Quantum calculation

Similar MNDOjcalculations for N, O, F compounds using bond parameters for O—F and N—F permitted enthalpies of unknown compounds such as F N(0F)3 to be predicted and possible syntheses evaluated (96). [The input data to this set of calculations included a wrong value for Aiff(F(g,) = 270.3 kJmol Mt should be noted that experimental heats of formation of atoms are needed in all these calculations.] 

Ab initio calculations may be applied to isomerization reactions or bond separation reactions in which the bond type persists and correlation energies are unlikely to alter. For example, 

The value of Aff (F2NOF) derived from bond separation energies of this reaction was 55.7 kJ mol. This compared with the empirical MNDO calculation of -85.8 kJ mol (172). 

At the present time, semiempirical quantum calculations applied to a restricted range of fluorine compounds cannot be said to be more successful than other empirical methods, such as Sanderson s, although they yield other molecular properties in addition to enthalpies. 

The quantum chemical calculations for the 7-norbomadienyl ion have confirmed its unsymmetrical bishomoaromatic structure. The first calculations for this ion were made as early as 1963 but this was done by using the method LCAO MO in the n-electron approximation at the same time the nondassical electron delocalization in the 7-norbomadienyl cation does not obviously have the 7c-character, but is intermediate between jt- and a-delocalizations. More reliable, therefore, are the Jesuits obtained in 1971-1972 by the CNDO/2 and the MINDO/2 method with all the valent electrons taken into account. According to these calculations, the positve charge is mainly concentrated on C, C, but not on C and C  

As shown by Dewar s calculations in the process of bridge-flipping the symmetrical structure corresponds to the transition state and not to the intermediate, the energetic barrier amounting to 26 kcal/mole (according to Winstein s experimental data, it is 19.6 kcal/mole). 

The aim of this section is to show that the experimentally obtained ionization thresholds displayed in Fig. 7.3 can be reproduced by numerical quantum calculations conducted within the framework of the SSE model discussed in detail in Chapter 6. Since the SSE model is one-dimensional, it is surprising that it should be possible to use this model with any hope of success for the description of the manifestly three-dimensional experiments with real Rydberg atoms in the laboratory. Therefore, the main point here is to motivate and to justify the use of a one-dimensional model for the description of Rydberg atoms in a strong linearly polarized radiation field. 

In standard introductory text books, the quantum mechanics of the hydrogen atom is usually discussed in spherical coordinates. In the spherical description, neglecting the electron spin, the hydrogen states are classified with the help of three quantum numbers, the principal quantum number n, the angular quantum number I and the magnetic quantum number m. The hydrogen wave functions are given by 

In parabolic coordinates the hydrogen states are known as the Stark states. They are classified with the help of three quantum numbers. 

Prom (7.2.6) and the fact that Lq x) = const, it can be seen that (f 5l ) is locahzed around r w z, whereas (f 5n ) is locaUzed around r w — Thus, the extremal Stark states are quasi-one-dimensional highly elongated states. This is illustrated in Fig. 7.4, which shows Kt1-S4 )P as a three-dimensional plot in the x — z plane. 

In atomic units the hydrogen atom in a Unearly polarized microwave field of frequency u and field strength is given by 

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Baumert T, Engel V, Meier Ch and Gerber G 1992 High laser field effects in multiphoton ionization of Na2 -experiment and quantum calculations Chem. Rhys. Lett. 200 488... 

Zhang D H and Zhang J Z H 1995 Quantum calculations of reaction probabilities for HO + CO and bound states of HOCO J. Chem. Phys. 103 6512... 

Wang D and Bowman J M 1992 Reduced dimensionality quantum calculations of mode specificity in OH + H2 H2O + HJ. Chem. Phys. 96 8906... 

The relative shift of the peak position of the rotational distiibution in the presence of a vector potential thus confirms the effect of the geometric phase for the D + H2 system displaying conical intersections. The most important aspect of our calculation is that we can also see this effect by using classical mechanics and, with respect to the quantum mechanical calculation, the computer time is almost negligible in our calculation. This observation is important for heavier systems, where the quantum calculations ai e even more troublesome and where the use of classical mechanics is also more justified. 

How to cap the quantum calculation so that there are no dangling electron s or bonds in the quan turn m eeh an ical calculation wdi ilc still preservin g th c desired effect of the classical portion (which is now there, only in principle ). 

The second aspect is more fundamental. It is related to the very nature of chemistry (quantum chemistry is physics). Chemistry deals with fuzzy objects, like solvent or substituent effects, that are of paramount importance in tautomerism. These effects can be modeled using LFER (Linear Free Energy Relationships), like the famous Hammett and Taft equations, with considerable success. Quantum calculations apply to individual molecules and perturbations remain relatively difficult to consider (an exception is general solvation using an Onsager-type approach). However, preliminary attempts have been made to treat families of compounds in a variational way [81AQ(C)105]. 

Fig. 5.14. Quantum calculations of the spectral shape with (—) and without...

Gianturco F. A., Serna S., Sanna N. Dynamical decoupling in the quantum calculations of transport coefficients. I. Coupled state results for He-N2 gaseous mixture, Mol. Phys. 74, 1071-87 (1991). 

Labarre JF (1978) Conformational Analysis in Inorganic Chemistry Semi-Empirical Quantum Calculation vs. Experiment. 35 1-35 Lammers M, Follmann H (1983) The Ribonucleotide Reductases A Unique Group of Metalloenzymes Essential for Cell Proliferation. 54 27-91 Le Brun NE, Thomson AJ, Moore GR (1997) Metal Centres of Bacterioferritins of Non-Heam-Iron-Containing Cyrochromes 6557. 88 103-138... 

What is the main difference in the use of quantum calculations between group I and II ... 

When quantum calculations, at the ab initio and at the semiempirical level, gained foot in the realm of chemistry, a steadily increasing number of experimentalists began to use quantum calculations as a supplement in the exposition of their findings. In many case this was - and still is - nothing more that an ornament, like decorations on a cake. This use of quantum chemistry has been, in general, harmless, because results in contrast with experimental evidence have been rarely published, and this production may be considered now as a sort of advertising for the new-born computational chemistry. A more serious use of the facilities offered by the computational techniques is done by scientists provided of... 

The foundation of our approach is the analytic calculations of the perturbed wave-functions for a hydrogenic atom in the presence of a constant and uniform electric field. The resolution into parabolic coordinates is derived from the early quantum calculation of the Stark effect (29). Let us recall that for an atom, in a given Stark eigenstate, we have ... 

Labarre, J. F. Conformational Analysis in Inorganic Chemistry Semi-Empirical Quantum Calculation vs. Experiment. Vol. 35, pp. 1-35. 

The E-state is based solely on atom connectivity information obtained from the molecular graph, without any input from the molecular geometry or sophisticated quantum calculations. We start this chapter with a brief presentation of the relevant notions of graph theory and continue with the definitions of a couple of important graph matrices. Then the molecular connectivity indices are mentioned... 

Quantum calculations on metal-assisted tautomerization indicate a substantial stabilization to protonation of the endocyclic nitrogen atoms (99). In the case of HgCHg, adducts are formed by binding at either A-N6 or C-N4, which increases the stability of the respective N1H+ or N3H+ protonated species by 10-14 kcal/mol. For Pt11 binding at C-N4 the effect is much greater at 30-34 kcal/mol. 

In order to run a MM calculation, the parameters Kr, req, Kg, 0eq, Vn, y, Aab, Bab, and the charges Qa must be adjusted for different molecules or residues, usually to reproduce some experimental property or quantum calculation. The term force field refers to a specific set of those parameters, derived to work together. Besides the program, the name Amber is also used to refer to the particular family of force fields according to Eq. (1-1), although in this case the proper reference to the force field should also include the specific version details (e.g. Amber ff99SB [3], ff03 [4], etc.). 

Lee T, York D, Yang W (1996) Linear-scaling semiempirical quantum calculations for macromolecules. J Chem Phys 105(7) 2744-2750... 

Section 2 mainly focuses on the current efforts to improve the accuracy of quantum calculations using simplified empirical model forms. McNamara and Hillier, in Chapter 5, summary their work on improving the description of the interactions in biological systems via their optimized semiempirical molecular models. Piquemal and co-workers present recent advances in the classical molecular methods, aiming at better reproduction of high-level quantum descriptions of the electtostatic interactions in Chapter 6. In Chatper 7, Cui and Elstner describe a different semiempir-... 

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