Saturable Absorption of Free-Electron Laser Radiation by Graphite near the Carbon K-Edge.

The interaction of intense light with matter gives rise to competing nonlinear responses that can dynamically change material properties. Prominent examples are saturable absorption (SA) and two-photon absorption (TPA), which dynamically increase and decrease the transmission of a sample depending on pulse intensity, respectively. The availability of intense soft X-ray pulses from free-electron lasers (FELs) has led to observations of SA and TPA in separate experiments, leaving open questions about the possible interplay between and relative strength of the two phenomena. Here, we systematically study both phenomena in one experiment by exposing graphite films to soft X-ray FEL pulses of varying intensity. By applying real-time electronic structure calculations, we find that for lower intensities the nonlinear contribution to the absorption is dominated by SA attributed to ground-state depletion; our model suggests that TPA becomes more dominant for larger intensities (>1014 W/cm2). Our results demonstrate an approach of general utility for interpreting FEL spectroscopies.

TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings.

We present an algorithm for efficient calculation of analytic nonadiabatic derivative couplings between spin-adiabatic, time-dependent density functional theory states within the Tamm-Dancoff approximation. Our derivation is based on the direct differentiation of the Kohn-Sham pseudowavefunction using the framework of Ou et al. Our implementation is limited to the case of a system with an even number of electrons in a closed shell ground state, and we validate our algorithm against finite difference at an S1/T2 crossing of benzaldehyde. Through the introduction of a magnetic field spin-coupling operator, we break time-reversal symmetry to generate complex valued nonadiabatic derivative couplings. Although the nonadiabatic derivative couplings are complex valued, we find that a phase rotation can generate an almost entirely real-valued derivative coupling vector for the case of benzaldehyde.

Multiple-Time Step Ab Initio Molecular Dynamics Based on Two-Electron Integral Screening.

A multiple-timestep ab initio molecular dynamics scheme based on varying the two-electron integral screening method used in Hartree-Fock or density functional theory calculations is presented. Although screening is motivated by numerical considerations, it is also related to separations in the length- and timescales characterizing forces in a molecular system: Loose thresholds are sufficient to describe fast motions over short distances, while tight thresholds may be employed for larger length scales and longer times, leading to a practical acceleration of ab initio molecular dynamics simulations. Standard screening approaches can lead, however, to significant discontinuities in (and inconsistencies between) the energy and gradient when the screening threshold is loose, making them inappropriate for use in dynamics. To remedy this problem, a consistent window-screening method that smooths these discontinuities is devised. Further algorithmic improvements reuse electronic-structure information within the dynamics step and enhance efficiency relative to a naïve multiple-timestepping protocol. The resulting scheme is shown to realize meaningful reductions in the cost of Hartree-Fock and B3LYP simulations of a moderately large system, the protonated sarcosine/glycine dipeptide embedded in a 19-water cluster.

The requisite electronic structure theory to describe photoexcited nonadiabatic dynamics: nonadiabatic derivative couplings and diabatic electronic couplings.

Electronically photoexcited dynamics are complicated because there are so many different relaxation pathways: fluorescence, phosphorescence, radiationless decay, electon transfer, etc. In practice, to model photoexcited systems is a very difficult enterprise, requiring accurate and very efficient tools in both electronic structure theory and nonadiabatic chemical dynamics. Moreover, these theoretical tools are not traditional tools. On the one hand, the electronic structure tools involve couplings between electonic states (rather than typical single state energies and gradients). On the other hand, the dynamics tools involve propagating nuclei on multiple potential energy surfaces (rather than the usual ground state dynamics). In this Account, we review recent developments in electronic structure theory as directly applicable for modeling photoexcited systems. In particular, we focus on how one may evaluate the couplings between two different electronic states. These couplings come in two flavors. If we order states energetically, the resulting adiabatic states are coupled via derivative couplings. Derivative couplings capture how electronic wave functions change as a function of nuclear geometry and can usually be calculated with straightforward tools from analytic gradient theory. One nuance arises, however, in the context of time-dependent density functional theory (TD-DFT): how do we evaluate derivative couplings between TD-DFT excited states (which are tricky, because no wave function is available)? This conundrum was recently solved, and we review the solution below. We also discuss the solution to a second, pesky problem of origin dependence, whereby the derivative couplings do not (strictly) satisfy translation variance, which can lead to a lack of momentum conservation. Apart from adiabatic states, if we order states according to their electronic character, the resulting diabatic states are coupled via electronic or diabatic couplings. The couplings between diabatic states |ΞA⟩ and |ΞB⟩ are just the simple matrix elements, ⟨ΞA|H|ΞB⟩. A difficulty arises, however, because constructing exactly diabatic states is formally impossible and constructing quasi-diabatic states is not unique. To that end, we review recent advances in localized diabatization, which is one approach for generating adiabatic-to-diabatic (ATD) transformations. We also highlight outstanding questions in the arena of diabatization, especially how to generate multiple globally stable diabatic surfaces.

Derivative couplings between TDDFT excited states obtained by direct differentiation in the Tamm-Dancoff approximation.

Working within the Tamm-Dancoff approximation, we calculate the derivative couplings between time-dependent density-functional theory excited states by assuming that the Kohn-Sham superposition of singly excited determinants represents a true electronic wavefunction. All Pulay terms are included in our derivative coupling expression. The reasonability of our approach can be established by noting that, for closely separated electronic states in the infinite basis limit, our final expression agrees exactly with the Chernyak-Mukamel expression (with transition densities from response theory). Finally, we also validate our approach empirically by analyzing the behavior of the derivative couplings around the T1/T2 conical intersection of benzaldehyde.

Analysis of localized diabatic states beyond the condon approximation for excitation energy transfer processes.

In a previous paper [ Fatehi , S. ; et al. J. Chem. Phys. 2013 , 139 , 124112 ], we demonstrated a practical method by which analytic derivative couplings of Boys-localized CIS states can be obtained. In this paper, we now apply that same method to the analysis of triplet-triplet energy transfer systems studied by Closs and collaborators [ Closs , G. L. ; et al. J. Am. Chem. Soc. 1988 , 110 , 2652 ]. For the systems examined, we are able to conclude that (i) the derivative coupling in the BoysOV basis is negligible, and (ii) the diabatic coupling will likely change little over the configuration space explored at room temperature. Furthermore, we propose and evaluate an approximation that allows for the inexpensive calculation of accurate diabatic energy gradients, called the "strictly diabatic" approximation. This work highlights the effectiveness of diabatic state analytic gradient theory in realistic systems and demonstrates that localized diabatic states can serve as an acceptable approximation to strictly diabatic states.

Derivative couplings and analytic gradients for diabatic states, with an implementation for Boys-localized configuration-interaction singles.

We demonstrate that Boys-localized diabatic states do indeed exhibit small derivative couplings, as is required of quasidiabatic states. In doing so, we present a general formalism for calculating derivative couplings and analytic gradients for diabatic states. We then develop additional equations specific to the case of Boys-localized configuration-interaction singles (CIS)--in particular, the analytic gradient of the CIS dipole matrix--and we validate our implementation against finite-difference results. In a forthcoming paper, we will publish additional algorithmic and computational details and apply our method to the Closs energy-transfer systems as a further test of the validity of Boys-localized diabatic states.

Communication: Adjusting charge transfer state energies for configuration interaction singles: without any parameterization and with minimal cost.

In a recent article, we showed that configuration interaction singles (CIS) has a systematic bias against charge-transfer (CT) states: CT vertical excitation energies are consistently too high (by 1-2 eV) as compared with non-CT energies [J. E. Subotnik, J. Chem. Phys. 137, 071104 (2011)]. We now show that this CIS error can be corrected approximately by performing a single Newton-Raphson step to reoptimize orbitals, thus establishing a new set of orbitals which better balances ground and excited state energies. The computational cost of this correction is exactly that of one coupled-perturbed Hartree-Fock calculation, which is effectively the cost of the CIS calculation itself. In other words, for twice the computational cost of a standard CIS calculation, or roughly the same cost as a linear-response time-dependent Hartree-Fock calculation, one can achieve a balanced, size-consistent description of CT versus non-CT energies, ideally with the accuracy of a much more expensive doubles CIS(D) calculation.

Analytic derivative couplings between configuration-interaction-singles states with built-in electron-translation factors for translational invariance.

We present a method for analytically calculating the derivative couplings between a pair of configuration-interaction-singles (CIS) excited states obtained in an atom-centered basis. Our theory is exact and has been derived using two completely independent approaches: one inspired by the Hellmann-Feynman theorem and the other following from direct differentiation. (The former is new, while the latter is in the spirit of existing approaches in the literature.) Our expression for the derivative couplings incorporates all Pulay effects associated with the use of an atom-centered basis, and the computational cost is minimal, roughly comparable to that of a single CIS energy gradient. We have validated our method against CIS finite-difference results and have applied it to the lowest lying excited states of naphthalene; we find that naphthalene derivative couplings include Pulay contributions sufficient to have a qualitative effect. Going beyond standard problems in analytic gradient theory, we have also constructed a correction, based on perturbative electron-translation factors, for including electronic momentum and eliminating spurious components of the derivative couplings that break translational symmetry. This correction is general and can be applied to any level of electronic structure theory.

Nuclear quantum effects in the structure and lineshapes of the N2 near-edge x-ray absorption fine structure spectrum.

We study the relative ability of several models of x-ray absorption spectra to capture the Franck-Condon structure apparent from an experiment on gaseous nitrogen. In doing so, we adopt the Born-Oppenheimer approximation and a constrained density functional theory method for computing the energies of the x-ray-excited molecule. Starting from an otherwise classical model for the spectrum, we systematically introduce more realistic physics, first by substituting the quantum mechanical nuclear radial density in the bond separation R for the classical radial density, then by adding the effect of zero-point energy and other level shifts, and finally by including explicit rovibrational quantization of both the ground and excited states. The quantization is determined exactly, using a discrete variable representation (DVR). We show that the near-edge x-ray absorption fine structure (NEXAFS) spectrum can be predicted semiquantitatively within this framework. We also address the possibility of non-trivial temperature dependence in the spectrum. By using constrained density functional theory in combination with more accurate potentials, we demonstrate that it is possible to improve the predicted spectrum. Ultimately, we establish the predictive limits of our method with respect to vibrational fine structure in NEXAFS spectra.

Importance of electronic relaxation for inter-coulombic decay in aqueous systems.

Inspired by recent photoelectron spectroscopy experiments on hydroxide solutions, we have examined the conditions necessary for enhanced (and, in the case of solutions, detectable) inter-Coulombic decay (ICD)--Auger emission from an atomic site other than that originally excited. We present general guidelines, based on energetic and spatial overlap of molecular orbitals, for this enhancement of inter-Coulombic decay-based energy transfer in solutions. These guidelines indicate that this decay process should be exhibited by broad classes of biomolecules and suggest a design criterion for targeted radiooncology protocols. Our findings show that photoelectron spectroscopy cannot resolve the current hydroxide coordination controversy.