Energy different forms

This matrix represents an effective operator that still has to act on the bending functions/ (p),/ (p). A generalization of (24) to the case when the kinetic energy operator (i.e., the coefficients 7 and A) has a different form in the... 

The second application of the CFTI approach described here involves calculations of the free energy differences between conformers of the linear form of the opioid pentapeptide DPDPE in aqueous solution [9, 10]. DPDPE (Tyr-D-Pen-Gly-Phe-D-Pen, where D-Pen is the D isomer of /3,/3-dimethylcysteine) and other opioids are an interesting class of biologically active peptides which exhibit a strong correlation between conformation and affinity and selectivity for different receptors. The cyclic form of DPDPE contains a disulfide bond constraint, and is a highly specific S opioid [llj. Our simulations provide information on the cost of pre-organizing the linear peptide from its stable solution structure to a cyclic-like precursor for disulfide bond formation. Such... 

The second application of the CFTI protocol is the evaluation of the free energy differences between four states of the linear form of the opioid peptide DPDPE in solution. Our primary result is the determination of the free energy differences between the representative stable structures j3c and Pe and the cyclic-like conformer Cyc of linear DPDPE in aqueous solution. These free energy differences, 4.0 kcal/mol between pc and Cyc, and 6.3 kcal/mol between pE and Cyc, reflect the cost of pre-organizing the linear peptide into a conformation conducive for disulfide bond formation. Such a conformational change is a pre-requisite for the chemical reaction of S-S bond formation to proceed. The predicted low population of the cyclic-like structure, which is presumably the biologically active conformer, agrees qualitatively with observed lower potency and different receptor specificity of the linear form relative to the cyclic peptide. 

For this class of thiazoles most of the chemical and physicochemical studies are centered around the protomeric equilibrium and its consequences. The position of this equilibrium may be determined by spectroscopic and titrimetric methods, as seen in each section. A simple HMO (Hiickel Molecular Orbitals) treatment of 2-substituted compounds however, may, exemplify general trends. This treatment considers only protomeric forms 1 and 2 evidence for the presence of form 3 has never been found. The formation energy reported in Table 1 is the energy difference in f3 units. 

The CIS and trans forms of 1 2 dimethylcyclopropane are stereoisomers Stereoisomers are isomers that have their atoms bonded m the same order—that is they have the same constitution but they differ m the arrangement of atoms m space Stereoiso mers of the cis-trans type are sometimes referred to as geometric isomers You learned m Section 2 18 that constitutional isomers could differ m stability What about stereoisomers We can measure the energy difference between as and trans 1 2 dimethylcyclo propane by comparing their heats of combustion As illustrated m Figure 3 20 the two compounds are isomers and so the difference m their heats of combustion is a direct measure of the difference m their energies Because the heat of combustion of trans 1 2 dimethylcyclopropane is 5 kJ/mol (12 kcal/mol) less than that of its cis stereoisomer it follows that trans 1 2 dimethylcyclopropane is 5 kJ/mol (12 kcal/mol) more stable than as 1 2 dimethylcyclopropane... 

Resonance theory can also account for the stability of the allyl radical. For example, to form an ethylene radical from ethylene requites a bond dissociation energy of 410 kj/mol (98 kcal/mol), whereas the bond dissociation energy to form an allyl radical from propylene requites 368 kj/mol (88 kcal/mol). This difference results entirely from resonance stabilization. The electron spin resonance spectmm of the allyl radical shows three, not four, types of hydrogen signals. The infrared spectmm shows one type, not two, of carbon—carbon bonds. These data imply the existence, at least on the time scale probed, of a symmetric molecule. The two equivalent resonance stmctures for the allyl radical are as follows ... 

Results obtained at high temperatures indicate that the solubihties of the crystalline modifications of sihca are in the order tridymite > cristobahte > quartz, an order that parallels to some extent the chemical reactivity of these forms. Lower values for solubihty of crystalline as compared to amorphous sihca are consistent with the free-energy differences between them. 

Thorium [7440-29-1], a naturally occurring radioactive element, atomic number 90, atomic mass 232.0381, is the second element of the actinide ( f) series (see Actinides AND transactinides Radioisotopes). Discovered in 1828 in a Norwegian mineral, thorium was first isolated in its oxide form. For the light actinide elements in the first half of the. series, there is a small energy difference between and 5/ 6d7 electronic configurations. Atomic spectra... 

One interesting exception to the generalization that chair forms predominate in this series is shown by the tetrathian (44), which prefers the twist form in the solid phase, and also in CS2 solution at 0 C both chair and twist forms coexist in solution, with a free energy difference of ca. 3.5 kJ between them (67JA5978, 68JA2450). 

Many different forms of the energy balance have been used in fixed-bed adsorption studies. The form chosen for a particular study depends on the process considered (e.g., temperature swing adsorption or pressure swing adsorption) and on the degree of approximation that is appropriate. 

A prototype of such phenomena can be seen in even the simplest carboxylic acid, acetic acid (CH3CHOOH). Acidity is determined by the energy or free energy difference between the dissociated and nondissociated forms, whose energetics usually depend significantly on their conformation, e.g., the syn/anti conformational change of the carboxyl-ate group in the compound substantially affects the acid-base equilibrium. The coupled conformation and solvent effects on acidity is treated in Ref. 20. 

Physisorption occurs when, as a result of energy differences and/or electrical attractive forces (weak van der Waals forces), the adsorbate molecules become physically fastened to the adsorbent molecules. This type of adsorption is multilayered that is, each molecular layer forms on top of the previous layer with the number of layers being proportional to the contaminant concentration. More molecular layers form with higher concentrations of contaminant in solution. When a chemical compound is produced by the reaction between the adsorbed molecule and the adsorbent, chemisorption occurs. Unlike physisorption, this process is one molecule thick and irreversible... 

Fig. 10(b)). One of the reasons for the differences between both theories is a different form of a hard sphere part of the free energy functional. Segura et al. have used the expression resulting from the Carnahan-Starhng equation of state, whereas the Meister-Kroll-Groot approach requires the application of the PY compressibility equation of state, which produces higher oscillations. 

A few groups replace the Lennard-Jones interactions by interactions of a different form, mostly ones with a much shorter interaction range [144,146]. Since most of the computation time in an off-lattice simulation is usually spent on the evaluation of interaction energies, such a measure can speed up the algorithm considerably. For example, Viduna et al. use a potential in which the interaction range can be tuned... 

The RR and SS forms have exactly the same values for the energy and the dipole moment. The energy difference between them and the meso form is about 2.5 millihartrees, which corresponds to about 1.5 kcal moT. This is a small but significant difference in energy. 

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