Interplays of electron and nuclear motions along CO dissociation trajectory in myoglobin revealed by ultrafast X-rays and quantum dynamics calculations.

Ultrafast structural dynamics with different spatial and temporal scales were investigated during photodissociation of carbon monoxide (CO) from iron(II)-heme in bovine myoglobin during the first 3 ps following laser excitation. We used simultaneous X-ray transient absorption (XTA) spectroscopy and X-ray transient solution scattering (XSS) at an X-ray free electron laser source with a time resolution of 80 fs. Kinetic traces at different characteristic X-ray energies were collected to give a global picture of the multistep pathway in the photodissociation of CO from heme. In order to extract the reaction coordinates along different directions of the CO departure, XTA data were collected with parallel and perpendicular relative polarizations of the laser pump and X-ray probe pulse to isolate the contributions of electronic spin state transition, bond breaking, and heme macrocycle nuclear relaxation. The time evolution of the iron K-edge X-ray absorption near edge structure (XANES) features along the two major photochemical reaction coordinates, i.e., the iron(II)-CO bond elongation and the heme macrocycle doming relaxation were modeled by time-dependent density functional theory calculations. Combined results from the experiments and computations reveal insight into interplays between the nuclear and electronic structural dynamics along the CO photodissociation trajectory. Time-resolved small-angle X-ray scattering data during the same process are also simultaneously collected, which show that the local CO dissociation causes a protein quake propagating on different spatial and temporal scales. These studies are important for understanding gas transport and protein deligation processes and shed light on the interplay of active site conformational changes and large-scale protein reorganization.

Modeling L2,3-Edge X-ray Absorption Spectroscopy with Real-Time Exact Two-Component Relativistic Time-Dependent Density Functional Theory.

X-ray absorption spectroscopy is a powerful technique to probe local electronic and nuclear structure. There has been extensive theoretical work modeling K-edge spectra from first principles. However, modeling L-edge spectra directly with density functional theory poses a unique challenge requiring further study. Spin-orbit coupling must be included in the model, and a noncollinear density functional theory is required. Using the real-time exact two-component method, we are able to variationally include one-electron spin-orbit coupling terms when calculating the absorption spectrum. The abilities of different basis sets and density functionals to model spectra for both closed- and open-shell systems are investigated using SiCl4 and three transition metal complexes, TiCl4, CrO2Cl2, and [FeCl6]3-. Although we are working in the real-time framework, individual molecular orbital transitions can still be recovered by projecting the density onto the ground state molecular orbital space and separating contributions to the time evolving dipole moment.

Efficient Implementation of Variation after Projection Generalized Hartree-Fock.

Projected Hartree-Fock (PHF) theory can restore important symmetries to broken symmetry wave functions. Variation after projection (VAP) implementations make it possible to deliberately break and then restore a given symmetry by directly minimizing the projected energy expression. This technique can be applied to any symmetry that can be broken from relaxing constraints on single Slater determinant wave functions. For instance, generalized Hartree-Fock (GHF) wave functions are eigenfunctions of neither Sz nor S2. By relaxing these constraints, the wave function can explore a larger variational space and can reach lower energies than more constrained HF solutions. We have implemented spin-projected GHF (SGHF), which retains many of the advantages of breaking symmetry while also being a spin eigenfunction, with some notable improvements over previous implementations. Our new algorithm involves the formation of new intermediate matrices not previously discussed in the literature. Discretization of the necessary integration over the rotation group SO(3) is also accomplished much more efficiently using Lebedev grids. A novel scheme to incrementally build rotated Fock matrices is also introduced and compared with more standard approaches.

Can Excited State Electronic Coherence Be Tuned via Molecular Structural Modification? A First-Principles Quantum Electronic Dynamics Study of Pyrazolate-Bridged Pt(II) Dimers.

Materials and molecular systems exhibiting long-lived electronic coherence can facilitate coherent transport, opening the door to efficient charge and energy transport beyond traditional methods. Recently, signatures of a possible coherent, recurrent electronic motion were identified in femtosecond pump-probe spectroscopy experiments on a binuclear platinum complex, where a persistent periodic beating in the transient absorption signal's anisotropy was observed. In this study, we investigate the excitonic dynamics that underlie the suspected electronic coherence for a series of binuclear platinum complexes exhibiting a range of interplatinum distances. Results suggest that the long-lived coherence can only result when competitive electronic couplings are in balance. At longer Pt-Pt distances, the electronic couplings between the two halves of the binuclear system weaken, and exciton localization and recombination is favored on short time scales. For short Pt-Pt distances, electronic couplings between the states in the coherent superposition are stronger than the coupling with other excitonic states, leading to long-lived coherence.

Imaging ultrafast excited state pathways in transition metal complexes by X-ray transient absorption and scattering using X-ray free electron laser source.

This report will describe our recent studies of transition metal complex structural dynamics on the fs and ps time scales using an X-ray free electron laser source, Linac Coherent Light Source (LCLS). Ultrafast XANES spectra at the Ni K-edge of nickel(ii) tetramesitylporphyrin (NiTMP) were measured for optically excited states at a timescale from 100 fs to 50 ps, providing insight into its sub-ps electronic and structural relaxation processes. Importantly, a transient reduced state Ni(i) (π, 3dx2-y2) electronic state is captured through the interpretation of a short-lived excited state absorption on the low-energy shoulder of the edge, which is aided by the computation of X-ray transitions for postulated excited electronic states. The observed and computed inner shell to valence orbital transition energies demonstrate and quantify the influence of the electronic configuration on specific metal orbital energies. A strong influence of the valence orbital occupation on the inner shell orbital energies indicates that one should not use the transition energy from 1s to other orbitals to draw conclusions about the d-orbital energies. For photocatalysis, a transient electronic configuration could influence d-orbital energies up to a few eV and any attempt to steer the reaction pathway should account for this to ensure that external energies can be used optimally in driving desirable processes. NiTMP structural evolution and the influence of the porphyrin macrocycle conformation on relaxation kinetics can be likewise inferred from this study.

Ultrafast Excited State Relaxation of a Metalloporphyrin Revealed by Femtosecond X-ray Absorption Spectroscopy.

Photoexcited Nickel(II) tetramesitylporphyrin (NiTMP), like many open-shell metalloporphyrins, relaxes rapidly through multiple electronic states following an initial porphyrin-based excitation, some involving metal centered electronic configuration changes that could be harnessed catalytically before excited state relaxation. While a NiTMP excited state present at 100 ps was previously identified by X-ray transient absorption (XTA) spectroscopy at a synchrotron source as a relaxed (d,d) state, the lowest energy excited state (J. Am. Chem. Soc., 2007, 129, 9616 and Chem. Sci., 2010, 1, 642), structural dynamics before thermalization were not resolved due to the ∼100 ps duration of the available X-ray probe pulse. Using the femtosecond (fs) X-ray pulses of the Linac Coherent Light Source (LCLS), the Ni center electronic configuration from the initial excited state to the relaxed (d,d) state has been obtained via ultrafast Ni K-edge XANES (X-ray absorption near edge structure) on a time scale from hundreds of femtoseconds to 100 ps. This enabled the identification of a short-lived Ni(I) species aided by time-dependent density functional theory (TDDFT) methods. Computed electronic and nuclear structure for critical excited electronic states in the relaxation pathway characterize the dependence of the complex's geometry on the electron occupation of the 3d orbitals. Calculated XANES transitions for these excited states assign a short-lived transient signal to the spectroscopic signature of the Ni(I) species, resulting from intramolecular charge transfer on a time scale that has eluded previous synchrotron studies. These combined results enable us to examine the excited state structural dynamics of NiTMP prior to thermal relaxation and to capture intermediates of potential photocatalytic significance.

The consequences of improperly describing oscillator strengths beyond the electric dipole approximation.

The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strength can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.

Calibration of Energy-Specific TDDFT for Modeling K-edge XAS Spectra of Light Elements.

X-ray absorption spectroscopy (XAS) has become a powerful technique in chemical physics, because of advances in synchrotron technology that have greatly improved its temporal and spectroscopic resolution. Our recent work on energy-specific time-dependent density functional theory (ES-TDDFT) allows for the direct calculation of excitation energies in any region of the absorption spectrum, from UV-vis to X-ray. However, the ability of different density functional theories to model X-ray absorption spectra (XAS) of light elements has not yet been verified for ES-TDDFT. This work is a calibration of the ability of existing DFT kernels and basis sets to reproduce experimental K-edge excitation energies. Results were compared against 30 different transitions from gas-phase experiments. We focus on six commonly used density functionals (BHandHLYP, B3LYP, PBE1PBE, BP86, HSE06, LC-ωPBE) and various triple-ζ basis sets. The effects of core and diffuse functions are also investigated.

Energy-Specific Equation-of-Motion Coupled-Cluster Methods for High-Energy Excited States: Application to K-edge X-ray Absorption Spectroscopy.

Single-reference techniques based on coupled-cluster (CC) theory, in the forms of linear response (LR) or equation of motion (EOM), are highly accurate and widely used approaches for modeling valence absorption spectra. Unfortunately, these equations with singles and doubles (LR-CCSD and EOM-CCSD) scale as O(N6), which may be prohibitively expensive for the study of high-energy excited states using a conventional eigensolver. In this paper, we present an energy-specific non-Hermitian eigensolver that is able to obtain high-energy excited states (e.g., XAS K-edge spectrum) at low computational cost. In addition, we also introduce an improved trial vector for iteratively solving the EOM-CCSD equation with a focus on high-energy eigenstates. The energy-specific EOM-CCSD approach and its low-scaling alternatives are applied to calculations of carbon, nitrogen, oxygen, and sulfur K-edge excitations. The results are compared to other implementations of CCSD for excited states, energy-specific linear response time-dependent density functional theory (TDDFT), and experimental results with multiple statistical metrics are presented and evaluated.

Density of States Guided Møller-Plesset Perturbation Theory.

An integral formalism using a density-of-state framework has been developed for Møller-Plesset perturbation theory. This method is designed to compute the correlation energy correction for large systems with high density of states, such as polymers and nanostructures. The framework has the potential to lower the computational cost of perturbation theory, and such perspectives are discussed in this paper. This method has been implemented for the second- and third-order perturbation theory. Applications of the new methods to test cases of conjugated molecules show very good accuracy and significant savings in computational cost.