Additivity atomic contribution

The properties of the topologically defined atoms and their temporal changes are identified within a general formulation of subspace quantum mechanics. It is shown that the quantum mechanical partitioning of a system into subsystems coincides with the topological partitioning both are defined by the set of zero flux surfaces in Vp(r). Consequently the total energy and any other property of a molecular system are partitioned into additive atomic contributions. 

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

Fhe van der Waals and electrostatic interactions between atoms separated by three bonds (i.c. the 1,4 atoms) are often treated differently from other non-bonded interactions. The interaction between such atoms contributes to the rotational barrier about the central bond, in conjunction with the torsional potential. These 1,4 non-bonded interactions are often scaled down by an empirical factor for example, a factor of 2.0 is suggested for both the electrostatic and van der Waals terms in the 1984 AMBER force field (a scale factor of 1/1.2 is used for the electrostatic terms in the 1995 AMBER force field). There are several reasons why one would wish to scale the 1,4 interactions. The error associated wilh the use of an repulsion term (which is too steep compared with the more correct exponential term) would be most significant for 1,4 atoms. In addition, when two 1,4... 

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... 

In addition to electrophilic attack on the pyrrole ring in indole, there is the possibility for additions to the fused benzene ring. First examine the highest-occupied molecular orbital (HOMO) of indole. Which atoms contribute the most What should be the favored position for electrophilic attack Next, compare the energies of the various protonated forms of indole (C protonated only). These serve as models for adducts formed upon electrophilic addition. Which carbon on the pyrrole ring (C2 or C3) is favored for protonation Is this the same as the preference in pyrrole itself (see Chapter 15, Problem 2)1 If not, try to explain why not. Which of the carbons on the benzene ring is most susceptible to protonation Rationalize your result based on what you know about the reactivity of substituted benzenes toward electrophiles. Are any of the benzene carbons as reactive as the most reactive pyrrole carbon Explain. 

In the TT-electron theories, each first-row atom contributes a single basis function. For the all valence electron models there is now an additional complication in at some of the basis functions could be on the same atomic centre. So how should we treat integrals involving basis functions all on the same atomic centre such as... 

For local deviations from random atomic distribution electrical resistivity is affected just by the diffuse scattering of conduction electrons LRO in addition will contribute to resistivity by superlattice Bragg scattering, thus changing the effective number of conduction electrons. When measuring resistivity at a low and constant temperature no phonon scattering need be considered ar a rather simple formula results ... 

Table I reports the observed NMR linewidths for the H/3 protons of the coordinating cysteines in a series of iron-sulfur proteins with increasing nuclearity of the cluster, and in different oxidation states. We have attempted to rationalize the linewidths on the basis of the equations describing the Solomon and Curie contributions to the nuclear transverse relaxation rate [Eqs. (1) and (2)]. When dealing with polymetallic systems, the S value of the ground state has been used in the equations. When the ground state had S = 0, reference was made to the S of the first excited state and the results were scaled for the partial population of the state. In addition, in polymetallic systems it is also important to account for the fact that the orbitals of each iron atom contribute differently to the populated levels. For each level, the enhancement of nuclear relaxation induced by each iron is proportional to the square of the contribution of its orbitals (54). In practice, one has to calculate the following coefficient for each iron atom ...

In summary, despite the structural diversity exhibited by the silicates, their silicon atoms always have tetrahedral geometry. In addition, every outer oxygen atom contributes a net charge of -1 to the structure, while every inner oxygen atom is electrically neutral and has an Si—O—Si bond angle close to 109.5°. 

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. 

The epoxidation of electron-deficient alkenes, particularly a,P-unsaturated carbonyl compounds, continues to generate much activity in the literature, and this has been the subject of a recent concise review <00CC1215>. Additional current contributions in this area include a novel epoxidation of enones via direct oxygen atom transfer from hypervalent oxido-).3-iodanes (38), a process which proceeds in fair to good yields and with complete retention of... 

Several other molecular orbital models have been applied to the analysis of VCD spectra, primarily using CNDO wave functions. The nonlocalized molecular orbital model (NMO) is the MO analog of the charge flow models, based on atomic contributions to the dipole moment derivative (38). Currents are restricted to lie along bonds. An additional electronic term is introduced in the MO model that corresponds to s-p rehybridization effects during vibrational motion. 

Equation (11.8) reads The average of the expectation values of r — for the various valence AOs of atom I, weighted by the rations of the orbital populations to the total atomic population of atom I equals the inverse of the — / distance. For all their their simplicity, Eqs. (11.7) and (11.8) cannot be tested numerically by direct calculation. The reason is linked to the difficulty of partitioning the total electron density into atomic contributions, in spite of an important conceptual step forward due to Parr [219]. A practical step in the same direction is in the construction of suitable in situ valence atomic orbitals (VAO) from accurate ab initio computations [143], as advocated long ago by Mulliken [220] and discussed by Del Re [221]. As will be seen, such in situ VAOs do provide useful information, but they are of no help in solving the additional problem of assigning suitable populations to the orbitals and of dividing overlap populations into atomic contributions. In view of this situation, we take Eqs. (11.5) and (11.8) as statements whose validity rests on experimental evidence, at least for saturated hydrocarbons. 

Estimation of a with 5.3.1 requires solely the input of pi and parachor. Parachor can be derived from molecular structure with schemes based on group additivity. Exner [4] gives an excellent review and discussion of various group contribution methods for parachor. A very simple method has been developed by McGowan [5] employing only atomic contribution and the number of bonds, A bonds ... 

Additivity in Polyhaloalkanes A simple atom contribution model for polyhalo-methanes has been reported [32] ... 

Balaban et al. [33] studied the use of neural networks to establish relationships between halomethanes and atom contributions and between chlorofluorocarbons (C ] -C4) and atom contributions. In addition to atom contribution, their relationships include molecular descriptors (i.e., the Wiener and J indices). 

Method of Broto, Moreau, and Vandycke The method of Broto et al. [46] is an atom contribution method including one extra contribution for conjugated double bonds. The complete set of atom constants is given in Appendix F to illustrate the relative hydrophobicity of the different types of atom contributions. Atom types are differentiated by their environment depending on whether they are C atoms or heteroatoms. The C-atom environment is limited to the adjacent bonds and to the attached H atoms. For heteroatoms, the environment additionally includes nonhydrogen neighbors. The latter are divided into two classes (1) C atoms, for which the bond environment is considered and (2) heteroatoms, Z, irrespective of... 

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