Square geometry

High level molecular orbital calculations of cyclobutadiene itself and experimen tally measured bond distances of a stable highly substituted derivative both reveal a pat tern of alternating short and long bonds characteristic of a rectangular rather than square geometry... 

The total 7t-eIectron energy of benzene is 6a -I- 8)3, corresponding to a DE of 2)3. Cyclobutadiene is predicted to have a triplet ground state (for a square geometry) and zero... 

To have more measurements than unknowns, for a square geometry of the pupil and subpupils, one has to fulfill ... 

According to 6-31G calculations (90JA4155), the square geometry of the N4 fragment may be stabilized in the D4h structure of tetrazete dianion with two Li+ counteranions (246) that corresponds to a minimum on the PES. Also, the planar square 67r-electron structure corresponds to a minimum on the PES, as judged from ab initio calculations with the 6-31+G basis set (90JA4155). 

Table 15.9. Energies and derivatives of energies relating to the stability of the square geometry of cyclobutadiene.

Group theory predicts that if parent CB is square, it should show four IR active fundamentals (of which one was a degenerate C—H stretch expected to be of very weak intensity). On the other hand, if parent CB were rectangular, it should show seven IR active fundamentals of which two are weak C—H stretches. Since only three (rather than five) bands were observed in the IR spectrum of CB below 2000 cm Krantz and Newton concluded that CB must be square. They supported this conclusion with a force-field calculation, based on a square geometry, that reproduced the observed frequencies, including those of C -d, to within a few wavenumbers. On the other hand, Chapman conjectured that the absence of evidence for two different vicinally dideuterated CR-CL2 (which would be expected for rectangular CB-[Pg.827]

Heat equation in a square geometry with linear elements. Using the square section depicted in Fig. 10.10, we want to solve the steady-state conduction equation for a material of constant conductivity. 

We may conclude that the relative strengths of the a- and the rc-bonds determine the geometry of cyclobutadiene. For relatively weak rc-bonds, the resonance, together with the a-bonds, prevails to yield a square geometry. With stronger rc-bonds or weaker a-bonds the, expected, rectangular structure is produced. 

Oxidation of Co111 dithiocarbamates gives [Co(dtc)3]+ complexes which are low-spin d5 with magnetic moments between 2.2 and 2.7 BM. For the macrocyclic complex (17-F-IX) (formally CoIV) square geometry was confirmed by X-ray diffraction the compound has one unpaired electron and slowly oxidizes water, with reduction to H[Com(L)].M... 

Figure 15.14 (A) The ratio of chemiluminescent intensities after Mw pulses to intensity before Mw pulses is shown for glass (blue bar), the center of the square geometry (hatched red bar), and the comer (solid red bar). (B) Chemiluminescence signal in a multiplexed ftnmat is apfxoximately equivalent fi om all positions on the 8 mm square aluminum foil structure (dashed box) before the application of low power pulses and (C) significantly enhanced after the application of low power microwave pulses. Reproduced from J. Fluorescence 17 279-287 (2007).

Tetranuclear species showing square geometries are generated spontaneously on reaction of dinitro(ethane-l,2-diamine)palladium(II) or its platinum(II) analogue... 

Thulasidas et al. [2] found for capillary numbers Ca < 0.3 that upward flow gave a thicker liquid film than downward or horizontal flow, for both circular and square geometry. 

Figure 7 A monolithic structure with square channels with a nonuniform washcoat. The left cell illustrates how the washcoat conceptually is divided into slab regions along the sides and circlc-in-square geometry in the comers, for calculation of the effectiveness factor. (From Ref. 14.)...

For the TBR, spherical catalyst particles of uniform size with the catalytically active material either uniformly distributed throughout the catalyst or present in a shell were considered. For the MR, channels of square cross section were assumed to have walls covered by the washcoat distributed in such a way that the comers are approximated by the circle-in-square geometry, while the sides are approximated by a planar slab geometry. The volumetric load of catalytic material was a function of the washcoat thickness... 

Industrial experience with the three-phase MR is limited, since only few large-scale industrial plants are running in the world today. Very little has been published about these industrial reactors and reactor scale-up. Also, most modeling has been done on cylindrical channel geometry, while most industrial reactors use sinusoidal or square geometry. Hence this chapter mainly summarizes our own experience with three-phase monolith reactors, with limited reference to the literature. 

If the new bonds are formed in a suprafacial way, the process is referred to as [2, + 2J. The singlet states of the hypothetical H, molecule at square geometries c culated by Gerhartz et al. (1976) can be thought of as a simple model for thej electronic states involved. 

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