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Quantum mechanical approximation

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. [Pg.179]

Goldflam R., Kouri D. J. On accurate quantum mechanical approximations for molecular relaxation phenomena. Averaged... [Pg.289]

A first step toward quantum mechanical approximations for free energy calculations was made by Wigner and Kirkwood. A clear derivation of their method is given by Landau and Lifshitz [43]. They employ a plane-wave expansion to compute approximate canonical partition functions which then generate free energy models. The method produces an expansion of the free energy in powers of h. Here we just quote several of the results of their derivation. [Pg.392]

Quantum-mechanical approximation methods can be classified into three generic types (1) variational, (2) perturbative, and (3) density functional. The first two can be systematically improved toward exactness, but a systematic correction procedure is generally lacking in the third case. [Pg.710]

Levy, M. and Perdew, J. P. Success of quantum mechanical approximations for molecular geometries and electron-nuclear attraction expectation values gift of the Coulomb potential , J. Chem. Phys., 84 (1986), 4519-4523... [Pg.356]

The various types of successful approaches can be classified into two groups empirical model calculations based on molecular force fields and quantum mechanical approximations. In the first class of methods experimental data are used to evaluate the parameters which appear in the model. The shape of the potential surfaces in turn is described by expressions which were found to be appropriate by semiclassicala> or quantum mechanical methods. Most calculations of this type are based upon the electrostatic model. Another more general approach, the "consistent force field method, was recently applied to the forces in hydrogen-bonded crystals 48> 49>. [Pg.14]

As was also previously noted in Section 9.3.1, the completely general rigid-rotor Schrodinger equation for a molecule characterized by three unique axes and associated moments of inertia does not lend itself to easy solution. However, by pursuing a generalization of the classical mechanical rigid-rotor problem, one can derive a quantum mechanical approximation that is typically quite good. Within that approximation, the rotational partition function becomes... [Pg.363]

Quantum mechanical approximation of an infinitesimally thin fullerene sphere... [Pg.30]

Another, purely quantum mechanical approximation is the so-called time-dependent self-consistent field (TDSCF) method. For general reviews see Kerman and Koonin (1976), Goeke and Reinhard (1982), and Negele (1982). For applications to molecular systems see, for example, Gerber and Ratner (1988a,b). In the TDSCF method the wavepacket is separated according to... [Pg.88]

The complexity of individual halogenation mechanisms has become clear in more recent years from the diverse isomer distributions observed under different reaction conditions. Quantitative product studies are beginning to make a welcome appearance, but kinetic studies are almost wholly lacking. The recent kinetic work on the iodination of imidazole may signal the onset of improvement in this aspect. On the theoretical side, much attention has been given to the several possible quantum mechanical approximations applicable to heterocyclic substitution. Here again the lack of ample quantitative... [Pg.8]

The 1,2-dithiolium salts are electron-deficient compounds, and as such are very reactive and unselective towards nucleophilic reagents. Qualitative considerations based on the simple resonance theory, as well as refined quantum mechanical approximations (Section II, C, 1), indicate that the resonance hybrid is most closely described by the carbonium and sulfonium structures (1 and 60), whereas the decet (61) and long-bond (62) structures appear to be of little importance. As would be expected for a charge distribution indicated in 1, protons attached in positions 3 and 5 experience a relatively weak electron screening effect (Section II, C, 4).79c... [Pg.60]

Eor simplicity, however, let s adopt an atomic-level description of the molecular solution. As with the central-force models (Lemberg and Stillinger, 1975), the interactions treated could be sufficiently complicated as to form complex molecules, but we will focus on the interaction contributions to the chemical potentials of atoms. In that case, all = 1, and any quantum mechanical effects on the internal structures of molecules that may be formed will have to be described by the quantum mechanical approximations that are the target here. [Pg.54]

F. Barocchi, M. Moraldi, M, Zoppi, and J. D. Poll. Quantum mechanical approximation for collision induced light scattering Spectral Moments. Molec. Phys., 45 1193-1197 (1981). [Pg.474]

The expression avoided state touching (crossing) can refer to one of two situations (Salem et al., 1975). First, an avoided touching can be encountered along paths that pass close to a real state touching but miss the tip of the cones and do not quite reach the required values of Xy and Xj to enter the (F - 2)-dimensional intersection coordinate subspace. An example would be a path that does not quite preserve the high symmetry that is characteristic of some conical intersections. Second, it can be encountered upon improvement of a simpler quantum mechanical approximation in which a... [Pg.184]

The quantum-mechanical SCF method for obtaining the vibrational energy levels is a direct adaptation of the Hartree approximation for electronic struc-true calculations, which dates back to the early stages of quantum theory. The introduction of the method for vibrational modes is, however, rather recent and is due to Bowman and co-workers,6,7 Carney et al.,8 and Cohen et al.9 The semiclassical version of the SCF, the SC-SCF method, proposed by Gerber and Ratner,10 relies on the characteristically short de Broglie wavelengths typical of vibrational motions (as opposed to electronic ones) to gain some further simplification, but is otherwise based on the same physical considerations as the quantum-mechanical approximation. A brief review of the SCF and SC-SCF methods can be found in Ref. (11). [Pg.99]

In this contribution, a brief review will be presented of the techniques of conformational searching such as the systematic grid search, minimization schemes and molecular dynamics. Also discussed will be the relative merits and shortcomings of the various semi-empirical quantum mechanical approximations such as CNDO, MNDO, AMI, PM3 and PCH O. [Pg.109]

The semiempirical quantum mechanical approximation " that has been called CNDO/2 (for complete neglect of differential overlap) was used to calculate binding energies in the trigonal bipyramidal configuration and in a series of model situations that are pertinent to the TR and the BPR mechanisms in a variety of molecules. This approximation to the solution of the LCAO-SCF equations yields results that provide, at least, a trend in the real systems involved. It has been shown that, with reasonable approximations and parametrization, this method offers an adequate compromise with respect to the more rigorous and accurate but far more laborious and expensive ab initio methods. " ... [Pg.58]

We now discuss the second major quantum-mechanical approximation method, perturbation theory. [Pg.245]

M.Baer. A review of quantum-mechanical approximate treatments of three-body reactive systems. Adv. Chem. Phys. 49. 191-309 (1982). [Pg.277]

M. Baer, A Review of Quantum Mechanical Approximate Treatments of Three Body Reactive Systems, Advances in Chemical Physics, Vol. 49, eds., I Prigogine and S. A. Rice (Wiley, N.Y., 1982)191. [Pg.380]

Avery, J., Creation and Annihilation Operators, McGraw-Hill, New York, 1976. Chapter 2 formulates a number of quantum mechanical approximations, including the Hartree-Fock approximation, in the language of second quantization. [Pg.107]

Gamow(1928) and independently Condon and Gurney(1928,1929) have shown that such a penetration of an a particle through the potential harrier is possible in quantum mechanics. The mechanism is called tunneling. One can define a penetration factor (penetrability) P, which is the ratio of emergent and incident intensities. A detailed quantum-mechanical approximate theory gives the following expression for the penetration factor ... [Pg.118]

To quote from Schreckenback, Wolff, and Ziegler[67] chemical shifts are known to be sensitive to everything . Their list of factors include the following (1) relativity, (2) quantum mechanical approximation, (3) gauge problem, (4) basis set, (5) geometries, (6) reference compound, (7) condensed phase, temperature, and pressure. Relativistic effects, which are particularly important for heavy nuclei or light nucleus attached to a heavy one, will be discussed later. [Pg.139]

We have carried out reactive differential cross section measurements in CMB experiments [21,22] and determined the spatial distribution and energy distribution of the products from reaction (1) and (2). The results are compared with those of quasiclassical and quantum mechanical (approximate) dynamical computations on ab initio surfaces, which have been carried out by Schatz [13,25,26] and by Clary [12,26,27] at the experimental energies. [Pg.101]

Tables 11.11 and 11.12 demonstrate the relatively large dependence of the calculated water-adsorption energies on the nature of the quantum-mechanical approximation (HF or DFT) and type of basis set (PW or LCAO) within the same periodic-slab model. It should be noted that the results for the equivalent 2D and 3D slab models coincide if the sufficiently large vacuum gap for 3D model is used, see Sect. 11.1.3. Nevertheless, we can conclude that the Kohn ham Hamiltonian using both PW and LCAO basis sets gives the order of the adsorption energy that is in better agreement with the experimental observations. However, the relaxation of the surface atoms seems to be more appropriate to experimental data [804] in the case of the HF calculations. Tables 11.11 and 11.12 demonstrate the relatively large dependence of the calculated water-adsorption energies on the nature of the quantum-mechanical approximation (HF or DFT) and type of basis set (PW or LCAO) within the same periodic-slab model. It should be noted that the results for the equivalent 2D and 3D slab models coincide if the sufficiently large vacuum gap for 3D model is used, see Sect. 11.1.3. Nevertheless, we can conclude that the Kohn ham Hamiltonian using both PW and LCAO basis sets gives the order of the adsorption energy that is in better agreement with the experimental observations. However, the relaxation of the surface atoms seems to be more appropriate to experimental data [804] in the case of the HF calculations.
Theoretical calculations and quantum-mechanical approximations of the free surface energy at the interface between a solid metal and a melt have indicated that the surface free energy at the interface between relevant pairs, such as Cd-Ga, Zn-Hg, Zn-Sn, and Cu-Bi, can be lowered by an order of magnitude [36]. These theoretical calculations are mainly focused on illustrating the trends... [Pg.264]

Previously, we have treated orbitals as covering the molecule as a whole, and have not from the start restricted the orbitals to any one atom. Many molecular orbitals can be approximated as linear combinations of atomic orbitals. Another way to consider molecular wavefunctions is in terms of products of atomic orbitals. This is valence bond theory, and ultimately it is very useful for describing the structures of molecules. Valence bond (or VB) theory dates from 1927, when W. Heftier and F. W. London constructed the first successful quantum-mechanical approximation of the hydrogen molecule, H2. It was developed further by J. C. Slater (of Slater determinant fame) and Linus Pauling. [Pg.459]

Conversely, for slow collisions the combined system of incoming electron and target molecule has to be considered, leading in the exit channel to a full three-body problem. Quantum-mechanical (approximate) calculations are difficult and have been carried out only for a few selected examples. Therefore, other methods have been developed with the goal of obtaining reasonably accurate cross sections using either classical or semiclassical theories and by devising semiempirical formulae. Some of these concepts are based on the Born-Bethe formula [22] and on the observation that the ejection of an atomic electron with quantum numbers (n,J) is approximately proportional to the mean-square radius of the electron shell (n,J). This leads also to proposed correlations of the ionization cross section with polarizability, dia-... [Pg.1020]


See other pages where Quantum mechanical approximation is mentioned: [Pg.208]    [Pg.755]    [Pg.70]    [Pg.30]    [Pg.139]    [Pg.834]    [Pg.120]    [Pg.108]    [Pg.116]    [Pg.17]    [Pg.161]    [Pg.495]    [Pg.950]    [Pg.31]   


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Approximate Quantum Mechanical Calculation of Thermodynamic Properties

Approximate methods of quantum mechanics

Approximate techniques for alternative representations of quantum mechanics

Approximation methods quantum-mechanical

Computational quantum mechanics approximate orbital theories

MNDO approximation, semiempirical quantum mechanics/molecular

Oscillator approximation, quantum mechanical

Quantum mechanics Born-Oppenheimer approximation

Quantum mechanics methods approximation

Quantum mechanics semiclassical approximation

Quantum-mechanical treatment the first Born approximation

Quantum-mechanical treatment the second Born approximation

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