Bonded contributions

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

The next higher order of approximation, the first-order approximation, is obtained by estimating molecular properties by the additivity of bond contributions. In the following, we will concentrate on thermochemical properties only. 

In order to develop a quantitative interpretation of the effects contributing to heats of atomization, we will introduce other schemes that have been advocated for estimating heats of formation and heats of atomization. We will discuss two schemes and illustrate them with the example of alkanes. Laidler [11] modified a bond additivity scheme by using different bond contributions for C-H bonds, depending on whether hydrogen is bonded to a primary (F(C-H)p), secondary ( (C-H)g), or tertiary ( (C-H)t) carbon atom. Thus, in effect, Laidler also used four different kinds of structure elements to estimate heats of formation of alkanes, in agreement with the four different groups used by Benson. 

N is the number of point charges within the molecule and Sq is the dielectric permittivity of the vacuum. This form is used especially in force fields like AMBER and CHARMM for proteins. As already mentioned, Coulombic 1,4-non-bonded interactions interfere with 1,4-torsional potentials and are therefore scaled (e.g., by 1 1.2 in AMBER). Please be aware that Coulombic interactions, unlike the bonded contributions to the PEF presented above, are not limited to a single molecule. If the system under consideration contains more than one molecule (like a peptide in a box of water), non-bonded interactions have to be calculated between the molecules, too. This principle also holds for the non-bonded van der Waals interactions, which are discussed in Section 7.2.3.6. 

The accuracy of an additivity scheme can be increased by going from atomic contributions through bond contributions to group contributions. 

The value of the torsional energy increment has been variously estimated, but TORS = 0.42 kcal mol was settled on for the bond contribution method in MM3, In the full statistical method (see below), low-frequency torsional motion should be calculated along with all the others so the empirical TORS inererneut should be zero. In fact, TORS is not zero (Allinger, 1996). It appears that the TORS inererneut is a repository for an energy eiror or errors in the method that are as yet unknown. 

The activation energy for ro tation about a typical carbon-carbon double bond IS very high—on the order of 250 kj/mol (about 60 kcal/ mol) This quantity may be taken as a measure of the ir bond contribution to the to tal C=C bond strength of 605 kJ/mol (144 5 kcal/mol) in ethylene and compares closely with the value esti mated by manipulation of thermochemical data on page 191... 

We classify compounds as aromatic, if there is continuous conjugation around the ring, or non-aromatic. Aromatic compounds are further subdivided into those without exocyclic double bonds and those in which important canonical forms containing exocyclic double bonds contribute. 

The soft-nucleophile-soft-electrophile combination is also associated with a late transition state, in which the strength of the newly forming bond contributes significantly to the stability of the transition state. The hard-nucleophile-hffld-elechophile combination inqilies an early transition state with electrostatic attraction being more important than bond formation. The reaction pathway is chosen early on the reaction coordinate and primarily on the basis of charge distributiotL... 

Carbon has six electrons around the atomic core as shown in Fig. 2. Among them two electrons are in the K-shell being the closest position from the centre of atom, and the residual four electrons in the L-shell. TTie former is the Is state and the latter are divided into two states, 2s and 2p. The chemical bonding between neighbouring carbon atoms is undertaken by the L-shell electrons. Three types of chemical bonds in carbon are single bond contributed from one 2s electron and three 2p electrons to be cited as sp bonding, double bond as sp and triple bond as sp from the hybridised atomic-orbital model. 

In Chapter 3, we studied the topic of population analysis. In population analysis, we attempt a rough-and-ready numerical division of the electron density into atom and bond regions. In Mulliken theory, the bond contributions are divided up equally between the contributing atoms, giving the net charges. The aim of the present section is to answer the questions Are there atoms in Molecules , and if so, How can they be defined . According to Bader and coworkers (Bader, 1990) the answers to both questions are affirmative, and the boundaries of these atoms are determined by a particular property of the electron density. 

As can be seen from Table 2.4, the number of bonded contributions, bend and... 

The use of a cut-off distance reduces the fonnal scaling in the large system limit from atom - atoni since the non-bonded contributions now only are evaluated within the locSl sphere determined by the cut-off radius. However, a cut-off distance of 10 A is so large that the large system limit is not achieved in practical calculations. The actual scaling is thus more like where n is perhaps 1.5-1.8. In static applications,... 

In diamond, each carbon atom forms single bonds with four other carbon atoms arranged tetrahedrally around it The hybridization in diamond is sp3. The three-dimensional covalent bonding contributes to diamond s unusual hardness. Diamond is one of the hardest substances known it is used in cutting tools and quality grindstones (Figure 9.12). 

Here the favorable geometrical arrangement with two hydrogen bonds contributes 14 kcal to the stability of the hydrogen bonded product, (7). These are called inter-molecular hydrogen bonds (inter means between). 

The presence of these bonds contributes to the increase of the temperature of zero strength from 140 °C for PAN to 280—320 °C, as well as to a lower shrinkage at high temperatures. 

Originally the constant for the field/inductive effect was called the inductive constant ((jj). The field (through-space) contribution is, however, clearly larger than the inductive effect proper, i. e., the through-bond contribution. 

The formal charge at sulfur can be reduced to 0 by including one double bond contribution. This change gives rise to two expanded octet structures ... 

There are three cases The original p orbital may have contained two, one, or no electrons. Since the original double bond contributes two electrons, the total number of electrons accommodated by the new orbitals is four, three, or two. A typical example of the first situation is vinyl chloride, CH2—CH—CI. Although the p orbital of the chlorine atom is filled, it still overlaps with the double bond. The four electrons occupy the two molecular orbitals of lowest energies. This is our first example of resonance involving overlap between unfilled orbitals and a filled orbital. Canonical forms for vinyl chloride are... 

In contrast to chloride compounds, niobium oxides have a VEC of 14 electrons, due to an overall anti-bonding character of the a2u state, caused by a stronger Nb-O anti-bonding contribution. In some cases, the VEC cannot be determined unambiguously due to the uncertainty in the electron distribution between the clusters and additional niobium atoms present in the majority of the structures. The 14-electron compounds exhibit semiconducting properties and weak temperature-independent paramagnetism. Unlike niobium chlorides, the oxides do not exhibit a correlation between the electronic configuration and intra-cluster bond distances. 

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