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We describe a procedure for the calculation of quasi-diabatic states within the recently introduced DFT/MRCI(2) framework [S. P. Neville and M. S. Schuurman, J. Chem. Phys. 157, 164103 (2022)]. Based on an effective Hamiltonian formalism, the proposed procedure, which we term QD-DFT/MRCI(2), has the advantageous characteristics of being simultaneously highly efficient and effectively black box in nature while directly yielding both quasi-diabatic potentials and wave functions of high quality. The accuracy and efficiency of the QD-DFT/MRCI(2) formalism are demonstrated via the simulation of the vibronic absorption spectra of furan and chlorophyll a. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A newly parameterized combined density functional theory and multi-reference configuration interaction (DFT/MRCI) Hamiltonian, termed core-valence separation (CVS)-QE12, is defined for the computation of K-shell core-excitation and core-ionization energies. This CVS counterpart to the recently reported QE8 Hamiltonian [Costain et al., J. Chem. Phys, 160, 224106 (2024)] is parameterized by fitting to benchmark quality ab initio data. The definition of the CVS-QE12 and QE8 Hamiltonians differ from previous CVS-DFT/MRCI parameterizations in three primary ways: (i) the replacement of the BHLYP exchange–correlation functional with QTP17 to yield a balanced description of both core and valence excitation energies, (ii) the adoption of a new, three-parameter damping function, and (iii) the introduction of separate scaling of the core-valence and valence-valence Coulombic interactions. Crucially, the parameters of the CVS-QE12 Hamiltonian are obtained via fitting exclusively to highly accurate ab initio vertical core-excitation and ionization energies computed at the CVS-EOM-CCSDT level of theory. The CVS-QE12 Hamiltonian is validated against further benchmark computations and is found to furnish K-edge core vertical excitation and ionization energies exhibiting absolute errors ≤0.5 eV at low computational cost. [ABSTRACT FROM AUTHOR]

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 à (π3s/σ*) and B ̃ (π 3 s / 3 p / σ * ) states, we identify an excited-state electron transfer pathway involving the coupling of the à (π3s/σ*) and B ̃ (π 3 s / 3 p / σ * ) states and driven by N–H dissociation in the B ̃ (π 3 s / 3 p / 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 à (π3s/σ*) and B ̃ (π 3 s / 3 p / σ * ) states and may be the dominant relaxation pathway in the latter case. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A new combined density functional theory and multi-reference configuration interaction (DFT/MRCI) Hamiltonian parameterized solely using the benchmark ab initio vertical excitation energies obtained from the QUEST databases is presented. This new formulation differs from all previous versions of the method in that the choice of the underlying exchange–correlation (XC) functional employed to construct the one-particle (orbital) basis is considered, and a new XC functional, QTP17, is chosen for its ability to generate a balanced description of core and valence vertical excitation energies. The ability of the new DFT/MRCI Hamiltonian, termed QE8, to furnish accurate excitation energies is confirmed using benchmark quantum chemistry computations, and a mean absolute error of 0.16 eV is determined for the wide range of electronic excitations included in the validation dataset. In particular, the QE8 Hamiltonian dramatically improves the performance of DFT/MRCI for doubly excited states. The performance of fast approximate DFT/MRCI methods, p-DFT/MRCI and DFT/MRCI(2), is also evaluated using the QE8 Hamiltonian, and they are found to yield excitation energies in quantitative agreement with the parent DFT/MRCI method, with the two methods exhibiting a mean difference of 0.01 eV with respect to DFT/MRCI over the entire benchmark set. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 A 2 ′ (σ3px/3py) and A 1 ′ (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. [ABSTRACT FROM AUTHOR]

We investigate the sensitivity of X-ray absorption spectra, simulated using a general method, to properties of molecular excited states. Recently, Averbukh and co-workers [M. Ruberti et al., J. Chem. Phys. 140, 184107 (2014)] introduced an efficient and accurate L² method for the calculation of excited state valence photoionization cross-sections based on the application of Stieltjes imaging to the Lanczos pseudo-spectrum of the algebraic diagrammatic construction (ADC) representation of the electronic Hamiltonian. In this paper, we report an extension of this method to the calculation of excited state core photoionization cross-sections. We demonstrate that, at the ADC(2)x level of theory, ground state X-ray absorption spectra may be accurately reproduced, validating the method. Significantly, the calculated X-ray absorption spectra of the excited states are found to be sensitive to both geometric distortions (structural dynamics) and the electronic character (electronic dynamics) of the initial state, suggesting that core excitation spectroscopies will be useful probes of excited state non-adiabatic dynamics. We anticipate that the method presented here can be combined with ab initio molecular dynamics calculations to simulate the time-resolved X-ray spectroscopy of excited state molecular wavepacket dynamics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The dynamics of N-methylpyrrole following excitation at wavelengths in the range 241.5-217.0 nm were studied using a combination of time-resolved photoelectron spectroscopy (TRPES), ab initio quantum dynamics calculations using the multi-layer multi-configurational time-dependent Hartree method, as well as high-level photoionization cross section calculations. Excitation at 241.5 and 236.2 nm results in population of the A2(πσ*) state, in agreement with previous studies. Excitation at 217.0 nm prepares the previously neglected B1(π3py) Rydberg state, followed by prompt internal conversion to the A2(πσ*) state. In contrast with the photoinduced dynamics of pyrrole, the lifetime of the wavepacket in the A2(πσ*) state was found to vary with excitation wavelength, decreasing by one order of magnitude upon tuning from 241.5 nm to 236.2 nm and by more than three orders of magnitude when excited at 217.0 nm. The order of magnitude difference in lifetimes measured at the longer excitation wavelengths is attributed to vibrational excitation in the A2(πσ*) state, facilitating wavepacket motion around the potential barrier in the N-CH3 dissociation coordinate. [ABSTRACT FROM AUTHOR]

The dynamics of pyrrole excited at wavelengths in the range 242-217 nm are studied using a combination of time-resolved photoelectron spectroscopy and wavepacket propagations performed using the multi-configurational time-dependent Hartree method. Excitation close to the origin of pyrrole's electronic spectrum, at 242 and 236 nm, is found to result in an ultrafast decay of the system from the ionization window on a single timescale of less than 20 fs. This behaviour is explained fully by assuming the system to be excited to the A2(πσ*) state, in accord with previous experimental and theoretical studies. Excitation at shorter wavelengths has previously been assumed to result predominantly in population of the bright A1(ππ*) and B2(ππ*) states. We here present time-resolved photoelectron spectra at a pump wavelength of 217 nm alongside detailed quantum dynamics calculations that, together with a recent reinterpretation of pyrrole's electronic spectrum [S. P. Neville and G. A. Worth, J. Chem. Phys. 140, 034317 (2014)], suggest that population of the B1(πσ*) state (hitherto assumed to be optically dark) may occur directly when pyrrole is excited at energies in the near UV part of its electronic spectrum. The B1(πσ*) state is found to decay on a timescale of less than 20 fs by both N-H dissociation and internal conversion to the A2(πσ*) state. [ABSTRACT FROM AUTHOR]

Since the discovery of roaming as an alternative molecular dissociation pathway in formaldehyde (H2CO), it has been indirectly observed in numerous molecules. The phenomenon describes a frustrated dissociation with fragments roaming at relatively large interatomic distances rather than following conventional transition-state dissociation; incipient radicals from the parent molecule self-react to form molecular products. Roaming has been identified spectroscopically through static product channel– resolved measurements, but not in real-time observations of the roaming fragment itself. Using time-resolved Coulomb explosion imaging (CEI), we directly imaged individual “roamers” on ultrafast time scales in the prototypical formaldehyde dissociation reaction. Using high-level first-principles simulations of all critical experimental steps, distinctive roaming signatures were identified. These were rendered observable by extracting rare stochastic events out of an overwhelming background using the highly sensitive CEI method. [ABSTRACT FROM AUTHOR]

The involvement of intermediate Rydberg states in the relaxation dynamics of small organic molecules which, after excitation to the valence manifold, also return to the valence manifold is rarely observed. We report here that such a transiently populated Rydberg state may offer the possibility to modify the outcome of a photochemical reaction. In a time resolved photoelectron study on pyrrole and its methylated derivatives, N-methyl pyrrole and 2,5-dimethyl pyrrole, 6.2 eV photons (200 nm) are used to excite these molecules into a bright ππ* state. In each case, a π3p-Rydberg state, either the B1(π3py) or theA2(π3pz) state, is populated within 20-50 fs after excitation. Thewavepacket then proceeds to the lower lyingA2(πσ*) state within a further 20 fs, at which point two competing reaction channels can be accessed: prompt N-H (N-CH3) bond cleavage or return to the ground state via a conical intersection accessed after ring puckering, the latter of which is predicted to require an additional 100-160 fs depending on the molecule. [ABSTRACT FROM AUTHOR]

Ongoing developments in ultrafast x-ray sources offer powerful new means of probing the complex nonadiabatically coupled structural and electronic dynamics of photoexcited molecules. These non-Born-Oppenheimer effects are governed by general electronic degeneracies termed conical intersections, 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 (TRXAS) and photoelectron spectroscopy (TRXPS) of the prototypical unsaturated organic chromophore, ethylene, following excitation to its S2(pp*) 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 wave packet 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. [ABSTRACT FROM AUTHOR]

The non-radiative relaxation dynamics of pyrrole have been investigated using time-resolved photoelectron spectroscopy and quantum dynamics simulations. Following excitation of the A 2 ( 1 1 π σ ∗ ) state, we observe population flow out of the Franck-Condon region on a ≲ 50 fs timescale. Following excitation of the B 2 ( 2 1 π π ∗ ) state, we observe population being transferred to the A 2 ( 1 1 π σ ∗ ) state on a <50 fs timescale and subsequently out of the Franck-Condon region, also on a <50 fs timescale. Quantum dynamics calculations suggest that population is transferred from the B 2 ( 2 1 π π ∗ ) state through the A 2 ( 1 π 3 p z ) state to the B 1 ( 2 1 π σ ∗ ) state before being transferred to the A 2 ( 1 1 π σ ∗ ) state. [ABSTRACT FROM AUTHOR]

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 (<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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]