Bonding pair bond representation

Figure 2-12. Valence bond representation of the formation of a complex. The left hand form is the ionic representation with no covalent interaction between metal and ligand. The right-hand form shows the charge distribution which results from equal sharing of the lone pair.

In azole N-oxides the bond between the nitrogen and the oxygen atom is formed by an overlap of a lone pair orbital at the N-atom with an empty p-orbital at the oxygen atom. In the literature the N-O bond has been depicted as a dipolar single bond, a double bond, or as an arrow as shown in Scheme 2. The dipolar representation is used here. The double bond representation is usually applied in literature search engines. 

Although the molecular orbital description of bonding has some mathematical advantages, simple valence bond representations of structures are adequate for many purposes. The structures of molecules that have only single bonds (and in some cases unshared pairs of electrons on the... 

Figure 17-11. Valence bond representations of the cytosine-guanine base pair in the relevant electronic states (adapted from Ref. [53])...

There is a lot of delocalization in this structure, and usually these ligands are represented with a curved line to show the donation of both nitrogen lone pairs to the carbene C atom. You might prefer to include the formal + and - charges, but these compounds really do stretch the classical valence bond representation almost to breaking point, and conventionally the charges are not shown as they cancel out. 

It is useflil to show the valence bond representations of the complexes [CoFe] and [Co(NH3)6], which can then be compared with representations from the crystal field and molecular orbital theories to be discussed later. First, we must know from experiment that [CoF ] contains four unpaired electrons, whereas [Co(NH3)g] has all of its electrons paired. Each of the ligands, as Lewis bases, contributes a pair of electrons to form a coordinate covalent bond. The valence bond theory designations of the electronic structures are shown in Figure 2.7. The bonding is described as being covalent. Appropriate combinations of metal atomic orbitals are blended together to give a new set of orbitals, called hybrid orbitals. 

For example, the jump of a repton 6 in Fig. 1b from site 4 to site 3, corresponding to the motion of loop DDi through the gate between cells 4 and 3 in Fig. la, is described by the interchange of the last pair in the repton bond representation (100110) >( 100101). If oj = oj+i, their interchange does not lead to a new state and in the repton language implies that this transition is forbidden (e.g.. Jump of repton 3 in Fig. 1b in either direction). 

Figure B3.3.11. The classical ring polymer isomorphism, forA = 2 atoms, using/ = 5 beads. The wavy lines represent quantum spring bonds between different imaginary-time representations of the same atom. The dashed lines represent real pair-potential interactions, each diminished by a factor P, between the atoms, linking corresponding imaginary times.

It is useful to represent the polyelectronic wave function of a compound by a valence bond (VB) structure that represents the bonding between the atoms. Frequently, a single VB structure suffices, sometimes it is necessary to use several. We assume for simplicity that a single VB stiucture provides a faithful representation. A common way to write down a VB structure is by the spin-paired determinant, that ensures the compliance with Pauli s principle (It is assumed that there are 2n paired electrons in the system)... 

Figure 2-51. a) The rotational barrier in amides can only be explained by VB representation using two resonance structures, b) RAMSES accounts for the (albeit partial) conjugation between the carbonyl double bond and the lone pair on the nitrogen atom. 

The representation of non-bonding orbitals on an atom again uses the concept of. T-systems, though they may have any kind of hybridization (p, sp etc.), In Figure 2-56 the three possibilities arc shown lone pairs, radicals, and orbitals without electrons can be accommodated by this eoneept. 

Boranes are typical species with electron-deficient bonds, where a chemical bond has more centers than electrons. The smallest molecule showing this property is diborane. Each of the two B-H-B bonds (shown in Figure 2-60a) contains only two electrons, while the molecular orbital extends over three atoms. A correct representation has to represent the delocalization of the two electrons over three atom centers as shown in Figure 2-60b. Figure 2-60c shows another type of electron-deficient bond. In boron cage compounds, boron-boron bonds share their electron pair with the unoccupied atom orbital of a third boron atom [86]. These types of bonds cannot be accommodated in a single VB model of two-electron/ two-centered bonds. 

RAMSES is usually generated from molecular structures in a VB representation. The details of the connection table (localized charges, lone pairs, and bond orders) are kept within the model and are accessible for further processes. Bond orders are stored with the n-systems, while the number of free electrons is stored with the atoms. Upon modification oF a molecule (e.g., in systems dealing with reactions), the VB representation has to be generated in an adapted Form from the RAMSES notation. 

Internally, molecules can be represented several different ways. One possibility is to use a bond-order matrix representation. A second possibility is to use a list of bonds. Matrices are convenient for carrying out mathematical operations, but they waste memory due to many zero entries corresponding to pairs of atoms that are not bonded. For this reason, bond lists are the more widely used technique. 

Fig. 8. Planar representation of the (9M,0)-(5n,5n) knees, having a 36° bend angle produced by a heptagon-pentagon pair on the equatorial plane. The arrows show the dotted line of bonds where the knee N or N is connected to the corresponding straight tubules (a) knee N for n= 1 (b) stretched knee N , . for h = 1 and c=38 (c) general knees N and jV f.

Figure 11.11 Schematic representation of the bonding in NO complexes. Note that bending would withdraw an electron-pair from the metal centre to the N atom thus creating a vacant coordination site this may be a significant factor in the catalytic activity of such complexes. ...

Figure 19.18 Schematic representation of the orbital overlaps leading to M-CO bonding (a) a overlap and donation from the lone-pair on C into a vacant (hybrid) metal orbital to form a u M <—C bond, and (b) 7T overlap and the donation from a filled d or dj orbital on M into a vacant antibonding n orbital on CO to form a tt M—> C bond.

The following model is a representation of citric acid, the key substance in the so-called citric acid cycle by which food molecules are metabolized in the body. Only the connections between atoms are shown multiple bonds are not indicated. Complete the structure by indicating the positions of multiple bonds and lone-pair electrons (gray = C, red = O, ivory = H). 

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