Few-femtosecond electronic and structural rearrangements of CH4+ driven by the Jahn-Teller effect.

The Jahn-Teller effect (JTE) is central to the understanding of the physical and chemical properties of a broad variety of molecules and materials. Whereas the manifestations of the JTE in stationary properties of matter are relatively well studied, the study of JTE-induced dynamics is still in its infancy, largely owing to its ultrafast and non-adiabatic nature. For example, the time scales reported for the distortion of CH4+ from the initial Td geometry to a nominal C2v relaxed structure range from 1.85 fs over 10 ± 2 fs to 20 ± 7 fs. Here, by combining element-specific attosecond transient-absorption spectroscopy and quantum-dynamics simulations, we show that the initial electronic relaxation occurs within 5 fs and that the subsequent nuclear dynamics are dominated by the Q2 scissoring and Q1 symmetric stretching modes, which dephase in 41 ± 10 fs and 13 ± 3 fs, respectively. Significant structural relaxation is found to take place only along the e-symmetry Q2 mode. These results demonstrate that CH4+ created by ionization of CH4 is best thought of as a highly fluxional species that possesses a long-time-averaged vibrational distribution centered around a D2d structure. The methods demonstrated in our work provide guidelines for the understanding of Jahn-Teller driven non-adiabatic dynamics in other more complex systems.

Time-Resolved X-ray Photoelectron Spectroscopy: Ultrafast Dynamics in CS2 Probed at the S 2p Edge.

Recent developments in X-ray free-electron lasers have enabled a novel site-selective probe of coupled nuclear and electronic dynamics in photoexcited molecules, time-resolved X-ray photoelectron spectroscopy (TRXPS). We present results from a joint experimental and theoretical TRXPS study of the well-characterized ultraviolet photodissociation of CS2, a prototypical system for understanding non-adiabatic dynamics. These results demonstrate that the sulfur 2p binding energy is sensitive to changes in the nuclear structure following photoexcitation, which ultimately leads to dissociation into CS and S photoproducts. We are able to assign the main X-ray spectroscopic features to the CS and S products via comparison to a first-principles determination of the TRXPS based on ab initio multiple-spawning simulations. Our results demonstrate the use of TRXPS as a local probe of complex ultrafast photodissociation dynamics involving multimodal vibrational coupling, nonradiative transitions between electronic states, and multiple final product channels.

Antioxidant, pancreatic lipase, and α-amylase inhibitory properties of oat bran hydrolyzed proteins and peptides.

This work aimed to determine the antioxidant properties of identified hydrolyzed oat proteins and peptides, and their capacity to inhibit lipase and α-amylase. The protein hydrolysates retarded the oxidation of peanut oil by reducing peroxide values (up to 2.5-fold), relative to the control oil. Of the five tested peptides, P1 (YFDEQNEQFR), P3 (SPFWNINAH), and P4 (NINAHSVVY) significantly reduced the oxidation of linoleic acid. In the enzyme assays, P3 was the best lipase inhibitor (IC50 85.4 ± 3 µM) while P1 was the most potent inhibitor of α-amylase (IC50 37.5 ± 1.1 µM). The structure-activity relationship assessed using the CABS-dock computational model predicted that interactions between peptides and pancreatic lipase residues of Ser153 , His264 , and Asp177 were important for the inhibition. In the case of α-amylase, interactions with residues of the active sites (Asp197 , Glu233 , and Asp300 ), but not those of calcium- or chloride-binding domains, were important for the inhibition. PRACTICAL APPLICATIONS: In recent years, there have been many studies focussing on isolating multifunctional peptides from food and food waste with antioxidant and bioactivity potential to promote human health. Some of these antioxidant peptides have been found to be effective to prevent diseases and complications such as hypertension, cardiovascular disease, cancer, diabetes, and obesity. The peptides studied in this work showed a great potential to prevent oxidation in a lipid system and demonstrated a significant ability to reduce the enzymatic activity of lipase and α-amylase. These enzymes contribute to the digestion of fat and carbohydrate, and their inhibition can reduce the absorption of these macronutrients and make them a great target for designing antioxidant and anti-obesity compounds. With the multifunctional activity of oat bran-derived peptides, it is proposed that these peptides can be used in food formulations due to their antioxidant and potential anti-obesity properties.

Resolving competing conical intersection pathways: time-resolved X-ray absorption spectroscopy of trans-1,3-butadiene.

Time-resolved X-ray absorption spectroscopy is emerging as a uniquely powerful tool to probe coupled electronic-nuclear dynamics in photo-excited molecules. Theoretical studies to date have established that time-resolved X-ray absorption spectroscopy is an atom-specific probe of excited-state wave packet passage through a seam of conical intersections (CIs). However, in many molecular systems, there are competing dynamical pathways involving CIs of different electronic and nuclear character. Discerning these pathways remains an important challenge. Here, we demonstrate that time-resolved X-ray absorption spectroscopy (TRXAS) has the potential to resolve competing channels in excited-state non-adiabatic dynamics. Using the example of 1,3-butadiene, we show how TRXAS discerns the different electronic structures associated with passage through multiple conical intersections. trans-1,3-Butadiene exhibits a branching between polarized and radicaloid pathways associated with ethylenic "twisted-pyramidalized" and excited-state cis-trans isomerization dynamics, respectively. The differing electronic structures along these pathways give rise to different XAS signals, indicating the possibility of resolving them. Furthermore, this indicates that XAS, and other core-level spectroscopic techniques, offer the appealing prospect of directly probing the effects of selective chemical substitution and its ability to affect chemical control over excited-state molecular dynamics.

Sub-7-femtosecond conical-intersection dynamics probed at the carbon K-edge.

Conical intersections allow electronically excited molecules to return to their electronic ground state. Here, we observe the fastest electronic relaxation dynamics measured to date by extending attosecond transient-absorption spectroscopy (ATAS) to the carbon K-edge. We selectively launch wave packets in the two lowest electronic states (D0 and D1) of C2H4 + The electronic D1 → D0 relaxation takes place with a short time constant of 6.8 ± 0.2 femtoseconds. The electronic-state switching is directly visualized in ATAS owing to a spectral separation of the D1 and D0 bands caused by electron correlation. Multidimensional structural dynamics of the molecule are simultaneously observed. Our results demonstrate the capability to resolve the fastest electronic and structural dynamics in the broad class of organic molecules. They show that electronic relaxation in the prototypical organic chromophore can take place within less than a single vibrational period.

Propagative block diagonalization diabatization of DFT/MRCI electronic states.

We present a framework for the calculation of diabatic states using the combined density functional theory and multireference configuration interaction (DFT/MRCI) method. Due to restrictions present in the current formulation of the DFT/MRCI method (a lack of analytical derivative couplings and the inability to use non-canonical Kohn-Sham orbitals), most common diabatization strategies are not applicable. We demonstrate, however, that diabatic wavefunctions and potentials can be reliably calculated at the DFT/MRCI level of theory using a propagative variant of the block diagonalization diabatization method (P-BDD). The proposed procedure is validated via the calculation of diabatic potentials for LiH and the simulation of the vibronic spectrum of pyrazine. In both cases, the combination of the DFT/MRCI and P-BDD methods is found to correctly recover the non-adiabatic coupling effects of the problem.

The simulation of X-ray absorption spectra from ground and excited electronic states using core-valence separated DFT/MRCI.

We present an extension of the combined density functional theory (DFT) and multireference configuration interaction (MRCI) method (DFT/MRCI) [S. Grimme and M. Waletzke, J. Chem. Phys. 111, 5645 (1999)] for the calculation of core-excited states based on the core-valence separation (CVS) approximation. The resulting method, CVS-DFT/MRCI, is validated via the simulation of the K-edge X-ray absorption spectra of 40 organic chromophores, amino acids, and nucleobases, ranging in size from CO2 to tryptophan. Overall, the CVS-DFT/MRCI method is found to yield accurate X-ray absorption spectra (XAS), with consistent errors in peak positions of ∼2.5-3.5 eV. Additionally, we show that the CVS-DFT/MRCI method may be employed to simulate XAS from valence excited states and compare the simulated spectra to those computed using the established wave function-based approaches [ADC(2) and ADC(2)x]. In general, each of the methods yields excited state XAS spectra in qualitative and often quantitative agreement. In the instances where the methods differ, the CVS-DFT/MRCI simulations predict intensity for transitions for which the underlying electronic states are characterized by doubly excited configurations relative to the ground state configuration. Here, we aim to demonstrate that the CVS-DFT/MRCI approach occupies a specific niche among numerous other electronic structure methods in this area, offering the ability to treat initial states of arbitrary electronic character while maintaining a low computational cost and comparatively black box usage.

Vibronic interaction in CO3- photo-detachment: Jahn-Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries.

Recently, the negative ion photoelectron spectrum of CO3- was reported and the second lowest energy band is assigned to the close-lying 3E'' and 3E' states that undergo Jahn-Teller distortions (Chem. Sci., 2016, 7, 1142). This assignment is based on the Born-Oppenheimer approximation and the assumption of a static Jahn-Teller effect that distorts the CO3 structure from D3h to C2v symmetry. In this work, we employ a 4 states 6 modes vibronic coupling model to investigate the triplet band and uncover the dynamic and non-adiabatic nature of the Jahn-Teller and pseudo-Jahn-Teller interactions in the triplet states. The apparent four peaks progression in the band is studied in depth, and is found to consist of more than four transitions. By comparing the simulated spectra using the full model and the reduced-dimension 2 states 2 modes models, we characterize those transitions. The origin of the complexities of the spectrum is traced to the C-O nonbonding character of the orbitals that lose electron in the photo-detachment process. Methodology-wise, we derive and present the formalisms for arbitrary order expansions of all bimodal trigonal Jahn-Teller and pseudo-Jahn-Teller Hamiltonians in vibrational coordinates.

General Formalism of Vibronic Hamiltonians for Tetrahedral and Octahedral Systems: Problems That Involve T, E States and t, e Vibrations.

We derive expansion formulas up to arbitrary order in vibrational coordinates for the tetrahedral and octahedral vibronic Hamiltonians that involve T and E states, and t and e vibrations. These states feature both Jahn-Teller (JT) and pseudo-Jahn-Teller (pJT) effects, and the vibrations are the most JT and pJT active. We first derive the formulas for 92 problems of T and Td symmetries involving up to two vibrational modes. The formulas can be easily generalized to problems of Th, O, and Oh symmetries, as well as problems involving more than two vibrational modes. They can also be adapted to describe spin-orbit vibronic Hamiltonians of tetrahedral p-type problems. Overall, this work makes crucial preparations for future studies on vibronic coupling problems of tetrahedral and octahedral systems. Most importantly, a new, simple, modularized approach to construct vibronic Hamiltonians for a set of related problems, instead of particular problems one by one, is presented.

Revisiting the (E + A) ⊗ (e + a) problems of polyatomic systems with trigonal symmetry: general expansions of their vibronic Hamiltonians.

In this work, we derive general expansions in vibrational coordinates for the (E + A) ⊗ (e + a) vibronic Hamiltonians of molecules with one and only one C3 axis. We first derive the expansion for the lowest C3 symmetry. Additional symmetry elements systematically eliminate terms in the expansion. We compare our expansions with the previous results for two cases, the and the C3 (E + A) ⊗ e. The first comparison demonstrates the robustness, completeness, conciseness, and convenience of our formalism. There is a systematic discrepancy in the second comparison. We discuss the origin of the discrepancy and use a numerical example to corroborate our expansion. Our formalism covers 153 vibronic problems in 6 point groups. It also gives general expansions for the spin-orbit vibronic Hamiltonians of the p-type (E + A) ⊗ (e + a) problems.

Constricted Variational Density Functional Theory Approach to the Description of Excited States.

We review the theoretical foundation of constricted variational density functional theory and illustrate its scope through applications.

Applications of Time-Dependent and Time-Independent Density Functional Theory to Electronic Transitions in Tetrahedral d(0) Metal Oxides.

We present benchmark calculations on excitation energies based on time-dependent density functional theory (TDDFT) as well as orbital relaxed self-consistent and constricted variational DFT (RSCF-CV-DFT) with and without use of the Tamm-Dancoff approximation. The compilation contains results for the 3d complexes MnO4⁻, CrO4²â», and VO4³â», as well as the 4d congeners RuO4, TcO4⁻, and MoO4²â», and 5d homologues OsO4, ReO4⁻, and WO4²â». Considerations have been given to the local density approximation (LDA) and the functionals BP86 and PBE based on the generalized gradient approximation (GGA), as well as the hybrids B3LYP, BHLYP, and PBE0 and the length corrected functional LCBP86. We find for the 3d complexes that RSCF-CV-DFT fares better than TDDFT. Thus, in the case of RSCF-CV-DFT, the average root-mean-square deviations (RMSDs) are 0.25-0.3 eV for GGAs, 0.1 eV for B3LYP, and 0.45 eV for BHLYP. TDDFT affords RMSDs that on average range from 0.3 eV for local functionals to 0.7 eV for BHLYP with the largest fraction of Hartree-Fock (HF) exchange. TDDFT is seen to fare better among the heavier tetraoxo systems. For the 4d and 5d systems, the three functionals B3LYP, PBE0 with an intermediate fraction of HF exchange, and LCBP86 have the lowest RMSD of 0.2 eV, whereas the local functionals (LDA, BP86, BPE) and BHLYP with the highest HF fraction and LCBP86* have a somewhat larger RMSD of 0.3 eV. Nearly the same performance is observed for RSCF-CV-DFT with respect to the different functionals in the case of the 4d and 5d systems. Thus, for the heavier tetraoxo systems, the two DFT schemes are comparable in accuracy.

Applications of time-dependent and time-independent density functional theory to Rydberg transitions.

We have benchmarked the performance of time-independent density functional theory (ΔSCF and RSCF-CV-DFT) in studies on Rydberg transitions employing five different standard functionals and a diffuse basis. Our survey is based on 71 triplet or singlet Rydberg transitions distributed over nine different species: CO (7), CH2O (8), C2H2 (8), H2O (10), C2H4 (13), Be (6), Mg (6), and Zn (8). The best performance comes from the long-range corrected functional LCBP86 (ω = 0.4.) with an average root-mean-square deviation (RMSD) of 0.23 eV. Of similar accuracy are LDA and B3LYP, both with a RMSD of 0.24 eV. The largest RMSD of 0.32 eV comes from BP86 and LCBP86* (ω = 0.75). The performance of ΔSCF is considerably better than that of adiabatic time-dependent density functional theory (ATDDFT) and matches that of highly optimized long-range corrected functionals. However, it is not as accurate as ATDDFT based on highly tuned functionals. The reasonable success of ΔSCF is based on its well-documented ability to afford good estimates of ionization potentials (IP) and electron affinities (EA) even for simple local functionals after orbital relaxation has been taken into account. In ATDDFT based on semilocal functionals, both IP and -EA are poorly described, with errors of up to 5 eV. In the transition energy (ΔE = IP - EA), these errors are canceled to some degree. However, ΔE still carries an error exceeding 1 eV.

Role played by isopropyl substituents in stabilizing the putative triple bond in Ar'EEAr' [E = Si, Ge, Sn; Ar' = C6H3-2,6-(C6H3-2,6-Pr(i)2)2] and Ar*PbPbAr* [Ar* = C6H3-2,6-(C6H2-2,4,6-Pr(i)3)2].

A theoretical study of the bonding in ArEEAr (where E = Si, Ge, Sn, Pb; Ar = terphenyl ligand) revealed for the first time why bulky isopropyl substituents electronically are required in order to isolate stable ArEEAr species. This was accomplished by combining the natural orbitals for chemical valence (NOCV) method with the extended transition state (ETS) scheme. The NOCV-ETS analysis was based on two ArE fragments in their doublet ground state with the configuration σ(2)π(1). For E = Si, Ge, and Sn, it revealed one π-bond perpendicular to the CEEC plane and two σ/π-type bonds in the plane, whereas the ArPbPbAr system was found to have a single σ bond with a C-Pb-Pb trans-bent angle close to 90°. While similar bonding pictures have been obtained in previous model studies with Ar = H and CH3, the NOCV-ETS scheme was able to obtain quantitative estimates for the strength of various σ/π components without artificial truncations or twisting of the system. More importantly, NOCV-ETS analysis was able to show that the electronic influence of the isopropyl substituents on the σ/π components differs little from that found in a system where they are replaced by hydrogen. Instead, the favorable role of the isopropyl substituents is due to dispersive van der Waals attractions between Pr(i) groups on aryl rings attached to different E atoms as well as hyperconjugation involving donation into σ* orbitals on Pr(i). Dispersive interaction amounts to -27.5 kcal/mol (Si), -29.1 kcal/mol (Ge), -26.2 kcal/mol (Sn), and -44.0 kcal/mol (Pb). The larger dispersive stabilization for Pb reflects the fact that the longer Pb-Pb and Pb-C bonds sterically allow for more isopropyl groups with Ar = C6H3-2,6-(C6H2-2,4,6-Pr(i)3)2. This is compared to the other elements where Ar = C6H3-2,6-(C6H3-2,6-Pr(i)2)2. It is finally concluded from the analysis that real ArEEAr systems reveal little character of the EE bond in contrast to the findings of previous studies on model systems.

Calculation of exchange coupling constants in triply-bridged dinuclear Cu(II) compounds based on spin-flip constricted variational density functional theory.

The performance of the second-order spin-flip constricted variational density functional theory (SF-CV(2)-DFT) for the calculation of the exchange coupling constant (J) is assessed by application to a series of triply bridged Cu(II) dinuclear complexes. A comparison of the J values based on SF-CV(2)-DFT with those obtained by the broken symmetry (BS) DFT method and experiment is provided. It is demonstrated that our methodology constitutes a viable alternative to the BS-DFT method. The strong dependence of the calculated exchange coupling constants on the applied functionals is demonstrated. Both SF-CV(2)-DFT and BS-DFT affords the best agreement with experiment for hybrid functionals.