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We introduce a perturbative approximation to the combined density functional theory and multireference configuration interaction (DFT/MRCI) approach. The method, termed DFT/MRCI(2), results from the application of quasi-degenerate perturbation theory (QDPT) and the Epstein–Nesbet partitioning to the DFT/MRCI Hamiltonian matrix. The application of QDPT obviates the need to diagonalize the large DFT/MRCI Hamiltonian; electronic energies are instead obtained as the eigenvalues of a small effective Hamiltonian, affording an orders of magnitude savings in the computational cost. Most importantly, the DFT/MRCI(2) approximation is found to be of excellent accuracy, furnishing excitation energies with a root mean squared deviation from the canonical DFT/MRCI values of less than 0.03 eV for an extensive test set of organic molecules.

International audience; Time-resolved photo-electron spectroscopy (TRPES) has become one of the most widespread techniques for probing nonadiabatic dynamics in the excited electronic states of molecules. Furthermore, the complementary development of ab initio approaches for the simulation of TRPES signals has enabled an interpretation of these transient spectra in terms of the underlying coupled electronic-nuclear dynamics. In this perspective we discuss the current state of the art, including efforts to push femtosecond pulses into the vacuum ultraviolet and soft X-ray regimes as well as the utilization of novel polarizations to use time-resolved optical activity as a probe of nonadiabatic dynamics. We close this perspective with a forward-looking prospectus on the new areas of application for this technique.

We demonstrate attosecond transient-absorption spectroscopy (ATAS) at the carbon K-edge as a powerful technique to detect few-femtosecond electronic dynamics driven by conical intersections in gas-phase organic molecules, revealing the fastest electronic relaxation measured to date., International Conference on Ultrafast Phenomena, July 18–22, 2022, Montreal, QC, Canada

The optical formation of coherent superposition states, a wavepacket, can allow the study of zeroth-order states, the evolution of which exhibit structural and electronic changes as a function of time: this leads to the notion of a molecular movie. Intramolecular vibrational energy redistribution, due to anharmonic coupling between modes, is the molecular movie considered here. There is no guarantee, however, that the formed superposition will behave semi-classically (e.g. Gaussian wavepacket dynamics) or even as an intuitively useful zeroth-order state. Here we present time-resolved photoelectron spectroscopy (TRPES) studies of an electronically excited triatomic molecule wherein the vibrational dynamics must be treated quantum mechanically and the simple picture of population flow between coupled normal modes fails. Specifically, we report on vibronic wavepacket dynamics in the zeroth-order 3pσ2Σu Rydberg state of NO2. This wavepacket exemplifies two general features of excited state dynamics in polyatomic molecules: anharmonic multimodal vibrational coupling (forming polyads); nonadiabatic coupling between nuclear and electronic coordinates, leading to predissociation. The latter suggests that the polyad vibrational states in the zeroth-order 3p Rydberg manifold are quasi-bound and best understood to be scattering resonances. We observed a rapid dephasing of an initially prepared 'bright' valence state into the relatively long-lived 3p Rydberg state whose multimodal vibrational dynamics and decay we monitor as a function of time. Our quantum simulations, based on an effective spectroscopic Hamiltonian, describe the essential features of the multimodal Fermi resonance-driven vibrational dynamics in the 3p state. We also present evidence of polyad-specificity in the state-dependent predissociation rates, leading to free atomic and molecular fragments. We emphasize that a quantum molecular movie is required to visualize wavepacket dynamics in the 3pσ2Σu Rydberg state of NO2.

Roaming dynamics in real time Roaming is distinct from conventional reaction channels because of the unusual geometries that chemical systems use to bypass the minimum energy pathway. It is a relatively new phenomenon that is usually determined in experiments through spectroscopic characterization of the roaming products. Using a combination of time-resolved Coulomb explosion imaging and quasiclassical trajectory analysis, Endo et al. report real-time observation of individual fragments of the prototypical reaction of deuterated formaldehyde (D 2 CO) dissociation as they roam on ultrafast time scales. They show that roaming not only occurs several orders of magnitude earlier than previously expected but also that it can terminate in a radical (D + DCO) rather than the well-known molecular (D 2 + CO) product channel. Science , this issue p. 1072

Increasing attention has been given to amine–copper formate complexes for their use as low-cost printable conductive inks. The structure of amine ligands coordinated to copper centers has been reported to dictate the properties of copper molecular inks, such as stability and printability, thereby influencing the copper reduction pathway during the thermolysis. Yet, the underlying mechanism by which formate is oxidized when complexed with amine ligands is still not fully understood. Here, we propose a mechanistic pathway of copper formate dehydrogenation and decarboxylation and examine the critical role that amine ligands play in their thermal decomposition by employing first-principles electronic structure computations and experimental analyses of thermolysis reactions. Based on the computational characterization of the relevant reaction pathways for a number of primary and secondary amines as well as pyridine ligand complexes, we are the first to show that the hydrogen bonds formed between the amine ligand and formate are the key factors governing the activation energy, providing a design principle for the synthesis of organic ligands that can tune the height of the reaction barriers of the dehydrogenation and decarboxylation reactions. The calculations, confirmed by NMR studies, show that the reduction of Cu(II) to Cu(I) occurs in concert with the release of H2 via the dimerization of Cu(II) hydride. This result suggests that the monomeric elimination of H2 is not favorable for the Cu(II) to Cu(I) reduction and thus identifies dimeric amino copper formate as an important intermediate for copper reduction whose thermodynamic stabilities are also dictated by the nature of the amine ligands.

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.

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a powerful tool for the calculation of excited electronic states of large molecules. There exists, however, a large amount of superfluous configurations in a typical DFT/MRCI wave function. We show that this deadwood may be effectively removed using a simple configuration pruning algorithm based on second-order Epstein–Nesbet perturbation theory. The resulting method, which we denote p-DFT/MRCI, is shown to result in orders of magnitude saving in computational timings, while retaining the accuracy of the original DFT/MRCI method.

We combined tunable vacuum-ultraviolet time-resolved photoelectron spectroscopy (VUV-TRPES) with high-level quantum dynamics simulations to disentangle multistate Rydberg-valence dynamics in acetone. A femtosecond 8.09 eV pump pulse was tuned to the sharp origin of the A1(n3dyz) band. The ensuing dynamics were tracked with a femtosecond 6.18 eV probe pulse, permitting TRPES of multiple excited Rydberg and valence states. Quantum dynamics simulations reveal coherent multistate Rydberg-valence dynamics, precluding simple kinetic modeling of the TRPES spectrum. Unambiguous assignment of all involved Rydberg states was enabled via the simulation of their photoelectron spectra. The A1(ππ*) state, although strongly participating, is likely undetectable with probe photon energies ≤8 eV and a key intermediate, the A2(nπ*) state, is detected here for the first time. Our dynamics modeling rationalizes the temporal behavior of all photoelectron transients, allowing us to propose a mechanism for VUV-excited dynamics in acetone which confers a key role to the A2(nπ*) state.

We present the first vacuum ultraviolet time-resolved photoelectron spectroscopy (VUV-TRPES) study of photoisomerization dynamics in the paradigmatic molecule cis-stilbene. A key reaction intermediate in its dynamics, known as the phantom state, has often been invoked but never directly detected in the gas phase. We report direct spectral signatures of the phantom state in isolated cis-stilbene, observed and characterized through a combination of VUV-TRPES and ab initio multiple spawning (AIMS) nonadiabatic dynamics simulations of the channel-resolved observable. The high VUV probe photon energy tracks the complete excited-state dynamics via multiple photoionization channels, from initial excitation to its return to the "hot" ground state. The TRPES was compared with AIMS simulations of the dynamics from initial excitation, to the phantom-state intermediate (an S1 minimum), through to the ultimate electronic decay to the ground state. This combination revealed the unique spectral signatures and time-dependent dynamics of the phantom-state intermediate, permitting us to report here its direct observation.

The photochemistry of organic chromophores generally involves the co-evolution of the electronic and nuclear degrees of freedom. To obtain a specific and predetermined photochemical reaction outcome, chemical substitution can be used to selectively alter the underlying electronic potential energy surfaces to favor a particular reaction pathway. We show using ab initio simulation that the substitution of s- trans-1,3-butadiene with a cyano group can effectively "direct" a molecular wavepacket to particular regions of the seam of conical intersection and either favor or inhibit the photoinitiated cis-trans isomerization. The substituent is able to effect this control due to the formation of transient charge-separated electronic structures that arise during the nonadiabatic dynamical process. The atomic site at which this charge develops can be selectively stabilized (or destabilized) depending on the location of the cyano substituent and gives rise to a single dominant decay pathway. This work aims to demonstrate how the application of known electron density effects to ultrafast dynamics may be used to obtain desired photochemical reactions and properties.

Using time-resolved Coulomb explosion imaging (CEI) in an ultraviolet (UV) pump near infrared (NIR) probe experiment, we directly image the different dissociation dynamics in the formaldehyde molecule. Different pathways are distinguished from each other, despite their statistical nature. To extract such dynamics, hidden in a statistical background, calls for an elimination of noise. In our approach, we take advantage of CEI being a quasi-background-free technique., International Conference of Computational Methods in Sciences and Engineering ICCMSE 2020, April 29 – May 3, 2020, Crete, Greece (Virtual), Series: AIP Conference Proceedings

The optical formation of coherent superposition states, a wavepacket, can allow the study of zeroth-order states, the evolution of which exhibit structural and electronic changes as a function of time: this leads to the notion of a molecular movie. Intramolecular vibrational energy redistribution, due to anharmonic coupling between modes, is the molecular movie considered here. There is no guarantee, however, that the formed superposition will behave semi-classically (e.g. Gaussian wavepacket dynamics) or even as an intuitively useful zeroth-order state. Here we present time-resolved photoelectron spectroscopy (TRPES) studies of an electronically excited triatomic molecule wherein the vibrational dynamics must be treated quantum mechanically and the simple picture of population flow between coupled normal modes fails. Specifically, we report on vibronic wavepacket dynamics in the zeroth-order 3pσ2Σu Rydberg state of NO2. This wavepacket exemplifies two general features of excited state dynamics in polyatomic molecules: anharmonic multimodal vibrational coupling (forming polyads); nonadiabatic coupling between nuclear and electronic coordinates, leading to predissociation. The latter suggests that the polyad vibrational states in the zeroth-order 3p Rydberg manifold are quasi-bound and best understood to be scattering resonances. We observed a rapid dephasing of an initially prepared 'bright' valence state into the relatively long-lived 3p Rydberg state whose multimodal vibrational dynamics and decay we monitor as a function of time. Our quantum simulations, based on an effective spectroscopic Hamiltonian, describe the essential features of the multimodal Fermi resonance-driven vibrational dynamics in the 3p state. We also present evidence of polyad-specificity in the state-dependent predissociation rates, leading to free atomic and molecular fragments. We emphasize that a quantum molecular movie is required to visualize wavepacket dynamics in the 3pσ2Σu Rydberg state of NO2.

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.

Functional group substituents are a ubiquitous tool in ground-state organic chemistry often employed to fine-tune chemical properties and obtain desired chemical reaction outcomes. Their effect on photoexcited electronic states, however, remains poorly understood. To help build an intuition for these effects, we have studied ethylene, substituted with electron acceptor (cyano) and/or electron donor (methoxy) substituents, both theoretically and experimentally: using ab initio quantum molecular dynamics and time-resolved photoelectron spectroscopy. Our results show the consistent trend that photo-induced ethylenic dynamics is primarily localized to the carbon with the greater electron density. For doubly substituted ethylenes, the trend is additive when both substituents are located on opposite carbons, whereas the methoxy group (in concert with steric effects) dominates when both substituents are located on a single carbon atom. These results point to the development of rules for structure–dynamics correlations; in this case, a novel mechanistic ultrafast photochemistry for conjugated carbon chains employing long-established chemical concepts.

Electronic coherences in molecules are ultrafast charge oscillations on the Molecular Frame MF and their direct observation and separation from electronic population dynamics is challenging. Here we present a valence shell Lab Frame LF scattering method suited to probing electronic coherences in isolated systems. MF electronic coherences lead to LF electronic anisotropies observable by ultrafast angle resolved scattering. Moment analysis of the LF anisotropy completely separates electronic coherences from population dynamics, demonstrated in excited state NH3 using ultrafast time energy angle resolved photoelectron spectroscopy. This general approach applies equally to attosecond femtosecond electronic coherences in isolated systems

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.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 photochemical dynamics of double-bond-containing hydrocarbons is exemplified by the smallest alkenes, ethylene and butadiene. Chemical substituents can alter both decay timescales and photoproducts through a combination of inertial effects due to substituent mass, steric effects due to substituent size, and electronic (or potential) effects due to perturbative changes to the electronic potential energy surface. Here, we demonstrate the interplay of different substituent effects on 1,3-butadiene and its methylated derivatives using a combination of ab initio simulation of nonadiabatic dynamics and time-resolved photoelectron spectroscopy. The purely inertial effects of methyl substitution are simulated through the use of mass 15 "heavy-hydrogen" atoms. As expected from both inertial and electronic influences, the excited-state dynamics is dominated by pyramidalization at the unsubstituted carbon sites. Although the electronic effects of methyl group substitution are weak, they alter both decay timescales and branching ratios by influencing the initial path taken by the excited wavepacket following photoexcitation.

“Roamers” are directly observed in the prototypical roaming reaction in the formaldehyde molecule. Despite their statistical nature, roaming is well discriminated from the radical- and molecular dissociation channels, using Coulomb explosion imaging and theoretical modeling., International Conference on Ultrafast Phenomena 2020, Nov. 16-19, 2020, Washington, D.C.

The energetic and structural trends in the minimum energy conical intersections of a series of substituted ethylenes are explained by the degree to which the chemical substituents polarize electron density across the C=C double bond. The addition of a substituent that significantly polarizes the electron density also reduces the magnitude of the large-amplitude pyramidalization motions required to reach a conical intersection and can thus very effectively “direct” these motions to occur at a specific carbon atom. These observations are summarized via the construction of a reduced dimensionality representation of the relevant potential energy surfaces inspired by a previously reported 3-state model for biradical systems. On-the-fly nonadiabatic dynamics simulations reveal that this effect dictates the dominant excited state decay pathway for acrylonitrile ( π -acceptor CN substituent) and vinylamine ( π -donor NH2 substituent). The ab initio multiple spawning simulations show that population transfer to the ground electronic state for both molecules occurs primarily in the regions around the substituent-altered minimum energy conical intersections, demonstrating that chemical substitution may be used to selectively alter photochemical pathways.

We report results from a novel fully ab initio method for simulating the time-resolved photoelectron angular distributions around conical intersections in CS_2. The technique employs wavepacket densities obtained with the multiple spawning method in conjunction with geometry- and energy-dependent photoionization matrix elements. The robust agreement of the calculated molecular-frame photoelectron angular distributions with measured values for CS_2 demonstrates that this approach can successfully illuminate, and disentangle, the underlying coupled nuclear and electronic dynamics around conical intersections in polyatomic molecules.

Following on from previous experimental and theoretical work [Neville et al., Nat. Commun. 7, 11357 (2016)], we report the results of a combined electronic structure theory and quantum dynamics study of the excited state dynamics of the pyrrole dimer following excitation to its first two excited states. Employing an exciton-based analysis of the A(π3s/σ*) and B(π3s/3p/σ*) states, we identify an excited-state electron transfer pathway involving the coupling of the A(π3s/σ*) and B(π3s/3p/σ*) states and driven by N–H dissociation in the B(π3s/3p/σ*) state. This electron transfer mechanism is found to be mediated by vibronic coupling of the B state, which has a mixed π3s/3p Rydberg character at the Franck-Condon point, to a high-lying charge transfer state of the πσ* character by the N–H stretch coordinate. Motivated by these results, quantum dynamics simulations of the excited-state dynamics of the pyrrole dimer are performed using the multiconfigurational time-dependent Hartree method and a newly developed model Hamiltonian. It is predicted that the newly identified electron transfer pathway will be open following excitation to both the A(π3s/σ*) and B(π3s/3p/σ*) states and may be the dominant relaxation pathway in the latter case.

The efficient, yet accurate, simulation of X-ray absorption spectra represents a significant challenge for ab initio electronic structure methods. Conventional approaches involve the explicit calculation of all core-excited states spanning the energy range of interest, even though only a small number of these states will contribute appreciably to the spectrum. We here report a different approach, based on a time-independent Chebyshev filter diagonalization scheme, which allows for the X-ray absorption spectrum to be computed without the explicit calculation of the core-excited eigenstates. Furthermore, in a subsequent postprocessing calculation, selected peaks may be analyzed via the calculation of natural transition orbitals, if desired. The scheme presented here is based on a refinement of the time-independent Chebyshev filter diagonalization approach. Previous formulations of this method have been characterized by a requirement for significant "user input" via the (sometimes unintuitive) tuning of various numerical parameters. To circumvent this, we introduce a new class of filters based on discrete prolate spheroidal sequences. We demonstrate that the resulting method, which we term Chebyshev-Slepian filter diagonalization, makes filter diagonalization essentially a black-box procedure. The Chebyshev-Slepian filter diagonalization method is implemented at the second-order algebraic diagrammatic construction level of theory and validated through the calculation of the X-ray absorption spectra of trifluoroacetonitrile and 1,4-benzoquinone.

We report how imaginary time wavepacket propagation may be used to efficiently calculate the lowest-lying eigenstates of the electronic Hamiltonian. This approach, known as the relaxation method in the quantum dynamics community, represents a fundamentally different approach to the solution of the electronic eigenvalue problem in comparison to traditional iterative subspace diagonalization schemes such as the Davidson and Lanczos methods. In order to render the relaxation method computationally competitive with existing iterative subspace methods, an extended short iterative Lanczos wavepacket propagation scheme is proposed and implemented. In the examples presented here, we show that by using an efficient wavepacket propagation algorithm the relaxation method is, at worst, as computationally expensive as the commonly used block Davidson-Liu algorithm, and in certain cases, significantly less so.

We present a general approach for the calculation and assignment of X-ray absorption spectra based on electronic wavepacket propagations performed using explicitly time-dependent electronic structure calculations. Such calculations have the appeal of yielding the entire absorption spectrum for the cost of a single set of electronic wavepacket propagations, obviating the need to explicitly calculate large numbers of core-excited states. The spectrum can either be calculated from the Fourier transform of the time-dependent dipole moment or from the Fourier transform of the wavepacket autocorrelation function. We propose that calculating the absorption spectrum using the latter approach will generally be the preferred option. This method has two important advantages. First, the autocorrelation functions can be obtained for twice the propagation time, resulting in a halving of the computational effort required to calculate the spectrum relative to the time-dependent dipole moment approach. Second, using the tools of filter diagonalisation, the autocorrelation functions may be used to determine the time-independent final core-excited states underlying the peaks of interest in the spectrum. The proposed scheme is validated by calculating and characterizing the X-ray absorption spectra of benzene and trifluoroacetonitrile at the time-dependent second-order algebraic diagrammatic construction level of theory.

Cyclopropane, the smallest organic ring compound, exhibits complex spectroscopy and excited state dynamics. In Paper I, we reinterpret the vacuum ultraviolet (VUV) electronic absorption spectrum of cyclopropane via ab initio computation. The first two bands in the VUV spectrum are simulated using wavepacket propagations employing the multiconfigurational time-dependent Hartee method and a newly parameterized linear vibronic coupling Hamiltonian. The parameters of the model Hamiltonian are obtained directly from high level multireference configuration interaction calculations. An analysis of the results, with an emphasis on previously neglected vibronic coupling effects, reveals that these vibronic coupling terms must be included in order to account for strong intensity borrowing effects. This treatment dramatically changes the assignment of much of the VUV spectrum, with intensity borrowing by the optically dark A2′(σ3px/3py) and A1′(σ3px/3py) states from the E′(σ3px/3py) state being found to give rise to almost all the spectral intensities below 8 eV. This is in stark contrast to previous studies, which attributed the first two bands to transitions to the E′(σ3px/3py) state. This highlights the limitations of assigning spectral features based solely on calculated electronic excitation energies and oscillator strengths. Furthermore, we address the significant but infrequently discussed difficulties involved in determining the electronic character of a wavepacket produced in the pump step of ultrafast pump-probe experiments for systems exhibiting strong vibronic coupling.

The vacuum-ultraviolet photoinduced dynamics of cyclopropane (C

The ultrafast excited state dynamics of the smallest polyene, trans-1,3-butadiene, were studied by femtosecond time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy. The evolution of the excited state wavepacket, created by pumping the bright 1Bu (ππ*) electronic state at its origin of 216 nm, is projected via one- and two-photon ionization at 267 nm onto several ionization continua. The results are interpreted in terms of Koopmans’ correlations and Franck-Condon factors for the excited and cationic states involved. The known predissociative character of the cation excited states is utilized to assign photoelectron bands to specific continua using TRPEPICO spectroscopy. This permits us to report the direct observation of the famously elusive S1(21Ag) dark electronic state during the internal conversion of trans 1,3-butadiene. Our phenomenological analysis permits the spectroscopic determination of several important time constants. We report the overall decay lifetimes of the 11Bu and 21Ag states and observe the re-appearance of the hot ground state molecule. We argue that the apparent dephasing time of the S2(11Bu) state, which leads to the extreme breadth of the absorption spectrum, is principally due to large amplitude torsional motion on the 1Bu surface in conjunction with strong non-adiabatic couplings via conical intersections, whereupon nuclear wavepacket revivals to the initial Franck-Condon region become effectively impossible. In Paper II [W. J. Glover et al., J. Chem. Phys. 148, 164303 (2018)], ab initio multiple spawning is used for on-the-fly computations of the excited state non-adiabatic wavepacket dynamics and their associated TRPEPICO observables, allowing for direct comparisons of experiment with theory.

The excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene (BD), has long been the subject of controversy due to its strong coupling, ultrafast time scales and the difficulties that theory faces in describing the relevant electronic states in a balanced fashion. Here we apply Ab Initio Multiple Spawning (AIMS) using state-averaged complete active space multistate second order perturbation theory [SA-3-CAS(4/4)-MSPT2] which describes both static and dynamic electron correlation effects, providing a balanced description of both the initially prepared bright 11Bu (ππ*) state and non-adiabatically coupled dark 21Ag state of BD. Importantly, AIMS allows for on-the-fly calculations of experimental observables. We validate our approach by directly simulating the time resolved photoelectron-photoion coincidence spectroscopy results presented in Paper I [A. E. Boguslavskiy et al., J. Chem. Phys. 148, 164302 (2018)], demonstrating excellent agreement with experiment. Our simulations reveal that the initial excitation to the 11Bu state rapidly evolves via wavepacket dynamics that follow both bright- and dark-state pathways as well as mixtures of these. In order to test the sensitivity of the AIMS results to the relative ordering of states, we considered two hypothetical scenarios biased toward either the bright 1Bu or the dark 21Ag state. In contrast with AIMS/SA-3-CAS(4/4)-MSPT2 simulations, neither of these scenarios yields favorable agreement with experiment. Thus, we conclude that the excited state non-adiabatic dynamics in BD involves both of these ultrafast pathways.

The nonadiabatic coupling of electronic and vibrational degrees of freedom is the defining feature of electronically excited states of polyatomic molecules. Once considered a theoretical curiosity, conical intersections (CIs) are now generally accepted as being the dominant source of coupled charge and vibrational energy flow in molecular excited states. Passage through CIs leads to the conversion of electronic to vibrational energy, which drives the ensuing photochemistry, isomerization being a canonical example. It has often been remarked that the CI may be thought of as a transition state in the excited state. As such, we expect that both the direction and the velocity of approach to the CI will matter. We explore this suggestion by looking for dynamical aspects of passage through CIs and for analogies with well-known concepts from ground-state reaction dynamics. Great progress has been made in the development of both experimental techniques and ab initio dynamics simulations, to a degree that direct comparisons may now be made. Here we compare time-resolved photoelectron spectroscopy results with on-the-fly ab initio multiple spawning calculations of the experimental observables, thereby validating each. We adopt a phenomenological approach and specifically concentrate on the excited-state dynamics of the C=C bond in unsaturated hydrocarbons. In particular, we make use of selective chemical substitution (such as replacing an H atom by a methyl group) so as to alter the inertia of certain vibrations relative to others, thus systematically varying (mass-weighted) directions and velocities of approach to a CI. Chemical substituents, however, may affect both the nuclear and electronic components of the total wave function. The former, which we call an inertial effect, influences the direction and velocity of approach. The latter, which we call a potential effect, modifies the electronic structure and therefore the energetic location and topography of the potential energy surfaces involved. Using a series of examples, we discuss both types of effects. We argue that there is a need for dynamical pictures and simple models of nonadiabatic dynamics at CIs and hope that the phenomenology presented here will help inspire such developments.

Ongoing developments in ultrafast X-ray sources offer powerful new means of probing the com- plex non-adiabatically coupled structural and electronic dynamics of photoexcited molecules. These non-Born-Oppenheimer effects are governed by general electronic degeneracies termed conical in- tersections which play a key role, analogous to that of a transition state, in the electronic-nuclear dynamics of excited molecules. Using high level ab initio quantum dynamics simulations, we studied time-resolved X-ray absorption and photoelectron spectroscopy (TRXAS and TRXPS, respectively) of the prototypical unsaturated organic chromophore, ethylene, following excitation to its S2 state. The TRXAS in particular is highly sensitive to all aspects of the ensuing dynamics. These X-ray spectroscopies provide a clear signature of the wavepacket dynamics near conical intersections, related to charge localization effects driven by the nuclear dynamics. Given the ubiquity of charge localization in excited state dynamics, we believe that ultrafast X-ray spectroscopies offer a unique and powerful route to the direct observation of dynamics around conical intersections., 5 pages, 4 figures

The vacuum ultraviolet photoinduced dynamics of cyclopropane C3H6 were studied using time resolved photoelectron spectroscopy TRPES in conjunction with ab initio quantum dynamics simulations. Following excitation at 160.8 nm, and subsequent probing via photoionization at 266.45 nm, the initially prepared wave packet is found to exhibit a fast decay lt;100 fs that is attributed to the rapid dissociation of C3H6 to ethylene C2H4 and methylene CH2 . The photodissociation process proceeds via concerted ring opening and C C bond cleavage in the excited state. Ab initio multiple spawning simulations indicate that ring opening occurs prior to dissociation. The dynamics simulations were subsequently employed to simulate a TRPES spectrum, which was found to be in excellent agreement with the experimental result. On the basis of this agreement, the fitted time constants of 35 20 and 57 35 fs were assigned to prompt i dissociation on the lowest lying excited state, prepared directly by the pump pulse, and ii non adiabatic relaxation from higher lying excited states that lead to delayed dissociation, respectively

The excited state dynamics of a d0 vanadium(V) oxido ligand-to-metal charge transfer (LMCT) complex, VOLF, were investigated via a combination of static optical and X-ray absorption (XAS) spectroscopy, transient optical absorption spectroscopy, and time-dependent density functional theory (TD-DFT). Upon excitation of the LMCT in the visible region, transient absorption data reveal that internal conversion traps the excited carrier population into a long-lived charge transfer state of 3dxy electron character, S1(dxy). The internal conversion is substantiated by an isosbestic point in the transient absorption data, two nearby charge transfer states that couple well by TD-DFT, multiple rates in the ground state recovery, and the decay kinetics of an excited state absorption with the energy of a d-d transition in O K-edge XAS spectra. The long lifetime (∼420 ps) of S1(dxy) can be ascribed to its poor optical and vibrational coupling to a distorted ground state (S0*) via a negligible electronic dipole transition in TD-DFT. The lack of luminescence or an identifiable triplet state also suggests attributing the lifetime to electronic contributions. In conjunction with its strong visible absorption and reduction potential, the long-lived LMCT suggests that molecules such as VOLF could have potential utility for energy conversion applications. Moreover, the results show that internal conversion between two nearby charge transfer states, differentiated by their 3d character, can form a long-lived charge transfer excitation, broadly informing the discovery of 3d metal-centered optical absorbers with long-lived charge transfer lifetimes.

We present derivation and implementation of the Multi-Configurational Strong-Field Approximation with Gaussian nuclear Wave Packets (MC-SFA-GWP) -- a version of the molecular strong-field approximation which treats all electronic and nuclear degrees of freedom, including their correlations, quantum-mechanically. The technique allows, for the first time, realistic simulation of high-harmonic emission in polyatomic molecules without invoking reduced-dimensionality models for the nuclear motion or the electronic structure. We use MC-SFA-GWP to model isotope effects in high-harmonics generation (HHG) spectroscopy of methane. The HHG emission in this molecule transiently involves strongly vibronically-coupled $^2F_2$ electronic state of the $\rm CH_4^+$ cation. We show that the isotopic HHG ratio in methane contains signatures of: a) field-free vibronic dynamics at the conical intersection (CI); b) resonant features in the recombination cross-sections; c) laser-driven bound-state dynamics; as well as d) the well-known short-time Gaussian decay of the emission. We assign the intrinsic vibronic feature (a) to a relatively long-lived ($\ge4$ fs) vibronic wave packet of the singly-excited $\nu_4$ ($t_2$) and $\nu_2$ ($e$) vibrational modes, strongly coupled to the components of the $^2F_2$ electronic state. We demonstrate that these physical effects differ in their dependence on the wavelength, intensity, and duration of the driving pulse, allowing them to be disentangled. We thus show that HHG spectroscopy provides a versatile tool for exploring both conical intersections and resonant features in photorecombination matrix elements in the regime not easily accessible with other techniques.

We triply ionize the van der Waals bound carbon monoxide dimer with intense ultrashort pulses and study the breakup channel $(\mathrm{CO}{)}_{2}^{3+}\ensuremath{\rightarrow}{\mathrm{C}}^{+}+{\mathrm{O}}^{+}+{\mathrm{CO}}^{+}$. The fragments are recorded in a cold target recoil ion momentum spectrometer. We observe a fast ${\mathrm{CO}}^{2+}$ dissociation channel in the dimer, which does not exist for the monomer. We found that a nearby charge breaks the symmetry of a ${\mathrm{X}}^{3}\mathrm{\ensuremath{\Pi}}$ state of ${\mathrm{CO}}^{2+}$ and induces an avoided crossing that allows a fast dissociation. Calculation on the full dimer complex shows the coupling of different charge states, as predicted from excimer theory, gives rise to electronic state components not present in the monomer, thereby enabling fast dissociation with higher kinetic energy release. These results demonstrate that the electronic structure of molecular cluster complexes can give rise to dynamics that is qualitatively different from that observed in the component monomers.

How do atoms move within a molecule? What are the paths they take? Coulomb Explosion Imaging combined with a multi-color pump probe scheme allows us to address these questions with a table top setup. Since the momentum information of molecular fragments is preserved at the moment of explosion, we can deduce the fragment’s momentary position, representing the structure of the molecule. We have studied isomerization and dissociation events through the movement of protons, deuterons and electrons, taking advantage of the rich statistics this technique provides. In the case of proton migration in the acetylene cation, we were able to identify an isotope dependent to- and fro isomerization behavior [1]. Presently, we are expanding our studies on more complex processes. Aside from passively studying dynamics, we have also actively controlled the electron localization in small molecules [2] using two-color mid-infrared asymmetric laser fields.The manipulation of protons, the lightest atomic fragments in molecule...

High-harmonic spectroscopy probes molecular dynamics using electrons liberated from the same molecule earlier in the laser cycle. It affords sub-Ångstrom spatial and subfemtosecond temporal resolution. Nuclear dynamics in the intermediate cation influence the spectrum of the emitted high-harmonic photons through an autocorrelation function. Here, we develop an analytical approach for computing short-time nuclear autocorrelation functions in the vicinity of conical intersections, including laser-induced and nonadiabatic coupling between the surfaces. We apply the technique to two molecules of current experimental interest, C6H6 and C6H5F. In both molecules, high-harmonics generated within the same electronic channel are not sensitive to nonadiabatic dynamics, even in the presence of substantial population transfer. Calculated autocorrelation functions exhibit significant deviations from the expected Gaussian decay and may undergo revivals at short (∼1.5 fs) times. The associated phase of the nuclear wavepacket provides a possible experimental signature.

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.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 ins...

We have investigated nuclear dynamics in bound and dissociating acetylene molecular ions in a time-resolved reaction microscopy experiment with a pair of few-cycle pulses. Different ionization processes were observed for acetylene. These time-dependent ionization processes are simulated using semi-classical on-the-fly dynamics revealing the underling mechanisms.

We report a joint experimental and theoretical study on the ultrafast excited state dynamics of allene and a series of its methylated analogues (1,2-butadiene, 1,1-dimethylallene, and tetramethylallene) in order to elucidate the conical intersection mediated dynamics that give rise to ultrafast relaxation to the ground electronic state. We use femtosecond time-resolved photoelectron spectroscopy (TRPES) to probe the coupled electronic-vibrational dynamics following UV excitation at 200 nm (6.2 eV). Ab initio multiple spawning (AIMS) simulations are employed to determine the mechanistic details of two competing dynamical pathways to the ground electronic state. In all molecules, these pathways are found to involve as follows: (i) twisting about the central allenic C-C-C axis followed by pyramidalization at one of the terminal carbon atoms and (ii) bending of allene moiety. Importantly, the AIMS trajectory data were used for ab initio simulations of the TRPES, permitting direct comparison with experiment. For each molecule, the decay of the TRPES signal is characterized by short (30 fs, 52 fs, 23 fs) and long (1.8 ps, 3.5 ps, [306 fs, 18 ps]) time constants for 1,2-butadiene, 1,1-dimethylallene, and tetramethylallene, respectively. However, AIMS simulations show that these time constants are only loosely related to the evolution of electronic character and actually more closely correlate to large amplitude motions on the electronic excited state, modulating the instantaneous vertical ionization potentials. Furthermore, the fully substituted tetramethylallene is observed to undergo qualitatively different dynamics, as displacements involving the relatively massive methyl groups impede direct access to the conical intersections which give rise to the ultrafast relaxation dynamics observed in the other species. These results show that the branching between the "twisting" and "bending" pathways can be modified via the selective methylation of the terminal carbon atoms of allene. The interplay between inertial and potential effects is a key to understanding these dynamical branching pathways. The good agreement between the simulated and measured TRPES confers additional confidence to the dynamical picture presented here. (C) 2016 AIP Publishing LLC.

We use the ab initio multiple spawning method with potential energy surfaces and nonadiabatic coupling vectors computed from multistate multireference perturbation theory (MSPT2) to follow the dynamics of ethylene after photoexcitation. We introduce an analytic formulation for the nonadiabatic coupling vector in the context of MSPT2 calculations. We explicitly include the low-lying 3s Rydberg state which has been neglected in previous ab initio molecular dynamics studies of this process. We find that although the 3s Rydberg state lies below the optically bright ππ* state, little population gets trapped on this state. Instead, the 3s Rydberg state is largely a spectator in the photodynamics, with little effect on the quenching mechanism or excited state lifetime. We predict the time-resolved photoelectron spectrum for ethylene and point out the signature of Rydberg state involvement that should be easily observed.

We have investigated nuclear dynamics in bound and dissociating acetylene molecular ions in a time-resolved reaction microscopy experiment with a pair of few-cycle pulses. Vibrating bound acetylene cations or dissociating dications are produced by the first pulse. The second pulse probes the nuclear dynamics by ionization to higher charge states and Coulomb explosion of the molecule. For the bound cations, we observed vibrations in acetylene (HCCH) and its isomer vinylidene (CCHH) along the CC-bond with a periodicity of around 26 fs. For dissociating dication molecules, a clear indication of enhanced ionization is found to occur along the CH- and CC-bonds after 10 fs to 40 fs. The time-dependent ionization processes are simulated using semi-classical on-the-fly dynamics revealing the underling mechanisms.

We introduce an algorithm to solve the secular equation that arises in the time independent multimode expansion of the quadratic vibronic coupling problem in parallel. The implementation can handle expansions of arbitrary length, with the open-ended character of the algorithm achieved through the use of fine grained parallelism to partition the trial vectors. The characteristics of the algorithm are discussed and its utility is illustrated by determining a model photoelectron spectrum of the ethoxy radical (C 2 H 5 O) using a vibronic expansion involving more than 1 billion vibronic basis states. This calculation also represents the first determination of a photoelectron spectrum obtained using a diabatic Hamiltonian obtained with a recently introduced ab initio surface reshaping procedure.

We have demonstrated a generally applicable tabletop approach utilizing a 266nm femtosecond laser pulse pump, 800nm pulse probe, coupled with Coulomb explosion imaging (CEI). We have investigated two simple chemical reactions in C2H2 + simultaneously: proton transfer and C=C bond-breaking, triggered by multiphoton ionization to excited states. Too and fro proton migration results are in excellent agreement with new ab initio trajectory simulations which predict isomerization timescales and pathways., 29th International Conference on Photonic, Electronic and Atomic Collisions, ICPEAC 2015, 22 July 2015 through 28 July 2015

In this joint experimental and theoretical study we characterize the complete dynamical "life cycle" associated with the photoexcitation of the singlet carbene cyclopropenylidene to the lowest lying optically bright excited electronic state: from the initial creation of an excited-state wavepacket to the ultimate fragmentation of the molecule on the vibrationally hot ground electronic state. Cyclopropenylidene is prepared in this work using an improved synthetic pathway for the preparation of the precursor quadricyclane, thereby greatly simplifying the assignment of the molecular origin of the measured photofragments. The excitation process and subsequent non-adiabatic dynamics have been previously investigated employing time-resolved photoelectron spectroscopy and are now complemented with high-level ab initio trajectory simulations that elucidate the specific vibronic relaxation pathways. Lastly, the fragmentation channels accessed by the molecule following internal conversion are probed using velocity map imaging (VMI) so that the identity of the fragmentation products and their corresponding energy distributions can be definitively assigned.

The first high-resolution molecular movie of proton migration in the acetylene cation is obtained using a tabletop multiphoton pump-probe approach—an alternative to demanding free-electron-lasers and other VUV light sources when ionizing from the HOMO-1., Series: Springer Proceedings in Physics