Mulliken bond order

The Mulliken bond order for the bond between atoms A and B is the total population for the A/B overlap region ... 

Bond angle of N-Nd-N (degree) Overlap interval of Nd-N Mulliken bond order Net charge on N... 

The net charge on lutetium is 0.948 and the Lu-C bond is predominantly covalent with 31% ionic characters and the Mulliken bond order of Lu-C bond is 0.497. 

The off-diagonal terms of the P S matrix betv een pairs of atomic orbitals centered on different atoms can be used to define the Mulliken bond order between atom A and atom B Bab) -... 

Moreover, the bond order-weighted Wiener index was proposed by applying the —> Wiener operator Wi to a variant of the multigraph distance matrix D(7t), where the conventional bond orders are replaced by the Mulliken bond orders [ Jalbout and Li, 2003c]. Then, the bond order-weighted Wiener index was defined as... 

A = Mulliken Bond Order B = Lowdin Bond Order. 

It has been shown that the increase in the nucleophilic nature of the oxygen atom makes it possible to form a strong interaction between the CO molecule and the tin cation as shown in Table 16. As emerges from these data the Mulliken bond order increases and the distance decreases between the O and Sn " atoms if the tin atom is charged. However, the increase of the positive charge on the... 

Table 14 Bond lengths and Mulliken bond orders of the carbon-oxygen bond in the carbon monoxide molecule and in CO -H Sn " ...

Defining ethane, ethylene and acetylene to have bond orders of 1, 2 and 3, the constant a-is found to have a value of approximately 0.3 A. For bond orders less than 1 (i.e. breaking and fonning single bonds) it appears that 0.6 A is a more appropriate proportionality constant. A Mulliken style measure of the bond strength between atoms A and B can be defined from the density matrix as (note that this involves the elements of the product of the D and S matrices). 

The tables below give some examples of atomic charges and bond orders calculated by various methods as a function of the basis set at the HF level of theory. It is evident that the Mulliken and Ldwdin methods do not converge as the basis set is increased, and the values in general behave unpredictably. Especially the presence of diffuse functions lead to absurd behaviours, as the aug-cc-pVXZ basis sets illustrate for CH4. Note also that... 

For yq the overlap population 2clcyS12 is positive, and the electron is bonding for yr2 it is negative, and the electron is antibonding. The sum of the values 2clc2Sl2 of all occupied orbitals of the molecule, the Mulliken overlap population, is a measure of the bond strength or bond order (b.o.) ... 

In this chapter, we use the definitions of bond order and valence indices provided by Mayer [4-6] (for a historical account, see Ref. [6a] and for other types of bond indices, see Ref. [6b]). In terms of electronic structure theory, they represent an extension to Mulliken s population analysis. The bond order is defined as... 

This consideration is corroborated by calculations at different levels of theory [11-13], showing that 1,2-additions to C q occur preferentially at a and (3 bonds between C(l) and C(2) and C(5) and C(6), respectively (Figure 13.2). Also, Mulliken charges on the fullerene core have been used in predicting the regiochemistry of nucleophilic additions to C70 [11]. Finally, 7t-bond orders have also been employed to evaluate the reactivity of different types of bonds [14-16]. 

At the end of Section 10.1 the Mulliken overlap population is mentioned as a quantity related to the bond order. A corresponding quantity for solids was introduced by R. Hoffmann the crystal orbital overlap population (COOP). It is a function that specifies the bond strength in a crystal, all states being taken into account by the Mulliken overlap populations Its calculation requires a powerful computer however, it can... 

---