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Journal articles on the topic 'Ensemble density-functional theory'

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Author: Grafiati

Published: 25 May 2024

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1

Oliveira, L. N., E. K. U. Gross, and W. Kohn. "Ensemble-Density functional theory for excited states." International Journal of Quantum Chemistry 38, S24 (March 17, 1990): 707–16. http://dx.doi.org/10.1002/qua.560382470.

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2

Gould, Tim, and Stefano Pittalis. "Density-Driven Correlations in Ensemble Density Functional Theory: Insights from Simple Excitations in Atoms." Australian Journal of Chemistry 73, no. 8 (2020): 714. http://dx.doi.org/10.1071/ch19504.

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Ensemble density functional theory extends the usual Kohn-Sham machinery to quantum state ensembles involving ground- and excited states. Recent work by the authors [Phys. Rev. Lett. 119, 243001 (2017); 123, 016401 (2019)] has shown that both the Hartree-exchange and correlation energies can attain unusual features in ensembles. Density-driven (DD) correlations – which account for the fact that pure-state densities in Kohn-Sham ensembles do not necessarily reproduce those of interacting pure states – are one such feature. Here we study atoms (specifically S–P and S–S transitions) and show that the magnitude and behaviour of DD correlations can vary greatly with the variation of the orbital angular momentum of the involved states. Such estimations are obtained through an approximation for DD correlations built from relevant exact conditions, Kohn-Sham inversion, and plausible assumptions for weakly correlated systems.

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3

Ulbrich, Michael, Zaiwen Wen, Chao Yang, Dennis Klöckner, and Zhaosong Lu. "A Proximal Gradient Method for Ensemble Density Functional Theory." SIAM Journal on Scientific Computing 37, no. 4 (January 2015): A1975—A2002. http://dx.doi.org/10.1137/14098973x.

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4

Pribram-Jones, Aurora, Zeng-hui Yang, John R. Trail, Kieron Burke, Richard J. Needs, and Carsten A. Ullrich. "Excitations and benchmark ensemble density functional theory for two electrons." Journal of Chemical Physics 140, no. 18 (May 14, 2014): 18A541. http://dx.doi.org/10.1063/1.4872255.

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5

White, J. A., A. González, F. L. Román, and S. Velasco. "Density-Functional Theory of Inhomogeneous Fluids in the Canonical Ensemble." Physical Review Letters 84, no. 6 (February 7, 2000): 1220–23. http://dx.doi.org/10.1103/physrevlett.84.1220.

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6

Hernando, J. A. "Density functional theory in the canonical ensemble: I. General formalism." Journal of Physics: Condensed Matter 14, no. 3 (December 24, 2001): 303–17. http://dx.doi.org/10.1088/0953-8984/14/3/302.

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7

Heinonen, O., M. I. Lubin, and M. D. Johnson. "Ensemble Density Functional Theory of the Fractional Quantum Hall Effect." Physical Review Letters 75, no. 22 (November 27, 1995): 4110–13. http://dx.doi.org/10.1103/physrevlett.75.4110.

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8

Gonżález, A., J. A. White, F. L. Román, and S. Velasco. "Density functional theory of fluids in the isothermal-isobaric ensemble." Journal of Chemical Physics 120, no. 22 (June 8, 2004): 10634–39. http://dx.doi.org/10.1063/1.1739395.

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9

Lubin, M. I., O. Heinonen, and M. D. Johnson. "Spin-ensemble density-functional theory for inhomogeneous quantum Hall systems." Physical Review B 56, no. 16 (October 15, 1997): 10373–82. http://dx.doi.org/10.1103/physrevb.56.10373.

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10

Heinonen, O., M. I. Lubin, and M. D. Johnson. "Ensemble density functional theory for inhomogeneous fractional quantum hall systems." International Journal of Quantum Chemistry 60, no. 7 (1996): 1443–55. http://dx.doi.org/10.1002/(sici)1097-461x(1996)60:7<1443::aid-qua26>3.0.co;2-3.

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11

Lee, Seunghoon, Woojin Park, Hiroya Nakata, Michael Filatov, and Cheol Ho Choi. "Recent advances in ensemble density functional theory and linear response theory for strong correlation." Bulletin of the Korean Chemical Society 43, no. 1 (November 7, 2021): 17–34. http://dx.doi.org/10.1002/bkcs.12429.

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12

Gedeon, Johannes, Jonathan Schmidt, Matthew J. P. Hodgson, Jack Wetherell, Carlos L. Benavides-Riveros, and Miguel A. L. Marques. "Machine learning the derivative discontinuity of density-functional theory." Machine Learning: Science and Technology 3, no. 1 (December 15, 2021): 015011. http://dx.doi.org/10.1088/2632-2153/ac3149.

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Abstract Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit dependency of the functionals on the particle number or the infamous derivative discontinuity at integer particle numbers. Here we propose a solution to these problems by training a neural network as the universal functional of density-functional theory that (a) depends explicitly on the number of particles with a piece-wise linearity between the integer numbers and (b) reproduces the derivative discontinuity of the exchange-correlation energy. This is achieved by using an ensemble formalism, a training set containing fractional densities, and an explicitly discontinuous formulation.

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13

von Lilienfeld, O. Anatole, and Mark E. Tuckerman. "Molecular grand-canonical ensemble density functional theory and exploration of chemical space." Journal of Chemical Physics 125, no. 15 (October 21, 2006): 154104. http://dx.doi.org/10.1063/1.2338537.

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14

Filatov, Michael, Seunghoon Lee, Hiroya Nakata, and Cheol Ho Choi. "Computation of Molecular Electron Affinities Using an Ensemble Density Functional Theory Method." Journal of Physical Chemistry A 124, no. 38 (September 8, 2020): 7795–804. http://dx.doi.org/10.1021/acs.jpca.0c06976.

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15

Gould, Tim. "Approximately Self-Consistent Ensemble Density Functional Theory: Toward Inclusion of All Correlations." Journal of Physical Chemistry Letters 11, no. 22 (November 10, 2020): 9907–12. http://dx.doi.org/10.1021/acs.jpclett.0c02894.

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16

Filatov, Michael, Seunghoon Lee, and Cheol Ho Choi. "Computation of Molecular Ionization Energies Using an Ensemble Density Functional Theory Method." Journal of Chemical Theory and Computation 16, no. 7 (May 18, 2020): 4489–504. http://dx.doi.org/10.1021/acs.jctc.0c00218.

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17

Pastorczak, Ewa, and Katarzyna Pernal. "A road to a multiconfigurational ensemble density functional theory without ghost interactions." International Journal of Quantum Chemistry 116, no. 11 (February 19, 2016): 880–89. http://dx.doi.org/10.1002/qua.25107.

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18

Farid, Behnam. "From the density-functional theory to `density-free' approximation schemes; a one-particle-ensemble formalism." Journal of Physics: Condensed Matter 8, no. 35 (August 26, 1996): 6337–55. http://dx.doi.org/10.1088/0953-8984/8/35/005.

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19

Gould, Tim, Stefano Pittalis, Julien Toulouse, Eli Kraisler, and Leeor Kronik. "Asymptotic behavior of the Hartree-exchange and correlation potentials in ensemble density functional theory." Physical Chemistry Chemical Physics 21, no. 36 (2019): 19805–15. http://dx.doi.org/10.1039/c9cp03633d.

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We show that the Hartree-exchange and correlation potentials of ensemble systems can have unexpected features, including non-vanishing asymptotic constants and non-trivial screening of electrons. These features are demonstrated here on Li, C, and F.

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20

Moon, Kevin, Kumar Sricharan, Kristjan Greenewald, and Alfred Hero. "Ensemble Estimation of Information Divergence †." Entropy 20, no. 8 (July 27, 2018): 560. http://dx.doi.org/10.3390/e20080560.

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Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The theory of optimally weighted ensemble estimation is generalized to derive a divergence estimator that achieves the parametric rate when the densities are sufficiently smooth. Guidelines for the tuning parameter selection and the asymptotic distribution of this estimator are provided. Based on the theory, an empirical estimator of Rényi-α divergence is proposed that greatly outperforms the standard kernel density plug-in estimator in terms of mean squared error, especially in high dimensions. The estimator is shown to be robust to the choice of tuning parameters. We show extensive simulation results that verify the theoretical results of our paper. Finally, we apply the proposed estimator to estimate the bounds on the Bayes error rate of a cell classification problem.

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21

Chattaraj, P. K., S. Sengupta, and A. Poddar. "Quantum fluid density functional theory of chemical reactivity in a two-state ensemble." Journal of Molecular Structure: THEOCHEM 501-502 (April 2000): 339–52. http://dx.doi.org/10.1016/s0166-1280(99)00444-3.

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22

White, J. A., and A. Gonz lez. "The extended variable space approach to density functional theory in the canonical ensemble." Journal of Physics: Condensed Matter 14, no. 46 (November 13, 2002): 11907–19. http://dx.doi.org/10.1088/0953-8984/14/46/302.

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23

Marzari, Nicola, David Vanderbilt, and M. C. Payne. "Ensemble Density-Functional Theory forAb InitioMolecular Dynamics of Metals and Finite-Temperature Insulators." Physical Review Letters 79, no. 7 (August 18, 1997): 1337–40. http://dx.doi.org/10.1103/physrevlett.79.1337.

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24

Senjean, Bruno, Erik D. Hedegård, Md Mehboob Alam, Stefan Knecht, and Emmanuel Fromager. "Combining linear interpolation with extrapolation methods in range-separated ensemble density functional theory." Molecular Physics 114, no. 7-8 (December 15, 2015): 968–81. http://dx.doi.org/10.1080/00268976.2015.1119902.

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25

von Lilienfeld, O. Anatole, and M. E. Tuckerman. "Alchemical Variations of Intermolecular Energies According to Molecular Grand-Canonical Ensemble Density Functional Theory." Journal of Chemical Theory and Computation 3, no. 3 (April 6, 2007): 1083–90. http://dx.doi.org/10.1021/ct700002c.

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26

Hirakawa, Teruo, Teppei Suzuki, David R. Bowler, and Tsuyoshi Miyazaki. "Canonical-ensemble extended Lagrangian Born–Oppenheimer molecular dynamics for the linear scaling density functional theory." Journal of Physics: Condensed Matter 29, no. 40 (September 1, 2017): 405901. http://dx.doi.org/10.1088/1361-648x/aa810d.

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27

Nygaard, Cecilie R., and Jeppe Olsen. "The energy, orbitals and electric properties of the ozone molecule with ensemble density functional theory." Molecular Physics 111, no. 9-11 (July 2013): 1259–70. http://dx.doi.org/10.1080/00268976.2013.810792.

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28

Filatov, Michael, Fang Liu, Kwang S. Kim, and Todd J. Martínez. "Self-consistent implementation of ensemble density functional theory method for multiple strongly correlated electron pairs." Journal of Chemical Physics 145, no. 24 (December 28, 2016): 244104. http://dx.doi.org/10.1063/1.4972174.

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29

Paragi, G., I. K. Gyémánt, and V. E. VanDoren. "Investigation of exchange-correlation potentials in ensemble density functional theory: parameter fitting and excitation energy." Journal of Molecular Structure: THEOCHEM 571, no. 1-3 (August 2001): 153–61. http://dx.doi.org/10.1016/s0166-1280(01)00561-9.

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30

Gould, Tim. "Toward routine Kohn–Sham inversion using the “Lieb-response” approach." Journal of Chemical Physics 158, no. 6 (February 14, 2023): 064102. http://dx.doi.org/10.1063/5.0134330.

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Kohn–Sham (KS) inversion, in which the effective KS mean-field potential is found for a given density, provides insights into the nature of exact density functional theory (DFT) that can be exploited for the development of density functional approximations. Unfortunately, despite significant and sustained progress in both theory and software libraries, KS inversion remains rather difficult in practice, especially in finite basis sets. The present work presents a KS inversion method, dubbed the “Lieb-response” approach, that naturally works with existing Fock-matrix DFT infrastructure in finite basis sets, is numerically efficient, and directly provides meaningful matrix and energy quantities for pure-state and ensemble systems. Some additional work yields potential. It thus enables the routine inversion of even difficult KS systems, as illustrated in a variety of problems within this work, and provides outputs that can be used for embedding schemes or machine learning of density functional approximations. The effect of finite basis sets on KS inversion is also analyzed and investigated.

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31

Filatov, Michael, Seunghoon Lee, and Cheol Ho Choi. "Description of Sudden Polarization in the Excited Electronic States with an Ensemble Density Functional Theory Method." Journal of Chemical Theory and Computation 17, no. 8 (July 28, 2021): 5123–39. http://dx.doi.org/10.1021/acs.jctc.1c00479.

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32

Alam, Md Mehboob, Killian Deur, Stefan Knecht, and Emmanuel Fromager. "Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states." Journal of Chemical Physics 147, no. 20 (November 28, 2017): 204105. http://dx.doi.org/10.1063/1.4999825.

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33

Filatov, Michael, Miquel Huix-Rotllant, and Irene Burghardt. "Ensemble density functional theory method correctly describes bond dissociation, excited state electron transfer, and double excitations." Journal of Chemical Physics 142, no. 18 (May 14, 2015): 184104. http://dx.doi.org/10.1063/1.4919773.

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34

Filatov, Michael, Fang Liu, and Todd J. Martínez. "Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism." Journal of Chemical Physics 147, no. 3 (July 21, 2017): 034113. http://dx.doi.org/10.1063/1.4994542.

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35

Franck, Odile, and Emmanuel Fromager. "Generalised adiabatic connection in ensemble density-functional theory for excited states: example of the H2 molecule." Molecular Physics 112, no. 12 (November 11, 2013): 1684–701. http://dx.doi.org/10.1080/00268976.2013.858191.

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36

Belleflamme, Fabian, Anna-Sophia Hehn, Marcella Iannuzzi, and Jürg Hutter. "A variational formulation of the Harris functional as a correction to approximate Kohn–Sham density functional theory." Journal of Chemical Physics 158, no. 5 (February 7, 2023): 054111. http://dx.doi.org/10.1063/5.0122671.

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Accurate descriptions of intermolecular interactions are of great importance in simulations of molecular liquids. We present an electronic structure method that combines the accuracy of the Harris functional approach with the computational efficiency of approximately linear-scaling density functional theory (DFT). The non-variational nature of the Harris functional has been addressed by constructing a Lagrangian energy functional, which restores the variational condition by imposing stationarity with respect to the reference density. The associated linear response equations may be treated with linear-scaling efficiency in an atomic orbital based scheme. Key ingredients to describe the structural and dynamical properties of molecular systems are the forces acting on the atoms and the stress tensor. These first-order derivatives of the Harris Lagrangian have been derived and implemented in consistence with the energy correction. The proposed method allows for simulations with accuracies close to the Kohn–Sham DFT reference. Embedded in the CP2K program package, the method is designed to enable ab initio molecular dynamics simulations of molecular solutions for system sizes of several thousand atoms. Available subsystem DFT methods may be used to provide the reference density required for the energy correction at near linear-scaling efficiency. As an example of production applications, we applied the method to molecular dynamics simulations of the binary mixtures cyclohexane-methanol and toluene-methanol, performed within the isobaric-isothermal ensemble, to investigate the hydrogen bonding network in these non-ideal mixtures.

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37

Perdew, John P., and Espen Sagvolden. "Exact exchange-correlation potentials in spin-density functional theory and their discontinuities at unit electron number." Canadian Journal of Chemistry 87, no. 10 (October 2009): 1268–72. http://dx.doi.org/10.1139/v09-057.

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The exact exchange-correlation potential of Kohn–Sham density functional theory is known to jump discontinuously by a spatial constant as the average electron number, N, crosses an integer in an open system of fluctuating electron number, with important physical consequences for charge transfers and band gaps. We have recently constructed an essentially exact exchange-correlation potential vxc for N electrons (0 ≤ N ≤ 2) in the presence of a –1/r external potential, i.e., for a ground ensemble of H+ ion, H atom, and H– ion densities. That construction illustrates the discontinuity at N = 1, where it equals IH – AH, the positive difference between the ionization energy and the electron affinity of the hydrogen atom. Here we construct the corresponding essentially exact spin-up and spin-down exchange-correlation potentials vxc,↑ and vxc,↓ of the Kohn–Sham spin-density functional theory, more commonly used for electronic structure calculations, for the ground ensemble with most-negative z-component of spin (or equivalently in the presence of a uniform magnetic field of infinitesimal strength). The potentials vxc, vxc,↑, and vxc,↓, which vanish as r → ∞ (except when N approaches an integer from above), are identical for 0 ≤ N ≤ 1 and for N = 2 but not for 1 < N < 2. We find that the majority or spin-down potential has a spatially constant discontinuity at N = 1 equal to IH – AH. The minority or spin-up potential has a discontinuity which is this constant in one order of limits, but is a spatially varying function in a different order of limits. This order-of-limits problem is a consequence of a special circumstance: the vanishing of the spin-up density at N = 1.

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38

Marut, Clotilde, Bruno Senjean, Emmanuel Fromager, and Pierre-François Loos. "Weight dependence of local exchange–correlation functionals in ensemble density-functional theory: double excitations in two-electron systems." Faraday Discussions 224 (2020): 402–23. http://dx.doi.org/10.1039/d0fd00059k.

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We discuss the construction of first-rung weight-dependent exchange–correlation density-functional approximations for He and H₂ specifically designed for the computation of double excitations within Gross–Oliveira–Kohn-DFT.

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39

Deur, Killian, and Emmanuel Fromager. "Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation." Journal of Chemical Physics 150, no. 9 (March 7, 2019): 094106. http://dx.doi.org/10.1063/1.5084312.

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40

Sergiievskyi, Volodymyr P., Guillaume Jeanmairet, Maximilien Levesque, and Daniel Borgis. "Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections." Journal of Physical Chemistry Letters 5, no. 11 (May 20, 2014): 1935–42. http://dx.doi.org/10.1021/jz500428s.

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41

De Proft, Frank, Shubin Liu, and Robert G. Parr. "Chemical potential, hardness, hardness and softness kernel and local hardness in the isomorphic ensemble of density functional theory." Journal of Chemical Physics 107, no. 8 (August 22, 1997): 3000–3006. http://dx.doi.org/10.1063/1.474657.

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42

Filatov, Michael, Seung Kyu Min, and Kwang S. Kim. "Non-adiabatic dynamics of ring opening in cyclohexa-1,3-diene described by an ensemble density-functional theory method." Molecular Physics 117, no. 9-12 (September 7, 2018): 1128–41. http://dx.doi.org/10.1080/00268976.2018.1519200.

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43

Ham, Hyung Chul, J. Adam Stephens, Gyeong S. Hwang, Jonghee Han, Suk Woo Nam, and Tae Hoon Lim. "Pd ensemble effects on oxygen hydrogenation in AuPd alloys: A combined density functional theory and Monte Carlo study." Catalysis Today 165, no. 1 (May 2011): 138–44. http://dx.doi.org/10.1016/j.cattod.2011.02.006.

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44

Liu, Fang, Michael Filatov, and Todd J. Martínez. "Analytical derivatives of the individual state energies in ensemble density functional theory. II. Implementation on graphical processing units (GPUs)." Journal of Chemical Physics 154, no. 10 (March 14, 2021): 104108. http://dx.doi.org/10.1063/5.0041389.

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45

Barrio, L., P. Liu, J. A. Rodríguez, J. M. Campos-Martín, and J. L. G. Fierro. "A density functional theory study of the dissociation of H2 on gold clusters: Importance of fluxionality and ensemble effects." Journal of Chemical Physics 125, no. 16 (October 28, 2006): 164715. http://dx.doi.org/10.1063/1.2363971.

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46

Moreira, Ibério de P. R., Ramon Costa, Michael Filatov, and Francesc Illas. "Restricted Ensemble-Referenced Kohn−Sham versus Broken Symmetry Approaches in Density Functional Theory: Magnetic Coupling in Cu Binuclear Complexes." Journal of Chemical Theory and Computation 3, no. 3 (March 10, 2007): 764–74. http://dx.doi.org/10.1021/ct7000057.

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47

ORLOV, N. Y. "Theoretical models of hot dense plasmas for inertial confinement fusion." Laser and Particle Beams 20, no. 4 (October 2002): 547–49. http://dx.doi.org/10.1017/s0263034602204024.

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Results are presented for a theoretical model, known as the ion model (IM), recently elaborated to calculate the radiative opacity of a hot dense plasma. The density functional theory is used to obtain the general set of self-consistent field equations that describe the state of the whole ensemble of plasma atoms and ions. Theoretical features of the Hartree–Fock–Slater model, the detail configuration account, and the IM are considered. The IM is used for optimal selections of compound chemical compositions for laser and heavy ion target designs.

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48

Szyrmer, Wanda, and Isztar Zawadzki. "Snow Studies. Part IV: Ensemble Retrieval of Snow Microphysics from Dual-Wavelength Vertically Pointing Radars." Journal of the Atmospheric Sciences 71, no. 3 (February 27, 2014): 1171–86. http://dx.doi.org/10.1175/jas-d-12-0286.1.

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Abstract Based on the theory developed in Part III, this paper introduces a new method to retrieve snow microphysics from ground-based collocated X- and W-band vertically pointing Doppler radars. To take into account the variety of microphysical relations observed in natural precipitating snow and to quantify the uncertainty in the retrieval results caused by this variety, the retrieval is formulated using the ensemble-based method. The ensemble is determined by the spread of uncertainties in the microphysical descriptions applied to map the same radar observables to the retrieved quantities. The model descriptors use diverse assumptions concerning functional forms of particle size distribution and mass–velocity relations, all taken from previous observational studies. The mean of each ensemble is assumed to be the best estimate of the retrieval while its spread is defined by the standard deviation that characterizes its uncertainty. The main retrieved products are the characteristic size, the snow mass content, and the density parameter, as well as the vertical air motion. Four observables used in the retrieval are the difference in reflectivities and in Doppler velocities at two wavelengths, together with the equivalent reflectivity factor and Doppler velocity at X band. The solutions that are not consistent with all four observables after taking into account their estimated measurement errors are eliminated from the ensembles. The application of the retrieval algorithm to the real data yields a snow microphysical description that agrees with the snow characteristics seen in the vertical profile of the observed Doppler spectrum.

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49

Pola, Martina, Michal A. Kochman, Alessandra Picchiotti, Valentyn I. Prokhorenko, R. J. Dwayne Miller, and Michael Thorwart. "Linear photoabsorption spectra and vertical excitation energies of microsolvated DNA nucleobases in aqueous solution." Journal of Theoretical and Computational Chemistry 16, no. 04 (April 4, 2017): 1750028. http://dx.doi.org/10.1142/s0219633617500286.

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Employing density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations in combination with the semiclassical nuclear ensemble method, we have simulated the photoabsorption spectra of the four canonical DNA nucleobases in aqueous solution. In order to model the effects of solvation, for each nucleobase, a number of solvating water molecules were explicitly included in the simulations, and additionally, the bulk solvent was represented by a continuous polarizable medium. We find that the effect of the solvation shell in general is significant, and its inclusion improves the realism of the spectral simulations. The involvement of lone electron pairs in the hydrogen bonding with the solvating water molecules has the effect of systematically increasing the energies of vertical excitation into the [Formula: see text]-type states. Apart from a systematic blue shift of around [Formula: see text][Formula: see text]eV observed in the absorption peaks, the calculated photoabsorption spectra reproduce the measured ones with good accuracy. The photoabsorption spectra are dominated by excited states with [Formula: see text] and partial [Formula: see text] character. No low-energy charge transfer states are observed with the use of the CAM-B3LYP and M06-2X functionals.

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50

XIANG, YUANTAO, and A. JAMNIK. "STRINGENT VERIFICATION OF THIRD ORDER + SECOND ORDER PERTURBATION DENSITY FUNCTION THEORY: BASED ON SHORT-RANGE SQUARE WELL POTENTIAL." International Journal of Modern Physics B 24, no. 32 (December 30, 2010): 6291–306. http://dx.doi.org/10.1142/s021797921005764x.

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A recently proposed third order + second order perturbation density functional theory (DFT) approach is made self-contained by using a virial pressure from the Ornstein–Zernike integral equation theory as input to determine the numerical value of an associated physical parameter. An exacting examination is formulated by applying the self-contained perturbation DFT approach to a short-range square well fluid of low temperatures subject to various external fields and comparing the theoretical results for density profiles to the corresponding grand canonical ensemble Monte Carlo simulation results. The comparison seems favorable for the third order + second order perturbation DFT approach as a self-contained and accurate predictive approach. It is surprisingly found that this self-contained third order + second order perturbation DFT approach is displayed outstandingly even if a deep SW perturbation term is being accounted for by a second order perturbation expansion. A discussion is presented about potential opportunity for this perturbation scheme.

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