Optimal 1st-principles tuning

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]

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.

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.

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.

Salzner, U. ; Baer, R. Koopmans' springs to life. J. Chem. Phys. 2009, 131, 231101.Abstract

The meaning of orbital energies (OOEs) in Kohn–Sham (KS) density functional theory (DFT) is subject to a longstanding controversy. In local, semilocal, and hybrid density functionals (DFs) a Koopmans’ approach, where OOEs approximate negative ionization potentials (IPs), is unreliable. We discuss a methodology based on the Baer–Neuhauser–Livshits range-separated hybrid DFs for which Koopmans’ approach “springs to life.” The OOEs are remarkably close to the negative IPs with typical deviances of ±0.3 eV down to IPs of 30 eV, as demonstrated on several molecules. An essential component is the ab initio motivated range-parameter tuning procedure, forcing the highest OOE to be exactly equal to the negative first IP. We develop a theory for the curvature of the energy as a function of fractional occupation numbers to explain some of the results.

Livshits, E. ; Baer, R. ; Kosloff, R. Deleterious Effects of Long-Range Self-Repulsion on the Density Functional Description of O-2 Sticking on Aluminum. J. Phys. Chem. A 2009, 113, 7521–7527. Publisher's VersionAbstract

Density functional theory (DFT) with semilocal functionals such as the local-density and generalized gradients approximations predicts that the dissociative adsorption of oxygen on Al (111) goes through without a barrier in stark contradiction to experimental findings. This problem motivated our study of the reaction of oxygen colliding with a small aluminum cluster Al-5. We found semilocal functionals predict a minute barrier to sticking, associated with smeared long-range charge transfer from the metal to the oxygen. Hybrid B3LYP predicts a larger barrier while the range-separated the Baer-Neuhauser-Livshits (BNL, Phys. Chem. Chem. Phys. 2007, 9, 2932.) functional finds a more prominent barrier. BNL predicts short-ranged and more abrupt charge transfer from the surface to the oxygen. We conclude that spurious self-repulsion inherent in semilocal functionals causes early electron-transfer, long-range attraction toward the surface and low reaction barriers for these systems. The results indicate that the missing DFT barrier for O-2 sticking on Al (111) may be due to Spurious self-repulsion.

Eisenberg, H. R. ; Baer, R. A new generalized Kohn-Sham method for fundamental band-gaps in solids. Phys. Chem. Chem. Phys. 2009, 11, 4674–4680. Publisher's VersionAbstract

We developed a method for calculating the ground-state properties and fundamental band-gaps of solids, using a generalized Kohn-Sham approach combining a local density approximation (LDA) functional with a long-range explicit exchange orbital functional. We found that when the range parameter is selected according to the formula gamma = A/(epsilon(infinity) (epsilon) over tilde) where epsilon(infinity) is the optical dielectric constant of the solid and (epsilon) over tilde = 0.84 and A = 0.216 a(0)(-1), predictions of the fundamental band-gap close to the experimental values are obtained for a variety of solids of different types. For most solids the range parameter g is small (i.e. explicit exchange is needed only at long distances) so the predicted values for lattice constants and bulk moduli are similar to those based on conventional LDA calculations. Preliminary calculations on silicon give a general band structure in good agreement with experiment.

Andzelm, J. ; Rinderspacher, B. C. ; Rawlett, A. ; Dougherty, J. ; Baer, R. ; Govind, N. Performance of DFT Methods in the Calculation of Optical Spectra of TCF-Chromophores. J. Chem. Theory Comput. 2009, 5 2835–2846.Abstract

We present electronic structure calculations of the ultraviolet/visible (UV?vis) spectra of highly active push?pull chromophores containing the tricyanofuran (TCF) acceptor group. In particular, we have applied the recently developed long-range corrected Baer-Neuhauser-Livshits (BNL) exchange-correlation functional. The performance of this functional compares favorably with other density functional theory (DFT) approaches, including the CAM-B3LYP functional. The accuracy of UV-vis results for these molecules is best at low values of attenuation parameters (\gamma) for both BNL and CAM-B3LYP functionals. The optimal value of \gamma is different for the charge-transfer (CT) and valence excitations. The BNL and PBE0 exchange correlation functionals capture the CT states particularly well, while the ???* excitations are less accurate and system dependent. Chromophore conformations, which considerably affect the molecular hyperpolarizability, do not significantly influence the UV?vis spectra on average. As expected, the color of chromophores is a sensitive function of modifications to its conjugated framework and is not significantly affected by increasing aliphatic chain length linking a chromophore to a polymer. For selected push?pull aryl-chromophores, we find a significant dependence of absorption spectra on the strength of diphenylaminophenyl donors.

Livshits, E. ; Baer, R. A Density Functional Theory for Symmetric Radical Cations from Bonding to Dissociation. J. Phys. Chem. A 2008, 112, 12789–12791. Publisher's VersionAbstract

It has been known for quite some time that approximate density functional (ADF) theories fail disastrously when describing the dissociative symmetric radical cations R2+. By considering this dissociation limit, previous work has shown that Hartree-Fock (HF) theory favors the R+1-R-0 charge distribution, whereas DF approximations favor the R+(0.5)-R+0.5. Yet, general quantum mechanical principles indicate that both these (as well as all intermediate) average charge distributions are asymptotically energy degenerate. Thus, HF and ADF theories mistakenly break the symmetry but in a contradicting way. In this letter, we show how to construct system-dependent long-range corrected (LC) density functionals that can successfully treat this class of molecules, avoiding the spurious symmetry breaking. Examples and comparisons to experimental data is given for R = H, He, and Ne, and it is shown that the new LC theory improves considerably the theoretical description of the R-2(+) bond properties, the long-range form of the asymptotic potential curve, and the atomic polarizability. The broader impact of this finding is discussed as well, and it is argued that the widespread semiempirical approach which advocates treating the LC parameter as a system-independent parameter is in fact inappropriate under general circumstances.

Livshits, E. ; Baer, R. A well-tempered density functional theory of electrons in molecules. Phys. Chem. Chem. Phys. 2007, 9 2932–2941. Publisher's VersionAbstract

This Invited Article reports extensions of a recently developed approach to density functional theory with correct long-range behavior (R. Baer and D. Neuhauser, Phys. Rev. Lett., 2005, 94, 043002). The central quantities are a splitting functional \gamma[n] and a complementary exchange-correlation functional E_\gammaXC[n]. We give a practical method for determining the value of \gamma in molecules, assuming an approximation for E_\gammaXC is given. The resulting theory shows good ability to reproduce the ionization potentials for various molecules. However it is not of sufficient accuracy for forming a satisfactory framework for studying molecular properties. A somewhat different approach is then adopted, which depends on a density-independent \gamma and an additional parameter w eliminating part of the local exchange functional. The values of these two parameters are obtained by best-fitting to experimental atomization energies and bond lengths of the molecules in the G2(1) database. The optimized values are \gamma = 0.5 a_0^-1 and w = 0.1. We then examine the performance of this slightly semi-empirical functional for a variety of molecular properties, comparing to related works and experiment. We show that this approach can be used for describing in a satisfactory manner a broad range of molecular properties, be they static or dynamic. Most satisfactory is the ability to describe valence, Rydberg and inter-molecular charge-transfer excitations.

Baer, R. ; Neuhauser, D. A density functional theory with correct long-range asymptotic behavior. Phys. Rev. Lett. 2005, 94, 043002.Abstract

We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. Using a simple approximation, we develop an electronic structure theory that combines a new local correlation energy (based on Monte Carlo calculations applied to the homogeneous electron gas) and a combination of local and explicit long-ranged exchange. The theory is applied to several first-row atoms and diatomic molecules where encouraging results are obtained: good description of the chemical bond at the same time allowing for bound anions, reasonably accurate affinity energies, and correct polarizability of an elongated hydrogen chain. Further stringent tests of DFT are passed, concerning ionization potential and charge distribution under large bias