Limits of the creation of electronic wave packets using time-dependent density functional theory

Explicitly time-dependent density functional theory (TDDFT) has often been suggested as the method of choice for controlling the correlated dynamics of many electron systems. However, it is not yet clear which control tasks can be achieved reliably and how this depends on the functionals used. In this article, we show that the control task of creating a simple wave packet, having a population of 50% in the excited state, can indeed be achieved if a certain condition is fulfilled. This result is in contrast to the observation that a full population inversion is extremely difficult to achieve. In addition, we identify a rule to predict when TDDFT produces the correct wave packet. To illustrate our findings, we study the molecules Li(2)C(2), Li(7)OH, and B(2)N(2)CO using two different functionals as well as time-dependent Hartree-Fock (TDHF). To assess the performance of TDDFT and TDHF, we compare with time-dependent configuration interaction calculations.     

Adiabatic squeezing of molecular wave packets by laser pulses

Strong pulse sequences can be used to control the position and width of the molecular wave packet. In this paper we propose a new scheme to maximally compress the wave packet in a quasistatic way by freezing it at a peculiar adiabatic potential shaped by two laser pulses. The dynamic principles of the scheme and the characteristic effect of the different control parameters are presented and analyzed. We use two different molecular models, electronic potentials modeled by harmonic oscillators, with the same force constants, and the Na(2) dimer, to show the typical yield that can be obtained in compressing the initial (minimum width) molecular wave function.     

Formulation of magnetically perturbed time-dependent density functional theory

A formulation of time-dependent density functional theory (TDDFT) in the presence of a static imaginary perturbation is derived. A perturbational approach is applied leading to corrections to various orders in the quantities of interest, namely, the excitation energies and transition densities. The perturbed TDDFT equations are relatively straightforward to derive but the resulting expressions are rather cumbersome. Simplifications of these equations are suggested. Both the simplified and full expressions are used to obtain equations for first- and second-order corrections to the excitation energy, the first-order correction to the transition density, and the corrections for both quantities to first-order in two different perturbations. This formulation, called magnetically perturbed TDDFT, details how conventional TDDFT calculations can be corrected to allow for the inclusion of a static magnetic field and/or spin-orbit coupling.     

Excitation energies from range-separated time-dependent density and density matrix functional theory

Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other excitations is in general much better than that offered by TD-DFT-LDA or TD-DMFT-BB approximations if the range-separation parameter is properly chosen. The latter remains an open problem.     

Theoretical and numerical assessments of spin-flip time-dependent density functional theory

Spin-flip time-dependent density functional theory (SF-TD-DFT) with the full noncollinear hybrid exchange-correlation kernel and its approximate variants are critically assessed, both formally and numerically. As demonstrated by the ethylene torsion and the C(2v) ring-opening of oxirane, SF-TD-DFT is very useful for describing nearly degenerate situations. However, it may occasionally yield unphysical results. This stems from the noncollinear form of the generalized gradient approximation, which becomes numerically instable in the presence of spin-flip excitations from the closed- to vacant-shell orbitals of an open-shell reference. To cure this defect, a simple modification, dubbed as ALDA0, is proposed in the spirit of adiabatic local density approximation (ALDA). It is applicable to all kinds of density functionals and yields stable results without too much loss of accuracy. In particular, the combination of ALDA0 with the Tamm-Dancoff approximation is a promising tool for studying global potential energy surfaces. In addition to the kernel problem, SF-TD-DFT is also rather sensitive to the choice of reference states, as demonstrated by the spin multiplet states of closed-shell molecules of H(2)O, CH(2)O, and C(2)H(4). Surprisingly, SF-TD-DFT with pure density functionals may also fail for valance excitations with large orbital overlaps, at variance with the spin-conserving counterpart (SC-TD-DFT). In this case, the inclusion of a large amount of Hartree-Fock exchange is mandatory for quantitative results. Nonetheless, for spatially degenerate cases such as CF, CH, and NH(+), SF-TD-DFT is more advantageous than SC-TD-DFT, unless the latter is also space adapted. These findings are very instructive for future development and applications of TD-DFT.     

Adiabatic approximation of time-dependent density matrix functional response theory

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.     

Prediction of high-valent iron K-edge absorption spectra by time-dependent density functional theory

In recent years, a number of high-valent iron intermediates have been identified as reactive species in iron-containing metalloproteins. Inspired by the interest in these highly reactive species, chemists have synthesized Fe(IV) and Fe(V) model complexes with terminal oxo or nitrido groups, as well as a rare example of an Fe(VI)-nitrido species. In all these cases, X-ray absorption spectroscopy has played a key role in the identification and characterization of these species, with both the energy and intensity of the pre-edge features providing spectroscopic signatures for both the oxidation state and the local site geometry. Here we build on a time-dependent DFT methodology for the prediction of Fe K- pre-edge features, previously applied to ferrous and ferric complexes, and extend it to a range of Fe(IV), Fe(V) and Fe(VI) complexes. The contributions of oxidation state, coordination environment and spin state to the spectral features are discussed. These methods are then extended to calculate the spectra of the heme active site of P450 Compound II and the non-heme active site of TauD. The potential for using these methods in a predictive manner is highlighted.     

A theoretical study on quantum control of photodissociation dynamics by ultrashort chirped laser pulses

By a wavepacket propagation, we demonstrate the possibility of controlling the photodissociation branching ratio between two fragment channels by a single ultrashort linearly chirped laser pulse. It is found that a negatively chirped pulse of a moderate chirp rate completely prohibits the production of one of the photofragment channels. Two characteristics of chirped laser pulses contribute to this remarkable effect: the mechanism of adiabatic rapid passage (ARP) for the population transfer between the ground and excited states and the intrapulse pump‐dump process for determining the branching ratio. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 525–532, 1999     

All-electron time-dependent density functional theory with finite elements: time-propagation approach

We present an all-electron method for time-dependent density functional theory which employs hierarchical nonuniform finite-element bases and the time-propagation approach. The method is capable of treating linear and nonlinear response of valence and core electrons to an external field. We also introduce (i) a preconditioner for the propagation equation, (ii) a stable way to implement absorbing boundary conditions, and (iii) a new kind of absorbing boundary condition inspired by perfectly matched layers.     

Tuning nonlinear optical and optoelectronic properties of vinyl coupled triazene chromophores: a density functional theory and time-dependent density functional theory investigation

Triazenes are a unique class of polyazo compounds containing three consecutive nitrogen atoms in an acyclic arrangement and are promising NLO candidates. In the present work, a series of 15 donor-π-acceptor type vinyl coupled triazene derivatives (VCTDs) with different acceptors (-NO(2), -CN, and -COOH) have been designed, and their structure, nonlinear response, and optoelectronic properties have been studied using density functional theory and time-dependent density functional theory methods. B3LYP/6-311g(d,p) optimized geometries of the designed candidates show delocalization from the acceptor to donor through a π-bridge. Molecular orbital composition analysis reveals that HOMO is stabilized by the π-bridge, whereas acceptors play a major role in the stabilization of LUMO. Among the three acceptors, nitro derivatives are found to be efficient NLO candidates, and tri- and di-substituted cyano and carboxylic acid derivatives also show reasonably good NLO response. The effect of solvation on these properties has been studied using PCM calculations. From TDDFT calculations, the computed absorption spectra of these candidates lie in the range of 350-480 nm in the gas phase and have positive solvatochromism. The ground-state stabilization interactions are accounted from NBO calculations. In an effort to substantiate the thermal stability of the designed candidates, computations have been done to identify the weak interactions in the systems through NCI and AIM analysis. In summary, 10 out of 15 designed candidates are found to have excellent NLO and optoelectronic properties.     

Structure, spectroscopy, and reactivity properties of porphyrin pincers: a conceptual density functional theory and time-dependent density functional theory study

Porphyrin and pincer complexes are both important categories of compounds in biological and catalytic systems. The idea to combine them is computationally investigated in this work. By employment of density functional theory (DFT), conceptual DFT, and time-dependent DFT approaches, structure, spectroscopy, and reactivity properties of porphyrin pincers are systematically studied for a selection of divalent metal ions. We found that the porphyrin pincers are structurally and spectroscopically different from their precursors and are more reactive in electrophilic and nucleophilic reactions. A few quantitative linear/exponential relationships have been discovered between bonding interactions, charge distributions, and DFT chemical reactivity indices. These results are implicative in chemical modification of hemoproteins and understanding chemical reactivity in heme-containing and other biologically important complexes and cofactors.     

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.     

Absorption spectra of blue-light-emitting oligoquinolines from time-dependent density functional theory

Recently, it has been discovered that a series of four conjugated oligomers, oligoquinolines, exhibits many desirable properties of organic materials for developing high-performance light-emitting diodes: good blue color purity, high brightness, high efficiency, and high glass-transition temperatures. In this work, we investigate the optical absorption of oligoquinolines in the gas phase and chloroform (CHCl3) solution, respectively, using time-dependent density functional theory with the adiabatic approximation for the dynamical exchange-correlation potential. Our calculations show that the first peak of optical absorption corresponds to the lowest singlet excited state, whereas several quasi-degenerate excited states contribute to the experimentally observed higher-frequency peak. We find that, compared with the gas phase, there is a moderate red shift in excitation energy in solution due to the solute-solvent interaction simulated using the polarizable continuum model. Our results show that the lowest singlet excitation energies of oligoquinolines in chloroform solution calculated with the adiabatic hybrid functional PBE0 are in a good agreement with experiments. Our simulated optical absorption agrees well with the experimental data. Finally, analysis of the natural transition orbitals corresponding to the excited states in question underscores the underlying electronic delocalization properties.     

Production of color centers in PMMA by ultrashort laser pulses

We report here the creation of color centers in commercial, transparent PMMA samples by ultrashort pulses from a Ti:Sapphire laser emitting at 800 nm, with spatial control. Although the 800 nm photon energy is not sufficient to ionize the polymer, the centers are created following a multiphotonic absorption that causes the ionization. We propose that the free electrons quivering motion on the pulse electric field displaces atoms from its equilibrium positions, creating free radicals and double bonds that coalesce into color centers. The absorption and emission spectra of the centers were measured, but a dose-like curve could not be built due to the presence of damages created along with the centers that scatter the excitation and emission lights due to the commercial sample's poor optical quality.     

Dynamical quantum-electrodynamics embedding: Combining time-dependent density functional theory and the near-field method

We develop an approach for dynamical (ω > 0) embedding of mixed quantum mechanical (QM)∕classical (or more precisely QM∕electrodynamics) systems with a quantum sub-region, described by time-dependent density functional theory (TDDFT), within a classical sub-region, modeled here by the recently proposed near-field (NF) method. Both sub-systems are propagated simultaneously and are coupled through a common Coulomb potential. As a first step we implement the method to study the plasmonic response of a metal film which is half jellium-like QM and half classical. The resulting response is in good agreement with both full-scale TDDFT and the purely classical NF method. The embedding method is able to describe the optical response of the whole system while capturing quantum mechanical effects, so it is a promising approach for studying electrodynamics in hybrid molecules-metals nanostructures.     

Resonance vibrational Raman optical activity: a time-dependent density functional theory approach

We present a method to calculate both on- and off-resonance vibrational Raman optical activities (VROAs) of molecules using time-dependent density functional theory. This is an extension of a method to calculate the normal VROA by including a finite lifetime of the electronic excited states in all calculated properties. The method is based on a short-time approximation to Raman scattering and is, in the off-resonance case, identical to the standard theory of Placzek. The normal and resonance VROA spectra are calculated from geometric derivatives of the different generalized polarizabilites obtained using linear response theory which includes a damping term to account for the finite lifetime. Gauge-origin independent results for normal VROA have been ensured using either the modified-velocity gauge or gauge-included atomic orbitals. For the resonance VROA only the modified-velocity gauge has been implemented. We present some initial results for H(2)O(2) and (S)-methyloxirane and compare with predictions from a simple two-state approximation.     

Exploring odd-even effects of simple oligomer-like DRCNnT series: a study based on density functional theory/time-dependent density functional theory calculations

Odd-even effects of short-circuit current density and power conversion efficiency (PCE) are an interesting phenomenon in some organic solar cells. Although some explanations have been given, why they behave in such a way is still an open question. In the present work, we investigate a set of acceptor-donor-acceptor simple oligomer-like small molecules, named the DRCNnT (n = 5-9) series, to give an insight into this phenomenon because the solar cells based on them have high PCE (up to 10.08%) and show strong odd-even effects in experiments. By modeling the DRCNnT series and using density functional theory, we have studied the ground-state electronic structures of the DRCNnT (n = 5-9) series in condensed phase. The calculated results reproduce the experimental trends well. Furthermore, we find that the exciton-binding energies of the DRCNnT series may be one of the key parameters to explain this phenomenon because they also show odd-even effects. In addition, by studying the effects of alkyl branch and terminal group on odd-even effects of dipole moment, we find that eliminating one or two alkyl branches does not break the odd-even effects of dipole moments, but eliminating one or two terminal groups does. Finally, we conclude that removing one alkyl branch close to the terminal group of DRCN5T can decrease highest occupied molecular orbital (HOMO) energy (thus increasing open circuit voltage) and increase dipole moment (thus enhancing charge separation and short-circuit current). This could be a new and simple method to increase the PCE of DRCN5T-based solar cells.     

S-matrix theory of high harmonic generation and ionization of coherently ro-vibrating linear molecules by intense ultrashort laser pulses

A theory of high harmonic generation and ionization of coherently rotating and vibrating linear molecules by a delayed pair of intense ultrashort laser pulses is presented. It correlates the nuclear motions in real time with the modulation of the harmonic emission and ionization signals as a function of the time-delay between the exciting and the probing pulses. An illustrative analytical example of the excitation and detection of the clock-motion associated with the “0–1” vibrational oscillation of a diatomic molecule is also given.     

Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method

An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the self-consistent field as well as the predictor–corrector time integration schemes. The Coulomb contribution to the Kohn–Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two- and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.     

Brief review related to the foundations of time-dependent density functional theory

The electron density n(r,t), which is the central tool of time-dependent density functional theory, is presently considered to be derivable from a one-body time-dependent potential V(r,t), via one-electron wave functions satisfying a time-dependent Schrödinger equation. This is here related via a generalized equation of motion to a Dirac density matrix now involving t. Linear response theory is then surveyed, with a special emphasis on the question of causality with respect to the density dependence of the potential. Extraction of V(r,t) for solvable models is also proposed.