Rudy's D.F.T. Page



Density Functional Theory is non-perturbative way of solving the quantum many body problem. The approach relies on the observation that ground state energy of any quantum system is uniquely determined by the particle density. Traditionally, we start with some external potential, solve for a wave-function, and then using the wave-function, calculate observable properties. D.F.T tells us that we can, in principle, start with a density and solve for a potential. This observation suggests a natural scheme by which we can more readily analyze quantum systems. We map the original system to a non-interacting system with the same density but a different external potential. It is relatively easy to solve this non-interacting problem and to recover many useful physical properties like the total energy. The only part of the energy which must be approximated is the exchange correlation contribution. For the most part, finding better approximations to this exchange correlation energy is the business of DFT. The DFT scheme is in contrast to more costly schemes which require complicated Green's functions or many particle wave equations to determine the energy. Like D.F.T. these traditional methods are rigorous in principle, but applying these other methods is often prohibitively slow and produces more information than is needed to obtain useful physical quantities.



In my opinion, several common misconceptions about DFT are:
  • LDA is DFT. No, the local density approximation is an approximation to DFT.
  • Exact DFT approximates the many body effects in a local way. No, the exact EXC is as complicated and non-local as all the many body effects!
  • The exact KS potential must be nonlocal. No, it's local because it is the functional derivative of Exc!
  • DFT does not work for excited states. Not exactly true, see the Runge-Gross theorem.
  • DFT gives poor band gaps. Not known, little is known about the exact derivative discontinuity; it might even fortuitously vanish.

    For more information about D.F.T. see my advisor's homepage .

    REFERS.TXT is a reasonably complete list of all the major references in Density Functional Theory.

    My research notes are unavailable to the general public. Sorry.

    For D.F.T. homework solutions, see D.F.T. Solutions Manual . You will need a password to get these solutions. To get that, you'll need my permission. Write and tell me why tou need to use these solutions.



    My Current Research Projects
    The Infinite Coupling Limit The exchange-correlation energy of an electronic system can be written as an integral over the coupling constant, from zero to one, at fixed density (the adiabatic connection formula). A model, strictly correalted electrons (SCE), has been propsed for the behavior of the integrand in the limit of infinite coupling strength. We investigate the Hooke's atom in this limit. This analysis test the SCE hypothesis and reveals insights into the highly correlated limit.
    Insulator Band Gaps from Exact Exchange Calculations It has long been known that DFT band gaps should not agree with the experimental values. This is due to a disconitinuity in the exact functional as the number of electrons changes. However, it has been shown that using exact exchange along with LDA correlation does, in fact, give results close to the experimental values. The reason for this is yet unknown. To examine whether this is an accident or not, we are performing a series of calculations on Van der Waals insulators and ionic crystals.
    Spin Scaling Uniform scaling of the electronic density is a fundamental and useful concept in Density Functional Theory. Though unusual, it is useful to study systems in which only one spin channel is scaled. We consider some general properties of spin scaling transformation and look at the performance of existing functionals on various spin scaled atoms. Such scaling results contain information which may be useful for the improvement of present functional approximations for Ec.
    An Hybrid Exchange Energy Density Functional Hybrid density functionals have produced more accurate results in D.F.T. by a factor of three. It is interesting to consider whether a hybrid scheme would work else where. For example, it would be nice to hybridize the exchange potentials so that they have the correct asymptotic behavior yet retain the same energetic behavior. Several schemes have been introduced to make hybrid potentials. Typically, these potentials are not functional derivatives of an energy functional and thereby make little sense. We are trying to devise a scheme to hybridize the exchange energy density so that the corrected potential is a functional derivative.


    My e-mail address is: rmagyar@graviton.rutgers.edu.

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