Freeon dynamics

In the first volume of Advances in Quantum Chemistry [1] I published an article called Spin-Free Quantum Chemistry. Since then I have broadened this concept considerably and have changed the name of the subject to "freeon dynamics". The word "freeon1 means "free-of-spin" and not the common refrigerant. Freeon dynamics is a viable alternative (for light atoms and for molecules with light atoms) to the more-conventional fermion dynamics. The raison d etre for freeon dynamics is that it is conceptually and computationally simpler than fermion dynamics and so is consistent with Ockham s razor ... 

Central to freeon dynamics is the indistinguishability of electrons this property is a symmetry which is expressed in terms of the symmetric group, Sn> the group of permutations on the indices of the N identical electrons. The irreducible-representation-spaces (IRS) of Sn are uniquely labeled by Young diagrams denoted YD[X] where [X] is a partition of N and where YD[X] is an array of N boxes in columns of nondecreasing lengths. The Hamiltonian for a system of N identical particles commutes with the elements of Sn- By the... 

From all this one must conclude that the determinantal and second-quantized formulations should be regarded as a poor man s group theory which, while convenient, hides the basic freeon dynamics. These fermion methods have the additional disadvantage that their antisymmetric fermion functions are not normally pure spin (freeon) states so that spin-projection may be required. A method for avoiding (approximately) spin projection is the employment of the variation principle to approximate the ground state e. g., unrestricted Hartree-Fock theory. Finally the use of the fermion formulations has lead to the spin paradigm as a replacement for the more fundamental freeon dynamics. 

These facts appear to be unknown to most chemists even after thirty years. During this period I have presented freeon dynamics, on separate occasions, to Nobel-Laureate Robert Mulliken and to my research professor, Henry Eyring, after which I was asked by each whether "they had to learn that stuff ". I was able to assure them that their reputations would not suffer through the neglect of freeon dynamics. Even now after thirty years freeon dynamics does not appear in the standard quantum chemistry texts with the noteworthy exception of Roy McWeeny s Methods of Molecular Quantum Mechanics [2] Consequently the title of this article has been taken to be Freeon Dynamics. A Novel Theory of Atoms and Molecules. When, at the onset of my research on freeon dynamics, I told Norman Hackerman, a former office-mate and at that time president of the University of Texas, that I had an idea for a novel way to do quantum mechanics but that I did not know whether I would be able to acquire the necessary... 

In this, my third contribution, I apply freeon dynamics to problems of interest in chemistry and physics and compare with the results obtained by the spin paradigm. In particular I will apply freeon dynamics to the following "spin phenomena" i) spin exchange, ii) spin superexchange, iii) spin polarization, iii) spin density, iv) high-and low-spin states of the transition-metal ions, v) the periodic table, vi) ferromagnetism, vii) spin waves and viii) high-Tc superconductivity. 

Freeon dynamics provides a dynamically-correct replacement for the faulty spin paradigm. In particular its freeon Gel fand diagrams are a dynamically correct replacement for spin arrows as a "primitive pattern of understanding". 

In this section the simplicity of freeon dynamics is illustrated by its application to polyenes [6]. Here I relate molecular-orbital Gel fand states to atomic-orbital Gel fand states and then relate the atomic-orbital Gel fand states to valence bond states. Note that this construction provides a theoretical basis for the Rumer rule i.e., for the number of linearly independent valence bond states. We then use this freeon dynamics to explicate the spin paradigm. 

Benzene played an important role in my development of freeon dynamics. I knew, by the Rumer rule, that benzene had five canonical structures (i. e., five linearly independent wave functions). These are the two Kekule structures and the three Dewar structures. From this I surmised that the singlet IRS for N = M = 6 should be of five dimensions. On consulting the symmetric group textbooks I... 

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