Session F58: DFT and Beyond IV

Long-Range Correlations in Density Functional Theory

Accurate and low-cost reproduction of electron correlations remains one of the most difficult problems in chemical physics. Enormous progess has been made on dealing with short-range correlations. But long-range correlations remain challenging, despite contributing to a range of important quantum chemical problems including dispersion forces [1-2], strong correlations [3-4] and charge transfer excitations [5]. This talk will discuss the origins of key types of long-range correlations in density functional theory, and consider physical, chemical and mathematical perspectives on the problem. It will discuss some low-cost solutions to difficult problems in the field, introduced by the author and others, and will highlight some of the challenges that lie ahead. It will stress the importance of the universal functional in devising new approximations, and how quantum state ensembles can help, even in "mundane" cases.

[1] T Gould, S Lebègue, JG Ángyán and T Bučko, J. Chem. Theory Comput. 12, 5920–5930 (2016)
[2] M. Kim, W. J. Kim, T. Gould, E. K. Lee, S. Lebègue, H. Kim, doi://10.26434/chemrxiv.7938137.v2 (2019)
[3] T. Gould and S. Pittalis, Phys. Rev. Lett. 123, 016401 (2019).
[4] T. Gould and S. Vuckovic, Accepted in J. Chem. Phys; doi://10.26434/chemrxiv.9730250.v1 (2019)
[5] T. Gould, L. Kronik, and S. Pittalis, J. Chem. Phys. 148, 174101 (2018).   

Embedding tools to improve density functionals.

As is well known, standard approximations to the exchange-correlation (XC) functional often do not yield accurate energies and/or spin-densities when chemical bonds are stretched. We use density embedding theory to examine the behavior of the non-additive contribution to the XC energy and to propose physically-motivated approximations for this contribution as atoms dissociate. We also discuss a recent approach to develop improved approximations for the non-additive non-interacting kinetic energy, and why this is a challenging problem.
  

Kohn-Sham accuracy at a fraction of the cost: Nonlocal subsystem DFT and orbital-free DFT

Subsystem DFT enables first principles simulations to approach realistic time- and length-scales, and most importantly sheds light on the dynamical behavior of complex systems. The accuracy of subsystem DFT is dependent on the quality of the employed nonadditive Kinetic Energy Density Functionals (KEDF). As these are customarily of semilocal character (i.e., they depend locally on the value of the density and its gradient), so far subsystem DFT has only been able to approach weakly interacting subsystems. In this presentation, we employ latest-generation nonlocal KEDF^1,2 in subsystem DFT³ and orbital-free DFT⁴ simulations. Our results are of KS-DFT accuracy while still keeping the computational cost at a fraction of typical KS-DFT algorithms. The developed KEDFs are accurate enough also in the context of orbital-free DFT where we show they are able to approach million-atom semiconductor systems arranged in complex structures featuring Schottky barriers and space-charge regions.

1. W. Mi and M. Pavanello, Phys. Rev. B, 100, 041105 (2019)
2. W. Mi, A. Genova, and M. Pavanello, J. Chem. Phys., 148, 184107 (2018)
3. W. Mi and M. Pavanello, submitted.
4. X. Shao, W. Mi and M. Pavanello, in preparation.   

Absolutely Localized Multi-reference DFT Embedding

While density functional theory (DFT) has been a workhorse for quantum mechanical chemical calculations, current implementations have several deficiencies. Systems which require a multireference description are often poorly described by current DFT methods. Quantum embedding methods provide a strategy for performing localized highly accurate calculations on chemical systems while not incurring high cost computational scaling. Dividing a system into absolutely localized subsystems -- described by only the basis functions of the subsystem atoms -- can significantly reduce computational cost. The Huzinaga projection operator based absolute localization wavefunction embedded in DFT (WF-in-DFT) embedding methods match full system WF energy differences across a diverse test set including multi-reference WF calculations embedded in DFT. We have also studied large metal organic framework (MOF) cluster models, specifically gas adsorption on an Fe-MOF-74 cluster model and can achieve within 0.22 kcal/mol of the full system CASPT2 energy at a fraction of the computational cost. The absolute localization WF-in-DFT method allows for highly accurate calculations on multireference systems beyond the scope of current techniques.   

Towards an orbital-free kinetic energy density functional for molecular systems

A new kinetic energy density functional (KEDF) for systems composed of many atoms (molecular systems) is proposed. This KEDF contains the full von-Weizsacker KEDF as well as correction terms ("Pauli KEDF") appropriate for describing fermionic systems. Two of these correction terms are investigated: one from approximations based on the kinetic energy of fermions in an infinite well potential and the other from suitable averages of the kinetic energies of atoms. The peformance of these new KEDFs will be presented as well as possible routes for further development.   

Analytic inversion procedure for the exact non-additive kinetic potential functional Vnad

The non-additive kinetic potential functional V^nad is a key issue in density-dependent embedding methods, such as Frozen Density Embedding Theory and Partition-DFT. V^nad is a bifunctional of pairs of specific electron densities ρ_A and ρ_B. We report here an inversion procedure to generate reference V^nad for weakly overlapping ρ_A and ρ_B. To obtain the exact V^nad we used an analytical inversion procedure that we proposed (M. Banafsheh, T.A. Wesolowski, Int. J. Quant. Chem. 118 (2018): e25410). We discuss the constraints on the choice of electron densities to assure their admissibility. Mathematical challenges of satisfying these constraints will be presented in detail. The potential at small overlap is constructed for various diatomic systems of four electrons at different interatomic distances. These results are compared with the potential obtained using common kinetic functional approximations. V^nad is also presented for some diatomic systems including more than 4 electrons in which two electrons are localized with high precision in space and the accuracy of V^nad is assured. We are now studying the forward Kohn-Sham problem for some small diatomic systems using the analytically inverted potential and comparing with the standard Kohn-Sham approach.   

Bond energies of molecules using optimal transport theory for the strictly-correlated-electron (SCE) limit of Density-Functional-Theory

Standard Kohn-Sham DFT starts from a mean-field approximation: the kinetic energy is modeled exactly, while the electron-electron interactions are modeled through a split into a mean-field term, and corrections from the exchange-correlation term. The SCE limit starts from the opposite limit: the electron-electron interactions are assumed to dominate over the kinetic energy, and hence it is a semi-classical limit. It is hence well suited to study strongly-correlated situations, e.g. bond breaking. While the SCE limit includes many-body interactions, it can be identified as a problem from Optimal Transport theory with Coulomb cost function. Hence it can be solved by a nested optimization in its dual (Kantorovich) formulation. We incorporate the Kantorovich solution within the KS-DFT framework and solve it using the finite element method. Bond-energy curve is obtained using this method for hydrogen molecule, and is compared against other exchange-correlation models to show the improved results. We then investigate bond-breaking in ethane and other small molecules using the SCE limit.   

How accurate can a metaGGA+vdW functional be simultaneously for chemisorption and physisorption of molecular adsorption on transition metal surfaces?

Understanding molecular adsorption on transition metal surfaces underpins many problems in heterogeneous catalysis. Accurately predicting the adsorption energies has been a challenging task as simultaneously capturing chemical and van der Waals (vdW) bonds in a single functional is difficult. In this work, we combine the semi-local meta-GGA made simple (MGGA_MS) functional with the rvv10 vdW correction [1-3]. We re-parametrize the functional by fitting to the atomization energies of covalently bonded molecules and the Ar2 binding curve. The resulting MGGA_MS + rVV10 is validated against a set of 38 systems including chemisorption and physisorption features with experimental [4] adsorption data.


[1] J Sun, R Haunschild, B Xiao, et. al., J. Chem. Phys. 138, 044113 (2013)
[2] O A Vydrov and T Van Voorhis, J. Chem. Phys. 133, 244103 (2010)
[3] R Sabatini, T Gorni, S de Gironcoli, Phys. Rev. B 87, 041108 (2013)
[4] J Wellenorff, T L. Silbaugh, D Gracia-Pintos, et. al., Surf. Sci. 640, 36-44 (2015)   

Asymptotic behavior of the exchange-correlation energy density and the Kohn-Sham potential in density functional theory: exact results and strategy for approximations

Density functional theory (DFT) is nowadays the leading theoretical framework for quantum description of materials from first principles. The predictive power of DFT critically depends on an accurate approximation to the generally unknown exchange-correlation (xc) energy functional. Approximations to the xc functional can be constructed from first principles by satisfying known properties of the exact functional. In this talk I focus on two such exact properties: the asymptotic behavior of the xc energy density per particle, e_xc[n](r), and the asymptotic behavior of the Kohn-Sham potential, v_xc[n](r), in finite many-electron systems. It is shown that these two properties are independent: fulfillment of one does not guarantee the other. In this process, a new quantity, the xc hole response function, is defined, some of its properties are deduced and its exact exchange part is analytically derived. A strategy for development of advanced approximations for exchange and correlation with a correct asymptotic behavior is suggested [1].

[1] E. Kraisler, Isr. J. Chem., accepted. https://doi.org/10.26434/chemrxiv.9917189.v1   

Methods of corrections to to GEA approximations of the Pauli potential

In recent years many advances have been made in Orbital-Free Density Functional Theory (OFDFT), which attempts to remove orbitals from the Kohn-Sham DFT approach, either completely, or by approximating the kinetic energy density from meta-GGA exchange correlation functionals. The difficulty in OFKE models is in modeling the Pauli energy, the contribution to the KE of Pauli statistics. One aspect of this problem is correctly producing the OF Pauli potential, the functional derivative of the Pauli KE. Recent mathematical analysis of orbital free kinetic energy models based on Gradient Expansion Approximations (GEA)s, like the Airy gas model, have offered insight in modeling the Pauli potential for neutral atoms. However all of these models suffer from gross inaccuracies in the nuclear cusp region, as well as an unexpected deviation in the core. The exact Pauli potential approaches a constant near the nucleus related eigenvalue of the lowest occupied atomic orbital, but all GEAs become infinitely negative at the singularity. We propose a smooth non-analytic stitching function to correct the error in the near nuclear region for Pauli potential GEAs, and explore the outer core. This is similar to work done by Perdew and Constantin as well as previous work from this group done on KEDs.   

Practical Density Functional Theory Beyond the Zero-Sum Limit: M11plus

Conventional approximate DFT functionals are based on what exchange would be a nearly homogeneous electron gas. This model effectively uses like-spin exchange to model opposite-spin correlation, producing a "zero-sum" tradeoff in performance for some classes of problems, including bond energies vs. barrier heights or valence vs. Rydberg excitations. We argue that including new ingredients in a functional can provide beyond-zero-sum broad accuracy. We demonstrate this by adding a new ingredient to the flexible M11 long-range-corrected hybrid meta functional form. The new ingredient is an inexpensive rung-3.5 bound to the exact exchange energy density. The M11 form was reoptimized with these terms, producing a functional called M11plus. Tests for thermochemistry, kinetics, and response properties suggest M11plus is one of the most broadly accurate occupied-orbital-only DFT functionals available to date.   

Numerical analysis of thermodynamic limit extrapolation power-laws in the uniform electron gas using connectivity-twist-averaged coupled cluster doubles theory

We recently developed a coupled-cluster theory method in the uniform electron gas (UEG) for improving twist averaging in solids [1]. The method finds a special twist angle that gives comparable results to conventional twist averaging at a reduced cost. Here, we apply this new method to calculate the thermodynamic limit energies of the uniform electron gas across a range of densities. The high-density limit is then used to derive general power laws for extrapolation. Time permitting, we will also show preliminary results for real systems using the Vienna ab-initio software package [2][3].

[1] Mihm, T. N.; McIsaac, A. R.; Shepherd, J. J. J. Chem. Phys. 2019, 150 (19), 191101. https://doi.org/10.1063/1.5091445.
[2] Kresse, G.; Furthmüller, J., Phys. Rev. B 1996, 54 (16), 11169–11186. https://doi.org/10.1103/PhysRevB.54.11169
[3] https://www.vasp.at