Molecular bond representation

NH3 dipole moment in the molecular bond representation. The first global description of the dipole moments of ammonia was reported by Marquardt et al. [66] who computed ab initio DMSs of NH3 using the MP2/ aug-cc-pVQZ and MCSCF/aug-cc-pVQZ levels of theory. This was also the first work where the MB-representation was used for describing DMSs of an XY3 molecule, formulated as follows ... 

This symmetrized molecular bond representation (denoted as SMB ) has been used by Yurchenko et al. [80] to resolve a similar issue encountered in connection with representing the polarizability tensor of NH in terms of analytical functions. The subscripts of the functions (T = A (, E, E[) in Eqs. (61-63) refer to irreducible representations [7] of T>3h(M) has... 

The most well-known and at the same time the earliest computer model for a molecular structure representation is a wire frame model (Figure 2-123a). This model is also known under other names such as line model or Drciding model [199]. It shows the individual bonds and the angles formed between these bonds. The bonds of a molecule are represented by colored vector lines and the color is derived from the atom type definition. This simple method does not display atoms, but atom positions can be derived from the end and branching points of the wire frame model. In addition, the bond orders between two atoms can be expressed by the number of lines. 

Fig. A. Molecular-orbital representation of the 1-centrc F-Xe-F bond, (a) The possible combinations of colinear p, atomic orbitals, and (b) the energies of the resulting MOs (schematic).

On the basis of these values one can conclude that, with increasing bond orders, the force constants rise, suggesting that the S—O bond of sulphoxides should have more semipolar character than that of sulphones. Furthermore, molecular diffraction measurements20 and Parachors21 for sulphoxides also suggest that the S—O bond in sulphoxides should have a semipolar single-bond representation while the S—O bond in sulphones is described by double bonds or better as the resonance hybride shown in Scheme 1. 

Covalent bonds form between atoms with similar electronegativities. In these reactions, electrons do not migrate from one atom to another as they do in ionic bonds they are shared by the atoms in the molecule. A good way to visualize this was proposed by Gilbert Lewis, a chemist at the University of California, Berkeley. His representations of molecular bonds are called Lewis dot structures. These structures use dots to denote the valence electrons of an element or molecule. 

Whilst this demonstrates that calculations using the methods of this paper may prove very useful in studies of molecules containing only low-Z atoms, a major objective has been to study systems containing heavier atoms. So far, only a limited number of molecular calculations have been carried out with BERTHA at the DHF level, mainly in connection with studies of hyperfine and PT-odd effects in heavy polar molecules such as YbF [33] and TIF [13]. The reader is referred to the literature for an assessment of these calculations and for technical details on the construction of basis sets which must not only describe molecular bonding properly but also give a good representation of spinors close to the heavy nuclei to handle the short-range electron-nuclear electroweak interactions. 

Figure 13.1 In large systems that require explicit representation, understanding bond-making/-bond-breaking processes can often be accomplished using a quantum mechanical representation of only a portion of the full system, with a molecular mechanics representation of the rest...

A satisfactory theoretical model for ethylene oxide should take into account as many as possible of the physical properties discussed above, but should be able to predict or explain its chemical properties as well. Three such ogodels have been proposed which are based on molecular-orbital theory s 1-3W.1 ° and two more which conform rather to tho valence-bond representation of chemical structure.1M, W 7 The relative merits of all these models have been discussed in recent reviews.8 7 1301... 

Figure 3.25. Molecular orbital representations of the bonding structure of the parent bishomoaromatic dication C4H82+ (604) and cyclobutadiene dication C4H42+ (605).

Valence-bond representation Molecular-orbital representation it bonding and multicenter it bonds Shapes of molecules Coordination compounds Isomerism Bonding in metals... 

Fig. 9 may be viewed, also, as a localized molecular orbital representation of, e.g., a hydrocarbon (cf. Fig. 13, ref. 7). Thus, replacement of (i) the domains of the Si4+ cations (the atomic cores of silicon atoms) by the domains of C4+ cations (the atomic cores of carbon atoms r = 0.15 A 2>), (ii) the domains of the bridging (i.e., bonding) oxide ions by the domains of the electron-pairs of aliphatic carbon-carbon single bonds (r 0.6e A 40)), and (iii) the domains of the non-bridging oxide ions by the domains of the protonated electron-pairs of carbon-hydrogen bonds... 

The molecular structure of S2N2, as shown in Fig. 16.7.2(a), is aZ)2h square-planar ring with S-N edge 165 pm, somewhat analogous to the isoelectronic cation S + (Fig. 16.4.2). The valence-bond representations of the S2N2 molecule are as follows ... 

Although the molecular orbital description of bonding has some mathematical advantages, simple valence bond representations of structures are adequate for many purposes. The structures of molecules that have only single bonds (and in some cases unshared pairs of electrons on the... 

Fig. 1. Schematic molecular orbital representation of the dative w-type bond.

Fig. 3. Schematic molecular orbital representation of the ethylene-platinum bond. Reproduced from J. Chatt and L. A. Duncanson, J. Chem. Soc. 2939 (1953), by permission of the Chemical Society.

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