Quantum theory, experimental foundation

The experimental foundation of the quantum theory of atomic structure as put forward by Bohr, lies in the stability of the atom and in the existence of discrete energy levels and the ability of the atom to absorb and emit energy only in quanta, as demonstrated by the discontinuous nature of atomic spectra and by the critical potential measurements of Franck and Hertz. Bohr postulated that the atom could only exist in a limited number of orbits or stationary states, which were defined by the quantum condition that the angular momentum can assume only certain limited values which are given by the expressioiT ... 

The determination of the universal functions LXs(X,T) or MXs(X,T) is a fundamental task of physics. This was solved experimentally towards the end of the 19th century, but a theoretical basis for the measured data was first found by M. Planck4 in 1900. Through assumptions, which later formed one of the foundations of quantum theory, he was able to formulate the law for the spectral intensity... 

The experimental method of electron impact, mentioned in the introduction, enables the energy levels of the atomic systems to be determined in a purely empirical manner. Comparison of these determinations with the theoretical values provides a test of the foundations of the quantum theory as far as they have hitherto been developed. 

All science is based on a number of postulates. Quanmm mechanics has also elaborated a system of postulates that have been formulated to be as simple as possible and yet to be consistent with experimental results. Postulates are not supposed to be proved-their justification is efficiency. Quantum mechanics, the foundations of which date from 1925 and 1926, still represents the basic theory of phenomena within atoms and molecules. This is the domain of chemistry, biochemistry, and atomic and nuclear physics. Further progress (quantum electrodynamics, quantum field theory, and elementary particle theory) permitted deeper insights into the structure of the atomic nucleus but did not produce any fundamental revision of our understanding of atoms and molecules. Matter as described by non-relativistic quantum mechanics represents a system of electrons and nuclei, treated as pointlike particles with a definite mass and electric... 

The quantum mechanical model of atomic structure is based on a set of postulates that can only be justified on the basis of their ability to rationalize experimental behavior. However, the foundations of quantum theory have their origins in the field of classical wave mechanics. The fundamental postulates are as follows ... 

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

Quantum chemical simulations based on density functional theory (DFT) are widely regarded as reaching the appropriate compromise between chemical accuracy and the need to study structurally complex extended materials in order to tackle problems associate with heterogeneous catalysis involving alloys. A review of DFT and heterogeneous catalysis can be found in the previous SPR and that review also listed several general reviews of applications and foundations of DFT. Experimental and theoretical studies of monolayer bimetallic surfaces were recently reviewed. In... 

With this replacement of the strong collider assumption now commonplace, the term RRKM theory has become largely synonymous with quantum TST for unimolecular reactions, and we use this terminology here. The foundations of RRKM theory have been tested in depth with a wide variety of inventive theoretical and experimental studies [9]. While these tests have occasionally indicated certain limitations in its applicability, for example to timescales of a picosecond or longer, the primary conclusion remains that RRKM theory is quantitatively valid for the vast majority of conditions of importance to chemical kinetics. The H + O2 HO2 OH + O reaction is an example of an important reaction where deviations from RRKM predictions are significant [10, 11]. The foundations of RRKM theory and TST have been aptly reviewed in various places [7, 9, 12-15]. Thus, the present chapter begins with only a brief... 

Dunitz wrote of these equations Debye s paper, published only a few months after the discovery of X-ray diffraction by crystals, is remarkable for the physical intuition it showed at a time when almost nothing was known about the structure of solids at the atomic level. Ewald described how The temperature displacements of the atoms in a lattice are of the order of magnitude of the atomic distances The result is a factor of exponential form whose exponent contains besides the temperature the order of interference only [h,k,l, hence sin 9/M]. The importance of Debye s work, as stressed by Ewald,was in paving the way for the first immediate experimental proof of the existence of zero-point energy, and therewith of the quantum statistical foundation of Planck s theory of black-body radiation. ... 

The Schrodinger equation does not provide a complete theory of quantum mechanics. Schrodinger, Heisenberg, and others devised several postulates (unproved fundamental assumptions) that form a consistent logical foundation for nonrelativistic quantum mechanics. In any theory based on postulates, the validity of the postulates is tested by comparing the consequences of the postulates with experimental fact. The postulates of quantum mechanics do pass this test. These postulates can be stated in slightly different ways. We will state five postulates in a form similar to that of Mandl and Levine. The first two postulates were introduced in Chapter 15 without calling them postulates. We now state them explicitly ... 

The concept of calculating the interaction energy of two chemical systems A and B perturbatively is not at all a new idea. The first intermolecular perturbation expansion was proposed [22] just a few years after the foundations of quantum mechanics had been laid. Since then, numerous other expansions, now known under a common name of symmetry-adapted perturbation theory, have been introduced and the perturbation theory of intermolecular forces is now a fully mature approach. Thanks to the development of the many-body SAPT [23] and of a general-utility closed-shell SAPT computer code [24], the perturbative approach to intermolecular interactions has been successfully applied to construct PESs for numerous interacting dimers of theoretical and experimental interest [19-21,25-27]. One of the notable achievements of SAPT is an accurate description of the interactions between water molecules [21,28-32]. A recent paper by Keutsch et al. [33] compares the complete spectra of the water dimer with theoretical predictions obtained using an empirical potential fitted to extensive spectroscopic data, and with the predictions from a SAPT potential. These comparisons show that the latter potential probably provides the best current characterization of the water dimer force field. In another recent application, an SAPT PES for heUum in-... 

Since all chemistry has solid quantum foundations, one cannot expect any surprises in the future in this or any other field, although many unexpected experimental results will certainly appear. The role of theoretical chemistry will increase as new methods (bear in mind the tremendous impact of Density Functional Theory (DFT) [62]) and new hardware (quantum computers [63]) will become available. Remember however, that the goal of theoretical chemistry should be to predict. Quoting Kitaigorodskii in a lecture in 1975 A first-rate theory predicts a second-rate theory forbids and a third rate theory explains after the event [64,65]. 

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