Electron-bond order

The off-diagonal elements of P corresponding to directly bonded atoms are referred to as (7r-electron) bond orders. Hexatriene shows bond-length alternation there are distinct single and double bonds. Notice that the bond orders for the bonded atom pairs show a related alternation. 

It was noted many years ago that the rr-electron bond orders correlated well with experimental bond lengths. Simple relationships such as... 

The MO methods have been used to calculate the ir-electronic bond orders in unprotonated cytosine, and the bond lengths have been calculated on the basis of these quantities in the customary way.168a The qualitative agreement (Fig. 2) between the theoretical and experimental values is, in general, good, the best being obtained by means of the simple tt-HMO method. The 77-bond orders or total bond overlap populations calculated by different methods can be found in several papers 1t-HMO calculations on cytosines, see reviews1 140,170-172 n-SC... 

Here Aq = qv (X) — q (CeHgF) is the -electron charge density on the fluorine atom in X relative to fluorobenzene Aq c is the corresponding difference in jt-electron bond order for the FC bond Aqc is the corre-... 

The first term is essentially the total 7r-electron bond order for bonded sites, since v+ is the Hiickel model (1) for a ring with e = 0 and t = -1 between neighbors. 

Several MO methods have been applied to calculate the 7T-electronic bond orders (or total bond overlap populations) of uracil, thymine, and some of their derivatives. They can be found in the following papers tt-HMO calculations on uracils and thymines, see reviews ° ° 7T-SC HMO (w-technique) calculations on forms 32 and 28 of uracil and thymine, 1-methyluracil and 1-methylthymine tt-SCF MO calculations on uracil forms 27,29-31,i ... 

Formula Name Bonding electrons Antibonding electrons Bond order Bond length (pm)... 

We take half the difference because we are used to thinking of bonds as pairs of electrons. A bond order of 1 represents a single bond, a bond order of 2 represents a double bond, and a bond order of 3 represents a triple bond. Because MO theory also treats molecules containing an odd number of electrons, bond orders of 1/2,3/2, or 5/2 are possible. 

Tetrahedral CH4 is familiar in electronic disposition each hydrogen is bound to carbon by an sp -hybridized atomic orbital (AO), and each Csp /Hls localized molecular orbital (MO) is a normal electron-pair single bond (occupancy 2. 0 electrons, bond order 1.00). Nonintuitively, the four equivalent bonds do not reflect four equivalent valence AOs on caibon, but rather are a mathematical constmct based on different valence energy levels (—25, -14, -14, —14 eV at the STO-3G level), which can be experimentally detected [28, 29]. 

This becomes in particular apparent if one studies the electron bond order density distributions. 

The fermion operators and create and annihilate an electron with spin a at carbon n, with partial double and single bonds at sites 2n,2n- 1, and 2n, 2/i+ I in Fig. 6.1. Coulson s mobile 7r-electron bond order [14] is the operator defined by Eq. (1). The familiar eigenvalues of Hq 8) are... 

This article provides a comprehensive review of modem approaches to analysis of electronic wavefunctions. Diverse definitions of properties such as atomic charges, energies, and valences, bond orders and energies, specialized orbitals, and similarities of atoms and molecules are presented. The merits and shortcomings of these definitions are discussed, Particular emphasis is placed on rigorous interpretive tools which produce quantities that can be regarded as tme quantum mechanical observables. Because of their lack of generality, approaches to quantification of chemical concepts that are limited to certain classes of molecules or electronic stmcture methods (such as n -electron bond orders in Hiickel theory) are not mentioned. 

Number of Bonding Electrons Numbn of Anti-Bonding Electrons Bond Order... 

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