An Alternative Notation

Since the vast majority of nitrosyl complexes conform to the 18- and 16-electron rules, it seems reasonably to focus the notation on these parameters rather than the modified d-electron count proposed by Enemark and Feltham. Furthermore, the more routine nature of single-crystal X-ray measurements these days and the possibility of accurately estimating the M-N-O bond angle from spectroscopic data means that this parameter can be incorporated in the notation using the short hand introduced in Table 1, i.e. 180-160° I (linear), 140-160° i (intermediate), 110-140° b (bent). 

Complexes with bent b nitrosyls - NO is a 1 eiectron donor 

Complex with an intermediate I nitrosyi - NO is a 3 or 1 electron donor 

In common with Enemark—Feltham, the new notation makes no attempt to define the formal charges on the nitrosyl ligand and the formal metal oxidation state but focuses attention on the geometry of the nitrosyl, the metal s coordination number and the total electron count. As De La Cruz and Sheppard have recently pointed out [26] in their extensive analysis of the vihratiOTial data for nitrosyl complexes, the great majority of them conform to 18- and 16-electron rules, and therefore, this parameter establishes whether the molecirle has a closed shell. The total electron count has important chemical implications since it indicates whether the compound is likely to undergo electrochemical conversion or nucleophilic addition in order to achieve an 18-electron configuration. 

For complexes where metal oxidatirm states and spin states have been designated on the basis of reliable theoretical or spectroscopic data and it is felt necessary to 

---

The total number of bits set on A is a + c. and the total number of bits set on B is b + c. These totals form the basis of an alternative notation that uses a instead of a + c, and b instead oib + c [16]. This notation, however, lumps together similarity and dissimilarity components" - a disadvantage when interpreting a similarity measure. 

As a device for describing the effect of temperature on solution nonideality, it is entirely suitable to think of Eq. (8.115) as offering an alternate notation which accomplishes the desired effect with p and as adjustable parameters. We note, however, that the left-hand side of Eq. (8.115) contains only one such parameter, x, while the right-hand side contains two p and . Does this additional parameter have any physical significance ... 

An alternative notation involves the use of the so-called gradient operator V (pronounced del ),... 

If only one set of polarization functions is used, an alternative notation in terms of is also widely used. The 6-31G=i basis is identical to 6-31G(d), and b-SlG ts is identical to 6-31G(d,p). A special note should be made for the 3-21G basis. The 3-21G basis is basiciy too small to support polarization functions (it becomes unbalanced). However, the 3-21G basis by itself performs poorly for hypervalent molecules, such as sulfoxides and sulfones. This can be substantially improved by adding a set of d-functions. The 3-2IG basis has only d-functions on second row elements (it is sometimes denoted 3-21G(=f=) to indicate this), and should not be considered a polarized basis. Rather, the addition of a set of d-functions should be considered an ad hoc repair of a known flaw. 

A time-line/sequence form This diagram highlights the sequences of interactions, at the cost of interobject dependencies otherwise, it captures the same information as the graph version. Again, multiparty joint actions, such as entire use case occurrences, require an alternative notation to the arrow. 

In the adsorption studies we have discussed, the expansion of the unit mesh is the same in both directions, but this need not be the case. Examples in which the expansion along different axes of the mesh varies are p(4 x 2)—O for the adsorption of 02 on Mo(l 11), p(3 x 15)—O for 02 on Pt(l 11), c(4 x 2)—S for H2S on Au(100), and c(9 x 5)—CO for CO on W(110). Somorjai (1981, 1994) has assembled extensive tables of this sort of information. Note that many but not all adsorbates are dissociated on the metal surfaces. Finally, it is not necessary for the supernet and the substrate to show the same angles between sides of their respective meshes. The Wood notation does not apply in these cases, but an alternative notation exists... 

An alternative notation for the preceding equations is given in Appendix A. 10-2. 

By convention, surface superlattices are given names like 31/2 x 1 R 30° this is Wood s 20 notation of 1964 [8], [9]. This notation describes the symmetry of the superlattice, but does not identify its origin—that is, the exact point where the superlattice is anchored (even though this is a very desirable datum for aficionados of chemisorption). The 3m x 1 R 30° superlattice means that (1) the fls and b axes of the superlattice crystal lie in the plane of the surface of index hkl (whose axes we call abM and bbki), (2) the first superlattice axis as is 31/2 times longer than the first surface axis fl(3) the second superlattice axis bs is equal in length to the second surface axis b/ h (4) these two superlattice axes fls and bs are then rotated by 30° clockwise. An alternative notation uses... 

Let C Hj be the (chemical) formula of a benzenoid hydrocarbon. An alternative notation is given by... 

The Ipo AO refers to 2pz, which has the axial symmetry of arr-bond. Likewise, 2pn refers to 2px or 2py, which are positioned to form tt-bonds. An alternative notation for diatomic MO s which specifies their atomic origin and bond-ing/antibonding character is the following ... 

In a few cases, the Pearson symbol fails to differentiate between two crystalline allotropes of the element. In such an event the space group is added to the parentheses. If this still fails to distinguish the allotropes, the characteristically different lattice parameters will have to be cited. An alternative notation involving compound type may also be useful (see Section IR-4.2.5 and Chapter IR-11). 

While this compact notation is convenient for the experienced user, to grasp the basic concepts a rough description may be preferable. Therefore, for the beginners that is not familiar with the concepts of statistical mechanics we reiterate the presentation of the abstract theory using an alternative notation equivalent to what is common in the fluid dynamic literature [40] [61]. The purpose is to provide introductory ideas about the practical implications of the Liouville equations describing the ensemble flow in P-space. 

Vectors are represented by symbols such as a, b,... and their respective magnitudes are given by a, A, ..., or just a, b,... An alternative notation, OP, is sometimes used when we wish to describe a displacement in space between two points (in this case, points O and P). 

In the mathematical literature, the random variables are often denoted by (0 and the realizations of those variables by x(t) [31, 32], An alternative notation is to denote the random variables by capital letters, and the realizations by lower case ones. These distinctions are often ignored by physicists, for economy of notation. We shall, in our discussion of the Langevin equation, adapt the physicists s notation. The distinction becomes more important in the calculation of drift and diffusion coefficients and is consequently adhered to in the appendices. 

Note that here both the probabilities of growth and the probability of termination are independent on the length of the chain. This is in fact an alternate notation of a Markov process and is a cascade. Each term 5... e is associated with the probability of the formation of a polymer chain of the respective degree of polymerization that is p P). It is immediately seen that because r = 1 the total probability for all the chains generated becomes 1. On the other hand, from the second equation in the set (17.1), r can be calculated to be r = e/ — m). This can be inserted into the first equation in the set (17.1). 

It is common to use an alternative notation for the electron-electron interaction integrals (rr ss ) = (rs r s ), i.e., with the complex conjugate spin orbitals, belonging to the operators, on the left. One can introduce the compact notation (rs tu) = (rs fn) — rs vt) for an antisymmetric interaction integral and write... 

We denoted the hydrogen-atom bound-state wave functions by three subscripts that give the values of n, I, and m. In an alternative notation, the value of / is indicated by a letter ... 

If only one set of polarization functions is used, an alternative notation in terms of is also widely used. The 6-31G basis is identical to 6-31G(d), and 6-31G is identical to 6-31G(d,p). A special note should be made for the 3-21G basis. The 3-21G... 

The Maxwell equations have an alternative notation, which involves two new quantities the scalar potential 4> and the vector potential A, which replace and // ... 

Mingos DMP (2014) A review of complexes of ambivalent and ambiphilic Lewis acid/bases with symmetry signatures and an alternative notation for these non-innocent ligands. J Organomet Chem 751 153-173. doi 10.1016/j.jorganchem.2013.08.033... 

---