Population analysis bond order

We have obtained the bond overlap population (BOP) and net charge of the ions by the Mulliken population analysis in order to discuss the bonding state of the Li and N ions. 

Table 1 Populations and Bond Orders Using Mulliken and Lowdin Analysis ...

Table 2 Populations and Bond Orders of C3HJ with the 3-21G and 3-21 + G Basis Sets Using Mulliken and Lowdin Analysis ...

Chemists are able to do research much more efficiently if they have a model for understanding chemistry. Population analysis is a mathematical way of partitioning a wave function or electron density into charges on the nuclei, bond orders, and other related information. These are probably the most widely used results that are not experimentally observable. 

Natural bond order analysis (NBO) is the name of a whole set of analysis techniques. One of these is the natural population analysis (NPA) for obtaining... 

NBO (natural bond order) the name of a set of population analysis techniques NDO (neglect of differential overlap) the fundamental assumption behind many semiempirical methods... 

Table 3.40 displays the calculated 0b charges from natural population analysis (NPA) for all unique B atoms. This table also includes comparison of the NPA charges with corresponding zeroth-order (ZO) estimates given by Lipscomb, which are based essentially on the formal charges for conjectured three-center bond and. s /vx-code assignments for each species (to be discussed below). 

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... 

Information about the possible structures of molybdate and its pro-tonated forms in solution has been obtained from molecular orbital calculations (62). By considering bond orders obtained from a Mulli-ken population analysis and the agreement between experimental and theoretical UV spectra it was concluded that [Mo04]2 and [HMoOt I are tetrahedral and that the neutral acid is octahedral. For the latter a somewhat distorted octahedral structure based on the formula Mo02(OH)2(H20)2 was proposed (62). The alternative structure Mo03(H20)3 was not taken into account in the calculations. 

Several computational studies have addressed whether the dipolar cycloaddition of nitronates is a concerted or stepwise process (93,100). Natural population analysis reveals that their is very little zwitterionic character in the transition state. The formation of the C C bond marginally precedes the C—O bond on the basis of calculated bond lengths and orders in the transition structure. These calculations also show that the reaction is a concerted process that is shghtly asynchronous. In addition, the cycloaddition likely proceeds through an early transition state and is overall an exothermic process. 

R. S. Mulliken,/. Chem. Phys., 23, 1833, 1841 (1955). Electronic Population Analysis on LCAO-MO Molecular Wavefunctions. I. (no subtitle). II. Overlap Populations, Bond Orders, and Covalent Bond Energies. 

Assigning atom charges and bond orders involves calculating the number of electrons belonging to an atom or shared between two atoms, i.e. the population of electrons on or between atoms hence such calculations are said to involve population analysis. Earlier schemes for population analysis bypassed the problem of defining the space occupied by atoms in molecules, and the space occupied by bonding electrons, by partitioning electron density in a somewhat arbitrary way. The earliest such schemes were utilized in the simple Hiickel or similar methods [256], and related these quantities to the basis functions (which in these methods are essentially valence, or even just p, atomic orbitals see Section 4.3.4). The simplest scheme used in ab initio calculations is Mulliken population analysis [257]. 

In order to evaluate the strength of the bonding between two atoms, the BO is calculated by the Mulliken population analysis. The atomic bond order BOab between atoms A and B is defined as... 

Mulliken, R.S., Electronic population analysis on ICAO—MO molecular wave functions II. Overlap populations, bond orders, and covalent bond energies. J.Chem.Phys. (1955) 23 1841-1846. 

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