Quantum-mechanical calculations, for

This is a question of reaction prediction. In fact, this is a deterministic system. If we knew the rules of chemistry completely, and understood chemical reactivity fully, we should be able to answer this question and to predict the outcome of a reaction. Thus, we might use quantum mechanical calculations for exploring the structure and energetics of various transition states in order to find out which reaction pathway is followed. This requires calculations of quite a high degree of sophistication. In addition, modeling the influence of solvents on... 

Kripsonsov and quantum mechanical calculations for the metal-solution interface, 174... 

Metal-solution interface, quantum mechanical calculations for (Kripsonsov), 174 Metal-water affinity, 177 Micro-balance, quartz crystal, 578 Microwave circuit, 446 for Faraday rotation, 454 Microwave conductivity... 

Quantum chemical calculations, 172 Quantum chemical method, calculations of the adsorption of water by, 172 Quantum mechanical calculations for the metal-solution interface (Kripsonsov), 174 and water adsorption, 76 Quartz crystal micro-balance, used for electronically conducting polymer formation, 578... 

In his pioneering work Baetzold used the Hartree-Fock (HF) method for quantum mechanical calculations for the cluster structure (the details are summarized in Reference 33). The value of the HF procedure is that it yields the best possible single-determinant wave function, which in turn should give correct values for expectation values of single-particle operators such as electric moments and... 

An essential requirement for such stabilisation is that the carbocation should be planar, for it is only in this configuration that effective delocalisation can occur. Quantum mechanical calculations for simple alkyl cations do indeed suggest that the planar (sp2) configuration is more stable than the pyramidal (sp3) by = 84 kJ (20 kcal) mol-1. As planarity is departed from, or its attainment inhibited, instability of the cation and consequent difficulty in its formation increases very rapidly. This has already been seen in the extreme inertness of 1-bromotriptycene (p. 87) to SN1 attack, due to inability to assume the planar configuration preventing formation of the carbocation. The expected planar structure of even simple cations has been confirmed by analysis of the n.m.r. and i.r. spectra of species such as Me3C SbF6e they thus parallel the trialkyl borons, R3B, with which they are isoelectronic. 

The utility of spline functions to molecular dynamic studies has been tested by Sathyamurthy and Raff by carrying out quassiclassical trajectory and quantum mechanical calculations for various surfaces. However, the accuracy of spline interpolation deteriorated with an increase in dimension from 1 to 2 to 3. Various other numerical interpolation methods, such as Akima s interpolation in filling ab initio PES for reactive systems, have been used. 

This simple consideration led to a number of highly sophisticated quantum-mechanical calculations for methylene, such as extended Hiickel, MINDO/2 and 3, and ab initio calculations. The results of these calculations are presented in Table 3. 

The main advances in analysis of organolithium compounds are related to their structural characterization by instrumental methods. These rely heavily on NMR spectroscopy and, when possible, on crystallographic methods, although other spectroscopic and physicochemical techniques are occasionally employed. A modern approach to the solution of complex analytical problems involves, in addition to the evidence afforded by these experimental techniques, consideration of quantum mechanical calculations for certain structures. The results of such calculations support or deny hypothetical assumptions on structural features of a molecule or possible results of a synthetic path. The following two examples illustrate these proceedings. 

The entanglement time and area depend on the thickness of nonhnear crystal, the type of nonlinear interaction, and piunping conditions. Their chosen values are close to those used in [73]. Together, they yield the critical flux density of 0c = 3 x 10 cm. This results in the entangled photon absorption cross-section = 2.95 x 10 cm. The latter estimate falls between the values obtained earlier from quantum-mechanical calculations for Na (6.0 X 10-3° K2CsSb (2.6 x lO cm ) [73]. 

It was pointed out in Section 4-2 that the configuration sp8, which has promotion energy about 200 kcal/mole relative to the ground configuration 2s22p2, is the basis of the quadrivalent state of the carbon atom and is shown by quantum-mechanical calculations for methane to contribute about 49 percent to this valence state. Now let us consider the iron atom, for which spectroscopic energy levels are shown on... 

The elongation, A/, can be evaluated from quantum mechanical calculations. For a rough estimation, a value of... 

Quantum-mechanical calculations for individual initial vibrational states enhancement of cross section by vibrational excitation 448... 

Wintgen, D., Holle, A, Wiebusch, G., Main, J., Friedrich, H., and Welge, K.-H. (1986). Precision measurements and exact quantum mechanical calculations for diamagnetic Rydberg states in hydrogen, J. Phys. B 19, L557-L561. 

In a manner analogous to that described above for nitroethylene, again all quantum mechanical calculations for DADNE were performed with the Gaussian 98 program package [22]. Intrinsic reaction coordinate (IRC) analysis was carried out for each transition state to make sure that it is the transition structure connecting the desired reactants and products. For all structures with an even number of electrons, a restricted (doubly occupied... 

There have been no papers with experimental thermochemical data for 1,2,3-thiadiazoles. Thermochemical data derived from quantum mechanical calculations for 1,2,3-thiadiazoles are also not available. These areas clearly are worthy of greater research attention. 

Quantum mechanical calculations for the 1,3-dithiolylium ion, benzo-1,3-dithiolylium ion, l,3-dithiol-2-one and l,3-dithiole-2-thione have been carried out with the simple LCAO MO method <66AHC(7)39). According to these calculations, the lowest electron density was found at the 2-position of the 1,3-dithiolylium cation, and the C(4)—C(5) bond order corresponded approximately to that of an isolated C—C double bond. A delocalization energy of 105 kJ mol-1 has been calculated for this cation. For the benzo-l,3-dithiolylium ion it was found that nucleophilic attack should take place in the 2-position but electrophilic substitution at the 4-position. 

---