Cyclic theory

Much of world history exhibits a pattern of political cycles, superimposed on the cycles of day and night, full moon to full moon, seasons, droughts and IcKusts. No wonder that cyclical theories of history and visions of the eternal return are so attractive. But things can also get steadily worse or steadily better. The trend may be masked by cycles, but not indefinitely. Destruction of the environment is often nearly impossible to undo. Two thousand years ago the land around the Mediterranean, includ-... 

Friend88 specifically criticized Werner s theory and emphasized the differences between his own latent valencies and Werner s Nebenvalenzen. He applied his new theory of valency to ammonium salts, metal ammines and halide double salts , and he proposed that for hexacoordinate central atoms a hexatomic shell forms around the metal but that all the elements or groups are joined together by latent valencies and not necessarily to the metal itself. In 1916, Friend applied his cyclic theory of complexes in detail to the structures of the chlorides of hexaamminecobalt(III), chloro-pentaamminecobalt(III) and dichlorotetraamminecobalt(III) and emphasized four basic differences between his theory and Werner s.89... 

The theory for staircase voltammetry is more complex compared to the linear scan (or cyclic) theory. This is because more parameters must be taken into ac-... 

Pick s second law of difflision enables predictions of concentration changes of electroactive material close to the electrode surface and solutions, with initial and boundary conditions appropriate to a particular experiment, provide the basis of the theory of instrumental methods such as, for example, potential-step and cyclic voltanunetry. 

Adopting the view that any theory of aromaticity is also a theory of pericyclic reactions [19], we are now in a position to discuss pericyclic reactions in terms of phase change. Two reaction types are distinguished those that preserve the phase of the total electi onic wave-function - these are phase preserving reactions (p-type), and those in which the phase is inverted - these are phase inverting reactions (i-type). The fomier have an aromatic transition state, and the latter an antiaromatic one. The results of [28] may be applied to these systems. In distinction with the cyclic polyenes, the two basis wave functions need not be equivalent. The wave function of the reactants R) and the products P), respectively, can be used. The electronic wave function of the transition state may be represented by a linear combination of the electronic wave functions of the reactant and the product. Of the two possible combinations, the in-phase one [Eq. (11)] is phase preserving (p-type), while the out-of-phase one [Eq. (12)], is i-type (phase inverting), compare Eqs. (6) and (7). Normalization constants are assumed in both equations ... 

Other techniques that work well on small computers are based on the molecules topology or indices from graph theory. These fields of mathematics classify and quantify systems of interconnected points, which correspond well to atoms and bonds between them. Indices can be defined to quantify whether the system is linear or has many cyclic groups or cross links. Properties can be empirically fitted to these indices. Topological and group theory indices are also combined with group additivity techniques or used as QSPR descriptors. 

Several theories have been proposed to explain the corrosion-fatigue phenomena. One is that cyclic stressing causes repeated rupture of protective coatings. Corrosion-fatigue cracks propagate as the coating is successively reformed and ruptured along a plane. 

Monocyclic conjugated polyenes are referred to as annulenes, and there exists ample experimental evidence to support the conclusions based on application of HMO theory to neutral and charged annulenes. The relationship between stability and structure in cyclic conjugated systems will be explored more fully in Chapter 9. 

Aromaticity is usually described in MO terminology. Cyclic structures that have a particularly stable arrangement of occupied 7t molecular orbitals are called aromatic. A simple expression of the relationship between an MO description of stmcture and aromaticity is known as the Hiickel rule. It is derived from Huckel molecular orbital (HMO) theory and states that planar monocyclic completely conjugated hydrocarbons will be aromatic when the ring contains 4n + 2 n electrons. HMO calculations assign the n-orbital energies of the cyclic unsaturated systems of ring size 3-9 as shown in Fig. 9.1. (See Chapter 1, Section 1.4, p. 31, to review HMO theory.)... 

The study of 8-N compounds is one of the most active areas of current inorganic research many novel cyclic and acyclic compounds are being prepared which have unusual stmctures and which pose considerable problems in terms of simple bonding theory. The discoveiy in 1975 that the polymer (8N)jc is a metal whose conductivity increases with decrease in... 

Although azafulvalenes as yet comprise a small class of cyclic cross-conjugated compounds, they have been the subject of a variety of theoretical investigations spanning a range from the Hiickel (HMO) theory to the... 

Benzene is described by molecular orbital theory as a planar, cyclic, conjugated molecule with six it electrons. According to the Htickel rule, a molecule must have 4n + 2 77 electrons, where n - 0, 1, 2, 3, and so on, to be aromatic. Pianar, cyclic, conjugated molecules with other numbers of tt electrons are antiaromatic. 

How can we predict whether conrotatory or disrotatory motion will occur in a given case According to frontier orbital theory, the stereochemistry of an electro-cyclic reaction is determined by the symmetry of the polyene HOMO. The electrons in the HOMO are the highest-energy, most loosely held electrons, and are therefore most easily moved during reaction. For thermal reactions, the ground-state... 

For PPV-imine and PPV-ether the oxidation potential, measured by cyclic voltammetry using Ag/AgCl as a reference are ,M.=0.8 eV and 0.92 eV, respectively. By adopting the values 4.6 eV and 4.8 eV for the work functions of a Ag/AgCl and an 1TO electrode, respectively, one arrives at zero field injection barriers of 0.4 and 0.55 eV. These values represent lower bounds because cyclic voltammetry is carried out in polar solvents in which the stabilization cncigy of radical ions exceeds that in a polymer film, where only electronic polarization takes place. E x values for LPPP and PPPV are not available but in theory they should exceed those of PPV-imine and PPV-ether. 

For more detailed information on the theory of cyclic voltammetry, and the interpretation of cyclic voltammograms, see references (1,7,19,20). 

Much of the variation in these time series for the past 700 kyr can be described by a combination of a 100 kyr cycle plus additional cycles with periods of 20 and 40 kyr. This result immediately suggests that the ice-age cycles are caused by variations in the amount and seasonality of solar radiation reaching the Earth (insolation), because the 20, 40, and 100 kyr periods of climate history match the periods of cyclic variations in Earth s orbit and axial tilt, line hypothesis that these factors control climate was proposed by Milutin Milankovitch in the early part of the 20th century and is widely known as "Milankovitch Theory." It is now generally accepted that the Milankovitch variations are the root cause of the important 20 and 40 kyr climate cycles. The 100 kyr cycle, however, proves to be a puzzle. The magnitude of the insolation variation at this periodicity is relatively trivial, but the 100 kyr cycle dominates the climate history of the last 700 kyr. Further,... 

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