Computational studies expansion

Palma, R. and P.M. Curmi. 1999. Computational studies on mutant protein stability the correlation between surface thermal expansion and protein stability. Protein Sci... 

The scientific interests of Huzinaga are numerous. He initially worked in the area of solid-state theory. Soon, however, he became interested in the electronic structure of molecules. He studied the one-center expansion of the molecular wavefunction, developed a formalism for the evaluation of atomic and molecular electron repulsion integrals, expanded Roothaan s self-consistent field theory for open-shell systems, and, building on his own work on the separability of many-electron systems, designed a valence electron method for computational studies on large molecules. 

A computational study at the HF/6-31G level revealed that the activation energy of the ring expansion reaction of cyclopropylnitrene 570 toward azetine 2 was 2.84 kcal mol-1, whereas the activation energy of the fragmentation toward ethylene and HCN was 0.64 kcalmoF1 (Scheme 72) <2002TL745>. 

We have in the present paper investigated two fundamentally different, yet complementary, routes to computational studies of radical hyperfine structures. On the one hand, we have the highly accurate MRCI - based approaches, which are able to predict hyperfine structures of small systems to very high accuracy. The role and importance of higher than double excitations in the configuration expansions has been elucidated by means of detailed case studies on a number of first row atoms, as well some selected molecular systems. We have also demonstrated how a newly developed method, the MRD-CI/Bk method, by means of a perturbative method is able to incorporate the effects... 

The first serious computational study employed a CASSCF wavefunction followed by a Cl expansion. However, the active space employed for the geometry optimization only included the in-plane t-orbitals of the triple bond, which neglects the true symmetry of the species involved the Cj-Cg o-bond in 40 is included in the active while the C3-C4 o-bond is not. 

More recent computational studies have taken advantage of the vast expansion of computational capabilities in that they are able to follow the evolution of a molecular system in time under the influence of extant molecular interactions and fields of influence of the different constituent atoms. This has been the work of Brady and coworkers most recently described in the report by Matthews etal noted above. It is indeed the first computational study that is consistent with the observations of long-period helical organization noted in Figures 1 and 2. Further studies are ongoing and promise to enhance the understanding of the phenomenology of celluloses at the nanoscale level. 

The expanding application of computational chemistry is reflected by amplified discussion of this area, especially density function theory (DFT) calculations in Chapter 1. Examples of computational studies are included in subsequent chapters that deal with specific structures, reactions and properties. Chapter 2 discusses the principles of both configuration and conformation, which were previously treated in two separate chapters. The current emphasis on enantioselectivity, including development of many enantioselective catalysts, prompted the expansion of the section on stereoselective reactions to include examples of enantioselective reactions. Chapter 3, which covers the application of thermodynamics and kinetics to organic chemistry, has been reorganized to place emphasis on structural effects on stability and reactivity. This chapter lays the groundwork for later chapters by considering stability effects on carbocations, carbanions, radicals, and carbonyl compounds. 

That this form does indeed hold had been demonstrated for the cavitation of glassy polypropylene (Mott et al. 1993) in a computational study furnishing the validity of this extension of the universal binding-energy relation to symmetrical bulk response. The additional attraction of this expression is that it points out directly that application of a pressure produces symmetrical elastic compaction in an isotropic solid. However, more interestingly, one notes that, when dilatation is imposed, the bulk modulus monotonically decreases and eventually, at a dilatation of 1 /p, vanishes. This also leads to the observation that, if dilatation results from thermal expansion in response to a temperature increase, the bulk modulus also decreases. This simple observation represents the essence of the temperature dependence of all other elastic constants in anisotropic solids, beyond the mere effect on the bulk... 

The mechanism of catalytic epoxide-expansion carbonylation has been the subject of several investigations. Because the catalytic formation of 3-lactones from epoxides generates a new carbonyl compound, it is easily monitored by in situ IR spectroscopy. In addition to kinetic and reactivity studies, computational studies - have been conducted to probe the mechanism of epoxide-expansion carbonylation. The mechanistic aspects of the carbonylation chemistry based on these results are presented in this section. 

Computational studies indicate that Cu-catalysed ring expansion of vinyloxiranes involves a dual-Cu step with the catalysts involved in the bond forming and breaking process and the diastereospeciticity of this reaction controlled by the Cu migration step (Scheme 74)7° ... 

Generation data to complement the planning study were plentiful. As long as the utilities owned the physical facilities and were in control of future facility expansion, data were generally a nonissue. The parameters of generating plants were dialed into the calculations or computers, similar to transmission. Obviously, alternate locations for new plants could be evaluated, and oftentimes studies were finalized some ten years ahead of construction, with only limited analysis required as the in-seivicc date approached. 

A common finding of computational PECD studies is that a relatively large partial wave expansion, typically running to niax > 15 is required. Chiral molecules necessarily are of very low, or no, symmetry, and hence are quite... 

Under general hypotheses, the optimisation of the Bayesian score under the constraints of MaxEnt will require numerical integration of (29), in that no analytical solution exists for the integral. A Taylor expansion of Ao(R) around the maximum of the P(R) function could be used to compute an analytical expression for A and its first and second order derivatives, provided the spread of the A distribution is significantly larger than the one of the P(R) function, as measured by a 2. Unfortunately, for accurate charge density studies this requirement is not always fulfilled for many reflexions the structure factor variance Z2 appearing in Ao is comparable to or even smaller than the experimental error variance o2, because the deformation effects and the associated uncertainty are at the level of the noise. 

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