Session F01: Density Functional Theory and Beyond I

Density-Corrected SCAN Meta-GGA*

The strongly constrained and appropriately normed (SCAN) [1] meta-generalized gradient approximation satisfies 17 exact constaints on the density functional for the exchange-correlaton energy, and works well on its own self-consistent density for many atoms, molecules, and condensed phases. But density-corrected [2] SCAN, which evaluates SCAN on a "better" density such as that of Hartree-Fock theory, is often more accurate, and strikingly so for energy barriers [3] and for water clusters and liquid water [4]. For water, the accuracy of density-corrected SCAN approaches that of coupled cluster theory. The likely reason for this is that Hartree-Fock theory more correctly tends to localize an integer electron number within each system fragment, while computationally-efficient density functionals may not [5].

[1] J. Sun. A. Ruzsinszky, and J.P. Perdew, Phys. Rev. Lett. 115, 036402 (2015).

[2] M.-C. Kim, E. Sim, and K. Burke, Phys. Rev. Lett. 111, 073003 (2013).

[3] G. Santra and J.A. Martin, J. Chem. Theory Comput. 17, 1368 (2021).

[4] S. Dasgupta, E. Lambros, J.P. Perdew, and F. Paesani, Nature Commun., to appear. 

[5] J.P. Perdew, R.G. Parr, M. Levy, and J.L. Balduz, Phys. Rev. Lett. 49, 1691 (1982).     

Testing the r2SCAN density functional for the thermodynamical stability of solids with and without the van der Waals correction

Density functional theory has emerged as a powerful tool for predicting the thermodynamic stability of solid-state compounds, and improvements to the underlying exchange-correlation functional can make those predictions more reliable. The newly developed r²SCAN meta-GGA functional enhances the numerical stability of SCAN [1] while retaining its accuracy on molecules and solids [2]. Meanwhile, the combination of SCAN with the rVV10 long-range correlation is known to be reliable for studying layered materials [3]. Here, we compare the performance of SCAN, r²SCAN, SCAN+rVV10, and r²SCAN+rVV10 for predicting formation energies, volumes, and band gaps. The test set consists of 1015 solids displaying a wide range of bonding environments, chemistries, and properties. Additionally, we assess the thermodynamic stability of compounds by calculating the enthalpy of decomposition with respect to the appropriate competing phases.

 

[1] J. Sun, A. Ruzsinszky, and J. Perdew, Physical Review Letters 115, 1 (2015).

[2] J. W. Furness, A. D. Kaplan, J. Ning, J. Perdew, and J. Sun, The Journal of Physical Chemistry Letters 11, 8208 (2020).

[3] H. Peng, Z. Yang, J. Perdew, and J. Sun, Phys. Rev. X 6, 041005 (2016).   

FLO-SIC & F-Electron Systems

            Systems containing f-electrons are of growing importance as new applications exploiting their unique magnetic properties are developed. However, electronic structure theories lack the efficiency or accuracy necessary to study them. Density Functional Theory (DFT) offers an appealing approach to study f-electron systems, yet self-interaction error plagues the theory’s ability to accurately model f-electrons. Additional treatment, such as FLO-SIC [1], is generally required. NRLMOL has been generalized to include f-electrons and FLO-SIC, as well as improvements in efficiency which alleviate the difficulties of FLO-SIC calculations, namely, finding FOD starting points and calculating the coulomb potential in a timely fashion. We present these improvements along with optimized FOD positions for Cs to Rn and examples of the effect of FLO-SIC on ligated f-electron systems.

 

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

The Fermi-Löwdin self-interaction correction for spin transition systems

(Semi)-local density functional approximations underestimate the magnitude of the highest-occupied orbital (HO) eigenvalue, thereby narrowing the HO-LU (lowest-occupied orbital) gap. This inaccuracy can be attributed to self-interaction error (SIE). For spin transition systems like Fe(II) compounds, which show a transition between a low-spin state (S = 0) and a high-spin state (S=2) at a critical temperature, this underestimation can be substantial [1,2], and leads to electron configurations with incorrect energy. In this work we have applied the Fermi-Löwdin self-interaction correction [3], as well as different many-body perturbation approximations, to investigate how SIE affects the transition.   

Complex Fermi-Löwdin orbitals for Perdew-Zunger self-interaction correction

The Fermi-Löwdin orbital self-interaction correction [1] (FLO-SIC) is a size extensive and unitarily invariant approach for implementing the Perdew-Zunger self-interaction correction [2] (PZ-SIC) to density functional theory (DFT). The ingredients to define the FLO transformation are a set of orthonormal occupied orbitals and a set of parameters known as Fermi-orbital descriptors (FODs).  In the original FLO-SIC implementation, FODs are defined as real vectors. Here we define FODs to be complex vectors. This leads to a complex transformation and complex FLOs. The complex FLOs are expected to be smoother/less noded localized orbitals. Such orbitals are important to obtain accurate and larger SIC corrections, particularly for semi-local functionals [3,4]. In this work, we find the optimal complex FODs for atoms and small molecules and calculate the complex FLO-SIC total energies. Then we investigate the performance of the complex FLO-SIC method for atomization energies of the molecules.

1] J. Chem. Phys., 140, 121103 (2014).

[2] Phys. Rev. B, 23, 5048, (1981).

[3] Phys. Rev. A, 84, 050501 (2011).

[4] J. Chem. Phys., 150, 174102 (2019).

    

Lobedness, complex orbitals, and the self-interaction energies of multiple bonds

A size-extensive formulation of the Perdew-Zunger self-interaction correction (PZ-SIC) [1] can be accomplished using localized Fermi Löwdin orbitals (FLOs) [2]. However, real FLOs are noded and semi-local functionals introduce an error that reflects the incipient division of one electron into fragments of non-integer electron number [3].  With real FLOs, molecules with multiple bonds are under-bound and the FLOs associated with the multiple bonds are strongly noded.  This suggests that the under-binding is directly linked to the nodality.  We explore this link using a method that reduces the lobedness of these orbitals without altering the total electron density. This scheme effectively provides an upper bound on the PZ-SIC energy minimized in the variational space of complex orbitals [4,5] and yields a lower energy solution than with the original orbitals, thereby improving the atomization energies of the molecules.

1. J.P. P. and A. Z., Phys. Rev. B 23, 5048 (1981)

2. M. R. P., A. R., and J. P. P., J. Chem. Phys. 140, 121103 (2014)

3. C. S. et al., J. Chem. Phys. 150, 174102 (2019)

4. M. R. P., R. A. H., and C. C. L., J. Chem. Phys. 80, 1972 (1984)

5. S. K., P. K., and H. J., Phys. Rev. A 84, 050501(R) (2011)   

Hyperfine Interactions for Small Molecules using Fermi-Löwdin Orbital Based Self-Interaction Corrected DFT

Hyperfine interactions play an important role in characterizing electronic structure using EPR or NMR, as well as in designing qubit systems. The major component of the hyperfine interaction energy, the Fermi-contact (FC) term, is proportional to the electron spin density at the nuclear position. The FC term tends to be significantly underestimated in density-functional theory (DFT) methods due to self-interaction errors (SIE), arising from approximate exchange-correlation functionals, which results in significant electron- and spin-density delocalization. A recently developed self-interaction correction (SIC) method is based on Fermi-Löwdin orbitals (FLO), which depend on the positions of Fermi-Orbital Descriptors (FODs). The FLO-SIC method has been successfully applied to various systems; however, its performance for the FC term has not been assessed yet. We carried out FLO-SIC calculations on small transition metal-based molecules and computed the FC term in each case. The starting set of FODs for each calculation was generated using the symmetries of the system, as well as the Lewis structures predicted with natural bond orbital theory. The results from the FLO-SIC method are compared with those from the SIC-free generalized-gradient approximation method and experiments.   

Bond length alternation of π-conjugated polymers predicted by the Fermi-Löwdin orbital self-interaction correction

π-conjugated polymers have found practical applications in various fields, in part due to the high delocalization of electrons through the polymer axis. For electronic structure methods (ESMs), the correct description of the delocalization level can be characterized by the bond length difference between multiple and single bonds, or bond length alternation (BLA), and is a critical test for electron correlation effects and removal of self-interaction error. The accurate theoretical determination of the BLA remains a significant challenge for traditional ESMs, such as density functional theory (DFT). Here, the BLAs of five oligomers are analyzed using the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method, which was proposed as a tool to remove one-electron self-interaction from approximate DFT. The BLAs for oligomers of increasing length were extrapolated to the polymer limit and compared to DFT and MP2 results. To analyze the delocalization level predicted by each method, the Natural Bond Orbital analysis was used to quantify the deviation of the relaxed structures from the ideal Lewis structures. Our results reveal that the FLOSIC improves the calculated BLA over LSDA and PBE, but it tends to overcorrect, in line with observations for other properties.

    

Chemical bonding theories as guides for self-interaction corrections

Fermi-orbital descriptors (FODs), i.e., electron positions, can be used to form Fermi--Löwdin orbitals (FLO), a special set of localized orbitals which can be used in combination with the Perdew--Zunger self-interaction correction (SIC) in the FLO-SIC method. We show how FODs can be used to initialize, interpret and justify SIC solutions in a common chemical picture within various SIC approaches.[1]

Additionally, we show that using Lewis' theory as the starting point can lead to artifactual dipole moments of up to 1 Debye, while Linnett SIC dipole moments are in better agreement with experimental values. We suggest using the dipole moment as a diagnostic of symmetry breaking in SIC and monitoring it in all SIC  calculations. We show that Linnett structures can often be seen as superpositions of Lewis structures and propose Linnett structures as a simple way to describe aromatic systems in SIC with reduced symmetry breaking.[1]

[1] K. Trepte et. al, arXiv:2109.08199 [physics.comp-ph] (2021)