Session H31: Advances in Density Functional Theory IV

Extensions of time density functional theory to QED: QED-Chemistry

n this talk we will review the recent advances within density-functional and many-body based schemes to describe spectroscopic properties of complex systems with special emphasis to modelling time and spatially resolved electron spectroscopies We will discuss the theoretical approaches developed in the group for the characterisation of matter out of equilibrium, the control material processes at the electronic level and tailor material properties, and master energy and information on the nanoscale to propose new devices with capabilities. We will focus on examples linked to the efficient conversion of light into electricity or chemical fuels ("artificial photosynthesis") and the design on new nanostructured based optoelectronic devices based on inorganic nanotubes, among others. The goal is to provide a detailed, efficient, and at the same time accurate microscopic approach for the ab-initio description and control of the dynamics of decoherence and dissipation in quantum many-body systems. With the help of quantum optimal control (QOC) theory and the mastery over spectroscopy we could direct the movement of electrons, selectively trigger chemical reactions and processes, and create new materials   

Advances in time-dependent current-density functional theory

In this work we solve the problem of the gauge dependence of molecular magnetic properties (magnetizabilities, circular dichroism) using time-dependent current-density functional theory [1]. We also present a new functional that accurately describes the optical absorption spectra of insulators, semiconductors and metals [2]\\ [1] N. Raimbault, P.L. de Boeij, P. Romaniello, and J.A. Berger Phys. Rev. Lett. 114, 066404 (2015)\\ [2] J.A. Berger, Phys. Rev. Lett. 115, 137402 (2015)   

The particle-particle random phase approximation and beyond -- insight from the superconductive Gorkov perspective and implications of an efficient truncation scheme

As an excited-state electronic structure method, the particle-particle random phase approximation (ppRPA) satisfactorily resolves many challenges for the time-dependent density functional theory (TDDFT)/particle-hole (ph) RPA, e.g. absence of double excitations, diradicals, singlet-to-triplet instability, etc. Given that the ppRPA equation has been derived from the pairing potential linear response, we derive it using the propagator approach using the superconductive Gorkov formalism. Systematic higher-order contributions are added to the ppRPA, yielding the pp Bethe-Salpeter equation (BSE). This development can be combined with our recently proposed truncation scheme, which makes typical ppRPA calculations up to 100 times faster than the Davidson's algorithm. Since the electron correlation is important in yielding good excitation energies for the ppRPA (the superiority of DFT reference states over Hartree-Fock ones, esp. for large systems), combining the two developments allows us to add the electron correlation into the ppRPA calculation at a modest formal scaling of O(N4), pushing the excitation energy calculations towards both larger systems and higher accuracy.   

Calculating excitation energies with particle-particle and particle-hole random phase approximation using accurate optimized effective potentials

With an accurate electron density, one can calculate the optimized effective potential (OEP) which gives Kohn-Sham energies and eigenvectors accurately. Such Kohn-Sham energies and eigenvectors are developed here for applications in excited state calculations. In this work, Kohn-Sham results from OEP with an accurate input electron density, i.e. CCSD density, are used in excitation energy calculations, within the particle-particle and particle-hole random phase approximation (pp-, ph-RPA). Tests on small molecules, for example, BH and CH$^{+}$, matches well with the EOM-CCSD calculation for low energy excited states. For N$_{2}$, CO and H$_{2}$O, our method describes the lower excitations well compared with the experimental data and improves the results from pp- and ph-RPA based on approximate density functional approximations. This approach is thus promising for applications in calculating accurate excitation energies.   

Singlet--Triplet Energy Gaps for Diradicals from Particle--Particle Random Phase Approximation

The particle--particle random phase approximation (pp-RPA) has been applied to the calculation of vertical and adiabatic singlet--triplet energy gaps for a variety of categories of diradicals, including diatomic diradicals, carbene-like diradicals, disjoint diradicals, four-$\pi $-electron diradicals, and benzynes are calculated. Except for some excitations in four-$\pi $-electron diradicals, where four-electron correlation may play an important role, the singlet--triplet gaps are generally well predicted by pp-RPA. With a relatively low O(r4) scaling, the pp-RPA with DFT references outperforms spin-flip configuration interaction singles. It is similar to or better than the (variational) fractional-spin method. For small diradicals such as diatomic and carbene-like ones, the error of pp-RPA is slightly larger than noncollinear spin-flip time-dependent density functional theory (NC-SF-TDDFT) with LDA or PBE functional. However, for disjoint diradicals and benzynes, the pp-RPA performs much better and is comparable to NC-SF-TDDFT with long-range corrected $\omega $PBEh functional and spin-flip configuration interaction singles with perturbative doubles (SF-CIS(D)). In particular, with a correct asymptotic behavior and being almost free from static correlation error, the pp-RPA with DFT references can well describe the challenging ground state and charge transfer excitations of disjoint diradicals in which almost all other DFT-based methods fail. Therefore, the pp-RPA could be a promising theoretical method for general diradical problems.   

Thermal connection formula and linear response time-dependent density functional theory for thermal ensembles

The finite-temperature adiabatic connection formula is cast as an integral over the temperature and used to write new relations between correlation components in terms of temperature and the coupling constant. Next, the van Leeuwen proof of time-dependent density functional theory is generalized to thermal ensembles, along with the Gross-Kohn relation and the fluctuation-dissipation theorem. These results are combined with the thermal connection formula to produce a method for generating new exchange-correlation approximations.   

Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory

We present a framework for obtaining solid-state charge and optical excitations and spectra from optimally tuned range-separated hybrid density functional theory, which allows for the accurate prediction of exciton binding energies. We demonstrate our approach through calculations of one- and two-particle excitations in pentacene, a molecular semiconducting crystal, where we find excellent agreement with experiments and prior computations. We show that with one adjustable parameter, our method accurately predicts band structures and optical spectra of Si and LiF, prototypical covalent and ionic solids. For a range of extended bulk systems, this method may provide a computationally inexpensive alternative to many-body perturbation theory, opening the door to studies of materials of increasing size and complexity [Phys. Rev. B 92, 081204(R), 2015].   

Exploring Level Alignment in Molecule-Metal Interfaces with Optimally-Tuned Range-Separated Hybrid Functionals

Molecule-metal interfaces are ubiquitous in nanoscale functional materials and energy related applications. Characterizing the electronic structure at molecule-metal interfaces, especially the level alignment between molecular frontier orbitals and the Fermi level of the combined system, is crucial for understanding charge dynamics. Density functional theory (DFT) has been successful in computing binding geometries and adsorption energies, but much less successful in predicting level alignment. This is because the latter depends on quasiparticle excitation energies, typically believed to be outside the reach of DFT. In this work, we apply the recently developed optimally-tuned range-separated hybrid functional to the electronic structure of a model molecule-metal interface - benzene on graphite - and elucidate parameters leading to agreement with experiment and with many-body perturbation theory.   

Chemically accurate description of aromatic rings interaction using quantum Monte Carlo

We present an accurate study of interactions between benzene molecules using wave function based quantum Monte Carlo (QMC) methods [1]. We compare our QMC results with density functional theory (DFT) using various van der Waals (vdW) functionals. This comparison enables us to tune vdW functionals. We show that highly optimizing the wave function and introducing more dynamical correlation into the wave function are crucial to calculate the weak chemical binding energy between benzene molecules. The good agreement among our results, experiments and quantum chemistry methods, is an important sign of the capability of the wave function based QMC methods to provide accurate description of very weak intermolecular interactions based on vdW dispersive forces. $\backslash $pardReferences:1] Sam Azadi, and R. E. Cohen, J. Chem. Phys. \textbf{143}, 104301 (2015).   

Study of a Quantum Dot in an Excited State

We have studied the first excited singlet state of a quantum dot via quantal density functional theory (QDFT). The quantum dot is represented by a 2D Hooke's atom in an external magnetostatic field. The QDFT mapping is from an excited singlet state of this interacting system to one of noninteracting fermions in a singlet ground state. The results of the study will be compared to (a) the corresponding mapping$^{1}$ from a ground state of the quantum dot and (b) to the similar mapping$^{2}$ from an excited singlet state of the 3D Hooke's atom. $^{1}$ T. Yang, X.-Y. Pan, and V. Sahni, PRA \textbf{83}, 042518 (2011) $^{2}$ M. Slamet and V. Sahni, IJQC \textbf{85}, 436 (2001)   

First-principles photoemission spectroscopy in DNA and RNA nucleobases from Koopmans-compliant functionals

The determination of spectral properties of the DNA and RNA nucleobases from first principles can provide theoretical interpretation for experimental data, but requires complex electronic-structure formulations that fall outside the domain of applicability of common approaches such as density-functional theory. In this work, we show that Koopmans-compliant functionals [1], constructed to enforce piecewise linearity in energy functionals with respect to fractional occupation-i.e., with respect to charged excitations-can predict not only frontier ionization potentials and electron affinities of the nucleobases with accuracy comparable or superior with that of many-body perturbation theory and high-accuracy quantum chemistry methods, but also the molecular photoemission spectra are shown to be in excellent agreement with experimental ultraviolet photoemsision spectroscopy data. The results highlight the role of Koopmans-compliant functionals as accurate and inexpensive quasiparticle approximations to the spectral potential, which transform DFT into a novel dynamical formalism where electronic properties, and not only total energies, can be correctly accounted for. Reference [1] N.L. Nguyen et al., PRL (2015).   

van der Waals Density Functional Theory vdW-DFq for Semihard Materials

There are a large number of materials with mild stiffness, which are not as soft as tissues and not as strong as metals. These semihard materials includes energetic materials, molecular crystals, layered materials, and van der Waals crystals. The integrity and mechanical stability are mainly determined by the interactions between instantaneously induced dipoles, the so called London dispersion force or van der Waals force. It is challenging to accurately model the structural and mechanical properties of these semihard materials in the frame of density functional theory where the non-local correlation functionals are not well known. Here we propose a van der Waals density functional named {\em vdW-DFq} to accurately model the density and geometry of semihard materials. Using $\beta$-cyclotetramethylene tetranitramine as a prototype, we adjust the enhancement factor of the exchange energy functional with generalized gradient approximations. We find this method to be simple and robust over a wide tuning range when calibrating the functional on-demand with experimental data. With a calibrated value $q=1.05$, the proposed vdW-DFq method shows good performance in predicting the geometries of 11 common energetic material molecular crystals and 3 typical layered van der Waals crystals.   

A non-empirical, parameter-free, hybrid functional for accurate calculations of optoelectronic properties of finite systems

The accurate prediction of optoelectronic properties of molecules and solids is a persisting challenge for current density functional theory (DFT) based methods. We propose a hybrid functional where the mixing fraction of exact and local exchange is determined by a non-empirical, system dependent function. This functional yields ionization potentials, fundamental and optical gaps of many, diverse systems in excellent agreement with experiments, including organic and inorganic molecules and nanocrystals. We further demonstrate that the newly defined hybrid functional gives the correct alignment between the energy level of the exemplary TTF-TCNQ donor-acceptor system.