Peak-shifting in real-time time-dependent density functional theory.

In recent years, the development and application of real-time time-dependent density functional theory (RT-TDDFT) has gained momentum as a computationally efficient method for modeling electron dynamics and properties that require going beyond a linear response of the electron density. However, the RT-TDDFT method within the adiabatic approximation can unphysically shift absorption peaks throughout the electron dynamics. Here, we investigate the origin of these time-dependent resonances observed in RT-TDDFT spectra. Using both exact exchange and hybrid exchange-correlation approximate functionals, adiabatic RT-TDDFT gives time-dependent absorption spectra in which the peaks shift in energy as populations of the excited states fluctuate, while exact wave function methods yield peaks that are constant in energy but vary in intensity. The magnitude of the RT-TDDFT peak shift depends on the frequency and intensity of the applied field, in line with previous studies, but it oscillates as a function of time-dependent molecular orbital populations, consistent with a time-dependent superposition electron density. For the first time, we provide a rationale for the direction and magnitude of the time-dependent peak shifts based on the molecular electronic structure. For three small molecules, H2, HeH(+), and LiH, we give contrasting examples of peak-shifting to both higher and lower energies. The shifting is explained as coupled one-electron transitions to a higher and a lower lying state. Whether the peak shifts to higher or lower energies depends on the relative energetics of these one-electron transitions.

Two-electron Rabi oscillations in real-time time-dependent density-functional theory.

We investigate the Rabi oscillations of electrons excited by an applied electric field in several simple molecular systems using time-dependent configuration interaction (TDCI) and real-time time-dependent density-functional theory (RT-TDDFT) dynamics. While the TDCI simulations exhibit the expected single-electron Rabi oscillations at a single resonant electric field frequency, Rabi oscillations in the RT-TDDFT simulations are a two-electron process. The existence of two-electron Rabi oscillations is determined both by full population inversion between field-free molecular orbitals and the behavior of the instantaneous dipole moment during the simulations. Furthermore, the Rabi oscillations in RT-TDDFT are subject to an intensity threshold of the electric field, below which Rabi oscillations do not occur and above which the two-electron Rabi oscillations occur at a broad range of frequencies. It is also shown that at field intensities near the threshold intensity, the field frequency predicted to induce Rabi oscillations by linear response TDDFT only produces detuned Rabi oscillations. Instead, the field frequency that yields the full two-electron population inversion and Rabi oscillation behavior is shown to be the average of single-electron transition frequencies from the ground S0 state and the doubly-excited S2 state. The behavior of the two-electron Rabi oscillations is rationalized via two possible models. The first model is a multi-photon process that results from the electric field interacting with the three level system such that three level Rabi oscillations may occur. The second model suggests that the mean-field nature of RT-TDDFT induces paired electron propagation.

Ab initio molecular dynamics simulations of aqueous triflic acid confined in carbon nanotubes.

Ab initio molecular dynamics simulations were performed to investigate the effects of nanoscale confinement on the structural and dynamical properties of aqueous triflic acid (CF3SO3H). Single-walled carbon nanotubes (CNTs) with diameters ranging from ∼11 to 14 Å were used as confinement vessels, and the inner surface of the CNT were either left bare or fluorinated to probe the influence of the confined environment on structural and dynamical properties of the water and triflic acidic. The systems were simulated at hydration levels of n = 1-3 H2O/CF3SO3H. Proton dissociation expectedly increased with increasing hydration. Along with the level of hydration, hydrogen bond connectivity between the triflic acid molecules, both directly and via a single water molecule, played a role on proton dissociation. Direct hydrogen bonding between the CF3SO3H molecules, most commonly found in the larger bare CNT, also promoted interactions between water molecules allowing for greater separation of the dissociated protons from the CF3SO3(-) as the hydration level was increased. However, this also resulted in a decrease in the overall proportion of dissociated protons. The confinement dimensions altered both the hydrogen bond network and the distribution of water molecules where the H2O in the fluorinated CNTs tended to form small clusters with less proton dissociation at n = 1 and 2 but the highest at n = 3. In the absence of nearby hydrogen bond accepting sites from H2O or triflic acid SO3H groups, the water molecules formed weak hydrogen bonds with the fluorine atoms. In the bare CNT systems, these involved the CF3 groups of triflic acid and were more frequently observed when direct hydrogen bonding between CF3SO3H hindered potential hydrogen bonding sites. In the fluorinated tubes, interactions with the covalently bound fluorine atoms of the CNT wall dominated which appear to stabilize the hydrogen bond network. Increasing the hydration level increased the frequency of the OH···F (CNT) hydrogen bonding which was highly pronounced in the smaller fluorinated CNT indicating an influence on the confinement dimensions on these interactions.

Adsorption and diffusion of the Rh and Au adatom on graphene moiré/Ru(0001).

Detailed density functional theory calculations have been performed to investigate the adsorption and diffusion of the Rh and Au adatom on the graphene moiré superstructure on Ru(0001). The adsorption energies of each adatom in all of the non-equivalent C-top and C6 ring center sites on the graphene moiré have been calculated. The resulting potential energy surfaces encompass the entire graphene moiré unit cell and shows that the adsorption of both Rh1 and Au1 is most stable in the fcc region on the graphene moiré. The minimum-energy diffusion path between adjacent moiré cells is identified to run mostly directly between the fcc and hcp regions for Au1, but deviates toward the mound region for Rh1. The global diffusion barrier is estimated to be 0.53 eV for Rh1 and 0.71 eV for Au1, corresponding to a hopping rate between adjacent moiré cells of ~10(3) s(-1) and ~1 s(-1) at 298 K, respectively. The consequences of different hopping rates to cluster nucleation have been explored by performing Monte Carlo-based statistical analysis, which suggests that diffusing species other than adatoms need to be taken into account to develop an accurate description of cluster nucleation and growth on this surface.

Quantum Zeno effect rationalizes the phonon bottleneck in semiconductor quantum dots.

Quantum confinement can dramatically slow down electron-phonon relaxation in nanoclusters. Known as the phonon bottleneck, the effect remains elusive. Using a state-of-the-art time-domain ab initio approach, we model the observed bottleneck in CdSe quantum dots and show that it occurs under quantum Zeno conditions. Decoherence in the electronic subsystem, induced by elastic electron-phonon scattering, should be significantly faster than inelastic scattering. Achieved with multiphonon relaxation, the phonon bottleneck is broken by Auger processes and structural defects, rationalizing experimental difficulties.

Ab initio time-domain study of the triplet state in a semiconducting carbon nanotube: intersystem crossing, phosphorescence time, and line width.

Motivated by recent experiments (J. Am. Chem. Soc. 2011, 133, 17156), we used nonadiabatic (NA) molecular dynamics implemented within ab initio time-domain density functional theory to investigate the evolution of the excited electronic singlet and triplet states in the (6,4) carbon nanotube (CNT). The simulation simultaneously included the NA electron-phonon interaction and the spin-orbit (SO) interaction and focused on the intersystem crossing (ISC) from the first excited singlet state (S(1)) to the triplet state (T(1)) and subsequent relaxation to the ground electronic state (S(0)). For the first time, the state-of-the-art methodology (Phys. Rev. Lett. 2005, 95, 163001; Phys. Rev. Lett. 2008, 100, 197402) has been advanced to include triplet states. The S(1)-T(1) ISC was calculated to occur within tens of picoseconds, in agreement with the experimental data. This time scale is on the same order as the S(1)-S(0) nonradiative decay time obtained previously for the (6,4) CNT. The homogeneous phosphorescence line width, which can be measured in single-molecule experiments, was predicted to be on the order of 10 meV at room temperature. This value is similar to the fluorescence line widths of CNTs suspended in air. The NA electron-phonon and SO couplings were found to be on the order of 1 meV; however, the former fluctuates much more than the latter, causing the ISC rate to be limited by the SO interaction rather than NA interaction. The electronic energy lost nonradiatively during ISC is deposited into high-frequency optical phonons of the CNT arising from C-C stretching motions. The calculations indicate that ISC can contribute to the nonradiative energy losses and low photoluminescence quantum yields observed in semiconducting CNTs.

Ab initio simulations of the effects of nanoscale confinement on proton transfer in hydrophobic environments.

Carbon nanotubes (CNTs) were functionalized with -CF(2)SO(3)H groups and hydrated with 1-3 water molecules per sulfonic acid group to investigate proton dissociation and transport in confined, hydrophobic environments. The distance between sulfonate groups was systematically varied from 6 to 8 Å, and three different CNTs were used to determine the effects of nanoscale confinement. The inner walls of the CNT were either functionalized with fluorine atoms to provide a localized negative charge or left bare to provide a more delocalized charge distribution. The use of ab initio molecular dynamics permitted the study of sulfonate solvation, proton dissociation, and the formation of a hydrogen bonding network without a priori assumptions. It was shown that decreasing the distance between sulfonate groups increased proton dissociation, as well as the interactions between water molecules. As the sulfonate distance increased, connectivity among the water molecules decreased as they formed more isolated clusters around the sulfonate groups. The sulfonate distance and geometry were the most dominant factors in proton dissociation; however, the hydrophobic environment and nanoscale confinement became more important as the distance between sulfonate groups increased.

Regarding the validity of the time-dependent Kohn-Sham approach for electron-nuclear dynamics via trajectory surface hopping.

The implementation of fewest-switches surface-hopping (FSSH) within time-dependent Kohn-Sham (TDKS) theory [Phys. Rev. Lett. 95, 163001 (2005)] has allowed us to study successfully excited state dynamics involving many electronic states in a variety of molecular and nanoscale systems, including chromophore-semiconductor interfaces, semiconductor and metallic quantum dots, carbon nanotubes and graphene nanoribbons, etc. At the same time, a concern has been raised that the KS orbital basis used in the calculation provides only approximate potential energy surfaces [J. Chem. Phys. 125, 014110 (2006)]. While this approximation does exist in our method, we show here that FSSH-TDKS is a viable option for computationally efficient calculations in large systems with straightforward excited state dynamics. We demonstrate that the potential energy surfaces and nonadiabatic transition probabilities obtained within the TDKS and linear response (LR) time-dependent density functional theories (TDDFT) agree semiquantitatively for three different systems, including an organic chromophore ligating a transition metal, a quantum dot, and a small molecule. Further, in the latter case the FSSH-TDKS procedure generates results that are in line with FSSH implemented within LR-TDDFT. The FSSH-TDKS approach is successful for several reasons. First, single-particle KS excitations often give a good representation of LR excitations. In this regard, DFT compares favorably with the Hartree-Fock theory, for which LR excitations are typically combinations of multiple single-particle excitations. Second, the majority of the FSSH-TDKS applications have been performed with large systems involving simple excitations types. Excitation of a single electron in such systems creates a relatively small perturbation to the total electron density summed over all electrons, and it has a small effect on the nuclear dynamics compared, for instance, with thermal nuclear fluctuations. In such cases an additional, classical-path approximation can be made. Third, typical observables measured in time-resolved experiments involve averaging over many initial conditions. Such averaging tends to cancel out random errors that may be encountered in individual simulated trajectories. Finally, if the flow of energy between electronic and nuclear subsystems is insignificant, the ad hoc FSSH procedure is not required, and a straightforward mean-field, Ehrenfest approach is sufficient. Then, the KS representation provides rigorously a convenient and efficient basis for numerically solving the TDDFT equations of motion.

Ab initio molecular dynamics simulations investigating proton transfer in perfluorosulfonic acid functionalized carbon nanotubes.

Proton dissociation and transfer were examined with ab initio molecular dynamics (AIMD) simulations of carbon nanotubes (CNT) functionalized with perfluorosulfonic acid (-CF(2)SO(3)H) groups with 1-3 H(2)O/SO(3)H. The CNT systems were constructed both with and without fluorine atoms covalently bound to the walls to elucidate the effects of the presence of a strongly hydrophobic environment, the fluorine, on proton dissociation, hydration, and stabilization. The simulations revealed that the dissociated proton was preferentially stabilized as a hydrated hydronium cation (i.e., Eigen like) in the fluorinated CNTs but as a Zundel (H(5)O(2)(+)) cation in the nonfluorinated CNTs. This feature is attributed to the fluorine atoms forming hydrogen bonds with the water molecules coordinated to the central hydronium ion.

Phonon-induced dephasing of excitons in semiconductor quantum dots: multiple exciton generation, fission, and luminescence.

Phonon-induced dephasing processes that govern optical line widths, multiple exciton (ME) generation (MEG), and ME fission (MEF) in semiconductor quantum dots (QDs) are investigated by ab initio molecular dynamics simulation. Using Si QDs as an example, we propose that MEF occurs by phonon-induced dephasing and, for the first time, estimate its time scale to be 100 fs. In contrast, luminescence and MEG dephasing times are all sub-10 fs. Generally, dephasing is faster for higher-energy and higher-order excitons and increased temperatures. MEF is slow because it is facilitated only by low-frequency acoustic modes. Luminescence and MEG couple to both acoustic and optical modes of the QD, as well as ligand vibrations. The detailed atomistic simulation of the dephasing processes advances understanding of exciton dynamics in QDs and other nanoscale materials.

Ab initio study of phonon-induced dephasing of electronic excitations in narrow graphene nanoribbons.

Vibrational dephasing of the lowest energy electronic excitations in the perfect (16,16) graphene nanoribbon (GNR) and those with the C2-bond insertion and rotation defects is studied with ab initio molecular dynamics. Compared to single-walled carbon nanotubes (SWCNTs) of similar size, GNRs shows very different properties. The dephasing in the ideal GNR occurs twice faster than that in the SWCNTs. It is induced primarily by the 1300 cm (-1) disorder mode seen in bulk graphite rather than by the 1600 cm (-1) C-C stretching mode as in SWCNTs. In contrast to SWCNTs, defects exhibit weaker electron-phonon coupling compared to the ideal system. Therefore, defects should present much less of a practical problem in GNRs compared to SWCNTs. The predicted optical line widths can be tested experimentally.

Nonradiative quenching of fluorescence in a semiconducting carbon nanotube: a time-domain ab initio study.

As shown experimentally, strong nonradiative decay channels exist in carbon nanotubes (CNT) and are responsible for low fluorescence yields. The decay of the electronic excitation to its ground state is simulated in the (6,4) semiconducting CNT with surface hopping in the Kohn-Sham representation, providing a unique time-domain atomistic description of fluorescence quenching. The decay in the ideal CNT is estimated to occur on a 150 ps time scale and is only weakly dependent on temperature. Vibrationally induced decoherence strongly influences the electronic relaxation. Defects decrease the excited state lifetime to tens of picoseconds, rationalizing the multiple decay time scales seen in experiments.

Ab initio study of vibrational dephasing of electronic excitations in semiconducting carbon nanotubes.

Phonon-induced dephasing of electronic transitions in semiconducting single-wall carbon nanotubes (CNT) is investigated by ab initio molecular dynamics. Pure-dephasing is shown to be the source of the photoluminescence linewidths observed experimentally in isolated CNTs at low and room temperatures. In ideal tubes, the dephasing is found to occur by coupling to optical phonons. The dephasing proceeds notably faster in the presence of some defects due to stronger coupling to local modes, suggesting that the defects can be identified in CNTs by broadened optical bands.

Time-domain ab initio simulation of electron and hole relaxation dynamics in a single-wall semiconducting carbon nanotube.

The electron and hole relaxation in the (7, 0) zigzag carbon nanotube is simulated in time domain using a surface-hopping Kohn-Sham density functional theory. Following a photoexcitation between the second van Hove singularities, the electrons and holes decay to the Fermi level on characteristic subpicosecond time scales. Surprisingly, despite a lower density of states, the electrons relax faster than the holes. The relaxation is primarily mediated by the high-frequency longitudinal optical (LO) phonons. Hole dynamics are more complex than the electron dynamics: in addition to the LO phonons, holes couple to lower frequency breathing modes and decay over multiple time scales.

Regioselective routes to disubstituted dibenzo crown ethers and their complexations.

Two isomers of bis(carbomethoxybenzo)-24-crown-8 (cis-BCMB24C8, 1, and trans-BCMB24C8, 2) were synthesized regiospecifically with acceptable to excellent yields. Cyclization in the presence of a template reagent, KPF(6), led to an essentially quantitative yield of the potassium complex of the crown ether 1; the isolated cyclization yield of pure was a remarkable 89%! The methods not only avoid the very difficult separation of the isomers, but also greatly shorten the synthesis time by eliminating syringe pump usage during cyclization. The complexations of the isomeric BCMB24C8 with dibenzylammonium hexafluorophosphate (10) were studied by NMR; association constants (Ka) for 1 and 2 with the dibenzylammonium cation are 190 and 312 M(-1), respectively. The X-ray crystal structures of crown ether and the complexes 1.KPF(6), 2.KPF(6) and pseudorotaxane 2.10 were determined.