
NSF Org: |
DMR Division Of Materials Research |
Recipient: |
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Initial Amendment Date: | May 13, 2005 |
Latest Amendment Date: | May 26, 2007 |
Award Number: | 0501588 |
Award Instrument: | Continuing Grant |
Program Manager: |
Daryl Hess
dhess@nsf.gov (703)292-4942 DMR Division Of Materials Research MPS Directorate for Mathematical and Physical Sciences |
Start Date: | June 15, 2005 |
End Date: | May 31, 2009 (Estimated) |
Total Intended Award Amount: | $0.00 |
Total Awarded Amount to Date: | $372,000.00 |
Funds Obligated to Date: |
FY 2006 = $124,000.00 FY 2007 = $124,000.00 |
History of Investigator: |
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Recipient Sponsored Research Office: |
6823 SAINT CHARLES AVE NEW ORLEANS LA US 70118-5665 (504)865-4000 |
Sponsor Congressional District: |
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Primary Place of Performance: |
6823 SAINT CHARLES AVE NEW ORLEANS LA US 70118-5665 |
Primary Place of
Performance Congressional District: |
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Unique Entity Identifier (UEI): |
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Parent UEI: |
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NSF Program(s): | CONDENSED MATTER & MAT THEORY |
Primary Program Source: |
app-0106 app-0107 |
Program Reference Code(s): |
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Program Element Code(s): |
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Award Agency Code: | 4900 |
Fund Agency Code: | 4900 |
Assistance Listing Number(s): | 47.049 |
ABSTRACT
TECHNICAL EXPLANATION The density functional theory of Kohn and Sham is now the most widely-used method of electronic structure calculation in both condensed matter physics and quantum chemistry. The many users of this theory make it the citation leader of all physics. To calculate the nuclear framework, ground state energy, and electron spin densities of an atom, molecule, bio-molecule, solid, surface, or nanostructure, it is only necessary to solve self-consistent quantum mechanical one-electron equations. The results would be exact if the exchange-correlation energy as a functional of the electron density were known exactly.
A ladder of approximations to the exchange-correlation energy, on which higher rungs are more complex and more accurate, may lead up to the reliable computer design of new materials, chemicals, pharmaceuticals, devices, and processes. The first three rungs of this ladder have now been completed by first-principles or fully non-empirical constructions that satisfy known exact constraints on the density functional: the local spin density approximation (employing only the local spin densities as local ingredients), the generalized gradient approximation or GGA (employing also the density gradients), and the meta-GGA (which introduces the orbital kinetic energy density).
This proposal addresses the fourth rung or hyper-GGA (which introduces the exact exchange energy density), and the fifth rung or generalized random phase approximation (which introduces the unoccupied Kohn-Sham orbitals). On the fourth rung, a local hybrid functional is proposed which preserves all the exact constraints satisfied by the fully non-empirical Tao-Perdew-Staroverov-
Scuseria meta-GGA, while adding semi-empirical refinements that should further improve the description of molecules. The need for empiricism on the fourth rung is explained. On the fifth rung, a fully non-empirical RPAE+ functional is proposed, based on the random phase approximation with higher-order exchange plus a meta-GGA correction for short-range correlation. RPAE+
satisfies essentially all known exact constraints. It includes full exact exchange, as well as the long-range van der Waals interaction which can be important for soft condensed matter and for bio-molecules. RPAE+ can also be used to construct realistic electron-ion pseudopotentials that speed up calculations.
The first three or four rungs of the ladder fail to be exact for one-electron densities (and that is the root of many related errors). The self-interaction correction of Perdew and Zunger 1981 fixes this problem, but seems to overcorrect in many-electron regions of space. A damping factor, involving the orbital kinetic energy density, is proposed to prevent this overcorrection. (The revised self-interaction correction is a U.S./Hungary research collaboration.)
A chemical reaction typically proceeds through or over an energy barrier at a "transition state". To predict the rate of the reaction, the barrier height must be calculated accurately. Barrier heights are seriously underestimated on the first three rungs of the ladder, but might be predicted usefully on the fourth rung or by application of the revised self-interaction correction.
Some residual constructions and tests will be made on the first three rungs. The optimized effective or Kohn-Sham potential will be constructed on the third and higher rungs, for comparison with the potential on the first two rungs. An orbital-free density functional for the kinetic energy will be sought, to speed up calculations for large systems.
This research involves the education of graduate and undergraduate students and the professional development of postdoctoral fellows.
NON-TECHNICAL EXPLANATION
This theoretical research will focus on further developing methods to calculate the electronic structure of atoms, molecules and solids. The research will have wide applications in a variety of fields including nanoscience. Collaborations will be carried out with researchers in Hungary. Students and postdoctoral associates will also be supported.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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