Session W01: Density Functional Theory and Beyond VII

Steady-State Density Functional Theory for Correlated Quantum Transport and Spectral Functions

Steady-State Density Functional Theory (i-DFT) is a formalism to describe open quantum systems in nonequilibrium steady states. i-DFT is based on the one-to-one correspondence between the pair density and steady current and the pair local potential and applied voltage. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential and an xc contribution to the voltage. After revisiting the fundamentals of i-DFT we apply the formalism to correlated quantum dots in the Coulomb blockade regime. We show that the well-known discontinuity of the DFT xc potential at integer particle number bifurcates at finite currents. The i-DFT formalism can also be used to calculate bulk spectral functions. We present an approximation to the xc voltage suited to describe a paradigm in the field of strongly correlated electrons, i.e., the Mott metal-insulator transition.   

Modelling the plateaus in the Kohn-Sham and Pauli potentials

Density functional theory (DFT) is the leading theoretical framework used to describe electronic structure of materials. The most common approach in DFT is that of Kohn and Sham describes a material – a system of N interacting electrons – via a fictitious system of N non-inteacting electrons subject to an effective potential termed the Kohn-Sham (KS) potential. The Kohn-Sham (KS) potential – a central quantity DFT – is known to build up plateaus and exhibit sharp spatial steps when describing the processes of dissociation, ionization, excitation and charge transfer. In this talk we show that the Pauli potential – a central quantity in orbital-free DFT (OF-DFT) and in the exact electron factorization (EEF) method – exhibits plateaus and steps, as well. We find the height of the plateau that builds up as a result of electron addition, we examine which terms of the Pauli potential contribute to the plateau (and which aren’t) and finally we model the spatial form of the plateau function. We back up our analytical findings by numerical examples. Our detailed analysis of the Pauli potential sheds light also on the step structure of the KS potential, which we discuss in our talk.   

Relativistic orbital-optimized density functional theory for core-level spectroscopy

X-ray spectroscopy is widely used to study local chemical environments by probing the electronic structure of the innermost orbitals and obtaining element specific spectral signatures.  Theory can assist in interpreting these features, but accurate modelling requires a description of orbital relaxation effects that are crucial for characterizing the core-hole. Moreover, as we explore elements of the periodic table with higher atomic numbers, relativistic effects become more relevant, especially for the prediction of K (1s) and L (2p) shell transitions. We combine orbital-optimized (OO) DFT with the spin-free exact two-component one electron model (SF-X2C1e) for scalar relativistic effects, to study K-edge X-Ray spectroscopies for elements of the third row and early transition metals of the periodic table. Our results show that the optimal protocol to simulate such effects is obtained when the SCAN density functional approximation is used with a local basis set that is flexible enough to describe the effects of orbital relaxation on the center of interest, predicting core-excitation energies to < 0.5 eV RMSE error for a wide range of molecules containing third row main group elements. We also present progress on the simulation of transition metal L-edges within this framework.   

The Exponential Ansatz in the Context of Density Functional Theory: Elimination of Fractional Charges and Implications for Optical Excitations

The exponential-ansatz operator is traditionally applied within coupled cluster theory to compute relatively accurate wave functions and related electronic properties of molecular systems. One of the most advantageous properties of this operator is its ability to offer size-consistent quantum methods. Motivated by such property, we discuss the application of this operator to density functional calculations. We show the adapted (non-Hermitian) coupled-cluster variational method and the exponential ansatz can eliminate (spurious) fractional charges for spin-symmetry-broken heterogenous molecular systems, whereas preserving a strong consistency with Kohn-Sham LDA calculations in cases where these perform reasonably well. For linear-response TDDFT calculations we show the exponential operator can also assist in the description of avoided-crossing regions, and the study of quantum states where multiple electrons are optically excited. Finally, we discuss the role of the self-interaction error in our methods involving the exponential operator.   

Incorporating Nuclear Quantum Effects in Molecular Dynamics Simulations with Multicomponent Density Functional Theory

Nuclear quantum effects play an important role in a variety of chemical and biological processes and substantially affect many fundamental properties of systems involving hydrogen atoms. However, the accurate inclusion of nuclear quantum effects remains a significant challenge for large-scale molecular simulations. We present an alternative formulation of equations of motion for molecular dynamics (MD) based on a constrained minimized energy surface (CMES). Since CMES inherently includes nuclear quantum effects, the resulting CMES-MD is able to capture nuclear quantum effects such as quantum delocalization effects and tunneling effects. In model systems, CMES-MD gives results that are comparable to or better than those from centroid molecular dynamics and ring-polymer molecular dynamics. In practical molecular systems, CMES can be obtained from constrained nuclear-electronic orbital density functional theory (cNEO-DFT), a multicomponent density functional theory that was recently developed in our group. The resulting cNEO-MD is employed to calculate the vibrational spectra of a series of small molecules and the results are compared to those from conventional ab initio molecular dynamics (AIMD) as well as from experiments. With the same formal computational scaling, cNEO-MD greatly outperforms AIMD in describing the vibrational modes with a significant hydrogen motion character, indicating the importance of nuclear quantum effects in molecular simulations. This work opens the door to the accurate and efficient simulation of chemical and biological systems with significant nuclear quantum effects using cNEO-MD.   

Reliable lattice dynamics from an efficient density functional

First principles predictions of lattice dynamics are of vital importance for a broad range of topics in materials science and condensed matter physics. The large-scale nature of lattice dynamics calculations and the desire to design novel materials with distinct properties demands that first principles predictions are accurate, transferable, efficient, and reliable for a wide variety of materials. In this work, we demonstrate that the recently constructed r2SCAN density functional meets this need for general systems by demonstrating phonon dispersions for typical systems with distinct chemical characteristics.  The functional's performance opens a door for phonon-mediated materials discovery from first principles calculations.   

First principles binding energy evaluation of host-guest inclusion complexes

Molecular capsulation is a key technique for biopharmaceuticals. The development of molecular capsules from the theory side requires a precise evaluation of binding energy between capsules and biopharmaceutical molecules. For this purpose, density functional theory (DFT) is a suitable evaluation method due to its good balance of calculation accuracy and cost. However, it is not straightforward to accurately evaluate van der Waals and exchange interactions using a pure exchange-correlation functional. Meanwhile, empirical corrections are known to significantly improve the accuracy. In this work, we benchmark CAM and D3 corrections applied to the B3LYP functional for the binding energy between plumbagin and cyclodextrins (β-cyclodextrin/methyl-β-cyclodextrin/2-O-hydroxypropyl-β-cyclodextrin). We calculate the reference binding energy by diffusion Monte Carlo (DMC) method. DMC accurately evaluates dispersion force without any practical approximations, unlike DFT. Both B3LYP and CAM-B3LYP give almost zero binding energies (i.e., do not reproduce binding). On the other hand, B3LYP-D3 and CAM-B3LYP-D3 give similar binding energies to DMC due to the D3 correction [1]. In this talk, we will also discuss the solvent effects on the binding energies.   

Diffusion Monte Carlo Study on Relative Stabilities of Boron Nitride Polymorphs

One of the most fundamental properties of boron nitride (BN), the phase diagram, is still under debate both theoretically and experimentally even though BN compounds have well-known industrial applications. The determination of the most stable BN's polymorph (hexagonal, rhombohedral, wurtzite, and zinc-blende) is difficult with ab-initio methods because subtle vdW interactions are relevant in some of the polymorphs. This makes quantitative calculations challenging. As a result, despite significant theoretical research, there is no consensus yet on the most stable structure. There are several contradicting theoretical reports. We applied one of the state-of-the-art ab-initio methods, fixed-node diffusion Monte Carlo (FNDMC), to the four known BN's polymorphs. We also performed phonon calculations to investigate thermal stability. Our FNDMC calculations showed that hexagonal BN is the most stable among the four polymorphs at 0 K. Our calculations of the contribution of phonons to the free energy confirmed that this is the case even at 300K. We compared our results to previous sophisticated studies such as MBD, RPA, RPAx, and CCSD(T). We found that RPAx and CCSD(T) are consistent with our FNDMC, whereas MBD and RPA are not.