Matrix atom connectivity

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-clcctron matrix (BE-matrix) was introduced in the Dugundji-Ugi model [39], It can be considered as an extension of the bond matrix or as a mod-ific atinn of Spialter s atom connectivity matrix [38], The BE-inatrix gives, in addition to the entries of bond values in the off-diagonal elements, the number of free valence electrons on the corresponding atom in the diagonal elements (e.g., 03 = 4 in Figure 2-18). 

Spialter L (1964) The atom connectivity matrix (ACM) and its characteristic polynomial (ACMCP), J Chem Doc 4 261... 

An analogous quantity, called the bond vertex degree 6f, is calculated from the - atom connectivity matrix C as ... 

The most well-known is the atom connectivity matrix C obtained from multigraphs using the -> conventional bond order jt to represent the adjacency between a pair of vertices ... 

Spialter, L. (1963). The Atom Connectivity Matrix (ACM) and its Characteristic Polynomial (ACMCP) A New Computer-Oriented Chemical Nomenclature. J.Am.Chem.Soc., 85, 2012-2013. 

To accormt for multiple bonds, atom connectivity matrix, —> adjacency matrix of a multigraph, and adjacency matrix of a general graph can be used instead of the adjacency matrix of a simple graph. To account for heteroatoms, different weighted adjacerucy matrices were proposed, such as the augmented ct acency matrix and chemical adjacency matrix. 

The bond vertex degree 5 is another local invariant that accounts for atom connectedness and also for bond multiplicity. It is calculated from the atom connectivity matrix C as the sum of row entries [Kier and Hall, 1986] ... 

The adjacency matrix of a multigraph is a variant of the atom connectivity matrix defined as [Janezic, Milicevic et al., 2007]... 

Atom connectivity matrix C of 5-methyl-l,3,4-oxathiazol-2-one VS, indicates the matrix row sums. 

Spialter, L. (1964b) The atom connectivity matrix characteristic polynomial (ACMCP) and its physico-geometric (topological) significance. 

In 1964, Spialter introduced the atom connectivity matrix (ACM) in an attempt to define algebraically a characteristic polynomial associated... 

The covalent bonds of a chemical constitution of an EM which contains a set of n atoms can be represented by an x ACM. The ACM were introduced in 1963 by Spialter 29) for documentation purposes. In an atom connectivity matrix B, each off-diagonal entry % indicates the formal bond order between an indexed pair of atoms, Aj and Aj. The ACM are symmetric matrices because the chemical bond is a symmetric relation. 

The atom-connectivity matrix, denoted by ACM, has been proposed by Spialter (1963, 1964a, 1964b) for use in computer-oriented chemical nomenclature. This matrix represents the structural formula of a molecule and is given by... 

It should also be pointed out that the roots of the atom-connectivity matrix concept go back at least to Balandin (1940), though there are indications that this concept is even older (Randic and Trinajstid, 1994). Balandin constructed property matrices by using the symbols of atoms making up the molecule as diagonal elements and molecular properties such as the interatomic distances (in A), bond dissociation energies (in kcal), and vibrational force constants (in cm x 10 ) as off-diagonal elements. 

---