Back to the exchange term

The long-range effects discussed so far result from the Coulomb interaction in the Fock equation for a regular polymer. There is, however, also an exchange contri- 

Electronic Motion in the Mean Field Periodic Systems 

In eontrast, the only guarantee of a satisfactory convergence of the sum ovei 

A metallic system is notorious for its HOMO-LUMO quasidegeneracy, therefore, we began to suspect that when the HOMO-LUMO gap decreases, the P p coefficients do not decay with j. 

Such things are most clearly seen when the simplest example is taken, and the hydrogen molecule at long intemuclear distance is the simplest prototype of a metal. Indeed, this is a system with half-filled orbital energy levels when the LCAO MO method is applied (in the simplest case two atomic orbitals). Note that, after 

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Time-dependent density functional theory (TDDFT) as a complete formalism [7] is a more recent development, although the historical roots date back to the time-dependent Thomas-Fermi model proposed by Bloch [8] as early as 1933. The first and rather successful steps towards a time-dependent Kohn-Sham (TDKS) scheme were taken by Peuckert [9] and by Zangwill and Soven [10]. These authors treated the linear density response of rare-gas atoms to a time-dependent external potential as the response of non-interacting electrons to an effective time-dependent potential. In analogy to stationary KS theory, this effective potential was assumed to contain an exchange-correlation (xc) part, r,c(r, t), in addition to the time-dependent external and Hartree terms ... 

Attempts to represent the three-body interactions for water in terms of an analytic function fitted to ab initio results date back to the work of dementi and Corongiu [191] and Niesar et al. [67]. These authors used about 200 three-body energies computed at the Hartree-Fock level and fitted them to parametrize a simple polarization model in which induced dipoles were generated on each molecule by the electrostatic field of other molecules. Thus, the induction effects were distorted in order to describe the exchange effects. The three-body potentials obtained in this way and their many-body polarization extensions have been used in simulations of liquid water. We know now that the two-body potentials used in that work were insufficiently accurate for a meaningful evaluation of the role of three-body effects. 

Carbon dioxide is constantly exchanged between the ocean and atmosphere. Each year the ocean and atmosphere exchange about 350 Gt CO2, with a net ocean uptake currently of about 8 Gt CO2. Because of this exchange, questions arise as to how effective ocean sequestration will be at keeping the CO2 out of the atmosphere. Specifically, is the sequestration permanent, and if not, how fast does the CO2 leak back to the atmosphere. Because there has been no long-term CO2 direct-injection experiment in the ocean, the long-term effectiveness of direct CO2 injection must be predicted based on observations of other oceanic tracers (e.g., radiocarbon) and on computer models of ocean circulation and chemistry. 

GO2 absorbed by the ocean through gas exchange has a variety of fates. Physical and biological mechanisms can return the GO2 back to the atmosphere or transfer carbon from the surface ocean to the deep ocean and ocean sediments through several transport processes termed the solubility , biological , and carbonate pumps. 

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