Session Y21: Density Functional Theory and Beyond V

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The recent revision [1] of the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (GGA) exchange-correlation functional into r²SCAN reduces the numerical instabilities and integration grid sensitivities exhibited by SCAN very substantially. Similar numerical difficulties plus high iteration counts impaired the utility of the otherwise successful deorbitalization of SCAN to SCAN-L, SCAN with density Laplacian dependence [2]. The suspected cause was the Laplacian dependence.
However, use of the identical de-orbitalization to generate r²SCAN-L [3] from r²SCAN is successful both in preserving the accuracy of r²SCAN and in reducing, drastically, the SCAN-L technical problems. The result is much faster calculations. On a set of 660 solid calculations with VASP, r²SCAN-L needed only 20% more time than PBE and only 30% of the time needed for r²SCAN. We provide validation data and discuss the remaining Laplacian-dependence issues, including the use of r²SCAN-L in orbital-free DFT calculations.

[1] J. Phys. Chem. Lett. 11, 8208 (2020).
[2] Phys. Rev. B 98, 115161 (2018)
[3] Phys. Rev. B 102, 121109(R) (2020).   

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In Kohn-Sham density functional theory, the kinetic energy (KE) functional is described by fictitious orbitals. These can create a computational bottleneck for large systems. Orbital-Free Density Functional Theory attempts to model the KE as a functional of ingredients derived from the density directly, avoiding the need for orbitals. In particular, the Perdew-Constantin metaGGA model [1] utilizes the Laplacian of the density to switch between slowly varying electron gas to the von Weizsacker or single electron-pair limits. It and later improvements [2] produce a highly accurate KE density, reproducing the shell structure of atoms for example. With the use of the Laplacian an issue arises of unphysical Pauli potentials that are difficult to find convergent solutions for. We construct a smoothness measure based on the variational description of Poisson's equation. Variational optimization of this measure for Laplacian-based model improve the Pauli potential's smoothness. For hydrogen, results are improved by a factor of 15 in best case scenarios. Results are mixed for atoms, with regions near the nucleus and far from the atom still unreliable.

[1] J. P. Perdew and L. A. Constantin, Phys. Rev. B 75, (2007).
[2] A. Cancio, D. Stewart and A. Kuna, JCP 144, (2016).   

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The binding of adsorbate molecules at metal sites is relevant for a number of applications such as catalysis and storage (H₂). In particular, metal organic frameworks (MOFs) with open mental sites are drawing attention for these applications. A recent study on a Cu(I)-substituted MOF^₁ showed that density functional theory (DFT) with LDA, PBE, and SCAN functionals tend to overestimate the adsorption energies of small molecules at Cu(I) centers. Another study² showed that the adsorption energies of H₂ molecules on monocationic 3d metals is overestimated by LDA, GGA, and mGGA functionals, while hybrid and double hybrid functionals tend to perform better. In this work we use the Fermi-Löwdin orbital (FLO) self interaction correction (SIC) method to compute adsorption energies of a series of small molecules on 3d transition metal cations. Results indicate that the FLO-SIC corrects LDA and PBE adsorption energies towards accurate reference values. We will also report results for molecular adsorption energies in cluster models of MOF binding sites.
¹Organometallics, 38, 3453-3459 (2019)
²J. Chem. Theory Comput., 16, 4963-4982 (2020)   

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Accurate description of weakly bound electrons is difficult for the semi-local density functional approximations. Here we study weakly bound electrons in molecules and clusters using self-interaction-corrected density functional methods. These are the recently proposed local scaled self-interaction-correction (LSIC) method[1] and the widely known Perdew-Zunger (PZ) self-interaction-correction (SIC) method. The SIC is determined using the Fermi-Löwdin localized orbitals in both methods. Our results from the density plot difference show that these clusters bind the extra electron in dipole bound states. We also estimate vertical detachment energies from the absolute of the highest occupied eigenvalues. Our results show that LSIC provides better agreement with reference CCSD(T) values than PZSIC and MP2.
[1]. Zope et al. J. Chem. Phys., 151, 214108, (2019).   

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Density-functional theory with extended Hubbard functionals is a powerful method for studying complex materials containing transition-metal and rare-earth elements, owing to its accuracy in correcting self-interactions and its low computational costs. There are two key elements in these formulations which are closely interconnected: i) the choice of the on-site U and inter-site V Hubbard parameters, and ii) the choice of the Hubbard manifold. Often, these are chosen empirically, disregarding both the goal of DFT functionals (reproducing total energies, not band gaps) and the nature of the Hubbard manifold used in the actual calculations. Having developed automated and reliable approaches for the non-empirical determination of the U and V parameters from density-functional perturbation theory [1], we highlight here the role played by the Hubbard manifold, comparing atomic orbitals (in different oxidation states and orthogonalized or not) and maximally localised Wannier functions. [1] I. Timrov et al., PRB 98, 085127 (2018).   

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Within density functional theory (DFT), adding a Hubbard U correction can mitigate some of the deficiencies of local and semi-local exchange-correlation functionals, while maintaining computational efficiency. However, the accuracy of DFT+U largely depends on the chosen Hubbard U values. We propose an approach to determining the optimal U parameters for a given material by machine learning. The Bayesian optimization (BO) algorithm is used with an objective function formulated to reproduce the band structures produced by more accurate hybrid functionals. This approach is demonstrated for transition metal oxides, europium chalcogenides, and narrow-gap semiconductors. The band structures obtained using the BO U values are in agreement with hybrid functional results. Additionally, comparison to the linear response (LR) approach to determining U demonstrates that the BO method is superior.   

Live

Hubbard U parameters quantify the many-electron self-interaction error associated with selected subspaces in approximate DFT. We describe the interpretation and calculation of its lesser-known counterpart, Hund's J, as a measure instead of subspace static correlation error. We show how Hund's J can be readily calculated like the Hubbard U using minimum-tracking [1] (constrained DFT based [2]) linear-response, sometimes as a cost-free by-product [3]. We demonstrate that J-moderated DFT+U yields rather satisfactory results for several oxides including MnO [3], TiO2 (rutile and anatase) [4], Cr2O3, and NiO [1]. We revise the parameter self-consistency condition in light of new results on the role of Hund's J [1].

[1] G. Moynihan, Ph.D. thesis, Trinity College Dublin (2018) http://hdl.handle.net/2262/82220
[2] D. D. O’Regan and G. Teobaldi, Phys. Rev. B 94, 035159 (2016).
[3] E. B. Linscott, D. J. Cole, M. C. Payne and D. D. O’Regan, Phys. Rev. B 98, 235157 (2018).
[4] O. K. Orhan and D. D. O'Regan, Phys. Rev. B 101, 245137 (2020).   

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The structure of a polymeric fluid is usually characterized by the intra- and inter-chain pair correlation functions (PCFs), which can be used to determine both the thermodynamic and dynamic properties. Few theories, however, are available to predict such microscopic structures, which require that the segment-segment correlation effects be explicitly taken into account. In the well-developed self-consistent polymer reference interaction site model (SC-PRISM) (Heine et al., Adv. Polym. Sci. 173, 209, 2005), the inter-chain PCFs are approximated by an intra-chain solvation pair potential, thus allowing its prediction of the intra- and inter-chain PCFs. On the other hand, Yu and Wu proposed an extended test-particle method (J. Chem. Phys. 118, 3835, 2003), enabling prediction of these quantities using polymer density-functional theories (PDFTs). Here we directly compare the intra- and inter-chain PCFs predicted by various versions of PDFTs and SC-PRISM calculations with those obtained from Monte Carlo simulations. A simple model system of tangent hard-sphere chains allows us to unambiguously quantify the accuracy of these predictions as a function of the chain length and hard-sphere packing density.   

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Graphene’s success for nanopore DNA sequencing has shown that it is possible to explore other potential single- and few-atom thick layers of elemental 2D materials beyond graphene (e.g. phosphorene and silicene), and also that these materials can exhibit fascinating and technologically useful properties for DNA base detection that are superior to those of graphene. Using density functional theory (DFT), we studied the interaction of DNA bases with finite-size nanomaterials from phosphorene and silicene. We observe that binding energies of DNA bases using nanopores and nanoribbon from phosphorene are smaller compared to graphene and silicene devices. This shows that minimal sticking of DNA bases to phosphorene’s surface is expected for phosphorene devices. Furthermore, both nanopore and nanoribbon devices from phosphorene show a characteristic change in the density of states for each base. The band gap of phosphorene is significantly changed compared to other nanomaterials (e.g., MoS₂, graphene, silicene, and h-BN) due to physisorption of bases on nanoribbon surface. Our findings show that phosphorene performs better than silicene and graphene, hence a promising material for DNA base detection using advanced detection principles such as transverse tunneling current measurement.   

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The meta-GGA class of functionals for the exchange-correlation (XC) energy in density functional theory (DFT) is conventionally constructed as a function of the density, its gradient, and the kinetic energy density (KED). Inclusion of the KED betters meta-GGAs accuracy but raises computational cost for some applications such as ab initio molecular dynamics simulations. That cost can be reduced by replacing the explicit orbital dependence in the KED with expressions using the Laplacian of the density. We calculate the exact KED and electron density of semiconductor solids with varying ionicity and atomic number using the ABINIT DFT plane-wave pseudopotential code. We visualize how well the exact KED can be represented by a single meta-GGA model in terms of the scaled density gradient and scaled Laplacian. We test the validity of recent deorbitalization strategies by comparing their predictions to the exact calculations. We find a near-universal linear correlation with the Laplacian and gradient of the density for regions outside of the atomic bond, which can be fit to a simple gradient expansion.   

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Electron transfer is fundamental process that occurs ubiquitously from energy conversion, molecular electronics to biochemistry. Effective generation of the diabatic states is needed for determination of parameters like reorganization energies and electronic coupling constants which are important for electron transfer study. Here, we discuss the recently developed oxidation-state constrained density functional theory (OS-CDFT) method [1] which specifically controls the oxidation states of transition metal ions. This is based on the previous approach for oxidation state determination [2]. Under OS-CDFT, we can obtain forces on ions for structural optimization. The electronic coupling constant can also be evaluated from the diabatic states. After that, we introduce its application to problems like electron transfer between solvated ferrous and ferric ions, polaron hopping in TiO₂ and in BiVO₄, and photoexcited electron transfer.

[1] C. Ku and P. H.-L. Sit. J. Chem. Theory Comput. 15, 4781 (2019)
[2] P. H.-L. Sit, R. Car, M. H. Cohen and A. Selloni. Inorg. Chem., 50, 10259 (2011).   

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We study the importance of self-interaction correction in density functional approximations for ion-water clusters, with different bonding patterns. For this purpose, we have used the Fermi-Löwdin orbital self-interaction correction (FLOSIC) [1] method to calculate binding energies (BE) of protonated water clusters (H₃O⁺(H₂O)_n, n=1-3 and 6), deprotonated water clusters (OH^-(H₂O)_n, n=1-6), small halide-water clusters (X^-(H₂O)_n, X=(F, Cl, Br), and n=1,2), and small alkali ion-water clusters (M⁺(H₂O)_n, M=(Li, Na, K), and n=1,2). We have considered three non-empirical exchange-correlation functionals namely, the local density approximation (LDA), the generalized gradient approximation (GGA) formulated by Perdew, Burke, Ernzerhof (PBE), and the strongly constrained and appropriately normed (SCAN) meta-GGA. We show that the FLOSIC method yields an improved description of BE for all systems that are connected at least with one hydrogen bond and that the error decreases with an increase in the size of an ion or equivalently decreases with the length of the hydrogen bond. However, FLOSIC strongly overestimates the bond dissociation energy of small alkali ion-water clusters.

1. M. R. Pederson, A. Ruzsinszky, and J. P. Perdew, J. Chem. Phys. 140, 121103 (2014).   

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Graphene’s success for nanopore DNA sequencing has shown that it is possible to explore other potential single- and few-atom thick layers of 2D elemental materials beyond graphene, and also that these materials can exhibit fascinating and technologically useful properties for DNA base detection that are superior to those of graphene. The buckled honeycomb lattice of silicene monolayer makes it an ideal material for rapid DNA sensing applications. Using density functional theory, we modeled and studied the interaction of silicene nanopore and nanoribbon with DNA bases. The ability of silicene to distinguish the individual DNA bases is then compared with graphene using three evaluation metrics, namely, binding energy, band gap, and density of states. In this talk, we will present the results of our research findings.   

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In wavefunction-based periodic solid calculations, converging calculations to the thermodynamic limit (TDL) is important due to the finite size effects. Many methods, such as additive corrections and twist averaging, have been developed to combat this error that is difficult to remove. These improve the overall accuracy of many quantum Monte Carlo methods. However, twist averaging can have higher costs as a calculation needs to be run at each twist angle. We developed a method for the uniform electron gas (UEG) we termed connectivity twist averaging (cTA) that helps combat this increased cost. In this method, we select a single twist angle that represents the twist averaging system and run a single wavefunction-based calculation, obtaining twist averaged results at a fraction of the cost. As we have only demonstrated the application of this method to the UEG using coupled cluster, here, I will show how this method can be applied to quantum Monte Carlo methods, using full configuration interaction quantum Monte Carlo, as well as applications to real systems using a modified version of the cTA method.   

On Demand

Polymer density-functional theories (PDFTs) are able to predict microscopic details that are often neglected by the more widely used polymer self-consistent field theory (PSCFT), and provide more accurate equations of state due to the incorporation of compressibility and the correlation effects. PDFTs are, however, numerically more complicated and less developed than PSCFT, particularly for systems with multi-dimensional inhomogeneity. Here we show that two popular PDFTs, one proposed by Yu and Wu (J. Chem. Phys. 117, 2368, 2002) and the other by Chapman and co-workers (J. Chem. Phys. 127, 244904, 2007), can be put into the same unified framework as the PSCFT. Later-versions (J. Chem. Phys. 118, 3835, 2003; J. Chem. Theory Comput. 8, 1393, 2012) are based on the modified fundamental measure theory to account for the hard-sphere excluded-volume effects, and the only difference between them lies in the excess Helmholtz free-energy density for intra-chain correlations. The unified framework will help promote the application of PDFTs by the broader polymer community. We also present improved numerical methods for faster and more accurate evaluation of the integrals in PDFTs for tangent hard-sphere chains which have discontinuous or non-differentiable integrands.