We consider the implications of a nonintegral occupation number of 3d and 4? electrons in a 3d transition element or compound, in a configuration such as 3d n+x 4:S 2~x , where x is a variable. In the energy-band problem, such fractional occupation numbers are common, but we pay particular attention to the atomic problem. We apply Hartree-Fock procedures to such a problem, using the formula for the average energy of all multiplets associated with the configuration, and vary not only the orbitals but the occupation numbers to minimize the energy. We consider both the non-spin-polarized and spin-polarized cases. This procedure, which is more general than the ordinary Hartree-Fock procedure, we shall call the hyper-Hartree-Fock method (HHF). We have carried through HHF calculations for fractional occupation numbers in the Co and Ni atoms, and have also treated these atoms by several schemes involving approximate statistical exchanges. We compare the results with the atomic spectra of these atoms. We find that the condition for minimum energy, in the HHF scheme, can be put in a form stating that one-electron energies E/' of the 3d and 4s orbitals must be equal; these quantities E/, which we call modified one-electron energies, are different from the ordinary one-electron energies Ei of Hartree-Fock theory, involving only one-half the self-energy correction met with in HF theory. These quantities E/, rather than the ordinary one-electron energies Ei, are the quantities which have the properties desired for one-electron energies in energy-band theory and Fermi statistics: The change in the total energy of the system, when an infinitesimal fraction of the electrons shifts from one orbital to another, rigorously equals the net change in the quantities E t f for the electrons which have made the shift. We show that the ordinary one-electron eigenvalues of the Kohn-Sham statistical exchange method form fairly good approximations to these HHF quantities E/, which explains why energy-band calculations using that exchange have had considerable success in studies of transition-element crystals and compounds. Preliminary mention is made of calculations under way by one of the authors (TMW) on the antiferromagnetic crystals MnO and NiO, in which an exchange potential set up according to the ideas presented here leads to energy bands describing correctly the electrical, magnetic, and optical behavior of these crystals, including the insulating properties and the crystal-field splitting of the 3d orbitals into the e 0 and h a components. r , , rr, . i J ences to all that earlier work here. Their general ","_ .. conclusion is that the occupation 3d n+1 As leads to energy * Work performed under the auspices of the National Science UJ-U^ , .,i . ^ ^ Foundation and the U.S. Atomic Energy Commission. bands ln better agreement with experiment than 1 J. C. Slater, T. M. Wilson, and J. H. Wood, Phys. Rev. 179, 3dHs 2 , but they leave open the question as to whether 28 (1969) The reader's attention is also called to the interesting a nonin...

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Self-consistent calculations of theCu + ion have been carried out using five different methods of approximating the Hartree-Fock exchange. These calculations have been compared with Hartree's Cu + calculation to test the accuracy of the various approximations and to interpret their interrelations. The best results were obtained from two quite different methods. The first, suggested by Uberman with modifications which we have introduced, uses a different local exchange potential for each orbital and gives a very good approximation to the Hartree-Fock method, but with considerable computational difficulty. The second amounts to multiplying the local potential proportional to the J power of the electronic charge density, suggested by the senior author in 1951, by a constant factor a chosen to minimize the total energy. This second method is much simpler to apply than the first and gives very nearly as good orbitals, as well as a very good total energy, but gives poor one-electron energies for the x-ray levels. The reasons for the different results are discussed. The latter method, which has been empirically arrived at by a number of the workers in the energy-band field, is probably the most useful one for practical calculation.

Experimental measurements and theoretical calculations are reported which may resolve some of the remaining difficulties associated with photoemission from anion vacancies in thermochemically reduced MgO crystals. The intensities of the 2.3and 3.2-eV luminescence bands are found to be strongly influenced by both the concentrations of H ioris and anion vacancies present, and also by the intensity of the -5.0-eV exciting light. Theoretical calculations predict that for a 'A~g relaxation of the surrounding ions the 'T&"and T&"electronic states of the F center are almost degenerate and -0.05 eV above the 'A~g state. The 'Tj"-+'A&~and the T&"~'A&~transition energies are predicted to be 2.2 and 2.9 eV, respectively.

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BackgroundAging involves multiple biologically complex processes characterized by a decline in cellular homeostasis over time leading to a loss and impairment of physiological integrity and function. Specific cellular hallmarks of aging include abnormal gene expression patterns, shortened telomeres and associated biological dysfunction. Like all organs, the lung demonstrates both physiological and structural changes with age that result in a progressive decrease in lung function in healthy individuals. Cigarette smoking accelerates lung function decline over time, suggesting smoking accelerates aging of the lung. Based on this data, we hypothesized that cigarette smoking accelerates the aging of the small airway epithelium, the cells that take the initial brunt of inhaled toxins from the cigarette smoke and one of the primary sites of pathology associated with cigarette smoking.MethodsUsing the sensitive molecular parameters of aging-related gene expression and telomere length, the aging process of the small airway epithelium was assessed in age matched healthy nonsmokers and healthy smokers with no physical manifestation of lung disease or abnormalities in lung function.ResultsAnalysis of a 73 gene aging signature demonstrated that smoking significantly dysregulates 18 aging-related genes in the small airway epithelium. In an independent cohort of male subjects, smoking significantly reduced telomere length in the small airway epithelium of smokers by 14% compared to nonsmokers.ConclusionThese data provide biologic evidence that smoking accelerates aging of the small airway epithelium.Electronic supplementary materialThe online version of this article (doi:10.1186/s12931-014-0094-1) contains supplementary material, which is available to authorized users.

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