Entity Linear

The entity SWEEP consists of a class containing the entities LINEAR SWEEP and ROTATIONAL SWEEP. 

The electronic wave functions of the different spin-paired systems are not necessarily linearly independent. Writing out the VB wave function shows that one of them may be expressed as a linear combination of the other two. Nevertheless, each of them is obviously a separate chemical entity, that can he clearly distinguished from the other two. [This is readily checked by considering a hypothetical system containing four isotopic H atoms (H, D, T, and U). The anchors will be HD - - TU, HT - - DU, and HU -I- DT],... 

The wave mechanics discussed in Chapter 2 is a linear theory. In order to develop the theory in a more formal manner, we need to discuss the properties of linear operators. An operator 4 is a mathematical entity that transforms a function ip into another function 0... 

The [Ni(NCS)f,]4 ion is almost perfectly octahedral, with Ni—N distances of around 209.5 pm and N—Ni—N angles around 89.5°. The Ni—N—C and N—C—S entities are practically linear.438,439 In [Ni(NCS)2L2] where L is a R-substituted pyridine, stereochemistry and spin state depend on the type and positions of R.431 While for 2-Me- and 2-Et-pyridine square planar complexes are observed, other pyridins lead to coordination polymers with pseudo-octahedral Ni11 due to N,S-bridging thiocyanate. Ni11 thiocyanato complexes have been studied quite intensively as hosts for inclusion compounds.440"442... 

From CdCl2, K[Ag(CN)2] (ratio 1 2), and NH3 at pH 10 (citrate buffer), colorless crystals of [Cd(NH3)2 Ag(CN)2 2] (P42/mbc, Z= 4) are formed. Therein, /nmv-Cd(NI I3)2 entities (2/m — C2h) are linked by slightly bent NC—Ag—CN units to form a puckered 2-D network with large, 24-membered meshes. Two of these networks (transformed into each other by the 42 operation, i.e., they are perpendicular) interpenetrate.1 3 Similar corrugated sheets occur in [trans-CA (4-Mepy)2 Ag(CN)2 2] (4-Mepy) (4-Mepy = 4-methylpyridin) (Ibca, Z= 16 all atoms in general positions) but here, they are pairwise interwoven in the same layer. The intercalated 4-Mepy molecules are located in the meshes of this layer.219 From the same reaction medium, [Cd(4-Mepy)4 Ag2(CN)3 ][Ag(CN)2] (C2/m, Z = 2) crystallizes after some days. Here, the Cd(4-Mepy)4 units (2jm — C2h) are linked by almost linear NC—Ag—(C,N)—Ag CN rods to form chains, which in turn are arranged in layers. Inserted between the chains or into the layers are linear [Ag(CN)2] anions.219... 

With simple Hg thiolates the structures of bis(ethanethiolato)mercury Hg(SEt)2321 and of the cysteamine complex [Hg S(CH2)2NH3 2]Cl2322 have reference character, as only weak or no secondary bonds are present, and therefore the central S—Hg—S entities can be considered to be unperturbed. In mercury bis(tri-t-butoxysilanethiolate) Hg[SSi(o-t-Bu)3], with a strictly linear S—Hg—S unit, two weak intramolecular O II g interactions obviously do not affect the bonding in this unit.323... 

The benzeneselenolates of mercury, [Hg(SePh)2] and (Bu4N)[Hg(SePh)3], both adopt simple structures, with mononuclear complex entities which posses near-linear Se—Hg—Se and near trigonal-planar HgSe3 cores, respectively.335... 

Figure 9.7. Separation of misorientation (Bg) and extension of the structural entities (1/ (L)) for known breadth of the primary beam (Bp) according to Ruland s streak method. The perfect linearization of the observed azimuthal integral breadth measured as a function of arc radius, s, shows that the orientation distribution is approximated by a Lorentzian with an azimuthal breadth Bs... 

Metal-complex stability is also related to the basic strength of the ligand entity. For a series of 1 2 complexes of the bidentate naphthylazophenol ligand (5.64) with copper(II) ion, the acidic dissociation constants (pKa) are linearly related to the stability constants (log K1 2), the more acidic groups forming the less stable complexes. Thus where X = N02 in structure 5.64 then pKa = 8.1 and log K1 2 = 17.2, and where X = OCH3 then pKa = 8.5... 

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