Shared-electron-number method

The shared-electron number (SEN) method was used for the evaluation of hydrogen bond energies. This method was developed for the evaluation of hydrogen bonds in compounds which cannot be decomposed into two parts such that the decomposition energy can be solely attributed to the broken hydrogen bond. Details of the SEN method are described in Ref. (82). 

The basic idea of the shared-electron-number (SEN) method [243] is to estimate the strength of a hydrogen bond by means of only one variable. This variable is the two-center shared-electron number ctha, which is related linearly to the hydrogen bond energy j ha. 

Historically, multiple theoretical descriptor-based approaches to H-bond strength ranking were proposed. That includes approaches based on group contribution method [46], electrostatic potentials [47], electrophilic superdelocalizability and self-atom polarizability [48], Quantum Theory of Atoms In Molecules (QTAIM) descriptors [49-51], the two-center shared electron number a and the product of ionization potential [45, 52], and local quantum mechanical molecular parameters, which quantify electrostatic, polarizability, and charge transfer contributions to H-bonding [53, 54],... 

Merrill 157). The basic assumptions and mathematical formalism of the BOC-MP and BEBO methods are quite different, however. Most important, in the BEBO method, following Lewis and Pauling, the bond order x is defined as the number of shared electron pairs, so that x may be smaller than, equal to, or larger than unity, reflecting fractional, single, or multiple A-B bonding, respectively. Furthermore, the BEBO method makes use of the power function E x) = -Q0xp, where p is some empirical constant. 

The forces that hold atoms together in compounds are called chemical bonds. One way that atoms can form bonds is by sharing electrons. These bonds are called covalent bonds, and the resulting collection of atoms is called a molecule. Molecules can be represented in several different ways. The simplest method is the chemical formula, in which the symbols for the elements are used to indicate the types of atoms present, and subscripts are used to indicate the relative numbers of atoms. For example, the formula for carbon dioxide is C02, meaning, of course, that each molecule contains 1 atom of carbon and 2 atoms of oxygen. 

Notice that the shared electron density, P is divided equally between the two atoms in question. The gross atomic charge on each atom is simply the sum of all the q, belonging to that atom minus the nuclear charge of the atom on which orbital XfA. is located. This is called the Mulliken population analysis. The computed charge on an atom of a molecule is influenced by a number of factors such as the basis set chosen, the exact details of H , and whether electron correlation is taken into consideration or not. The Mulliken scheme is arbitrary in that it partitions the shared electron density equally between the two atoms. There are many other methods for population analysis, some perhaps preferable in that they do not appear to be as method and basis set dependent as the Mulliken scheme. 

Laser ablation of compounds of almost all elements in the periodic table will produce the bare ion M+. Laser ablation and other methods of producing bare metal ions have been discussed in Section II.C.5. The bare metal ion has a coordination number of 0 and for most elements these ions will aggressively seek molecules able to share or donate electrons. Thus most bare transition metal ions will increase their coordination number by reacting with any donor, this even includes the inert gas atoms such as Xe (96). 

In general, the experimental resnlts presented emphasize some distinction between chemical and electrochemical electron-transfer reactions. At the same time, both kinds of reactions share a fair number of features. A greater combination of these two methods in the organic chemistry of ion-radicals would seem to be fruitful. 

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]. 

Mechanistic and Theoretical Studies of Phosphonium Ylides and the Wittig Reaction. - The physico-chemical nature of the P-C bond in phosphonium ylides is complex and, despite intensive research over many years, remains the subject of dispute Numerous theoretical studies of this problem have appeared in the scientific literature. A recent contribution to this area by Mitrasinovic uses sharing indices and sharing amplitudes to study P-C bonds in a number of tri-and penta-valent phosphorus species. Sharing indices and amplitudes are quantitative, orbital dependent, measurements of the degree to which an electron, as a wave, is shared between two spatial points in a many electron system. Ylides studied using this method include (1), (2) and (3). ... 

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