Chapter 1. Quantum Mechanics and Application to Molecular Structure

1961 ◽  
pp. 3-38
Keyword(s):  
Molecular Structure ◽  
Quantum Mechanics

Subsequent and Subsidiary? Rethinking the Role of Applications in Establishing Quantum Mechanics

2015 ◽  
Vol 45 (5) ◽  
pp. 641-702 ◽  
Author(s):  
Jeremiah James ◽  
Christian Joas
Keyword(s):  
Molecular Structure ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Mechanics ◽  
Theory Construction ◽  
Science Pedagogy ◽  
Old Quantum Theory ◽  
The Common ◽  
Complete Quantum

As part of an attempt to establish a new understanding of the earliest applications of quantum mechanics and their importance to the overall development of quantum theory, this paper reexamines the role of research on molecular structure in the transition from the so-called old quantum theory to quantum mechanics and in the two years immediately following this shift (1926–1928). We argue on two bases against the common tendency to marginalize the contribution of these researches. First, because these applications addressed issues of longstanding interest to physicists, which they hoped, if not expected, a complete quantum theory to address, and for which they had already developed methods under the old quantum theory that would remain valid under the new mechanics. Second, because generating these applications was one of, if not the, principal means by which physicists clarified the unity, generality, and physical meaning of quantum mechanics, thereby reworking the theory into its now commonly recognized form, as well as developing an understanding of the kinds of predictions it generated and the ways in which these differed from those of the earlier classical mechanics. More broadly, we hope with this article to provide a new viewpoint on the importance of problem solving to scientific research and theory construction, one that might complement recent work on its role in science pedagogy.

Quantum information theory

2009 ◽  
Author(s):  
Stephen Barnett
Keyword(s):  
Information Theory ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Quantum Information Theory ◽  
Quantum Circuits ◽  
Classical Counterpart ◽  
Theory Of Information ◽  
The Many

The astute reader might have formed the impression that quantum in formation science is a rather qualitative discipline because we have not, as yet, explained how to quantify quantum information. There are three good reasons for leaving this important question until the final chapter. Firstly, quantum information theory is technically demanding and to treat it at an earlier stage might have suggested that our subject was more complicated than it is. Secondly, there is the fact that many of the ideas in the field, such as teleportation and quantum circuits, are unfamiliar and it was important to present these as simply as possible. Finally, and most importantly, the theory of quantum information is not yet fully developed. It has not yet reached, in particular, the level of completeness of its classical counterpart. For this reason we can answer only some of the many questions we would like a quantum theory of information to address. Having said this, we can say that however, there are beautiful and useful mathematical results and it seems certain that these will continue to form an important part of the theory as it develops. We noted in the introduction to Chapter 1 that ‘quantum mechanics is a probabilistic theory and so it was inevitable that a quantum information theory would be developed’. A presentation of at least the beginnings of a quantitative theory is the objective of this final chapter. The entropy or information derived from a given probability distribution is, as we have seen, a convenient measure of the uncertainty associated with the distribution. If many of the probabilities are large, so that many of the possible events are comparably likely, then the entropy will be large. If one probability is close to unity, however, then the entropy will be small. It is convenient to introduce entropy in quantum mechanics as a measure of the uncertainty, or lack of knowledge, of the form of the state vector. If we know that our system is in a particular pure state then the associated uncertainty or entropy should be zero. For mixed states, however, it will take a non-zero value.

Multi-step modeling of liquid crystals using ab initio molecular packing and hybrid quantum mechanics/molecular mechanics simulations

2017 ◽  
Vol 16 (02) ◽  
pp. 1750012 ◽  
Author(s):  
Hang Hu ◽  
Alejandro D. Rey
Keyword(s):  
Molecular Structure ◽  
Quantum Mechanics ◽  
Raman Spectrum ◽  
Liquid Crystals ◽  
Molecular Mechanics ◽  
Crystal Structures ◽  
Molecular Interactions ◽  
Crystal Packing ◽  
Order Parameters ◽  
Molecular Structures

A density functional theory (DFT) based multi-step simulation method is used to characterize the detailed molecular structure and inter/intra- molecular interactions of two benchmark liquid crystals (LC) 5CB, 8CB and a novel tri-biphenyl ring bent core LC material. The method uses hybrid DFT at the B3LYP/6-31G* level to obtain molecular structure and Raman data. These results are fed to a crystal packing simulation to find possible crystal structures. A pico-second quantum mechanics/molecular mechanics (QM/MM) simulation model is built for the selected structures with lower overall energy as well as optimal density. The stabilized crystal structures are then extended into a super cell, heated and simulated using a mixed force field and nano-second molecular dynamics (MD). The described simulation process sequence provides predictions of molecular Raman spectrum, LC density, isotropic depolarization ratio, ratio of differential polarizability, order parameters, molecular structures, and rotating Raman spectrum of the different mesophases. The Raman spectra, order parameters and depolarization ratios all agree well with existing experimental and previous simulation results. The study of the novel tri-biphenyl ring bent core LC system shows that the ratio of differential polarizability depends on intra-molecular interactions. The findings presented in this manuscript contribute to the on-going efforts to establish links between LC molecular structures and their properties, including optical behavior.

Molecular structure in non-Born–Oppenheimer quantum mechanics

2004 ◽  
Vol 387 (1-3) ◽  
pp. 136-141 ◽  
Author(s):  
Mauricio Cafiero ◽  
Ludwik Adamowicz
Keyword(s):  
Molecular Structure ◽  
Quantum Mechanics

scholarly journals ORBITALS IN GENERAL CHEMISTRY, PART II: MATHEMATICAL REALITIES

Química Nova ◽  
2020 ◽  
Author(s):  
Guy Lamoureux ◽  
John Ogilvie
Keyword(s):  
Molecular Structure ◽  
General Chemistry ◽  
Quantum Mechanics ◽  
Constant Amplitude ◽  
Qualitative Explanation ◽  
Mathematical Functions ◽  
Atomic Orbitals ◽  
Two Factors

In Part II of a three-part series, we discuss two factors absent from textbooks of general chemistry that are important in a discussion of teaching orbitals. First, atomic orbitals are shown systematically to comprise algebraic formulae in coordinates of not one but four sets (spherical polar, paraboloidal, ellipsoidal, spheroconical coordinates). Each formula has its corresponding shape as a surface of constant amplitude; some visual examples are provided. Second, the argument that molecular structure is incompatible with quantum mechanics is presented. Despite the utility of orbitals as mathematical functions in various calculations, they are intrinsically complicated for the traditional purpose of qualitative explanation of molecular structure.

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