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Chapter 8
CREATING BONDS AND POLYHEDRA

To search for bonds and atoms connected by them, and to create coordination polyhedra, choose the “Edit” menu \(\Rightarrow \) “Bonds…”. At the top of the Bonds dialog box (Fig. 8.1), select a phase to edit. A list of bond specifications is shown at the lower half of the dialog box. GUI controls in the Search bonds and atoms frame box are used to edit a bond specification. They are disabled when no bond specification is selected in the list.

To add a new bond specification, click the [New] button at first, select atoms relevant to the bond, and edit minimum and maximum lengths. Modifications in the GUI control are applied to the list either immediately or after the focus (caret) has moved from a text box to another GUI control. To delete a bond specification, select it in the list, and then click the [Delete] button or press the \(<\)Delete\(>\) key. Clicking the [Clear] button deletes all the bond specifications in the list. Press the [OK] or [Apply] button to reflect editing results in the Graphics Area.

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Figure 8.1:Bonds dialog.

8.1 Specifications of Searching for Bonds

8.1.1 Search mode

Bonds and, in turn, atoms connected by them are searched in one of the following three search modes:

  • “Search A2 bonded to A1”
    \(A2\) atoms bonded to \(A1\) atoms are searched on the basis of user-specified minimum and maximum interatomic distances: {Min. length} and {Max. length}.
  • “Search atoms bonded to A1”
    All the atoms bonded to \(A1\) atoms are searched on the basis of user-specified {Min. length} and {Max. length} regardless of the species of the \(A2\) atoms.
  • “Search molecules”
    All the pairs of atoms are searched on the basis of user-specified {Min. length} and {Max. length}. Neither \(A1\) nor \(A2\) is specified in this option. This mode best meets searching for atoms and bonds in molecular crystals.

8.1.2 Boundary mode

The Boundary mode specifies the extent of searching for atoms. Basically, atoms and bonds are searched within a drawing boundary defined by ranges along \(x\), \(y\), and \(z\) axes, and by optional cutoff planes (see chapter 10.1). However, on selection of a proper Boundary mode, atoms and bonds outside the drawing boundary are also searched so that all the atoms in coordination polyhedra or molecules are included.

  • “Do not search atoms beyond the boundary”
    Only atoms within the drawing boundary are searched.
  • “Search additional atoms if A1 is included in the boundary”
    All the \(A2\) atoms bonded to \(A1\) atoms are searched even if \(A2\) atoms are placed outside the drawing boundary. If the \(A2\) and \(A1\) atoms are, respectively, located inside and outside the boundary, the \(A1\) atom is not searched. This mode is the default for the “Search A2 bonded to A1” and “Search atoms bonded to A1” modes.
  • “Search additional atoms recursively if either A1 or A2 is visible”
    All the pairs of \(A1\) and \(A2\) atoms are searched if either \(A1\) or \(A2\) has already been found. When using this mode in inorganic crystals, beware lest bonds are infinitely connected. This mode is the default for the “Search molecules” mode.

8.1.3 Options

  • “Search by label”
    On selection of this option, a pair of atoms is specified by labels of sites. When this option is unchecked, a pair of atoms is specified by elemental symbols.
  • “Show polyhedra”
    This option specifies that \(A1\) atoms are central atoms of coordination polyhedra. This option has no effect on bond specifications in the “Search molecules” mode because no coordination polyhedra are searched in that mode.

8.1.4 A pair of atoms

Atoms \(A1\) and \(A2\) may be specified by entering either elemental symbols or site names. The {A1} and {A2} list boxes list elemental symbols of atoms if option “Search by label” is unchecked (default). On the other hand, {A1} and {A2} list site labels if option “Search by label” is checked.

The minimum and maximum bond lengths, {Min. length} and {Max. length}, are input in the unit of Å. Though {Min. length} is usually set at zero, it may be positive when dealing with a disordered structure whose split-atom model gives seemingly very short bonds.

8.2 Operating Instructions

8.2.1 Creating coordination polyhedra

To build up coordination polyhedra, either the “Search A2 bonded to A1” or “Search atoms bonded to A1” mode should be selected. The central atoms of the coordination polyhedra must be specified as \(A1\). In the “Search molecules” mode, no coordination polyhedra are created because VESTA does not have any information about central atoms. In the first two bond search modes, the Boundary mode 2 (“Search additional atoms if A1 is included in the boundary”) enables us to search for all the \(A2\) atoms bonded to \(A1\) atoms so that no coordination polyhedra are truncated even if \(A2\) atoms lie outside the boundary. \(A1\) atoms lying outside the boundary are never searched.

To search for additional atoms bonded to \(A2\) atoms, use the Boundary mode 3 (“Search additional atoms recursively if either A1 or A2 is visible”). For example, if hydrogen atoms are coordinated to some \(A2\) atoms, those hydrogen atoms can be searched even if \(A2\) atoms lie outside the boundary (Fig. 8.2).

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Figure 8.2:Crystal structure of \(\delta \)-AlOOH, a high-pressure modification of aluminum oxide hydroxide, with displacement ellipsoids at a 99 % probability level [60]. The structures were drawn in a coordinate range from (0, 0, 0) to (1, 1.5, 1). O–H bonds were searched (A) in the “Search additional atoms if A1 is included in the boundary” mode and (B) in the “Search additional atoms recursively if either A1 or A2 is visible” mode. In (A), some H atoms were omitted when O atoms lay outside of the boundary specified in the Boundary dialog box. On the hand, all the H atoms bonded to O atoms displayed in the screen were searched in (B).

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Figure 8.3:Crystal structure of anthraquinone [61]. Bonds are searched in the “Search mole- cules” mode with the boundary modes (A) “Do not search atoms beyond the boundary” and (B) “Search additional atoms recursively if either A1 or A2 is visible”. In both cases, the bounding box has a range of coordinates from (0, 0, 0) to (1, 1, 1).

8.2.2 Searching for molecules and clusters

The “Search molecules” mode is similar to 406 instruction in ORTEP-III1 [62], i.e., “reiterative convoluting sphere of enclosure add.” This mode is generally used in combination with the Boundary mode 3 to avoid some atoms in molecules being “truncated” (omitted) even if they lie outside the boundary (Fig. 8.3). In this mode, neither \(A1\) nor \(A2\) is specified; only {Min. length} and {Max. length} are input.

A maximum distance of 1.6 Å is appropriate in typical organic compounds containing H, C, N, O, and F atoms having covalent radii of 0.32, 0.77, 0.74, 0.66, and 0.72 Å, respectively. Inputting a larger value may generates unreal bonds. To search for atoms and bonds in molecules and clusters containing larger atoms such as P, S, Cl, and Br having covalent radii of 1.10, 1.04, 0.99, and 1.14 Å, respectively, add bond specifications in the “Search A2 bonded to A1” mode in combination with the Boundary mode 3 (Fig. 8.4).

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Figure 8.4:Crystal structure of tetrakis(di-4-pyridylsulfane)dinitratocopper(II) [63]. Bonds are searched in the “Search molecules” mode with a maximum distance of 1.6 Å in combination with the “Search A2 bonded to A1” mode for Cu–N and S–C bonds. The Boundary mode 3 was used.

8.2.3 Applications of the “Search molecules” mode to inorganic crystals

In general, combination of the “Search molecules” mode and the Boundary mode 3 is unsuitable for inorganic compounds or metals because a network of bonds may continue infinitely in their structures. In practice, an infinite number of atoms must be searched in such a case. Nevertheless, VESTA actually searches and shows a huge number of atoms and bonds in a finite range because searching within a certain area ensures that all the atoms contained in molecules in the boundary are searched in cases of periodic structures.

There are exceptions where the combination of such modes is well-suited to search for bonds in inorganic crystals, e.g., searching for O\(-\)H bonds. Usually, no bonds are shorter than O\(-\)H ones; thus, the use of this mode is safe with a small value of {Max. length}. The maximum bond length of ca. 1.1 Å leads to a search for all the H atoms bonded to O atoms in the Graphics Area.

8.2.4 Searching for hydrogen bonds

To display X\(-\)H\(\dotsm \)Y hydrogen bonds, select the “Search A2 bonded to A1” mode in the Search mode frame box, set \(A1\) at H and \(A2\) at Y, and input the minimum and maximum distances of H\(\dotsm \)Y bonds in {Min. length} and {Max. length}. Styles of the H\(\dotsm \)Y bonds can be set at Objects tab in the Side Panel.

8.2.5 Visualizing cage-like structures

To represent cage-like voids in porous crystals by a polyhedral model, put a virtual site at the center of a cage (see page 123) and add a bond specification between the virtual site and atoms at corners of the cage. Then, to visualize framework structures with solid bonds, add a bond specification between the corner atoms. If Y atoms are bonded to X atoms at the corners, add X–Y bonds. All of these bond specifications should be given with the Boundary mode 2 so that neither atoms nor bonds in cages displayed are omitted (Fig. 8.5).

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Figure 8.5:Crystal structure of the tetragonal variant of chibaite represented by a polyhedral model [64].