Quantum description

As we shall see, in molecules as well as atoms, the interplay between the quantum description of the internal motions and the corresponding classical analogue is a constant theme. However, when referring to the internal motions of molecules, we will be speaking, loosely, of the motion of the atoms in the molecule, rather than of the fiindamental constituents, the electrons and nuclei. This is an extremely fundamental point to which we now turn. 

A1.3.3 DENSITY FUNCTIONAL APPROACHES TO QUANTUM DESCRIPTIONS OF CONDENSED PHASES... 

Ashkenazi G, Banin U, Bartana A, Ruhman S and Kosloff R 1997 Quantum description of the impulsive photodissociation dynamics of l, in solution Adv. Chem. Phys. 100 229... 

Goldman M 1988 Quantum Description of High-Resoiution NMR in Liquids (Oxford Clarendon)... 

Establishing precisely the conditions necessary to justify the transition from a microscopic, quantum description to such a macroscopic differential equation is an interesting question in theoretical physics. It has been treated in considerable detail (1) but rarely troubles practicing kineticists. 

The original FMM has been refined by adjusting the accuracy of the multipole expansion as a function of the distance between boxes, producing the very Fast Multipole Moment (vFMM) method. Both of these have been generalized tc continuous charge distributions, as is required for calculating the Coulomb interactioi between electrons in a quantum description. The use of FMM methods in electronic structure calculations enables the Coulomb part of the electron-electron interaction h be calculated with a computational effort which depends linearly on the number of basi functions, once the system becomes sufficiently large. 

Although an in-depth treatment is outside the scope of this book, it may be instructive to point out some of the features and problems in a relativistic quantum description of atoms and molecules. 

A classical description of M can for example be a standard force field with (partial) atomic charges, while a quantum description involves calculation of the electronic wave function. The latter may be either a semi-empirical model, such as AMI or PM3, or any of the ab initio methods, i.e. HF, MCSCF, CISD, MP2 etc. Although the electrostatic potential can be derived directly from the electronic wave function, it is usually fitted to a set of atomic charges or multipoles, as discussed in Section 9.2, which then are used in the actual solvent model. 

Abstract The statistical properties of the electromagnetic field find their origin in its quantum nature. While most experiments can be interpreted relying on classical electrodynamics, in the past thirty years, many experiments need a quantum description of the electromagnetic field. This gives rises to distinct statistical properties. 

Quantum description of light the wave/particle duality... 

To obtain single photon pulses, one can use the emission by a single dipole as shown below in section 21.3.1. The experiment was performed in 1977 by Kimble, Dagenais and Mandel (Kimble et al., 1977). They showed that single atoms from an atomic beam emitted light which, at small time scales, exhibited a zero correlation function. This result can not be explained through a semiclassical theory and requests a quantum description of light. 

We have shown in this chapter how some experiments made it necessary in some cases to use a quantum description of light instead of the standard semi-classical theory where only the atomic part is quantized. A brief description of different helds in terms of their statistical properties was also given. This description makes it possible to discriminate between the different sources using the intensity autocorrelation function (r). 

The new delightful book by Greenstein and Zajonc(9) contains several examples where the outcome of experiments was not what physicists expected. Careful analysis of the Schrddinger equation revealed what the intuitive argument had overlooked and showed that QM is correct. In Chapter 2, Photons , they tell the story that Einstein got the Nobel Prize in 1922 for the explaining the photoelectric effect with the concept of particle-like photons. In 1969 Crisp and Jaynes(IO) and Lamb and Scullyfl I) showed that the quantum nature of the photoelectric effect can be explained with a classical radiation field and a quantum description for the atom. Photons do exist, but they only show up when the EM field is in a state that is an eigenstate of the number operator, and they do not reveal themselves in the photoelectric effect. 

The molecular modelling approach, taking into account the pyruvate—cinchona alkaloid interaction and the steric constraints imposed by the adsorption on the platinum surface, leads to a reasonable explanation for the enantio-differentiation of this system. Although the prediction of the complex formed between the methyl pyruvate and the cinchona modifiers have been made for an ideal case (solvent effects and a quantum description of the interaction with the platinum surface atoms were not considered), this approach proved to be very helpful in the search of new modifiers. The search strategy, which included a systematic reduction of the cinchona alkaloid structure to the essential functional parts and validation of the steric constraints imposed to the interaction complex between modifier and methyl pyruvate by means of molecular modelling, indicated that simple chiral aminoalcohols should be promising substitutes for cinchona alkaloid modifiers. Using the Sharpless symmetric dihydroxylation as a key step, a series of enantiomerically pure 2-hydroxy-2-aryl-ethylamines... 

A combination of different approaches is at present the most convenient strategy. Most of the work done an complex material models adopts a classical formalism, disregarding for the moment quantum aspects, while there are significant progresses in quantum description of simple models [26]. 

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-... 

Statistical mechanics deals explicitly with the motion of particles. The common quantization procedure that provides a quantum description of classical particles by the introduction of operators, such as the momentum operator, p —> however, replaces the classical particle description by a wave... 

M. Goldman, Quantum Description of High-Resolution NMR in Liquids, Oxford University Press, Oxford, 1988, 54-69. 

See Louis de Broglie s remarks in an interview with Thomas Kuhn et al., January 7, 1963, Paris, no. 1 of 2 interviews, 67. The French physical chemists Jules Gueron and Michel Magat have remarked on the fact that no French physicist or chemist took part in the "swift creation of the quantum theory of the chemical bond and the quantum description of chemical reactions." Jules Gueron and Michel Magat, "A History of Physical Chemistry in France," Ann.Rev.P.Chem. 22 (1971) 123, on 7. 

Finally - and equally important - Jens contribution to the formal treatment of GOS based on the polarization propagator method and Bethe sum rules has been shown to provide a correct quantum description of the excitation spectra and momentum transfer in the study of the stopping cross section within the Bethe-Bloch theory. Of particular interest is the correct description of the mean excitation energy within the polarization propagator for atomic and molecular compounds. This motivated the study of the GOS in the RPA approximation and in the presence of a static electromagnetic field to ensure the validity of the sum rules. 

M. Goldman Quantum description of high-resolution NMR in liquids... 

In retrospect, one can see that Boltzmann s inspired conjecture (13.69) served, through (13.77), to anticipate an essential feature of the probabilistic quantum description that was to supplant classical determinism in the 20th century. Boltzmann and his followers specifically captured the key probabilistic feature (13.69) that could bring proper metric geometrical character (13.77) to macroscopic-level thermodynamic description, despite gross errors of then-current microscopic dynamical theory. 

First of all, consider the case when all normal vibrations are classical. This takes place if the condition a)k -4 T works well for all frequencies. In the classical case the probability of tunneling can be calculated with the help of the general formula (18) using the Franck-Condon approximation and the well-known [10] properties of quasi-classical wave functions. We will not dwell upon the details of transition from the quantum description to the... 

A quantum mechanical theory is in principle needed to describe molecular phenomena in both few-atom and many-atom systems. In some cases a single electronic state is involved, and it is possible to gain valuable insight using only classical molecular dynamics, which can be relatively easy to apply even for a system of many atoms. A quantum mechanical description of molecular phenomena is however clearly needed for electronic states, insofar these have pronounced wavemechanical properties. The need for a quantum description of nuclear motions in molecular dynamics is less apparent, but it is required in some important situations. If we consider a generic interaction between two species A(a) and B(j3) leading to formation of two others, C(7) and D(6), all of them in the specified quantum states, so that... 

I believe that these exciting discoveries of modem physics could be the basis for a new view of consciousness and the way it is coupled to our physical nature in the brain (Indeed, one of the fascinating aspects of Quantum theory which puzzles amd mystifies contemporary physicists is the way in which their quantum description of matter requires that they recognise the consciousness of the observer as a factor in certain experiments. This enigma has caused not a few physicists to take an interest in spirituality especially inclining them to eastern traditions like Taoism or Buddhism, and in time I hope that perhaps even the hermetic traditions might prove worthy of their interest). 

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