Atomic additive contributions

In the case of 9-acridyl nitrene, both of the ortho positions with respect to nitrene are occupied by fused benzene rings, which prevent the intramolecular insertion reaction and thereby stabilize the singlet nitrene to facilitate its conversion into the triplet state. Coordination to the lone pair of the oxygen or nitrogen atom additionally contributes to the stabilization of singlet nitrene when the reaction is carried out in ethanol or acetonitrile, respectively. 

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. 

In Section 7.1.2 a method for the calculation of mean molecular polarizability was presented. Mean molecular polarizability can be calculated from additive contributions of the atoms in their various hybridization states in a molecule (see Eq. (6)). Mean molecular polarizability, a, expresses the magnitude of the dipole moment, fi, induced into a molecule imder the influence of an external field, E (Eq. (15))... 

In such tables, typical chemical shifts are assigned to standard structure fragments (e.g., protons in a benzene ring). Substituents in these blocks (e.g., substituents in ortho, meta, or para positions) are assumed to make independent additive contributions to the chemical shift. These additive contributions are listed in a second series of tables. Once the tables are defined, the method is easy to implement, does not require databases, and is extremely fast. Predictions for a molecule with 50 atoms can be made in less than a second. On the other hand, it requires that the parent structure and the substituents are tabulated, and it considers no interaction... 

Information about the structure of a molecule can frequently be obtained from observations of its absorption spectrum. The positions of the absorption bands due to any molecule depend upon its atomic and electronic configuration. To a first approximation, the internal energy E oi a, molecule can be regarded as composed of additive contributions from the electronic motions within the molecule (Et), the vibrational motions of the constituent atoms relative to one another E ), and the rotational motion of the molecule as a whole (Ef) ... 

Enthalpy of Formation The ideal gas standard enthalpy (heat) of formation (AHJoqs) of chemical compound is the increment of enthalpy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard states, defined as the existing phase at a temperature of 298.15 K and one atmosphere (101.3 kPa). Sources for data are Refs. 15, 23, 24, 104, 115, and 116. The most accurate, but again complicated, estimation method is that of Benson et al. " A compromise between complexity and accuracy is based on the additive atomic group-contribution scheme of Joback his original units of kcal/mol have been converted to kj/mol by the conversion 1 kcal/mol = 4.1868 kJ/moL... 

The temperature-independent parachor [P] may be calculated by the additive scheme proposed by Quale.The atomic group contributions for this method, with contributions for silicon, boron, and aluminum from Myers,are shown in Table 2-402. At low pressures, where Pi. pc, the vapor density term may be neglected. Errors using Eq. (2-168) are normally less than 5 to 10 percent. 

In Eq. (4-62) Wq is the Larmor precessional frequency, and Tc is the correlation time, a measure of the rate of molecular motion. The reciprocal of the correlation time is a frequency, and 1/Tc may receive additive contributions from several sources, in particular I/t, where t, is the rotational correlation time, t, is, approximately, the time taken for the molecule to rotate through one radian. Only a rigid molecule is characterized by a single correlation time, and the value of Tc for different atoms or groups in a complex molecule may provide interesting chemical information. 

The total energy in ab initio theory is given relative to the separated particles, i.e. bare nuclei and electrons. The experimental value for an atom is the sum of all the ionization potentials for a molecule there are additional contributions from the molecular bonds and associated zero-point energies. The experimental value for the total energy of H2O is —76.480 a.u., and the estimated contribution from relativistic effects is —0.045 a.u. Including a mass correction of 0.0028 a.u. (a non-Bom-Oppenheimer effect which accounts for the difference between finite and infinite nuclear masses) allows the experimental non-relativistic energy to be estimated at —76.438 0.003 a.u. ... 

XLOGP [67, 68] is a further atom-additive method, as expressed by its almost exclusive use of atomic contributions. However, in contrast to pure atom-based methods correction rules are defined, to account for intramolecular interactions, which is typical for fragmental methods. 

In a-B12 the icosahedra are arranged as in a cubic closest-packing of spheres (Fig. 11.16). In one layer of icosahedra every icosahedron is surrounded by six other icosahedra that are linked by three-center two-electron bonds. Every boron atom involved contributes an average of electrons to these bonds, which amounts to -6 = 4 electrons per icosahedron. Every icosahedron is surrounded additionally by six icosahedra of the two adjacent layers, to which it is bonded by normal B-B bonds this requires 6 electrons per icosahedron. In total, this adds up exactly to the above-mentioned 10 electrons for the inter-icosahedron bonds. 

The use of theoretical methods in the study of bicyclic systems with P-, As-, Sb-, or Bi- bridgehead atoms has contributed to an increased understanding of the geometry, stability, and ring-strain effects of these systems. In addition, important data relating to basicity and the interpretation of nuclear magnetic resonance (NMR) and X-ray data have been generated. A vast majority of the work done has focused on P. 

An additional contributing factor to the mechanism of the present grafting reaction is the role of radiolytically produced hydrogen atoms. In the radiolysis of binary mixtures of aromatic and aliphatic compounds such as styrene-methanol, the concentration of aromatic strongly influences the G(H2) obtained from the methanol. In the most extensively studied binary mixtures of benzene-methanol (11) and pyridine-methanol (10), it is found that the yield of H atoms is important in determining product yields and types. Small additions (5%) of benzene and pyridine significantly reduce G(H2) from the methanol by scavenging H atoms. Above 5% additive, G(H2) is reduced further, but at a slower rate. These data for benzene-methanol and pyridine-methanol can be extrapolated... 

Decalin is constmcted from two cyclohexane units. In this case the second RHS term of Eq. (10.7), ( — 2 + 2m)(X — X ), accounts for 12 CH2 groups, but one additional contribution (i.e., that of two CH2 and two H atoms) is subtracted with respect to cyclohexane, that is, a total of two contributions with... 

The latter is in relation with those proposed by Deeth [30] and Berne [155]. Both involve the d-shell energy as an additional contribution to that of the MM scheme and use the AOM model with interpolated parameters to estimate the latter. In the case of the approach [30] there are two main problems. First is that the AOM parameters involved are assumed to depend only on the separation between the metal and donor atoms. This is obviously an oversimplification since from the formulae Eq. (25) it is clear that the lone pair orientation is of crucial importance. This is taken into account in the EHCF/MM method. Second important flaw is the absence of any correlation in describing the d-shell in the model [30]. This precludes correct description of the switch between different spin states of the open d-shell, although in some situations different spin states can be described uniformly. 

Since then, groups have been derived for heats of formation of solid nitroaromatics (Ref 20) and for solid and liquid nitroalkanes (Ref 22) Group Additivity. The basic idea behind Group Additivity is that chemical thermodynamic properties of molecules consist of contributions from the individual groups that make up the molecule. Group Additivity is therefore an extension of the series atom additivity, bond additivity,. . . , and turns out to be an excellent compromise between simplicity and accuracy... 

If sulfur or silicon, is present, the M + 2 will be more intense. In the case of a single sulfur atom, 34S contributes approximately 4.40% to the M + 2 peak for a single silicon in the molecule, 30Si contributes about 3.35% to the M + 2 peak (see Section 2.10.15). The effect of several bromine and chlorine atoms is described in Section 2.10.16. Note the appearance of additional isotope peaks in the case of multiple bromine and chlorine atoms. Obviously the mass spectrum should be routinely scanned for the relative intensities of the M + 2, M + 4, and higher isotope peaks, and the relative intensities should be carefully measured. Note that F and I are monoisotopic. 

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