Abstract
Further progress in pair-density functional theory (sometimes called 2-DFT) hinges on the development of computationally facile and quantitatively accurate models for the kinetic energy functional. In this paper we perform computational tests for two of the simplest models, the generalized Weizsäcker kinetic energy functional and its spin-resolved extension. Both of these models perform very poorly for atoms. The higher-order Weizsäcker functionals (based on the three-electron distribution function) perform better, but are still not successful. This suggests that an alternative approach for designing kinetic energy functionals of the pair density is needed.
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Becke A.D.: Phys. Rev. A 38, 3098 (1988)
Lee C., Yang W., Parr R.G.: Phys. Rev. B 37, 785 (1988)
Miehlich B., Savin A., Stoll H., Preuss H.: Chem. Phys. Lett. 157(3), 200 (1989)
Becke A.D.: J. Chem. Phys. 98, 5648 (1993)
Gorling A., Levy M.: Phys. Rev. B 47, 13105 (1993)
Gorling A., Levy M.: Phys. Rev. A 50, 196 (1994)
Tao J.M., Perdew J.P., Staroverov V.N., Scuseria G.E.: Phys. Rev. Lett. 91, 146401 (2003)
Staroverov V.N., Scuseria G.E., Tao J., Perdew J.P.: Phys. Rev. B 69, 075102 (2004)
Perdew J.P., Ruzsinszky A., Tao J.M., Staroverov V.N., Scuseria G.E., Csonka G.I.: J. Chem. Phys. 123, 062201 (2005)
Mori-Sanchez P., Wu Q., Yang W.T.: J. Chem. Phys. 123(6), 062204 (2005)
Ivanov S., Bartlett R.J.: J. Chem. Phys. 114, 1952 (2001)
Grabowski I., Hirata S., Ivanov S., Bartlett R.J.: J. Chem. Phys. 116, 4415 (2002)
Bartlett R.J., Lotrich V.F., Schweigert I.V.: J. Chem. Phys. 123(6), 062205 (2005)
Cohen A.J., Mori-Sanchez P., Yang W.T.: Science 321, 792 (2008)
Mori-Sanchez P., Cohen A.J., Yang W.T.: Phys. Rev. Lett. 102, 066403 (2009)
Ziesche P.: Phys. Lett. A 195, 213 (1994)
Ziesche P.: Int. J. Quantum Chem. 60, 1361 (1996)
Ayers P.W.: J. Math. Phys. 46, 062107 (2005)
Ayers P.W.: J. Math. Chem. 44, 311 (2008)
Davidson E.R.: Chem. Phys. Lett. 246, 209 (1995)
Gonis A., Schulthess T.C., Turchi P.E.A., Vanek J.: Phys. Rev. B 56, 9335 (1997)
Gonis A., Schulthess T.C., Vanek J., Turchi P.E.A.: Phys. Rev. Lett. 77, 2981 (1996)
Nagy A.: J. Chem. Phys. 125, 184104 (2006)
Nagy A., Amovilli C.: J. Chem. Phys. 121, 6640 (2004)
Nagy A.: Phys. Rev. A 66, 022505 (2002)
Nagy A., Amovilli C.: J. Chem. Phys. 128, 114115 (2008)
Ayers P.W., Davidson E.R.: Int. J. Quantum Chem. 106, 1487 (2006)
Ayers P.W., Davidson E.R.: Adv. Chem. Phys. 134, 443 (2007)
Ayers P.W., Golden S., Levy M.: J. Chem. Phys. 124, 054101 (2006)
Ayers P.W., Levy M.: J. Chem. Sci. 117, 507 (2005)
Ayers P.W., Levy M.: Chem. Phys. Lett. 416, 211 (2005)
Ayers P.W.: Phys. Rev. A 74, 042502 (2006)
Furche F.: Phys. Rev. A 70, 022514 (2004)
Higuchi M., Higuchi K.: Physica B-Condensed Matter 387, 117 (2007)
Higuchi M., Higuchi K.: Phys. Rev. A 75, 042510 (2007)
Higuchi M., Miyasita M., Kodera M., Higuchi K.: J. Phys. Condens. Matter 19, 365219 (2007)
Higuchi M., Miyasita M., Kodera M., Higuchi K.: J. Magn. Magn. Mater. 310, 990 (2007)
Pistol M.E.: Chem. Phys. Lett. 417, 521 (2006)
Pistol M.E.: Chem. Phys. Lett. 422, 363 (2006)
Pistol M.E.: Chem. Phys. Lett. 431, 216 (2006)
Pistol M.E.: Chem. Phys. Lett. 400, 548 (2004)
Pistol M.E.: Chem. Phys. Lett. 449, 208 (2007)
Kristyan S.: J. Mol. Struct. Theochem 858, 1 (2008)
Samvelyan S.K.: Int. J. Quantum Chem. 65(2), 127 (1997)
Higuchi K., Higuchi M.: Phys. Rev. B 69, 165118 (2004)
Higuchi K., Higuchi M.: J. Magn. Magn. Mater. 272(76), 659 (2004)
Higuchi M., Higuchi K.: Phys. Rev. B 69, 035113 (2004)
Levy M., Ziesche P.: J. Chem. Phys. 115, 9110 (2001)
Higuchi M., Higuchi K.: Phys. Rev. B 78, 125101 (2008)
Higuchi K., Higuchi M.: J. Phys. Condens. Matter 21, 064206 (2009)
Cuevas-Saavedra R., Ayers P.W.: Int. J. Quantum Chem. 109, 1699 (2009)
Pistol M.E., Almbladh C.O.: Chem. Phys. Lett. 480, 136 (2009)
Nagy A., Romera E.: Chem. Phys. Lett. 490, 242 (2010)
Higuchi M., Miyasita M., Higuchi K.: Int. J. Quantum Chem. 110, 2283 (2010)
Higuchi K., Higuchi M.: Phys. Rev. B 82, 155135 (2010)
Ayers P.W., Fuentealba P.: Phys. Rev. A 80, 032510 (2009)
Kryachko E.S., Ludena E.V.: Phys. Rev. A 43, 2179 (1991)
Ludena E.V.: J. Mol. Struct. Theochem 709, 25 (2004)
Ayers P.W., Liu S.B.: Phys. Rev. A 75, 022514 (2007)
Ludena E.V., Illas F., Ramirez-Solis A.: Int. J. Mod. Phys. B 22, 4398 (2008)
Weizsacker C.F.v.: Z.Physik 96, 431 (1935)
Acharya P.K., Bartolotti L.J., Sears S.B., Parr R.G.: Proc. Natl. Acad. Sci. 77, 6978 (1980)
Sears S.B., Parr R.G., Dinur U.: Isr. J. Chem. 19(1–4), 165 (1980)
D. Chakraborty, P.W. Ayers, Derivation of generalized von Weizsäcker kinetic energies from quasiprobability distribution functions, in Statistical Complexity: Applications in Electronic Structure, ed. by K. Sen (Springer, accepted)
Koga T., Tatewaki H., Thakkar A.J.: Phys. Rev. A 47, 4510 (1993)
http://www.unb.ca/fredericton/science/chem/ajit/f_download.htm
Clementi E., Roetti C.: Roothaan-Hartree-Fock Atomic Wavefunctions: Basis Functions and Their Coefficients for Ground and Certain Excited States of Neutral and Ionized Atoms, Z<=54. Academic, New York (1974)
Davidson E.R.: Reduced Density Matrices in Quantum Chemistry. Academic Press, New York (1976)
Coleman A.J., Yukalov V.I.: Reduced Density Matrices: Coulson’s Challenge. Springer, Berlin (2000)
March N.H., Santamaria R.: Int. J. Quantum Chem. 39(4), 585 (1991)
D. Chakraborty, P. W. Ayers. doi:10.1007/s10910-011-9861-0
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Chakraborty, D., Ayers, P.W. Failure of the Weizsäcker kinetic energy functional for one-, two-, and three-electron distribution functions. J Math Chem 49, 1810–1821 (2011). https://doi.org/10.1007/s10910-011-9860-1
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DOI: https://doi.org/10.1007/s10910-011-9860-1