# Research

2012
Refaely-Abramson, S. ; Sharifzadeh, S. ; Govind, N. ; Autschbach, J. ; Neaton, J. B. ; Baer, R. ; Kronik, L. Quasiparticle Spectra from a Nonempirical Optimally Tuned Range-Separated Hybrid Density Functional. Phys. Rev. Lett. 2012, 109, 226405. Publisher's VersionAbstract

We present a method for obtaining outer-valence quasiparticle excitation energies from a density-functional-theory-based calculation, with an accuracy that is comparable to that of many-body perturbation theory within the GW approximation. The approach uses a range-separated hybrid density functional, with an asymptotically exact and short-range fractional Fock exchange. The functional contains two parameters, the range separation and the short-range Fock fraction. Both are determined nonempirically, per system, on the basis of the satisfaction of exact physical constraints for the ionization potential and frontier-orbital many-electron self-interaction, respectively. The accuracy of the method is demonstrated on four important benchmark organic molecules: perylene, pentacene, 3,4,9,10-perylene-tetracarboxylic-dianydride (PTCDA), and 1,4,5,8-naphthalene-tetracarboxylic-dianhydride (NTCDA). We envision that for the outer-valence excitation spectra of finite systems the approach could provide an inexpensive alternative to GW, opening the door to the study of presently out of reach large-scale systems.

Kronik, L. ; Stein, T. ; Refaely-Abramson, S. ; Baer, R. Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals. J. Chem. Theory Comput. 2012, 8 1515–1531.Abstract

Excitation gaps are of considerable significance in electronic structure theory. Two different gaps are of particular interest. The fundamental gap is defined by charged excitations, as the difference between the first ionization potential and the first electron affinity. The optical gap is defined by a neutral excitation, as the difference between the energies of the lowest dipole-allowed excited state and the ground state. Within many-body perturbation theory, the fundamental gap is the difference between the corresponding lowest quasi-hole and quasi-electron excitation energies, and the optical gap is addressed by including the interaction between a quasi-electron and a quasi-hole. A long-standing challenge has been the attainment of a similar description within density functional theory (DFT), with much debate on whether this is an achievable goal even in principle. Recently, we have constructed and applied a new approach to this problem. Anchored in the rigorous theoretical framework of the generalized Kohn–Sham equation, our method is based on a range-split hybrid functional that uses exact long-range exchange. Its main novel feature is that the range-splitting parameter is not a universal constant but rather is determined from first principles, per system, based on satisfaction of the ionization potential theorem. For finite-sized objects, this DFT approach mimics successfully, to the best of our knowledge for the first time, the quasi-particle picture of many-body theory. Specifically, it allows for the extraction of both the fundamental and the optical gap from one underlying functional, based on the HOMO–LUMO gap of a ground-state DFT calculation and the lowest excitation energy of a linear-response time-dependent DFT calculation, respectively. In particular, it produces the correct optical gap for the difficult case of charge-transfer and charge-transfer-like scenarios, where conventional functionals are known to fail. In this perspective, we overview the formal and practical challenges associated with gap calculations, explain our new approach and how it overcomes previous difficulties, and survey its application to a variety of systems.

Jain, P. K. ; Ghosh, D. ; Baer, R. ; Rabani, E. ; Alivisatos, A. P. Near-field manipulation of spectroscopic selection rules on the nanoscale. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 8016–8019.Abstract

In conventional spectroscopy, transitions between electronic levels are governed by the electric dipole selection rule because electric quadrupole, magnetic dipole, and coupled electric dipole-magnetic dipole transitions are forbidden in a far field. We demonstrated that by using nanostructured electromagnetic fields, the selection rules of absorption spectroscopy could be fundamentally manipulated. We also show that forbidden transitions between discrete quantum levels in a semiconductor nanorod structure are allowed within the near-field of a noble metal nanoparticle. Atomistic simulations analyzed by an effective mass model reveal the breakdown of the dipolar selection rules where quadrupole and octupole transitions are allowed. Our demonstration could be generalized to the use of nanostructured near-fields for enhancing light-matter interactions that are typically weak or forbidden.

Jacobi, S. ; Baer, R. Variational grand-canonical electronic structure of Li+ Li at 10,000 K with second-order perturbation theory corrections. Theor. Chem. Acc. 2012, 131, 1113.Abstract

An ab initio variational grand-canonical electronic structure mean-field method, based on the Gibbs–Peierls–Bogoliubov minimum principle for the Gibbs free energy, is applied to the di-lithium (Li+Li) system at temperatures around T \approx 10,000 K and electronic chemical potential of μ \approx -0.1Eh. The method is an extension of the Hartree–Fock approach to finite temperatures. We first study the Li2 molecule at a frozen inter-nuclear distance of R = 3 \AA as a function of temperature. The mean-field electronic structure changes smoothly as temperature increases, up to 104 K, where a sharp spontaneous spin-polarization emerges as the variational mean-field solution. Further increase in the temperature extinguishes this polarization. We analyze the mean-field behavior using a correlated single-site Hubbard model and show it arises from an attempt of the mean-field to mimic the polarization of the spin–spin correlation function of the exact solution. Next, we keep constant the temperature at 104 K and examine the electronic structure as a function of inter-nuclear distance R. At R = 3.7 \AA, a crossing between two free energy states occurs: One state is “spin-unpolarized” (becomes lower in energy when R \ge 3.7 \AA), while the other is “spin polarized”. This crossing causes near-discontinuous jumps in calculated properties of the system and is associated with using the noninteracting electron character of our mean-field approach. Such problems will likely plague FT-DFT calculations as well. We use second-order perturbation theory (PT2) to study effects of electron correlation on the potential of mean force between the two colliding Li atoms. We find that PT2 correlation free energy at  104 K is larger than at 0 K and tends to restore the spin-polarized state as the lowest free energy solution.

Baratz, A. ; Baer, R. Nonmechanical Conductance Switching in a Molecular Tunnel Junction. J. Phys. Chem. Lett. 2012, 3 498–502.Abstract

We present a molecular junction composed of a donor (polyacetylene strands) and an acceptor (malononitrile) connected together via a benzene ring and coupled weakly to source and drain electrodes on each side, for which a gate electrode induces intramolecular charge transfer, switching reversibly the character of conductance. Using a new brand of density functional theory, for which orbital energies are similar to the quasiparticle energies, we show that the junction displays a single, gate-tunable differential conductance channel in a wide energy range. The gate field must align parallel to the displacement vector between donors and acceptor to affect their potential difference; for strong enough fields, spontaneous intramolecular electron transfer occurs. This event radically affects conductance, reversing the charge of carriers, enabling a spin-polarized current channel. We discuss the physical principles controlling the operation of the junction and find interplay of quantum interference, charging, Coulomb blockade, and electron-hole binding energy effects. We expect that this switching behavior is a generic property for similar donor-acceptor systems of sufficient stability.

Baer, R. ; Neuhauser, D. Communication: Monte Carlo calculation of the exchange energy. J. Chem. Phys. 2012, 137, 051103–4.Abstract

In recent generalized Kohn-Sham (GKS) schemes for density functional theory (DFT) Hartree-Fock type exchange is important. In plane waves and grid approaches the high cost of exchange energy calculations makes these GKS considerably more expensive than Kohn-Sham DFT calculations. We develop a stochastic approach for speeding up the calculation of exchange for large systems. We show that stochastic error per particle does not grow and can even decrease with system size (at a given number of iterations). We discuss several alternative approaches and explain how these ideas can be included in the GKS framework.

Baer, R. ; Rabani, E. Expeditious stochastic calculation of multiexciton generation rates in semiconductor nanocrystals. Nano Lett. 2012, 12, 2123–2128.Abstract

A stochastic method is developed to calculate the multiexciton generation (MEG) rates in semiconductor nanocrystals (NCs). The numerical effort scales near-linearly with system size allowing the study of MEG rates up to diameters and exciton energies previously unattainable using atomistic calculations. Illustrations are given for CdSe NCs of sizes and energies relevant to current experimental setups, where direct methods require treatment of over 1011 states. The approach is not limited to the study of MEG and can be applied to calculate other correlated electronic processes.

Ansbacher, T. ; Srivastava, H. K. ; Stein, T. ; Baer, R. ; Merkx, M. ; Shurki, A. Calculation of transition dipole moment in fluorescent proteins—towards efficient energy transfer. Phys. Chem. Chem. Phys. 2012, 14, 4109–4117.Abstract

Forster Resonance Energy Transfer (FRET) between fluorescent proteins (FPs) is widely used to construct fluorescent sensor proteins, to study intracellular protein-protein interactions and to monitor conformational changes in multidomain proteins. Although FRET depends strongly on the orientation of the transition dipole moments (TDMs) of the donor and acceptor fluorophores, this orientation dependence is currently not taken into account in FRET sensor design. Similarly, studies that use FRET to derive structural constrains typically assume a kappa(2) of 2/3 or use the TDM of green fluorescent protein, as this is the only FP for which the TDM has been determined experimentally. Here we used time-dependent density functional theory (TD-DFT) methods to calculate the TDM for a comprehensive list of commonly used fluorescent proteins. The method was validated against higher levels of calculation. Validation with model compounds and the experimentally determined TDM of GFP shows that the TDM is mostly determined by the structure of the pi-conjugated fluorophore and is insensitive to non-conjugated side chains or the protein surrounding. Our calculations not only provide TDM for most of the currently used FPs, but also suggest an empirical rule that can be used to obtain the TDMs for newly developed fluorescent proteins in the future.

2011
Refaely-Abramson, S. ; Baer, R. ; Kronik, L. Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned range-separated hybrid functional. Phys. Rev. B 2011, 84, 075144.Abstract

The fundamental and optical gaps of relevant molecular systems are of primary importance for organic-based photovoltaics. Unfortunately, whereas optical gaps are accessible with time-dependent density functional theory (DFT), the highest-occupied - lowest-unoccupied eigenvalue gaps resulting from DFT calculations with semi-local or hybrid functionals routinely and severely underestimate the fundamental gaps of gas-phase organic molecules. Here, we show that a range-separated hybrid functional, optimally tuned so as to obey Koopmans' theorem, provides fundamental gaps that are very close to benchmark results obtained from many-body perturbation theory in the GW approximation. We then show that using this functional does not compromise the possibility of obtaining reliable optical gaps from time-dependent DFT. We therefore suggest optimally tuned range-separated hybrid functionals as a practical and accurate tool for DFT-based predictions of photovoltaically relevant and other molecular systems.

Kuritz, N. ; Stein, T. ; Baer, R. ; Kronik, L. Charge-transfer-like $π$\ to $π$* excitations in time-dependent density functional theory: A conundrum and its solution. J. Chem. Theory Comput. 2011, 7 2408–2415.Abstract

We address the conundrum posed by the well-known failure of time-dependent DFT (TDDFT) with conventional functionals for "charge-transfer-like" excitations in oligoacenes. We show that this failure is due to a small spatial overlap in orbitals obtained from the underlying single-electron orbitals by means of a unitary transformation. We further show that, as in true charge-transfer excitations, this necessarily results in failure of linear-response TDDFT with standard functionals. Range-separated hybrid functionals have been previously shown to mitigate such errors but at the cost of an empirically adjusted range-separation parameter. Here, we explain why this approach should succeed where conventional functionals fail. Furthermore, we show that optimal tuning of a range-separated hybrid functional, so as to enforce the DFT version of Koopmans' theorem, restores the predictive power of TDDFT even for such difficult cases, without any external reference data and without any adjustable parameters. We demonstrate the success of this approach on the oligoacene series and on related hydrocarbons. This resolves a long-standing question in TDDFT and extends the scope of molecules and systems to which TDDFT can be applied in a predictive manner.

Livshits, E. ; Granot, R. S. ; Baer, R. A Density Functional Theory for Studying Ionization Processes in Water Clusters. J. Phys. Chem. A 2011, 115, 5735–5744. Publisher's VersionAbstract

A generalized Kohn-Sham (GKS) approach to density functional theory (DFT), based on the Baer-Neuhauser-Livshits range-separated hybrid, combined with ab initio motivated range-parameter tuning is used to study properties of water dimer and pentamer cations. The water dimer is first used as a benchmark system to check the approach. The present brand of DFT localizes the positive charge (hole), stabilizing the proton transferred geometry in agreement with recent coupled-cluster calculations. Relative energies of various conformers of the water dimer cation compare well with previously published coupled cluster results. The GKS orbital energies are good approximations to the experimental ionization potentials of the system. Low-lying excitation energies calculated from time-dependent DFT based on the present method compare well with recently published high-level "equation of motion-coupled-cluster" calculations. The harmonic frequencies of the water dimer cation are in good agreement with experimental and wave function calculations where available. The method is applied to study the water pentamer cation. Three conformers are identified: two are Eigen type and one is a Zundel type. The structure and harmonic vibrational structure are analyzed. The ionization dynamics of a pentamer water cluster at 0 K shows a fast <50 fs transient for transferring a proton from one of the water molecules, releasing a hydroxyl radical and creating a protonated tetramer carrying the excess hole.

Karolewski, A. ; Stein, T. ; Baer, R. ; Kümmel, S. Communication: Tailoring the optical gap in light-harvesting molecules. J. Chem. Phys. 2011, 134, 151101.Abstract

Systematically varying the optical gap that is associated with charge-transfer excitations is an important step in the design of light-harvesting molecules. So far the guidance that time-dependent density functional theory could give in this process was limited by the traditional functionals' inability to describe charge-transfer excitations. We show that a nonempirical range-separated hybrid approach allows to reliably predict charge-transfer excitations for molecules of practically relevant complexity. Calculated absorption energies agree with measured ones. We predict from theory that by varying the number of thiophenes in donor-acceptor-donor molecules, the energy of the lowest optical absorption can be tuned to the lower end of the visible spectrum. Saturation sets in at about five thiophene rings. (C) 2011 American Institute of Physics. [doi:10.1063/1.3581788]

2010
Stein, T. ; Eisenberg, H. R. ; Kronik, L. ; Baer, R. Fundamental gaps in finite systems from eigenvalues of a generalized Kohn-Sham method. Phys. Rev. Lett. 2010, 105, 266802.Abstract

We present a broadly applicable, physically motivated, first-principles approach to determining the fundamental gap of finite systems from single-electron orbital energies. The approach is based on using a range-separated hybrid functional within the generalized Kohn-Sham approach to density functional theory. Its key element is the choice of a range-separation parameter such that Koopmans’ theorem for both neutral and anion is obeyed as closely as possible. We demonstrate the validity, accuracy, and advantages of this approach on first, second and third row atoms, the oligoacene family of molecules, and a set of hydrogen-passivated silicon nanocrystals. This extends the quantitative usage of density functional theory to an area long believed to be outside its reach.

Paul, A. K. ; Adhikari, S. ; Baer, M. ; Baer, R. H2 + photodissociation by an intense pulsed photonic Fock state. Phys. Rev. A 2010, 81, 013412.Abstract

We study the photodissociation of the H+2 molecule by ultrashort Fock-state electromagnetic pulses (EMPs). We use the Born-Oppenheimer treatment combined with an explicit photon number representation via diabatic electrophoton potential surfaces for simplification of the basic equations. We discuss the issue of the number of photon states required and show that six photon states enable good accuracy for photoproduct kinetic energies of up to 3 eV. We calculate photodissociation probabilities and nuclear kinetic-energy (KE) distributions of the photodissociation products for 800 nm, 50-TW/cm2 pulses. We show that KE distributions depend on three pulse durations of 10, 20, and 45 fs and on various initial vibrational states of the molecule. We compare the Fock-state results to those obtained by “conventional,” i.e., coherent-state, laser pulses of equivalent electric fields and durations. The effects of the quantum state of EMPs on the photodissociation dynamics are especially strong for high initial vibrational states of H+2. While coherent-state pulses suppress photodissociation for the high initial vibrational states of H+2, the Fock-state pulses enhance it.

Rabani, E. ; Baer, R. Theory of multiexciton generation in semiconductor nanocrystals. Chem. Phys. Lett. 2010, 496, 227–235.Abstract

We develop a generalized framework based on a Green’s function formalism to calculate the efficiency of multiexciton generation in nanocrystal quantum dots. The direct/indirect absorption and coherent/incoherent impact ionization mechanisms, often used to describe multiexciton generation in nanocrystals, are reviewed and rederived from the unified theory as certain approximations. In addition, two new limits are described systematically – the weak Coulomb coupling limit and the semi-wide band limit. We show that the description of multiexciton generation in nanocrystals can be described as incoherent process and we discuss the scaling of multiexciton generation with respect to the photon energy and nanocrystal size. Illustrations are given for three prototype systems: CdSe, InAs and silicon quantum dots.

Baer, R. ; Rabani, E. Can Impact Excitation Explain Efficient Carrier Multiplication in Carbon Nanotube Photodiodes?. Nano Lett. 2010, 10, 3277–3282.Abstract

We address recent experiments (Science 2009, 325, 1367) reporting on highly efficient multiplication of electron?hole pairs in carbon nanotube photodiodes at photon energies near the carrier multiplication threshold (twice the quasi-particle band gap). This result is surprising in light of recent experimental and theoretical work on multiexciton generation in other confined materials, such as semiconducting nanocrystals. We propose a detailed mechanism based on carrier dynamics and impact excitation resulting in highly efficient multiplication of electron?hole pairs. We discuss the important time and energy scales of the problem and provide analysis of the role of temperature and the length of the diode.

Baer, R. Ground-State Degeneracies Leave Recognizable Topological Scars in the Electronic Density. Phys. Rev. Lett. 2010, 104, 073001.Abstract

In Kohn-Sham density functional theory (KS DFT) a fictitious system of noninteracting particles is constructed having the same ground-state (GS) density as the physical system of interest. A fundamental open question in DFT concerns the ability of an exact KS calculation to spot and characterize the GS degeneracies in the physical system. In this Letter we provide theoretical evidence suggesting that the GS density, as a function of position on a 2D manifold of parameters affecting the external potential, is â€øe}topologically scarredâ€ï¿½ in a distinct way by degeneracies. These scars are sufficiently detailed to enable determination of the positions of degeneracies and even the associated Berry phases. We conclude that an exact KS calculation can spot and characterize the degeneracies of the physical system.

Baer, R. ; Livshits, E. ; Salzner, U. Tuned Range-separated hybrids in density functional theory. Annu. Rev. Phys. Chem. 2010, 61, 85–109. Publisher's VersionAbstract

We review density functional theory (DFT) within the Kohn-Sham (KS) and the generalized KS (GKS) frameworks from a theoretical perspective for both time-independent and time-dependent problems. We focus on the use of range-separated hybrids within a GKS approach as a practical remedy for dealing with the deleterious long-range self-repulsion plaguing many approximate implementations of DFT. This technique enables DFT to be widely relevant in new realms such as charge transfer, radical cation dimers, and Rydberg excitations. Emphasis is put on a new concept of system-specific range-parameter tuning, which introduces predictive power in applications considered until recently too difficult for DFT.

2009
Stein, T. ; Kronik, L. ; Baer, R. Prediction of charge-transfer excitations in coumarin-based dyes using a range-separated functional tuned from first principles. J. Chem. Phys. 2009, 131, 244119–5.Abstract

We study the description of charge-transfer excitations in a series of coumarin-based donor-bridge-acceptor dyes. We show that excellent predictive power for the excitation energies and oscillator strengths in these systems is obtained by using a range-separated hybrid functional within the generalized Kohn–Sham approach to time-dependent density functional theory. Key to this success is a step for tuning the range separation parameter from first principles. We explore different methods for this tuning step, which are variants of a recently suggested approach for charge-transfer excitations [T. Stein et al., J. Am. Chem. Soc. 131, 2818 (2009)]. We assess the quality of prediction by comparing to excitation energies previously published for the same systems using the approximate coupled-cluster singles and doubles (CC2) method.

Stein, T. ; Kronik, L. ; Baer, R. Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory. J. Am. Chem. Soc. 2009, 131, 2818–2820.Abstract

We show how charge transfer excitations at molecular complexes can be calculated quantitatively using time-dependent density functional theory. Predictive power is obtained from range-separated hybrid functionals using nonempirical tuning of the range-splitting parameter. Excellent performance of this approach is obtained for a series of complexes composed of various aromatic donors and the tetracyanoethytene acceptor, paving the way to systematic nonempirical quantitative studies of charge-transfer excitations in real systems.