Bond/bonding orders

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. 

Bond Bond order Bond length /pm Mean bond enthalpy /(k J moi" )... 

Valence bond theory does agree fairly well with molecular orbital (MO) theory for homonuclear diatomic molecules that can obey the octet rule H2 (single bond, bond order = 1), Li2 (single bond, bond order = 1), N2 (triple bond, bond order = 3), 02 (double bond, bond order = 2), F2 (single bond, bond order = 1). However, for those molecules that don t, it is more difficult to know if they exist or not and what bond orders they have. MO theory allows us to predict that He2, Be2 and Ne2 do not exist since they have bond orders = 0, and that B2 has bond order = 1 and C2 has bond order = 2. 

Cremer and coworkers have shown that the analysis of p(r) provides a basis for a rigorous definition of homoaromaticity27 44. Utilizing the definitions of covalent bonding, bond order, -character and Tt-delocalization (Section III.E), they translated Winstein s definition of homoaromaticity14 (Section III. A) into density language27 44 ... 

It is characterized by double-bifurcation reactions with three directly connected first-order transition states. These are two transition states 570 and transition state 562. The chemical behavior of cation 560 is determined by the stereocomposition of a cyclo-propylcarbynyl cation moiety in conjugation with two vinyl group. The 9-barbaralyl cation 560 is characterized by four weak C—C single bonds (bond orders = 0.54 and 0.84) and one strong nonbonded interaction that can be easily broken and closed. 

Metal-metal bond bond order k (mdyn A ) fo(A)... 

Addition of Me2PCH2PMe2 in THF at room temperature leads to the red-brown paramagnetic dimer (106), which has an unusually short Co—Co bond (bond order 1.5 structure, Table 35) with each Co being formally at the 0.5 oxidation level. [Co(PEt3)4] also adds to the B,C skeleton of c/oso-carbonates to form paramagnetic (107) and diamagnetic (108) clusters (equation 86).436 Many uses for these electron-rich species will be found. 

Bohr theory (4.2) The first theory of the atom to propose that electrons in atoms were in definite energy levels, boiling point (14.2) The temperature at which a liquid changes to a gas at the prevailing pressure, boiling-point elevation (15.6) An increase in the boiling point of a solvent due to the presence of a solute, bond See covalent bond and ionic bond. bond order See total bond order. 

F]ch and Fyh are the stretching force constants of the corresponding stable bonds, bond order = 1)... 

The ETMC is essentially an interatomic distance matrix (Fig. 3.47), with the diagonal elements containing an electronic structural parameter (atomic charge, polarizability, HOMO energy, etc.). Off-diagonal elements for two atoms that are chemically bonded are used to store information regarding the bond (bond order, polarizability, etc.). Matrices for active compounds in a series are then searched for common features that are not shared by inactive compounds. The successful examples cited are predominately for small, relatively rigid structures where the conformational parameter does not confuse the analysis. 

Bond Bond Length (nm) Bond Order cr Bonds Bond Order 7t Bonds Position Interbond Angle (°)... 

The overall number of bonding and antibonding electrons determines the number of bonds (bond order) ... 

One shared pair single bond (-) Bond order = I... 

M. Barfield and M. Karplus, Valence-bond bond-order formulation for contact nuclear spin-spin coupling, J. Am. Chem. Soc., 91 (1969) 1-10. 

HCCH direction (Figure 6.9d), available for sideways overlap to form two 7r-bonds, one in the xy-plane and one in the yz-plane. This generates the triple bond description of the ethyne carbon to carbon bond, comprising one CT-bond and two 7r-bonds, bond order 3.0 and normally written as HC CH. 

Bond (bond order) (kcal mol b Bond (bond order) (kcal mol H... 

Results (Table I) from refinement of the powder neutron diffraction data for the Ce doped material, Bi 8 0 2 3 12 that significant structural alterations have resulcea from Ce incorporation into the solid The three Mo atoms are no longer chemically equivalent The coordination about Mo(l) is unchanged from that of the parent compound A second Mo atom contains two short (double) bonds to oxygen atoms These molybdate dioxo (dimolybdenyl) groups are believed to be an important feature for selective oxidation catalysis (7 ) The third Mo coordination sphere contains no Mo=0 bond Bond order calculations (27) about... 

Substitution Patterns Covers 12 different substitution patterns that typically occur. These patterns are based on replacing atom groups with chlorine atoms to treat them as similar. Four criteria can be defined for atom groups to be replaced atoms directly attached to aromatic rings, atoms attached to carbon-carbon multiple bonds, bond orders to substituents, and multiple substitutions by heteroatoms. 

Bond Bond Order Average Bond Length (pm) Average Bond Energy (kJ/mol)... 

This linear relationship exists for a variety of other C-C bonds, including those in strained ring molecules and even in carbocations. There is also a high-precision correlation (r = —0.998) for a series of bond lengths in aromatic compounds having differing bond orders, but it does not appear to hold for C-O or C-N bonds. Bond order in the AIM context has also been defined as ... 

The symbol is used to denote resonance. It is important to realize that we are not implying that benzene exists as an equilibrium mixture of the two forms. In that case, the symbol would have been used. Instead, each molecule is a hybrid, each carbon-carbon bond being halfway between a single and a double bond the C—C bond has a bond order of 1.5. The C—C bonds are all the same length, 0.140 nm, which is intermediate between the distance for a single bond (bond order — 1),... 

A number of compounds containing unusually short M-M bonds exhibit unusually high p(MM). For example, the Mo-Mo distance of Mo2(OAc)4 is only 2.09 A and its p(MM) is at 406 cm". According to Cotton, " this Mo-Mo bond consists of one cr-bond, two -jr-bonds and a S-bond (bond order 4). Such a quadruple bond is also expected for [Re2Clgf" which exhibits the p(ReRe) at 272 cm" with the Re-Re distance of 2.22 Table III-62 lists p(MM)... 

The intemuclear distance in the +1 ion should be greater than that in the neutral hydrogen molecule. The distance in the +2 ion will be arbitrarly large because there is no bond (bond order zero). 

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