Electron transfer in a crystalline cytochrome with four hemes

Diffusion of electrons over distances on the order of 100 μm has been observed in crystals of a small tetraheme cytochrome (STC) from Shewanella oneidensis [J. Huang et al. J. Am. Chem. Soc. 142, 10459-10467 (2020)]. Electron transfer between hemes in adjacent subunits of the crystal is slower and more strongly dependent on temperature than had been expected based on semiclassical electron-transfer theory. We here explore explanations for these findings by molecular-dynamics simulations of crystalline and monomeric STC. New procedures are developed for including time-dependent quantum mechanical energy differences in the gap between the energies of the reactant and product states and for evaluating fluctuations of the electronic-interaction matrix element that couples the two hemes. Rate constants for electron transfer are calculated from the time- and temperature-dependent energy gaps, coupling factors, and Franck-Condon-weighted densities of states using an expression with no freely adjustable parameters. Back reactions are considered, as are the effects of various protonation states of the carboxyl groups on the heme side chains. Interactions with water are found to dominate the fluctuations of the energy gap between the reactant and product states. The calculated rate constant for electron transfer from heme IV to heme Ib in a neighboring subunit at 300 K agrees well with the measured value. However, the calculated activation energy of the reaction in the crystal is considerably smaller than observed. We suggest two possible explanations for this discrepancy. The calculated rate constant for transfer from heme I to II within the same subunit of the crystal is about one-third that for monomeric STC in solution.

Extensive Analysis of the Parameters Influencing Radiative Rates Obtained through Vibronic Calculations

Defining a theoretical model systematically delivering accurate ab initio predictions of the fluorescence quantum yields of organic dyes is highly desirable for designing improved fluorophores in a systematic rather than trial-and-error way. To this end, the first required step is to obtain reliable radiative rates (kr), as low kr typically precludes effective emission. In the present contribution, using a series of 10 substituted phenyls with known experimental kr, we analyze the impact of the computational protocol on the kr determined through the thermal vibration correlation function (TVCF) approach on the basis of time-dependent density functional theory (TD-DFT) calculations of the energies, structures, and vibrational parameters. Both the electronic structure (selected exchange-correlation functional, application or not of the Tamm-Dancoff approximation) and the vibronic parameters (line-shape formalism, coordinate system, potential energy surface model, and dipole expansion) are tackled. Considering all possible combinations yields more than 3500 cases, allowing to extract statistically-relevant information regarding the impact of each computational parameter on the magnitude of the estimated kr. It turns out that the selected vibronic model can have a significant impact on the computed kr, especially the potential energy surface model. This effect is of the same order of magnitude as the difference noted between B3LYP and CAM-B3LYP estimates. For the treated compounds, all evaluated functionals do deliver reasonable trends, fitting the experimental values.

On the absolute photoionization cross section and threshold photoelectron spectrum of two reactive ketenes in lignin valorization: fulvenone and 2-carbonyl cyclohexadienone

We report the absolute photoionization cross section (PICS) of fulvenone and 2-carbonyl cyclohexadienone, two crucial ketene intermediates in lignin pyrolysis, combustion and organic synthesis. Both species were generated in situ by pyrolyzing salicylamide and dectected via imaging photoelectron photoion coincidence spectroscopy. In a deamination reaction, salicylamide loses ammonia yielding 2-carbonyl cyclohexadienone, a ketoketene, which further decarbonylates at higher pyrolysis temperatures to form fulvenone. We recorded the threshold photoelectron spectrum of the ketoketene and assigned the ground state (X̃⁺²A′′ ← X̃¹A′) and excited state (Ã⁺²A′ ← X̃¹A′) bands with the help of Franck–Condon simulations. Adiabatic ionization energies are 8.35 ± 0.01 and 9.19 ± 0.01 eV. In a minor reaction channel, the ketoketene isomerizes to benzpropiolactone, which decomposes subsequently to benzyne by CO₂ loss. Potential energy surface and RRKM rate constant calculations agree with our experimental observations that the decarbonylation to fulvenone outcompetes the decarboxylation to benzyne by almost two orders of magnitude. The absolute PICS of fulvenone at 10.48 eV was determined to be 18.8 ± 3.8 Mb using NH₃ as a calibrant. The PICS of 2-carbonyl cyclohexadienone was found to be 21.5 ± 8.6 Mb at 9 eV. Our PICS measument will enable the quantification of reactive ketenes in lignin valorization and combustion processes using photoionization techniques and provide advanced mechanistic and kinetics insights to aid the bottom-up optimization of such processes.

The absolute photoionization cross section (PICS) of these crucial ketene intermediates supports their quantification in lignin pyrolysis, combustion and organic synthesis.

Simulation of Ab Initio Optical Absorption Spectrum of β-Carotene with Fully Resolved S0 and S2 Vibrational Normal Modes

The electronic absorption spectrum of β-carotene (β-Car) is studied using quantum chemistry and quantum dynamics simulations. Vibrational normal modes were computed in optimized geometries of the electronic ground state S₀ and the optically bright excited S₂ state using the time-dependent density functional theory. By expressing the S₂-state normal modes in terms of the ground-state modes, we find that no one-to-one correspondence between the ground- and excited-state vibrational modes exists. Using the ab initio results, we simulated the β-Car absorption spectrum with all 282 vibrational modes in a model solvent at 300 K using the time-dependent Dirac-Frenkel variational principle and are able to qualitatively reproduce the full absorption line shape. By comparing the 282-mode model with the prominent 2-mode model, widely used to interpret carotenoid experiments, we find that the full 282-mode model better describes the high-frequency progression of carotenoid absorption spectra; hence, vibrational modes become highly mixed during the S₀ → S₂ optical excitation. The obtained results suggest that electronic energy dissipation is mediated by numerous vibrational modes.

Reliable Predictions of Benzophenone Singlet-Triplet Transition Rates: A Second-Order Cumulant Approach

Fermi golden rule and second-order cumulant expansion of the time-dependent density matrix have been used to compute from first principles the rate of intersystem crossing in benzophenone, using minimum-energy geometries and normal modes of vibrations computed at the TDDFT/CAM-B3LYP level. Both approaches yield reliable values of the S₁ decay rate, the latter being almost in quantitative agreement with the results of time-dependent spectroscopic measurements (0.154 ps^-1 observed vs 0.25 ps^-1 predicted). The Fermi golden rule slightly overestimates the decay rate of S₁ state (k_d = 0.45 ps^-1) but provides better insights into the chemico-physical parameters, which govern the transition from a thermally equilibrated population of S₁, showing that the indirect mechanism is much faster than the direct one because of the vanishingly small Franck-Condon weighted density of states at ΔE of transition.

Analytical Evaluation for Calculation of Two-Center Franck–Condon Factor and Matrix Elements

The Franck–Condon (FC) factor is defined as squares of the Franck–Condon (FC) overlap integral and represents one of the principle fundamental factors of molecular physics. The FC factor is used to determine the transition probabilities in different vibrational levels of the two electronic states and the spectral line intensities of diatomic and polyatomic molecules. In this study, new analytical formulas were derived to calculate Franck–Condon integral (FCI) of harmonic oscillators and matrix elements (xη, e−2cx, and e−cx2) including simple finite summations of binomial coefficients. These formulas are valid for arbitrary values. The results of formulas are in agreement with the results in the literature.

Insights into Geometric and Electronic Structures of VGe3-/0 Clusters from Anion Photoelectron Spectrum Assignment

The global minima of both neutral and anionic clusters of VGe₃^-/0 were determined using different quantum chemical methods (DFT, RCCSD(T), CASSCF/CASPT2). On the basis of the ground states identified, most excited bands in the anion photoelectron spectrum of VGe₃^- were assigned. The tetrahedral isomers of both charged states are the most stable ones. A singlet state (C_s^, 1A') of the tetrahedral isomer has the globally lowest energy on the potential hypersurface of VGe₃^-. Two states 1²A' and 1²A″ of the neutral tetrahedral isomer are nearly degenerate and identified as the competing ground state of VGe₃. From the anionic ground state, four of five bands in the anion photoelectron spectrum of VGe₃^- were determined to be the consequences of one-electron transitions starting from the anionic ground state ¹A'. Both nearly degenerate neutral ground states are responsible for generation of the first band. Two different transitions from the anionic ground state ¹A' to the first two nearly degenerate excited states (2²A' and 2²A″) of the neutral underlie the second lowest ionization band. Two higher levels of ionization recorded in the spectrum were assigned to the two higher excited states 4²A' and 5²A' of the neutral. Franck-Condon factor simulations of the first band were performed to obtain more insights into the experimental bands of the spectrum.

Titanium Digermanium: Theoretical Assignment of Electronic Transitions Underlying Its Anion Photoelectron Spectrum

Electronic structures of both the anionic and neutral triatomic species TiGe₂^-/0 were theoretically studied employing single-reference (DFT and RCCSD(T)) and multiconfigurational (CASSCF/CASPT2 and CASSCF/NEVPT2) methods with large basis sets. The ground state of TiGe₂^- (C_2v) was identified to be ⁴B₁, but the ²A₁ state is nearly degenerate, whereas the ³B₁ is clearly the ground state of the neutral TiGe₂ (C_2v). On the basis of the computed ground and excited states of both neutral and anionic structures, all electronic transitions giving rise to experimental anion photoelectron bands in the spectrum of TiGe₂^- can now be assigned. The X band of the anion photoelectron spectrum is attributed to a one-electron transition between two ground states ⁴B₁ → ³B₁. Three neutral excited states 2³A₂, 2⁵B₁, and 3⁵B₁ are energetically responsible for the B band upon one-electron photodetachement from the anionic ground state ⁴B₁. The C band is assigned to the transition ⁴B₁ → 2⁵A₁. A transition from the nearly degenerate ground state ²A₁ of the anion to the low-spin ¹A₁ of the final neutral state can be ascribed to the A band. Furthermore, the first two bands' progressions, whose normal vibrational modes were accessible from CASSCF/CASPT2 calculations, were also simulated by determination of multidimensional Franck-Condon factors.

Synthesis and Fluorescent Behaviour of 2-Aryl-4,5-dihydro-1H-1,2,4-triazoles

A series of new 4,5-dihydro-1H-1,2,4-triazoles was synthesized from amidrazones and acetylenedicarboxylic acid esters in the presence of pyridine in toluene. The synthesized compounds were characterized by ¹H, ¹³C NMR, FT-IR spectral analyses and XRD data. Optical studies revealed that most of the compounds reported here exhibited emission of blue or green-yellow light upon irradiation in acetone and showed Stokes shifts in the region of 70-96 nm and quantum yields of up to 45%. The interpretation of the experimental findings was supported by state-of-the-art quantum mechanical calculations.

Revisiting Vertical Models To Simulate the Line Shape of Electronic Spectra Adopting Cartesian and Internal Coordinates

Vertical models for the simulation of spectroscopic line shapes expand the potential energy surface (PES) of the final state around the equilibrium geometry of the initial state. These models provide, in principle, a better approximation of the region of the band maximum. At variance, adiabatic models expand each PES around its own minimum. In the harmonic approximation, when the minimum energy structures of the two electronic states are connected by large structural displacements, adiabatic models can breakdown and are outperformed by vertical models. However, the practical application of vertical models faces the issues related to the necessity to perform a frequency analysis at a nonstationary point. In this contribution we revisit vertical models in harmonic approximation adopting both Cartesian (x) and valence internal curvilinear coordinates (s). We show that when x coordinates are used, the vibrational analysis at nonstationary points leads to a deficient description of low-frequency modes, for which spurious imaginary frequencies may even appear. This issue is solved when s coordinates are adopted. It is however necessary to account for the second derivative of s with respect to x, which here we compute analytically. We compare the performance of the vertical model in the s-frame with respect to adiabatic models and previously proposed vertical models in x- or Q₁-frame, where Q₁ are the normal coordinates of the initial state computed as combination of Cartesian coordinates. We show that for rigid molecules the vertical approach in the s-frame provides a description of the final state very close to the adiabatic picture. For sizable displacements it is a solid alternative to adiabatic models, and it is not affected by the issues of vertical models in x- and Q₁-frames, which mainly arise when temperature effects are included. In principle the G matrix depends on s, and this creates nonorthogonality problems of the Duschinsky matrix connecting the normal modes of initial and final states in adiabatic approaches. We highlight that such a dependence of G on s is also an issue in vertical models, due to the necessity to approximate the kinetic term in the Hamiltonian when setting up the so-called GF problem. When large structural differences exist between the initial and the final-state minima, the changes in the G matrix can become too large to be disregarded.

A proposed new scheme for vibronically resolved time-dependent photoelectron spectroscopy: pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes)

We propose a new scheme for time-resolved photoelectron spectroscopy denoted as pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes). This scheme is comprised of two femtosecond laser (pump) pulses under cw illumination (probe). By changing the time-delay between pump and repump lasers one can manipulate the populations of vibronic levels in electronic excited states. The cw laser acts on for a long time and establishes resonance between excited states and the continuum photo-ionized states. Sharp spectra can be obtained from the resonance condition [formula: see text]. The intensities in the spectra are sensitive to the time-delay between the pump-repump pulses, but only depend on the populations of excited states, not the phase relations (coherence). As a result, each time-delayed snapshot spectrum is a weighted sum of so-called fingerprints, where a fingerprint is the vibrationally resolved photoelectron spectrum for a single vibronic excited state. The latter information can potentially be simulated reliably using vibronic models and wave packet propagation methods. In the easiest application of the experiment, different time-delays produce different spectra, for a single molecular system. This wealth of experimental data can be fitted to an, ideally small, set of theoretical fingerprints by adjusting the populations as fitting parameters. This technique might be able to distinguish between closely related molecular species. Adopting a different viewpoint, the proposed scheme can also be employed to monitor the time-dependent dynamics by changing the phase relationship between the pump and repump laser that can be viewed as a "control mechanism" employed in wave packet interferometry. Simplifications arise as the change in the spectra is due to the changing populations, not because of the coherence. In this paper, we outline the ideas behind the scheme and illustrate the ideas theoretically using simple model systems.

A Gaussian Wave Packet Propagation Approach to Vibrationally Resolved Optical Spectra at Non-Zero Temperatures

An effective time dependent approach based on a method that is similar to the Gaussian wave packet propagation (GWP) technique of Heller is developed for the computation of vibrationally resolved electronic spectra at finite temperatures in the harmonic, Franck-Condon/Hertzberg-Teller approximations. Since the vibrational thermal density matrix of the ground electronic surface and the time evolution operator on that surface commute, it is possible to write the spectrum generating correlation function as a trace of the time evolved doorway state. In the stated approximations, the doorway state is a superposition of the harmonic oscillator zero and one quantum eigenfunctions and thus can be propagated by the GWP. The algorithm has an O(N(3)) dependence on the number of vibrational modes. An application to pyrene absorption spectrum at two temperatures is presented as a proof of the concept.

Rapid intersystem crossings in anti bimanes

We have carried out first principles electronic structure calculations on the ground and excited valence states of syn and anti bimanes. While syn bimanes fluoresce strongly after photoexcitation to the first excited singlet state (S1) and are commonly used as fluorophores in biological labeling studies, anti bimanes largely phosphoresce at low temperatures. We show that this is due to subtle differences in the energetic ordering of excited singlet and triplet states within the isomers. In particular, T2 in anti bimanes is characterized by a π→π* transition and large exchange interactions with the singlet counterpart cause it to lie below and energetically close to S1 at the Franck-Condon region. This opens up a pathway for very fast intersystem crossing (ca. 10(11) s(-1)) from the optically bright S1 state to the triplet manifold, which effectively quenches fluorescence. On the other hand, T2 is energetically inaccessible to S1 in syn bimanes and intersystem crossing via S1→ T1 cannot compete effectively with fluorescence to S0. We have also located minimum energy conical intersections between S0 and S1 in bimanes. However, these structures are significantly distorted from their equilibrium geometries as well as energetically much higher than S1 at the Franck-Condon region. They are therefore not expected to play a part in the photophysics of bimanes after excitation to S1.

Hole delocalization over adenine tracts in single stranded DNA oligonucleotides

Adiabatic ionization energies of single stranded DNA oligonucleotides containing adenine tracts of different sizes have been computed at the DFT level and compared with the oxidation potentials determined by differential pulse voltammetry. Geometry optimizations have been performed at the full quantum mechanical level, including the sugar phosphate backbone and solvent effects. The observed progressive lowering of the ionization energy upon increasing the number of consecutive adenines is well predicted, the computed ionization potential shifts being in very good agreement with the experimental outcomes, both by using pure and hybrid functionals. The spin density of the oligonucleotide radical cations is distributed almost over the whole adenine tract, forming delocalized polarons.

Vibronic couplings and coherent electron transfer in bridged systems

A computational strategy to analyze the dynamics of coherent electron transfer processes in bridged systems, involving three or more electronic states, is presented.

Vibronic bandshape of the absorption spectra of dibenzoylmethanatoboron difluoride derivatives: analysis based on ab initio calculations

The nature of absorption bandshapes of dibenzoylmethanatoboron difluoride (DBMBF₂) derivatives is investigated using TDDFT and time-dependent linear vibronic coupling model.

Full dimensional Franck-Condon factors for the acetylene à (1)A(u)-X̃ (1)Σ(g)(+) transition. I. Method for calculating polyatomic linear-bent vibrational intensity factors and evaluation of calculated intensities for the gerade vibrational modes in acetylene

Franck-Condon vibrational overlap integrals for the à Au1-X̃ 1Σg+ transition in acetylene have been calculated in full dimension in the harmonic normal mode basis. The calculation uses the method of generating functions first developed for polyatomic Franck-Condon factors by Sharp and Rosenstock [J. Chem. Phys. 41(11), 3453-3463 (1964)], and previously applied to acetylene by Watson [J. Mol. Spectrosc. 207(2), 276-284 (2001)] in a reduced-dimension calculation. Because the transition involves a large change in the equilibrium geometry of the electronic states, two different types of corrections to the coordinate transformation are considered to first order: corrections for axis-switching between the Cartesian molecular frames and corrections for the curvilinear nature of the normal modes at large amplitude. The angular factor in the wavefunction for the out-of-plane component of the trans bending mode, ν4(″), is treated as a rotation, which results in an Eckart constraint on the polar coordinates of the bending modes. To simplify the calculation, the other degenerate bending mode, ν5(″), is integrated in the Cartesian basis and later transformed to the constrained polar coordinate basis, restoring the conventional v and l quantum numbers. An updated Ã-state harmonic force field obtained recently in the R. W. Field research group is evaluated. The results for transitions involving the gerade vibrational modes are in qualitative agreement with experiment. Calculated results for transitions involving ungerade modes are presented in Paper II of this series [G. B. Park, J. H. Baraban, and R. W. Field, "Full dimensional Franck-Condon factors for the acetylene à Au1-X̃ 1Σg+ transition. II. Vibrational overlap factors for levels involving excitation in ungerade modes," J. Chem. Phys. 141, 134305 (2014)].

A robust and effective time-independent route to the calculation of Resonance Raman spectra of large molecules in condensed phases with the inclusion of Duschinsky, Herzberg-Teller, anharmonic, and environmental effects

We present an effective time-independent implementation to model vibrational resonance Raman (RR) spectra of medium-large molecular systems with the inclusion of Franck-Condon (FC) and Herzberg-Teller (HT) effects and a full account of the possible differences between the harmonic potential energy surfaces of the ground and resonant electronic states. Thanks to a number of algorithmic improvements and very effective parallelization, the full computations of fundamentals, overtones, and combination bands can be routinely performed for large systems possibly involving more than two electronic states. In order to improve the accuracy of the results, an effective inclusion of the leading anharmonic effects is also possible, together with environmental contributions under different solvation regimes. Reduced-dimensionality approaches can further enlarge the range of applications of this new tool. Applications to imidazole, pyrene, and chlorophyll a1 in solution are reported, as well as comparisons with available experimental data.