Session C20: Electronic Structure Methods II

A DMC study on FePc electronic state

We performed fixed-node DMC calculations on an isolated FePc [Iron(II) Phthalocyanine] using CASSCF nodal surfaces, getting its ground state, $^3A_{2g}$ [$d^2_{z^2}d^{2}_{xz,yz}d^{2}_{xy}$]. Virial ratios for each state are achieved to be within 0.042\% around 2.0. Recent studies [1] are proposing a mixed state with $^3E_g(b)$ and $^3B_{2g}$ as the ground state, while past ab-initio calculations [2] are predicting $^3A_{2g}$ or $^3E_g(a)$, giving still controversial arguments even within isolated/no-LS coupling model. Under $D_{4h}$ ligand field parameter space, ($10D_q$, $D_t$, $D_s$), the state, $^3A_{2g}$, is reported to be possible as a ground state [3], while it is not when we restrict the space into 2-dim sub-space corresponding to more specified symmetry as in FePc with plane square alignment of neighboring N to Fe ('superposition model' [4]). Our optimized geometry also satisfies the same symmetry, and hence appears to be contradicting to the ligand theory[4]. [1] J. Fern\'{a}ndez-Rodr\'{i}guez {\it et al.}, Phys. Rev. B {\bf 91}, 214427 (2015). [2] K. Nakamura {\it et al.}, Phys. Rev. B {\bf 85}, 235129 (2012). [3] P.S. Miedema {\it et al.} , J. Phys.: Conf. Ser. {\bf 190} , 012143 (2009). [4] M.D. Kuz’min {\it et al.} , J. Chem. Phys. {\bf 138} , 244308 (2013).   

An effective model for LaTiO3 using first principles quantum Monte Carlo

The rare earth perovskites have long been of interest due in part to the interplay of their geometries and electronic properties. The perovskite LaTiO3 in particular is an antiferromagnetic insulator with a small 0.2 eV band gap that displays the GdFeO3 distortion at ambient pressure. We apply a new technique[1] to derive an effective model for LaTiO3 as a function of the distortion. Since this technique treats one and two-body degrees of freedom on an equal footing, we use it to evaluate the evolution of effective model parameters with changes in the lattice. We will report on the progress in assessing whether the insulating nature is due to the distortion, or vice versa. [1] Changlani, Zheng, and Wagner J. Chem. Phys. 143, 102814 (2015).   

Electronic and structural properties of M$_3$(HITP)$_2$ (M = Ni, Cu and Co) metal-organic frameworks

Theoretical and experimental works have demonstrated that electrical and structural properties of metal-organic frameworks (MOF) can be significantly changed by the identity of the metal center, leading to a potential strategy for tuning the selectivity of the material toward different types of technological applications. In this work, we use first principle calculations to investigate the electronic properties of 2D MOF M$_3$(HITP)$_2$ (M is Ni, Cu and Co and HITP = 2,3,6,7,10,11 – hexaiminotriphenylene). Our results show that for M=Ni and Co, the structures are perfect planar and there is a full charge delocalization in the 2D plane of stacking due to the predominance of $\pi-\pi$ bonding. The band structure for M = Ni shows that this material is a semiconductor with an indirect band gap of 132 meV, whilst for M = Co the band structure shows that this material is a ferromagnetic semiconductor with a direct band gap of 386 meV for spin down and a indirect band gap of 246 meV for spin up. For M=Cu, the material is a metal and adopts a distorted structure due to a different hybridization of the metal atom in comparison with its counterparts. We also propose a tight binding model that can represent the electronic structure near the Fermi level of this family of MOF.   

Band structure of correlated Sr$_2$RuO$_4$ using DFT+DMFT

The discovery of superconductivity in the cuprates stimulated investigations on materials sharing similar structural properties. Ruthenates, including Sr$_2$2RuO$_4$ became of great interest since they were found to be unconventional superconductors, possibly $p$-wave, at sufficiently low temperature. A lot of experimental data was acquired and analyzed over the past decade. Of particular interest is the discrepancy between the calculated and measured effective masses. In this presentaiton, we will present DFT+DMFT calculations as implemented in the ABINIT program to compute the electronic structure of Sr$_2$2RuO$_4$.   

A general optimization method applied to a vdW-DF functional for water

In particularly delicate systems, like liquid water, ab initio exchange and correlation functionals are simply not accurate enough for many practical applications. In these cases, fitting the functional to reference data is a sensible alternative to empirical interatomic potentials. However, a global optimization requires functional forms that depend on many parameters and the usual trial and error strategy becomes cumbersome and suboptimal. We have developed a general and powerful optimization scheme called data projection onto parameter space (DPPS) and applied it to the optimization of a van der Waals density functional (vdW-DF) for water. In an arbitrarily large parameter space, DPPS solves for vector of unknown parameters for a given set of known data, and poorly sampled subspaces are determined by the physically-motivated functional shape of ab initio functionals using Bayes' theory. We present a new GGA exchange functional that has been optimized with the DPPS method for 1-body, 2-body, and 3-body energies of water systems and results from testing the performance of the optimized functional when applied to the calculation of ice cohesion energies and ab initio liquid water simulations. We found that our optimized functional improves the description of both liquid water and ice when compared to other versions of GGA exchange.   

Solvated ions as defects in liquid water: A first-principles perspective

Understanding the electronic properties of solvated ions is crucial in order to control and engineer aqueous electrolytes for a wide variety of emerging energy and environmental technologies, including photocatalytic water splitting. In this talk, we present a strategy to evaluate electronic energy levels of simple solvated ions in aqueous solutions, using a combination of first-principles molecular dynamics simulations and many-body perturbation theory within the GW approximation. We considered CO$_3^{2-}$, HCO$_3^{-}$, NO$_3^{-}$, NO$_2^{-}$ ions and we show that by analogy to defects in semiconductors, these solvated ions may be classified as deep or shallow defects in liquid water. In particular CO$_3^{2-}$ and NO$_2^{-}$ ions behave as shallow defects, while HCO$_3^{-}$ and NO$_3^{-}$ as deep ones. We also show that the inclusion of many-body corrections constitutes significant improvement over conventional density functional theory calculations, yielding satisfactory agreement with photoemission experiments.   

Evaluation of Hamaker coefficients using Diffusion Monte Carlo method

We evaluated the Hamaker's constant for Cyclohexasilane to investigate its wettability, which is used as an ink of 'liquid silicon' in 'printed electronics'. Taking three representative geometries of the dimer coalescence (parallel, lined, and T-shaped), we evaluated these binding curves using diffusion Monte Carlo method. The parallel geometry gave the most long-ranged exponent, $\sim 1/r^6$, in its asymptotic behavior. Evaluated binding lengths are fairly consistent with the experimental density of the molecule. The fitting of the asymptotic curve gave an estimation of Hamaker's constant being around 100 [zJ]. We also performed a CCSD(T) evaluation and got almost similar result. To check its justification, we applied the same scheme to Benzene and compared the estimation with those by other established methods, Lifshitz theory and SAPT (Symmetry-adopted perturbation theory). The result by the fitting scheme turned to be twice larger than those by Lifshitz and SAPT, both of which coincide with each other. It is hence implied that the present evaluation for Cyclohexasilane would be overestimated.   

Exploring Reaction Mechanism on Generalized Force Modified Potential Energy Surfaces (G-FMPES) for Diels-Alder Reaction

We apply a recent formulation for searching minimum energy reaction path (MERP) and saddle point to atomic systems subjected to an external force. We demonstrate the effect of a loading modality resembling hydrostatic pressure on the trans to cis conformational change of 1,3-butadiene, and the simplest Diels-Alder reaction between ethylene and 1,3-butadiene. The calculated MERP and saddle points on the generalized force modified potential energy surface (G-FMPES) are compared with the corresponding quantities on an unmodified potential energy surface. Our study is performed using electronic structure calculations at the HF/6-31G** level as implemented in the AIMS-MOLPRO code. Our calculations suggest that the added compressive pressure lowers the energy of cis butadiene. The activation energy barrier for the concerted Diels-Alder reaction is found to decrease progressively with increasing compressive pressure.   

Fast molecular dynamics simulations using high-order forces and nonlocal operators in real space

We present a new modification to the finite-difference based real space pseudopotential density functional theory method as implemented in the code PARSEC. By using a high-order treatment of the nonlocal pseudopotential terms in the Hamiltonian, as well as integration performed during post-processing the wave functions, we improve the accuracy of total energy and interatomic forces. We perform molecular dynamics simulations for several systems, including organic molecules and small clusters. We demonstrate significant reduction in energy drift owing to the accuracy of our improved force calculations. Furthermore, the reduction in numerical noise as atoms move over the grid permits a larger grid spacing than would be possible with a conventional discretization.   

Real-space pseudopotential methods for calculating the vibrational Stark tuning rate

We introduce a real-space method based on pseudopotentials constructed within density functional theory for computing the vibrational Stark effect. With wave functions defined in real space and cluster boundary conditions, convergence is controlled solely by the grid spacing. Moreover, charged systems can be incorporated without a compensating background charge. Real space methods also have the advantage that neither polarization functions nor supercells are required to simulate external electric fields. We illustrate this method by calculating the Stark tuning rates of small carbonyls and nitriles. The use of high-order integration techniques allow for a coarser (less expensive) grid spacing. Perturbative methods for determining the tuning rate will also be discussed.   

Unbiased QM/MM approach using accurate multipoles from a linear scaling DFT calculation with a systematic basis set

The quantum mechanics/molecular mechanis (QM/MM ) method is a popular approach that allows to perform atomistic simulations using different levels of accuracy. Since only the essential part of the simulation domain is treated using a highly precise (but also expensive) QM method, whereas the remaining parts are handled using a less accurate level of theory, this approach allows to considerably extend the total system size that can be simulated without a notable loss of accuracy. In order to couple the QM and MM regions we use an approximation of the electrostatic potential based on a multipole expansion. The multipoles of the QM region are determined based on the results of a linear scaling Density Functional Theory (DFT) calculation using a set of adaptive, localized basis functions, as implemented within the BigDFT software package. As this determination comes at virtually no extra cost compared to the QM calculation, the coupling between QM and MM region can be done very efficiently. In this presentation I will demonstrate the accuracy of both the linear scaling DFT approach itself as well as of the approximation of the electrostatic potential based on the multipole expansion, and show some first QM/MM applications using the aforementioned approach.   

Large-scale All-electron Density Functional Theory Calculations using Enriched Finite Element Method

We present a computationally efficient method to perform large-scale all-electron density functional theory calculations by enriching the Lagrange polynomial basis in classical finite element (FE) discretization with atom-centered numerical basis functions, which are obtained from the solutions of the Kohn-Sham (KS) problem for single atoms. We term these atom-centered numerical basis functions as enrichment functions. The integrals involved in the construction of the discrete KS Hamiltonian and overlap matrix are computed using an adaptive quadrature grid based on gradients in the enrichment functions. Further, we propose an efficient scheme to invert the overlap matrix by exploiting its $LDL$ factorization and employing spectral finite elements along with Gauss-Lobatto quadrature rules. Finally, we use a Chebyshev polynomial based acceleration technique to compute the occupied eigenspace in each self-consistent iteration. We demonstrate the accuracy, efficiency and scalability of the proposed method on various metallic and insulating benchmark systems, with systems ranging in the order of 10,000 electrons. We observe a 50-100 fold reduction in the overall computational time when compared to classical FE calculations while being commensurate with the desired chemical accuracy.   

\textbf{Ultrafast Response of the Hubbard Model: Non-adiabatic TDDFT}$+$\textbf{DMFT versus Non-equilibrium DMFT Solution}

We study the ultrafast response of electrons in the one-band Hubbard model to an external laser-pulse perturbation by using the Non-adiabatic~Time-Dependent Density Functional Theory $+$ Dynamical Mean-Field Theory (TDDFT$+$DMFT) approach.~The corresponding~exchange-correlation kernel (XC) is obtained from the DMFT charge susceptibility by using the~Quantum Monte Carlo~solver for the impurity problem. Detailed analysis of the time-dependent excited charge density, the Fermi distribution function, and the spatially nonhomogeneous response (metallic domain growth), is performed for different~values for the carrier density and local Coulomb repulsion. We compare the results with~the corresponding~non-equilibrium DMFT~solutions, and demonstrate that non-adiabaticity (frequency-dependence) of the XC kernel is important in order to~reproduce the non-equilibrium~DMFT solution. Also, from the numerical results for the charge susceptibility,~we obtain an approximate analytical expression for the XC kernel.~Using this kernel, we reveal possible types of "elementary" excitations and the dynamics of metallic domain growth in the case of the one-band Hubbard model. Possible generalization of the approach to the multi-orbital case is discussed.   

Improving Boundary Conditions for Electronic Structure Calculations

Boundary conditions imposed on a local system joined to a much larger substrate system routinely introduce unphysical reflections that affect the calculation of electronic properties such as energies, charge densities, and densities of states. These problems persist in atomic cluster, slab, and supercell calculations alike. However, wave functions in real, physical systems do not reflect at artificial boundaries. Instead, they carry current smoothly across the surface separating the local system from the underlying medium. Haydock and Nex have derived a non-reflecting boundary condition that works well for discrete systems [Phys. Rev. B 75, 205121 (2006)]. Solutions satisfying their maximal breaking of time-reversal symmetry (MBTS) boundary condition carry current away from the boundary at a maximal rate---in much the same way as exact wave functions in physical systems. The MBTS approach has now been extended to studies employing continuous basis functions. In model systems, MBTS boundary conditions work well for calculating wave functions, eigenenergies, and densities of states. Results are reported for an Al(001) surface. Comparisons are made with slab calculations, embedding calculations, and experiment.