of the PBC dialog, show just the reference cell using the corresponding spin boxes ( ) in the Cell Replication section.
5-29 In the View tab of the PBC dialog, uncheck the checkbox.
5-30 We now have a face-centered cubic unit cell of diamond that gives the same crystal structure as that from the primitive unit cell we started with.