Distorted structures

The distorted structure can be replaced by a more reasonable structure using an empir ical molecular mechanics calculation This calculation which is invoked m Spartan Build by clicking on Minimize, automatically finds the structure with the smallest strain energy (m this case a structure with realistic bond distances and a boat conformation for the SIX membered ring)... 

In this exercise, we will examine three alkali metal trifluorides M=K, Na and Cs (drawn from the same study by Tozer and Sosa as Example 6.6). The structure can take on one of two forms, based on the angles 0 and resulting structure is T-shaped (left drawing below) if 0 is significantly greater than distorted structure results (right) ... 

Note that the structural form of each compound is implied by the presence (T-shaped structure) or absence (distorted structure) of the perturbed asymmetric stretching mode at about 550 cm . 

Hartree-Fock theory does quite a poor job of predicting the structures and frequencies for these compounds. It produces highly distorted structures in all three cases, and its computed frequencies bear little resemblance to the experimental observations. MP2 theory generally does better for the structures, although it fails to located a distorted structure for Na F3. The frequencies computed at the MP2 level also vary widely from experiment. 

Zinc and cadmium have the A 3 structure, but with abnormally large axial ratio (1-856 for zinc) instead of the value 1-633 corresponding to close packing. From the distances 2-660 A (for six bonds) and 2-907 A (for the other six) the bond numbers 0-54 and 0-21 have been deduced. If the axial ratio were normal each of the twelve bonds formed by a zinc atom with v = 4-5 would have bond number f. The assumption of the distorted structure permits a split into two classes with the more stable bond numbers and (or, probably, with the average valency of zinc equal to 4). 

A theoretical explanation for such an anomalous phenomenon in certain nonalternant hydrocarbons has first been attempted, in case of pentalene, by Boer-Veenendaal and Boer followed by Boer-Veenen-daal et Snyder and Nakajima and Katagiri for other related nonalternant hydrocarbons. By making allowance for the effects of <7-bond compression, these authors have shown that a distorted structure resembling either of the two Kekule-type structures is actually energetically favored as compared with the apparently-full symmetrical one. 

Further, if a certain distorted structure and its countertype in which the bond-length variation is reversed are not equivalent (e. g., the two Kekule-type structures in IV), these two structures should be differentiated as a starting geometry. 

In the anion radical of XXIII, the starting distorted structures belonging to the Og, bjg and b2u irreducible representations of point group D2k all converge into the unique set of bond lengths corresponding to... 

Djh, and the distorted structures belonging to converge into the other set of bond lengths corresponding to point group The stabilization energy which favors the structure is calculated to be 9.4 kcal mole ... 

Lighter elements show a stronger tendency to develop a stereochemically active lone pair than their heavier homologues. For instance, for antimony(III) more distorted structures are known than for bismuth(III) ]29]. 

A comparison of the total energies for a hypothetical complex with in the middle of the crown ether and with the total energies for the optimized geometries with Tr above the crown indicates, as expected, that the latter geometry is more stable [40]. A study of Pb(II) complexes also shows higher total energies for undistorted, compared to distorted, structures [43]. 

High quality is one of the criteria defined in the requirements section above. Since the program should run automatically in batch mode, we mean by quality control an internal check of the 3D structures produced by the structure generator itself. In general, the abilities of a fast, automatic structure builder to assess the quaUty of its models are rather limited since, for example, an exhaustive conformation analysis and energy optimization is impossible in most cases. However, there are a Umited number of simple quaUty checks to avoid trivially distorted structures ... 

Cussen EJ, Lynham DR, Rogers J (2006) Magnetic order arising from structural distortion structure and magnetic properties of Ba2LnMo06. J Chem Mater 18 2855-2866... 

Speaking of averages and denoting symbols by an overbar already means a generalization for distorted structures which will be discussed later. 

Scattering and Disorder. For structure close to random disorder the SAXS frequently exhibits a broad shoulder that is alternatively called liquid scattering ([206] [86], p. 50) or long-period peak . Let us consider disordered, concentrated systems. A poor theory like the one of Porod [18] is not consistent with respect to disorder, as it divides the volume into equal lots before starting to model the process. He concludes that statistical population (of the lots) does not lead to correlation. Better is the theory of Hosemann [158,211], His distorted structure does not pre-define any lots, and consequently it is able to describe (discrete) liquid scattering. The problems of liquid scattering have been studied since the early days of statistical physics. To-date several approximations and some analytical solutions are known. Most frequently applied [201,212-216] is the Percus-Yevick [217] approximation of the Ornstein-Zernike integral equation. The approximation offers a simple descrip-... 

Scattering Data of the Iterated Stochastic Structure. The computer simulation of the pure stochastic structure evolution process even yields the respective IDF and the scattering data [184], Here it becomes clear that a standard concept of arranged but distorted structure, the convolution polynomial, is not applicable to... 

History. Starting from the ID point statistics of Zernike and Prins [116] J. J. Hermans [128] designs various ID statistics of black and white rods. He applies these models to the SAXS curves of cellulose. Polydispersity of rod lengths is introduced by distribution functions, / , (,r)108. Hermans describes the loss of correlation along the series of rods by a convolution polynomial . One of Hermans lattice statistics is namedparacrystalby Hosemann [5,117]. Hosemann shows that the field of distorted structure is concisely treated by the methods of complex analysis. A controversial subject is Hosemann s extension of ID statistics to 3D [63,131,227,228],... 

In a fundamental paper [265] Ruland develops an advanced method for the analysis of scattering patterns showing moderate anisotropy. The deduction is based on a 3D model and the concept of highly oriented lattices. The addition of distortion terms makes sure that the theory is applicable to distorted structures and their scattering. 

The bands due to Fe(CO)4 are shown in Fig. 8. This spectrum (68) was particularly important because it showed that in the gas phase Fe(CO)4 had at least two vq—o vibrations. Although metal carbonyls have broad vC—o absorptions in the gas phase, much more overlapped than in solution or in a matrix, the presence of the two Vc—o bands of Fe(CO)4 was clear. These two bands show that in the gas phase Fe(CO)4 has a distorted non-tetrahedral structure. The frequencies of these bands were close to those of Fe(CO)4 isolated in a Ne matrix at 4 K (86). Previous matrix, isolation experiments (15) (see Section I,A) has shown that Fe(CO)4 in the matrix had a distorted C2v structure (Scheme 1) and a paramagnetic ground state. This conclusion has since been supported by both approximate (17,18) and ab initio (19) molecular orbital calculations for Fe(CO)4 with a 3B2 ground state. The observation of a distorted structure for Fe(CO)4 in the gas phase proved that the distortion of matrix-isolated Fe(CO)4 was not an artifact introduced by the solid state. 

An interesting new approach has been made possible by multiple quantum 27A1 MAS (MQMAS) NMR investigations of zeolites. Due to its nuclear electric quad-rupole moment, 27A1 exhibits broad lineshapes in distorted structural environments. 

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