Bond Ordering

Bundle (548) has pointed out that resonating, hybrid sp orbitals arc probably active in bonding in interstitial carbides and nitrides. 

there may be an ordering of the covalent portion of the bond, that is of the -p hybrid, to give covalent bonding along one axis and either ionic or bonding-band bonding in the perpendicular plane. This type of order seems to occur in CrN (see Chapter III, Section II-B-2). It is, of course, closely related to the ordering cited in Sections I-C-4 and I-C-5. 

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Fournier R and Salahub D R 1990 Chemisorption and magnetization A bond order-rigid band model Surf. Sol. 238 330-40... 

The systematic lUPAC nomenclature of compounds tries to characterize compounds by a unique name. The names are quite often not as compact as the trivial names, which are short and simple to memorize. In fact, the lUPAC name can be quite long and cumbersome. This is one reason why trivial names are still heavily used today. The basic aim of the lUPAC nomenclature is to describe particular parts of the structure (fi agments) in a systematic manner, with special expressions from a vocabulary of terms. Therefore, the systematic nomenclature can be, and is, used in database systems such as the Chemical Abstracts Service (see Section 5.4) as index for chemical structures. However, this notation does not directly allow the extraction of additional information about the molecule, such as bond orders or molecular weight. 

With such a matrix representation, the storage space is dependent only on the number of nodc.s (atoms) and independent of the number of bonds. As Figure 2-14 dcmon.stratcs, all the e.sscntial information in an adjacency matrix can also be lound in the much smaller non-rediindant matrix. But the adjacency matrix is unsuitable for reconstructing the constitution of a molecule, because it does not provide any information about the bond orders. 

Both the adjacency and distance matrices provide information about the connections in the molceular structure, but no additional information such as atom type or bond order. One type of matrix which includes more information, the Atom Connectivity Matrix (ACM), was introduced by Spialtcr and is discussed in Ref, [38]. This approach was eventually abandoned but is listed here because it was quite a unique approach. 

The bond matrix is related to the adjacency matrix but gives information also on the bond order of the connected atoms. Elements of the matrix obtain the value of 2 if there is a double bond between the atoms, c.g, between atoms 2 and 3... 

Adjactney matrix describes connections of atoms contains only 0 and 1 (bits) no bond types and bond orders no number of free electrons... 

Distunct matrix describes geometric distances no bond types or bond orders no number of free electrons cannot be represented by bits... 

There are many ways of presenting a connection table. One is first to label each atom of a molecule arbitrarily and to arrange them in an atom list (Figure 2-20). Then the bond information is stored in a second table with indices of the atoms that are connected by a bond. Additionally, the bond order of the corresponding coimection is stored as an integer code (1 = single bond, 2 = double bond, etc.) in the third column. 

Both tables, the atom and the bond lists, are linked through the atom indices. An alternative coimection table in the form of a redundant CT is shown in Figure 2-21. There, the first two columns give the index of an atom and the corresponding element symbol. The bond list is integrated into a tabular form in which the atoms are defined. Thus, the bond list extends the table behind the first two columns of the atom list. An atom can be bonded to several other atoms the atom with index 1 is connected to the atoms 2, 4, 5, and 6. These can also be written on one line. Then, a given row contains a focused atom in the atom list, followed by the indices of all the atoms to which this atom is bonded. Additionally, the bond orders are inserted directly following the atom in-... 

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. 

The most well-known and at the same time the earliest computer model for a molecular structure representation is a wire frame model (Figure 2-123a). This model is also known under other names such as line model or Drciding model [199]. It shows the individual bonds and the angles formed between these bonds. The bonds of a molecule are represented by colored vector lines and the color is derived from the atom type definition. This simple method does not display atoms, but atom positions can be derived from the end and branching points of the wire frame model. In addition, the bond orders between two atoms can be expressed by the number of lines. 

The optimization of the backtracking algorithm usually consists of an application of several heuristics which reduce the number of candidate atoms for mapping from Gq to Gj. These heuristics are based on local properties of the atoms such as atom types, number of bonds, bond orders, and ring membership. According to these properties the atoms in Gq and Gj are separated into different classes. This step is known in the literature as partitioning [13]. Table 6.1 illustrates the process of partitioning. 

Figure 10.1-3. Two regioisomeric products of the training data set and their corresponding physicochemical effects used as coding vectors bo bond order difference in tr-electro-...

Covalen t radii for all th e clem cn ts are readily available an d the bond orders of all bonds arc available from the molecular graph. Prior to describing the explicit default parameter scheme, it is nee-... 

As with atomic charges, the bond order is not a quantum mechanical observable and so anuus methods have been proposed for calculating the bond orders in a molecule. 

Table 2.6 Bond order obtained from the Mayer bond order scheme [Mayer 1983].

Mayer defined the bond order between two atoms as follows [Mayer 1983] ... 

P is the total spinless density matrix (P = P + P ) and P is the spin density matrix (P = p" + P ). For a closed-shell system Mayer s definition of the bond order reduces to ... 

The bond orders obtained from Mayer s formula often seem intuitively reasonable, as illustrated in Table 2.6 for some simple molecules. The method has also been used to compute the bond orders for intermediate structures in reactions of the form H -1- XH HX -1- H and X I- XH -H H (X = F, Cl, Br). The results suggested that bond orders were a useful way to describe the similarity of the transition structure to the reactants or to the products. Moreover, the bond orders were approximately conserved along the reaction pathway. 

As with methods for allocating electron density to atoms, the Mayer method is not necessarily correct, though it appears to be a useful measure of the bond order that conforms to accepted pictures of bonding in molecules. 

The Tersoff potential [Tersoff 1988] is based on a model known as the empirical bond-order potential. This potential can be written in a form very similar to the Finnis-Sinclair potential ... 

The key term is which is the bond order between the atoms i and j. This parameter depends upon the number of bonds to the atom i the strength of the bond between i and j decreases as the number of bonds fo fhe atom i increases. The original bond-order potential [Abell 1985] is mathematically equivalent to the Finnis-Sinclair model if the bond order by is given by ... 

The Tersoff potential was designed specifically for the group 14 elements and extends the basic empirical bond-order model by including an angular term. The interaction energy between two atoms i and j using this potential is ... 

The function/c is a smoothing function with the value 1 up to some distance Yy (typically chosen to include just the first neighbour shell) and then smoothly tapers to zero at the cutoff distance, by is the bond-order term, which incorporates an angular term dependent upon the bond angle 6yk- The Tersoff pofenfial is more broadly applicable than the Stillinger-Weber potential, but does contain more parameters. 

There are a number of different ways that the molecular graph can be conununicated between the computer and the end-user. One common representation is the connection table, of which there are various flavours, but most provide information about the atoms present in the molecule and their connectivity. The most basic connection tables simply indicate the atomic number of each atom and which atoms form each bond others may include information about the atom hybridisation state and the bond order. Hydrogens may be included or they may be imphed. In addition, information about the atomic coordinates (for the standard two-dimensional chemical drawing or for the three-dimensional conformation) can be included. The connection table for acetic acid in one of the most popular formats, the Molecular Design mol format [Dalby et al. 1992], is shown in Figure 12.3. 

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