Valence bond order

Under such circumstances, the E-X and X-Y bond distances should be strongly correlated in C.-T. spoke adducts. In fact, it is well known that for C.-T. spoke I2-adducts with S-donors a reciprocal correlation exists between (f(I-I) and rf(S-I), which was initially proposed by F.H. Herbstein and W. Schwotzer as a hyperbola.46 Assuming a valence (bond order) model for the description of the S-I-I system within C.-T. adducts, with n(I-I) + n(E-I) = 1... 

It is generally assumed that force constant is a measure of valence bond order. If so, this would imply that the force constant of a coordinated CO group would be a direct measure of the degree of metal-ligand back-donation. 

These results can be interpreted successfully in terms of Pauling s valence bond order concept. In the framework of this model, a chemical bond between X and H in diatomic molecule XH or between H and B in a HB molecule can be characterized by empirical valence bond orders Pxh and Phb decreasing exponentially with bond distance ... 

This equation implies that the difference between the usual covalent bond and the hydrogen bond is not qualitative but has only a quantitative character The hydrogen bond exhibits the smaller valence bond order. In these terms, for example, hydrogen bonds H- O in ice correspond to a covalent bonding of 5%. 

The difference between the usual covalent bond and a hydrogen bond is only quantitative in character The hydrogen bond exhibits the smaller valence bond order. 

Limbach et 1 performed DFT calculations on. I(N, 11) and 2hJ(N,N) couplings in the anion [C = N-L-N = C] (L = H, D) and in the cyclic bonded formamide dimer (HCNHNH2)2 to study how such couplings depend on the geometry of the hydrogen bond. To describe such a relationship they employed the valence bond order model and compared the NHN and FHF- hydrogen bonded systems. 

For a more precise method of calculating valence-bond orders, sec Clarkson Coulson Goodwin Tetrahedron... 

Element Valence Bond order Hybridization Radius Element Valence Bond order Hybridization Radius... 

For these complexes, the isotropic and 15N chemical shifts and the 15N chemical shift tensor elements were measured as a function of the hydrogen bond geometry. Lineshape simulations of the static powder 15N NMR spectra revealed the dipolar 2H-15N couplings and hence the corresponding distances. The results revealed several correlations between hydrogen bond geometry and NMR parameters which were analysed in terms of the valence bond order model. It was shown that the isotropic 15N chemical shifts of collidine and other pyridines depend in a characteristic way on the N-H distance. A correlation of the and 15N... 

According to the valence bond order concept as applied to the case of stretched H2 complexes by Limbach, there is a significant H-H bond order phh even at /hh = 1.6 A, implying that stretched dihydrogen complexes are not usefully considered as compressed dihydrides . 

For a more precise method of calculating valence-bond orders, see Clarkson, D. Coulson, C.A. Goodwin, T.H. Tetrahedron 1963, 19, 2153. See also Herndon, W.C. Parkanyi, C. J. Chem. Educ. 1976, 53, 689. 

To end up with a predictive pharmacophore model, it is necessary to start with reliable structural and biological data. First of all, it is important to have correct 3D structures of all compounds under study. Thus, atomic valences, bond orders, protonation state and stereochemistry have to be checked carefully. Also the consideration of different possible tautomers is necessary when the bioactive form is not exactly known. Another prerequisite is the existence of a similar binding mode of all ligands under study. Experimental data, from competition experiments or protein-ligand crystal structures, can clearly point out that the ligands interact with the same binding epitope in a similar way and not on distinct binding sites. 

With any hydrogen bond A-H B one can normally associate two distances, the A-H distance rj = for the diatomic unit AH, and the H---B distance t2 = r B for the diatomic unit HB. According to Pauling [38], one can associate with these distances so-called valence bond orders or bond valences, which correspond to the exponential distances ... 

Table 6.1 Shortest possible heavy atom distances of symmetric H-bonds predicted by the valence bond order model.

Figure 4.15. (a) Approach of H2 to M (origin) according to the valence bond order concept. The solid line was calculated using Eq. (4.14) as described in the text. The numbered points (identified in Grundemann et /.112) represent neutron diffraction data for H2 complexes (see Chapter 5) and hydrides, (b) Valence bond orders pMH and pHH as a function of the distance between M and the H2 center. Reprinted with permission from Grundemann et at.112 Copyright 1999 American Chemical Society. 

D structures of compounds used for pharmacophore modeling can be built using chemistry sofiware such as ChemBioDraw Ultra [18] or the compound builder of molecular modeling suites such as DiscoveryStudio [19], MOE [20], and Maestro [21]. After stmcture generation, the correctness of chemical properties, for example, atomic valences, bond orders, aromaticity definitions, stereochemistry, charges, and protonation states at physiological pH, has to be checked before compounds can be applied for VS studies [9]. 

Certain two-dimensional 5 = quantum antiferromagnets can imdergo a direct continuous quantum phase transition between two ordered phases, an antiferromagnetic Neel phase and the so-called valence-bond ordered phase (where translational invariance is broken). This is in contradiction to Landau theory, which predicts phase coexistence, an intermediate phase, or a first-order transition, if any. The continuous transition is the result of topological defects that become spatially deconfined at the critical point and are not contained in an LGW description. Recently, there has been a great interest in the resulting deconfined quantum critical points. ... 

This article provides a comprehensive review of modem approaches to analysis of electronic wavefunctions. Diverse definitions of properties such as atomic charges, energies, and valences, bond orders and energies, specialized orbitals, and similarities of atoms and molecules are presented. The merits and shortcomings of these definitions are discussed, Particular emphasis is placed on rigorous interpretive tools which produce quantities that can be regarded as tme quantum mechanical observables. Because of their lack of generality, approaches to quantification of chemical concepts that are limited to certain classes of molecules or electronic stmcture methods (such as n -electron bond orders in Hiickel theory) are not mentioned. 

Very recently, Singleton has suggested a new way of calculating isotope effects illustrated by the bromonium ion [61]. This method could possibly also be used for tautomeric systems. Another new approach is the multicomponent molecular orbital method for direct treatment of nuclear quantum effects [62]. The basic idea is to incorporate the nuclear wave function and in particular the proton wave function directly into the electronic structure calculation. This approach has great potential but has so far been tested only for secondary isotope effects on chemical shifts [63]. The geometric isotope effect has also been looked into based on Pauling valence-bond orders [20]. 

According to the valence bond order concept of Pauling [6] one can associate to both hydrogen bond distances valence bond orders given by... 

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