Biomedical subjects

Jianmin Tao

Publications and source records attributed to Jianmin Tao.

6 recordsLinked to original sources

PubMed2006

Time-dependent density-functional theory beyond the local-density approximation.

Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.

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PubMed2005

Nonempirical construction of current-density functionals from conventional density-functional approximations.

Density-functional approximations for the exchange-correlation energy Exc[n] of a many-electron ground state are highly developed and widely useful. When a paramagnetic current jp(r) is present, Vignale and Rasolt have extended the Kohn-Sham theorems and presented an additive correction valid to second order in the gauge-invariant vorticity nu=Delta x (jp/n):Exc[n, jp]=Exc[n, jp=0] + DeltaE(VR)(xc)[n, nu]. Apart from spin-polarization effects, their correction is unambiguous for a generalized gradient approximation (GGA). But for a meta-GGA (MGGA), one needs to know how to go back from the orbital kinetic energy density tau([n, jp];r) to tau([n,0];r); we show how to do this here. Numerical tests on the degeneracies for open-shell atoms show that current-density corrections reduce the error of GGA from 2 to 1 kcal/mol, and of MGGA from 5 to 2 kcal/mol.

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PubMed2005

Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits.

We present the case for the nonempirical construction of density functional approximations for the exchange-correlation energy by the traditional method of "constraint satisfaction" without fitting to data sets, and present evidence that this approach has been successful on the first three rungs of "Jacob's ladder" of density functional approximations [local spin-density approximation (LSD), generalized gradient approximation (GGA), and meta-GGA]. We expect that this approach will also prove successful on the fourth and fifth rungs (hyper-GGA or hybrid and generalized random-phase approximation). In particular, we argue for the theoretical and practical importance of recovering the correct uniform density limit, which many semiempirical functionals fail to do. Among the beyond-LSD functionals now available to users, we recommend the nonempirical Perdew-Burke-Ernzerhof (PBE) GGA and the nonempirical Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA, and their one-parameter hybrids with exact exchange. TPSS improvement over PBE is dramatic for atomization energies of molecules and surface energies of solids, and small or moderate for other properties. TPSS is now or soon will be available in standard codes such as GAUSSIAN, TURBOMOLE, NWCHEM, ADF, WIEN, VASP, etc. We also discuss old and new ideas to eliminate the self-interaction error that plagues the functionals on the first three rungs of the ladder, bring up other related issues, and close with a list of "do's and don't's" for software developers and users.

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PubMed2005

Test of a nonempirical density functional: short-range part of the van der Waals interaction in rare-gas dimers.

It is known that the nonempirical generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) provides a much more realistic description of the short-range part of the van der Waals (vdW) interaction than does the local spin density (LSD) approximation. In the present work, the ability of the higher-level nonempirical meta-GGA of Tao, Perdew, Staroverov, and Scuseria (TPSS) to describe vdW interaction is tested self-consistently in ten rare-gas dimers with Z< or =36. The one-parameter hybrid version (TPSSh) of the TPSS exchange-correlation functional is also included in this test. Calculations show that both TPSS and TPSSh functionals correctly yield vdW bonds in these dimers and significantly improve the prediction of bond lengths, binding energies, and harmonic vibrational frequencies over LSD. The rather close agreement of TPSS with PBE for these dimers confirms a principle of the TPSS construction: preservation of the PBE large-gradient behavior. More importantly, it suggests that TPSS can serve as a platform on which to construct a still-higher level of nonempirical functionals. Compared with the PBE GGA, TPSS, and TPSSh yield a slightly weaker binding. As for normally bonded molecules, TPSSh yields the most accurate vibrational frequencies. The typically too-long bond lengths and too-small binding energies of TPSS meta-GGA suggest the need for some long-range vdW interaction correction even in this class of systems. The effect of basis-set superposition error on the calculated properties of these vdW systems is investigated. We also show that the relatively strong anharmonic effects in the rare-gas dimers are described remarkably well by the Morse potential.

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PubMed2004

Meta-generalized gradient approximation: explanation of a realistic nonempirical density functional.

Tao, Perdew, Staroverov, and Scuseria (TPSS) have constructed a nonempirical meta-generalized gradient approximation (meta-GGA) [Phys. Rev. Lett. 91, 146401 (2003)] for the exchange-correlation energy, imposing exact constraints relevant to the paradigm densities of condensed matter physics and quantum chemistry. Results of their extensive tests on molecules, solids, and solid surfaces are encouraging, suggesting that this density functional achieves uniform accuracy for diverse properties and systems. In the present work, this functional is explained and details of its construction are presented. In particular, the functional is constructed to yield accurate energies under uniform coordinate scaling to the low-density or strong-interaction limit. Its nonlocality is displayed by plotting the factor F(xc) that gives the enhancement relative to the local density approximation for exchange. We also discuss an apparently harmless order-of-limits problem in the meta-GGA. The performance of this functional is investigated for exchange and correlation energies and shell-removal energies of atoms and ions. Non-self-consistent molecular atomization energies and bond lengths of the TPSS meta-GGA, calculated with GGA orbitals and densities, agree well with those calculated self-consistently. We suggest that satisfaction of additional exact constraints on higher rungs of a ladder of density functional approximations can lead to further progress.

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PubMed2003

Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids.

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.

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