Long-range Charge-transfer Excitations Research Articles

First-Principles Simulations of X-ray Transient Absorption for Probing Attosecond Electron Dynamics.

X-ray transient absorption spectroscopy (XTAS) is a promising technique for measuring electron dynamics in molecules and solids with attosecond time resolutions. In XTAS, the elemental specificity and spatial locality of core-to-valence X-ray absorption is exploited to relate modulations in the time-resolved absorption spectra to local electron density variations around particular atoms. However, interpreting these absorption modulations and frequency shifts as a function of the time delay in terms of dynamics can be challenging. In this paper, we present a first-principles study of attosecond XTAS in a selection of simple molecules based on real-time time-dependent density functional theory (RT-TDDFT) with constrained DFT to emulate the state of the system following the interaction with a ultraviolet pump laser. In general, there is a decrease in the optical density and a blue shift in the frequency with increasing electron density around the absorbing atom. In carbon monoxide (CO), modulations in the O K-edge occur at the frequency of the valence electron dynamics, while for dioxygen (O2) they occur at twice the frequency, due to the indistinguishability of the oxygen atoms. In 4-aminophenol (H2NC6H4OH), likewise, there is a decrease in the optical density and a blue shift in the frequency for the oxygen and nitrogen K-edges with increasing charge density on the O and N, respectively. Similar effects are observed in the nitrogen K-edge for a long-range charge-transfer excitation in a benzene (C6H6)–tetracyanoethylene (C6N4; TCNE) dimer but with weaker modulations due to the delocalization of the charge across the entire TCNE molecule. Additionally, in all cases, there are pre-edge features corresponding to core transitions to depopulated orbitals. These potentially offer a background-free signal that only appears in pumped molecules.

Revised M11 Exchange-Correlation Functional for Electronic Excitation Energies and Ground-State Properties.

The ability of Kohn-Sham density functional theory (KS-DFT) to accurately predict various types of electronic excitation energies with (necessarily approximate) exchange-correlation functionals faces several challenges. Chief among these is that valence excitations are usually inherently multiconfigurational and therefore best treated by functionals with local exchange, whereas Rydberg and charge-transfer excitations are often better treated with nonlocal exchange. The question arises regarding whether one can optimize a functional such that all three kinds of excitations (valence, Rydberg, and charge transfer, including long-range charge transfer) are treated in a balanced and accurate way. The goal of the present work is to try to answer that question and then to optimize a functional with the best possible balanced behavior. Of the variety of functional types available, we choose to use a range-separated hybrid meta functional for the following reasons: (i) Range separation allows the percentage of Hartree-Fock (HF) exchange to change with interelectronic separation, and therefore, one can have 100% HF exchange at large interelectronic separations, which gives good performance for long-range charge-transfer excitations, while the range separation allows one to simultaneously have smaller values of HF exchange at small and intermediate interelectronic separations, giving good performance for valence and Rydberg excitations. (ii) Meta functionals allow one to obtain better accuracy with high HF exchange than is possible with functionals whose local part depends only on spin densities and their gradients. This work starts with the range-separated hybrid meta functional M11 and reoptimizes it (with strong smoothness restraints) against electronic excitation energies and ground-state properties to obtain a new functional called revM11 that gives good performance for all three types of electronic excitations and at the same time gives very good predictions across the board for ground-state properties.

Short- and long-range corrected hybrid density functionals with the D3 dispersion corrections.

We propose a short- and long-range corrected (SLC) hybrid scheme employing 100% Hartree-Fock exchange at both zero and infinite interelectronic distances, wherein three SLC hybrid density functionals with the D3 dispersion corrections (SLC-LDA-D3, SLC-PBE-D3, and SLC-B97-D3) are developed. SLC-PBE-D3 and SLC-B97-D3 are shown to be accurate for a very diverse range of applications, such as core ionization and excitation energies, thermochemistry, kinetics, noncovalent interactions, dissociation of symmetric radical cations, vertical ionization potentials, vertical electron affinities, fundamental gaps, and valence, Rydberg, and long-range charge-transfer excitation energies. Relative to ωB97X-D, SLC-B97-D3 provides significant improvement for core ionization and excitation energies and noticeable improvement for the self-interaction, asymptote, energy-gap, and charge-transfer problems, while performing similarly for thermochemistry, kinetics, and noncovalent interactions.

First-principle study on the optical response of phosphorene

The optical response of phosphorene nanostructures was studied using time-dependent density functional theory (TDDFT). Compared with the absorption spectrum of graphene, that of the phosphorene nanostructure exhibits high absorbance in the ultraviolet region, which indicates a high light absorptivity. In a low-energy resonance zone, a spectral band extends to the entire near-infrared regions. When the impulse excitation polarizes in the armchair-edge direction, the low-energy plasmon in a few-layer phosphorene nanostructure shows an apparent long-range charge-transfer excitation but is significantly less pronounced along the zigzag-edge direction. The edge configuration significantly affects the absorption spectrum of monolayer phosphorene nanostructures. The armchair-edge and the zigzag-edge serve different functions in the absorption spectrum. Moreover, the absorption spectrum of the few-layer phosphorene nanostructure changes with the number of layers when the impulse excitation polarizes in the armchair-edge direction. In addition, the change in the low-energy resonance zone is significantly different from that in the high-energy resonance zone.

The Importance of Short- and Long-Range Exchange on Various Excited State Properties of DNA Monomers, Stacked Complexes, and Watson-Crick Pairs.

We present a detailed analysis of several time-dependent DFT (TD-DFT) methods, including conventional hybrid functionals and two types of nonempirically tuned range-separated functionals, for predicting a diverse set of electronic excitations in DNA nucleobase monomers and dimers. This large and extensive set of excitations comprises a total of 50 different transitions (for each tested DFT functional) that includes several n → π and π → π* valence excitations, long-range charge-transfer excitations, and extended Rydberg transitions (complete with benchmark calculations from high-level EOM-CCSD(T) methods). The presence of localized valence excitations as well as extreme long-range charge-transfer excitations in these systems poses a serious challenge for TD-DFT methods that allows us to assess the importance of both short- and long-range exchange contributions for simultaneously predicting all of these various transitions. In particular, we find that functionals that do not have both short- and full long-range exchange components are unable to predict the different types of nucleobase excitations with the same accuracy. Most importantly, the current study highlights the importance of both short-range exchange and a nonempirically tuned contribution of long-range exchange for accurately predicting the diverse excitations in these challenging nucleobase systems.

Molecular Excitation Energies from Time-Dependent Density Functional Theory Employing Random-Phase Approximation Hessians with Exact Exchange.

Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.

Discontinuous functional for linear-response time-dependent density-functional theory: The exact-exchange kernel and approximate forms

We present a detailed study of the exact-exchange (EXX) kernel of time-dependent density-functional theory with an emphasis on its discontinuity at integer particle numbers. It was recently found that this exact property leads to sharp peaks and step features in the kernel that diverge in the dissociation limit of diatomic systems [Hellgren and Gross, Phys. Rev. A 85, 022514 (2012)]. To further analyze the discontinuity of the kernel, we here make use of two different approximations to the EXX kernel: the Petersilka Gossmann Gross (PGG) approximation and a common energy denominator approximation (CEDA). It is demonstrated that whereas the PGG approximation neglects the discontinuity, the CEDA includes it explicitly. By studying model molecular systems it is shown that the so-called field-counteracting effect in the density-functional description of molecular chains can be viewed in terms of the discontinuity of the static kernel. The role of the frequency dependence is also investigated, highlighting its importance for long-range charge-transfer excitations as well as inner-shell excitations.

Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections.

By incorporating the improved empirical atom-atom dispersion corrections from DFT-D3 [Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys.2010, 132, 154104], two long-range corrected (LC) hybrid density functionals are proposed. Our resulting LC hybrid functionals, ωM06-D3 and ωB97X-D3, are shown to be accurate for a very wide range of applications, such as thermochemistry, kinetics, noncovalent interactions, frontier orbital energies, fundamental gaps, and long-range charge-transfer excitations, when compared with common global and LC hybrid functionals. Relative to ωB97X-D [Chai, J.-D.; Head-Gordon, M. Phys. Chem. Chem. Phys.2008, 10, 6615], ωB97X-D3 (reoptimization of ωB97X-D with improved dispersion corrections) is shown to be superior for nonbonded interactions, and similar in performance for bonded interactions, while ωM06-D3 is shown to be superior for general applications.

Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density-functional theory

We identify the key property that the exchange-correlation (XC) kernel of time-dependent density-functional theory must have in order to describe long-range charge-transfer excitations. We show that the discontinuity of the XC potential as a function of particle number induces a space- and frequency-dependent discontinuity of the XC kernel that diverges as $r\ensuremath{\rightarrow}\ensuremath{\infty}$. In a combined donor-acceptor system, the same discontinuity compensates for the vanishing overlap between the acceptor and donor orbitals, thereby yielding a finite correction to the Kohn-Sham eigenvalue differences. This mechanism is illustrated to first order in the Coulomb interaction.

Charge transfer in time-dependent density-functional theory via spin-symmetry breaking

Long-range charge-transfer excitations pose a major challenge for time-dependent density-functional approximations. We show that spin-symmetry breaking offers a simple solution for molecules composed of open-shell fragments, yielding accurate excitations at large separations when the acceptor effectively contains one active electron. Unrestricted exact-exchange and self-interaction-corrected functionals are performed on one-dimensional models and on the real LiH molecule within the pseudopotential approximation to demonstrate our results.

Charge-transfer excitation energies with a time-dependent density-functional method suitable for orbital-dependent exchange-correlation kernels

A time-dependent density-functional (TDDFT) response equation for the effective Kohn-Sham potential instead of the electron densities is presented that enables the use of orbital-dependent exchange-correlation kernels. In combination with the frequency-dependent exact-exchange kernel the present approach describes long-range charge-transfer excitations qualitatively correct in contrast to standard TDDFT methods, as shown by formal analysis and applications to molecular systems. Even charge-transfer excitations obtained with the adiabatic frequency-independent exact-exchange kernel exhibit a long-range dependence with the distance of the charge transfer, which, however, is too weak by a factor of 2. This indicates that it is not the frequency dependence of the kernel alone that leads to a correct description of charge-transfer excitations.

Systematic optimization of long-range corrected hybrid density functionals

A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such as dissociation of symmetric radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybrid density functionals.

Asymptotic correction of the exchange-correlation kernel of time-dependent density functional theory for long-range charge-transfer excitations.

Time-dependent density functional theory (TDDFT) calculations of charge-transfer excitation energies omegaCT are significantly in error when the adiabatic local density approximation (ALDA) is employed for the exchange-correlation kernel fxc. We relate the error to the physical meaning of the orbital energy of the Kohn-Sham lowest unoccupied molecular orbital (LUMO). The LUMO orbital energy in Kohn-Sham DFT--in contrast to the Hartree-Fock model--approximates an excited electron, which is correct for excitations in compact molecules. In CT transitions the energy of the LUMO of the acceptor molecule should instead describe an added electron, i.e., approximate the electron affinity. To obtain a contribution that compensates for the difference, a specific divergence of fxc is required in rigorous TDDFT, and a suitable asymptotically correct form of the kernel fxc(asymp) is proposed. The importance of the asymptotic correction of fxc is demonstrated with the calculation of omegaCT(R) for the prototype diatomic system HeBe at various separations R(He-Be). The TDDFT-ALDA curve omegaCT(R) roughly resembles the benchmark ab initio curve omegaCT CISD(R) of a configuration interaction calculation with single and double excitations in the region R=1-1.5 A, where a sizable He-Be interaction exists, but exhibits the wrong behavior omegaCT(R)<<omegaCT CISD(R) at large R. The TDDFT curve obtained with fxc (asymp) however approaches omegaCT CISD(R) closely in the region R=3-10 A. Then, the adequate rigorous TDDFT approach should interpolate between the LDA/GGA ALDA xc kernel for excitations in compact systems and fxc(asymp) for weakly interacting fragments and suitable interpolation expressions are considered.

Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn–Sham theory

Charge-transfer (CT) electronic excitation energies are known to be very poorly predicted by time-dependent density functional theory (TDDFT) using local exchange-correlation functionals. Insight into this observation is provided by a simple analysis of intermolecular CT excitations at infinite separation. It is argued that the first TDDFT CT excitation energy approximately underestimates the experimental excitation by the average of the integer discontinuities of the donor and acceptor molecules; errors are of the order of several electron volts.