*J Chem Theory Comput ; 19(19): 6577-6588, 2023 Oct 10.*

##### RESUMO

Trajectory surface hopping (TSH) is a widely used mixed quantum-classical dynamics method that is used to simulate molecular dynamics with multiple electronic states. In TSH, time-derivative coupling is employed to propagate the electronic coefficients and in that way to determine when the electronic state on which the nuclear trajectory is propagated switches. In this work, we discuss nonadiabatic TSH dynamics algorithms employing the curvature-driven approximation and overlap-based time derivative couplings, and we report test calculations on six photochemical reactions where we compare the results to one another and to calculations employing analytic nonadiabatic coupling vectors. We correct previous published results thanks to a bug found in the software. We also provide additional, more detailed studies of the time-derivative couplings. Our results show good agreement between curvature-driven algorithms and overlap-based algorithms.

*Phys Chem Chem Phys ; 25(15): 10447-10459, 2023 Apr 12.*

##### RESUMO

Photochemistry and photophysics processes involve structures far from equilibrium. In these reactions, there is often strong coupling between nuclear and electronic degrees of freedom. For first-row transition metals, Kß X-ray emission spectroscopy (XES) is a sensitive probe of electronic structure due to the direct overlap between the valence orbitals and the 3p hole in the final state. Here the sensitivity of Kß mainline (Kß1,3) XES to structural dynamics is analyzed by simulating spectral changes along the excited state dynamics of an iron photosensitizer [FeII(bmip)2]2+ [bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-pyridine], using both restricted active space (RAS) multiconfigurational wavefunction theory and a one-electron orbital-energy approach in density-functional theory (1-DFT). Both methods predict a spectral blue-shift with increasing metal-ligand distance, which changes the emission intensity for any given detection energy. These results support the suggestion that the [FeII(bmip)2]2+ femtosecond Kß XES signal shows oscillations due to coherent wavepacket dynamics. Based on the RAS results, the sensitivity to structural dynamics is twice as high for Kß compared to Kα, with the drawback of a lower signal-to-noise ratio. Kß sensitivity is favored by a larger spectral blue-shift with increasing metal-ligand distance and larger changes in spectral shape. Comparing the two simulations methods, 1-DFT predicts smaller energy shifts and lower sensitivity, likely due to missing final-state effects. The simulations can be used to design and interpret XES probes of non-equilibrium structures to gain mechanistic insights in photocatalysis.

*Phys Chem Chem Phys ; 25(14): 9761-9765, 2023 Apr 05.*

##### RESUMO

Excited State Intramolecular Proton Transfer in pyrrol pyridine is theoretically investigated using non-adiabatic dynamics simulations. The photochemical process is completely characterised: the reaction time, the total yield and the accessibility of the conical intersection are evaluated. Finally, new mechanistic interpretation are extracted: the proton transfer reaction in this molecule is shown to be driven by two complementary mechanisms.

*J Chem Theory Comput ; 19(6): 1827-1842, 2023 Mar 28.*

##### RESUMO

Photochemical reactions are widely modeled using the popular trajectory surface hopping (TSH) method, an affordable mixed quantum-classical approximation to the full quantum dynamics of the system. TSH is able to account for nonadiabatic effects using an ensemble of trajectories, which are propagated on a single potential energy surface at a time and which can hop from one electronic state to another. The occurrences and locations of these hops are typically determined using the nonadiabatic coupling between electronic states, which can be assessed in a number of ways. In this work, we benchmark the impact of some approximations to the coupling term on the TSH dynamics for several typical isomerization and ring-opening reactions. We have identified that two of the schemes tested, the popular local diabatization scheme and a scheme based on biorthonormal wave function overlap implemented in the OpenMOLCAS code as part of this work, reproduce at a much reduced cost the dynamics obtained using the explicitly calculated nonadiabatic coupling vectors. The other two schemes tested can give different results, and in some cases, even entirely incorrect dynamics. Of these two, the scheme based on configuration interaction vectors gives unpredictable failures, while the other scheme based on the Baeck-An approximation systematically overestimates hopping to the ground state as compared to the reference approaches.

*J Phys Chem A ; 126(34): 5692-5701, 2022 Sep 01.*

##### RESUMO

Following ionization by an extreme ultraviolet (XUV) attosecond pulse train, a polyatomic molecule can be promoted to more-than-one excited states of the residual ion. The ensuing relaxation dynamics is often facilitated by several reaction coordinates, making them difficult to disentangle by the usual spectroscopic means. Here, we show that in atto-chemistry isotope labeling can be an efficient tool for unraveling the relaxation pathways in highly excited photoionized molecules. Employing an XUV pump pulse and a near-infrared probe pulse, we found the nuclear as well as coupled electron-nuclear dynamics in ethylene to be almost 40% faster compared to that of its deuterated counterpart. The findings, which are supported by advanced nonadiabatic dynamics calculations, led to the identification of the relevant nuclear coordinates controlling the relaxation. Our experiment highlights the relevance of ultrashort XUV pulses to capture the isotopic effect in few-femtosecond molecular photodynamics.

*Phys Chem Chem Phys ; 24(3): 1638-1653, 2022 Jan 19.*

##### RESUMO

Chemiexcitation, the generation of electronic excited states by a thermal reaction initiated on the ground state, is an essential step in chemiluminescence, and it is mediated by the presence of a conical intersection that allows a nonadiabatic transition from ground state to excited state. Conical intersections classified as sloped favor chemiexcitation over ground state relaxation. The chemiexcitation yield of 1,2-dioxetanes is known to increase upon methylation. In this work we explore to which extent this trend can be attributed to changes in the conical intersection topography or accessibility. Since conical intersections are not isolated points, but continuous seams, we locate regions of the conical intersection seams that are close to the configuration space traversed by the molecules as they react on the ground state. We find that conical intersections are energetically and geometrically accessible from the reaction trajectory, and that topographies favorable to chemiexcitation are found in all three molecules studied. Nevertheless, the results suggest that dynamic effects are more important for explaining the different yields than the static features of the potential energy surfaces.

*J Phys Chem Lett ; 12(34): 8404-8415, 2021 Sep 02.*

##### RESUMO

Controlling matter with light has always been a great challenge, leading to the ever-expanding field of photochemistry. In addition, since the first generation of light pulses of attosecond (1 as = 10-18 s) duration, a great deal of effort has been devoted to observing and controlling electrons on their intrinsic time scale. Because of their short duration, attosecond pulses have a large spectral bandwidth populating several electronically excited states in a coherent manner, i.e., an electronic wavepacket. Because of interference, such a wavepacket has a new electronic distribution implying a potentially different and totally new reactivity as compared to traditional photochemistry, leading to the novel concept of "attochemistry". This nascent field requires the support of theory right from the start. In this Perspective, we discuss the opportunities offered by attochemistry, the related challenges, and the current and future state-of-the-art developments in theoretical chemistry needed to model it accurately.

*Phys Chem Chem Phys ; 23(35): 19155-19165, 2021 Sep 15.*

##### RESUMO

The cis â trans photo-isomerisation mechanism of azobenzene, after excitation to the nπ* and ππ* states, is revisited using high-level ab initio surface hopping mixed quantum-classical dynamics in combination with multi-reference CASSCF electronic structure calculations. A reduction of photoisomerisation quantum yield of 0.10 on exciting to the higher energy ππ* state compared to the lower energy nπ* state is obtained, in close agreement with the most recent experimental values [Ladányi et al., Photochem. Photobiol. Sci., 2017, 16, 1757-1761] which re-examined previous literature values which showed larger changes in quantum yield. By direct comparison of both excitations, we have found that the explanation for the decrease in quantum yield is not the same as for the reduction observed in the trans â cis photoisomerisation. In contrast to the trans â cis scenario, S1 â S0 decay does not occur at 'earlier' C-NîN-C angles along the central torsional coordinate after ππ* excitation, as in the cis â trans case the rotation about this coordinate occurs too rapidly. The wavelength dependency of the quantum yield is instead found to be due to a potential well on the S2 surface, from which either cis or trans-azobenzene can be formed. While this well is accessible after both excitations, it is more easily accessed after ππ* excitation - an additional 15-17% of photochromes, which under nπ* excitation would have exclusively formed the trans isomer, are trapped in this well after ππ* excitation. The probability of forming the cis isomer when leaving this well is also higher after ππ* excitation, increasing from 9% to 35%. The combination of these two factors results in the reduction of 0.10 of the quantum yield of photoisomerisation on ππ* excitation of cis-azobenzene, compared to nπ* excitation.

*Sci Rep ; 11(1): 2485, 2021 Jan 28.*

##### RESUMO

We present a new methodology for measuring few-femtosecond electronic and nuclear dynamics in both atoms and polyatomic molecules using multidimensional high harmonic generation (HHG) spectroscopy measurements, in which the spectra are recorded as a function of the laser intensity to form a two-dimensional data set. The method is applied to xenon atoms and to benzene molecules, the latter exhibiting significant fast nuclear dynamics following ionization. We uncover the signature of the sub-cycle evolution of the returning electron flux in strong-field ionized xenon atoms, implicit in the strong field approximation but not previously observed directly. We furthermore extract the nuclear autocorrelation function in strong field ionized benzene cations, which is determined to have a decay of [Formula: see text] fs, in good agreement with the [Formula: see text] fs obtained from direct dynamics variational multi-configuration Gaussian calculations. Our method requires minimal assumptions about the system, and is applicable even to un-aligned polyatomic molecules.

*Struct Dyn ; 7(4): 044102, 2020 Jul.*

##### RESUMO

Recently, coherent structural dynamics in the excited state of an iron photosensitizer was observed through oscillations in the intensity of Kα x-ray emission spectroscopy (XES). Understanding the origin of the unexpected sensitivity of core-to-core transitions to structural dynamics is important for further development of femtosecond time-resolved XES methods and, we believe, generally necessary for interpretation of XES signals from highly non-equilibrium structures that are ubiquitous in photophysics and photochemistry. Here, we use multiconfigurational wavefunction calculations combined with atomic theory to analyze the emission process in detail. The sensitivity of core-to-core transitions to structural dynamics is due to a shift of the minimum energy metal-ligand bond distance between 1s and 2p core-hole states. A key effect is the additional contraction of the non-bonding 3s and 3p orbitals in 1s core-hole states, which decreases electron-electron repulsion and increases overlap in the metal-ligand bonds. The effect is believed to be general and especially pronounced for systems with strong bonds. The important role of 3s and 3p orbitals is consistent with the analysis of radial charge and spin densities and can be connected to the negative chemical shift observed for many transition metal complexes. The XES sensitivity to structural dynamics can be optimized by tuning the emission energy spectrometer, with oscillations up to ±4% of the maximum intensity for the current system. The theoretical predictions can be used to design experiments that separate electronic and nuclear degrees of freedom in ultrafast excited state dynamics.

*J Chem Phys ; 152(21): 214117, 2020 Jun 07.*

##### RESUMO

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

*J Chem Theory Comput ; 16(6): 3989-4001, 2020 Jun 09.*

##### RESUMO

Machine learning techniques, specifically gradient-enhanced Kriging (GEK), have been implemented for molecular geometry optimization. GEK-based optimization has many advantages compared to conventional-step-restricted second-order truncated expansion-molecular optimization methods. In particular, the surrogate model given by GEK can have multiple stationary points, will smoothly converge to the exact model as the number of sample points increases, and contains an explicit expression for the expected error of the model function at an arbitrary point. Machine learning is, however, associated with abundance of data, contrary to the situation desired for efficient geometry optimizations. In this paper, we demonstrate how the GEK procedure can be utilized in a fashion such that in the presence of few data points, the surrogate surface will in a robust way guide the optimization to a minimum of a potential energy surface. In this respect, the GEK procedure will be used to mimic the behavior of a conventional second-order scheme but retaining the flexibility of the superior machine learning approach. Moreover, the expected error will be used in the optimizations to facilitate restricted-variance optimizations. A procedure which relates the eigenvalues of the approximate guessed Hessian with the individual characteristic lengths, used in the GEK model, reduces the number of empirical parameters to optimize to two: the value of the trend function and the maximum allowed variance. These parameters are determined using the extended Baker (e-Baker) and part of the Baker transition-state (Baker-TS) test suites as a training set. The so-created optimization procedure is tested using the e-Baker, full Baker-TS, and S22 test suites, at the density functional theory and second-order Møller-Plesset levels of approximation. The results show that the new method is generally of similar or better performance than a state-of-the-art conventional method, even for cases where no significant improvement was expected.

*Struct Dyn ; 7(2): 024101, 2020 Mar.*

##### RESUMO

Ultrafast non-adiabatic dynamics of the small heteroaromatic compound 2-thiopyridone has been studied with surface hopping simulations based on multi-configurational quantum chemistry. Initial excitation of the bright S 2 ( π , π * ) state is found to promptly relax to S 1 ( n , π * ) through in-plane motion. The subsequent dynamics are oppositely driven by out-of-plane motion, which results in both complex population transfers among all the available states and intersystem crossing predominantly through the "El-Sayed forbidden" S 1 ( n , π * ) to T 2 ( n , π * ) channel, through significant mixing of electronic excitation characters. Despite this complexity, the femto- to picosecond triplet population, expected from several spectroscopic measurements, is well described as a simple exponential decay of the singlet state manifold. No proton transfer is found in the reported trajectories, but two mechanisms for its possible mediation in previously reported experiments are proposed based on the observed structural dynamics: (i) ultrafast intra-molecular transfer driven by the initially coherent in-plane motion and (ii) inter-molecular solvent-mediated transfer driven by the out-of-plane modes that dominate the later motion.

*J Chem Phys ; 152(6): 064301, 2020 Feb 14.*

##### RESUMO

The influence of ring-puckering on the light-induced ring-opening dynamics of heterocyclic compounds was studied on the sample 5-membered ring molecules Î³-valerolactone and 5H-furan-2-one using time-resolved photoelectron spectroscopy and ab initio molecular dynamics simulations. In Î³-valerolactone, ring-puckering is not a viable relaxation channel and the only available reaction pathway is ring-opening, which occurs within one vibrational period along the C-O bond. In 5H-furan-2-one, the C=C double bond in the ring allows for ring-puckering which slows down the ring-opening process by about 150 fs while only marginally reducing its quantum yield. This demonstrates that ring-puckering is an ultrafast process, which is directly accessible upon excitation and which spreads the excited state wave packet quickly enough to influence even the outcome of an otherwise expectedly direct ring-opening reaction.

*Nat Commun ; 11(1): 634, 2020 Jan 31.*

##### RESUMO

The non-equilibrium dynamics of electrons and nuclei govern the function of photoactive materials. Disentangling these dynamics remains a critical goal for understanding photoactive materials. Here we investigate the photoinduced dynamics of the [Fe(bmip)2]2+ photosensitizer, where bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-pyridine, with simultaneous femtosecond-resolution Fe Kα and Kß X-ray emission spectroscopy (XES) and X-ray solution scattering (XSS). This measurement shows temporal oscillations in the XES and XSS difference signals with the same 278 fs period oscillation. These oscillations originate from an Fe-ligand stretching vibrational wavepacket on a triplet metal-centered (3MC) excited state surface. This 3MC state is populated with a 110 fs time constant by 40% of the excited molecules while the rest relax to a 3MLCT excited state. The sensitivity of the Kα XES to molecular structure results from a 0.7% average Fe-ligand bond length shift between the 1 s and 2p core-ionized states surfaces.

*J Chem Theory Comput ; 15(11): 5925-5964, 2019 Nov 12.*

##### RESUMO

In this Article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics, and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the Article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism, and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets.

*J Comput Chem ; 40(19): 1789-1799, 2019 Jul 15.*

##### RESUMO

Electronically excited states play important roles in many chemical reactions and spectroscopic techniques. In quantum chemistry, a common technique to solve excited states is the multiroot Davidson algorithm, but it is not designed for processes like X-ray spectroscopy that involves hundreds of highly excited states. We show how the use of a restricted active space wavefunction together with a projection operator to remove low-lying electronic states offers an efficient way to reach single and double-core-hole states. Additionally, several improvements to the stability and efficiency of the configuration interaction (CI) algorithm for a large number of states are suggested. When applied to a series of transition metal complexes the new CI algorithm does not only resolve divergence issues but also leads to typical reduction in computational time by 70%, with the largest savings for small molecules and large active spaces. Together, the projection operator and the improved CI algorithm now make it possible to simulate a wide range of single- and two-photon spectroscopies. © 2019 Wiley Periodicals, Inc.

*Chem Sci ; 10(8): 2298-2307, 2019 Feb 28.*

##### RESUMO

Molecular dynamics simulations are often key to the understanding of the mechanism, rate and yield of chemical reactions. One current challenge is the in-depth analysis of the large amount of data produced by the simulations, in order to produce valuable insight and general trends. In the present study, we propose to employ recent machine learning analysis tools to extract relevant information from simulation data without a priori knowledge on chemical reactions. This is demonstrated by training machine learning models to predict directly a specific outcome quantity of ab initio molecular dynamics simulations - the timescale of the decomposition of 1,2-dioxetane. The machine learning models accurately reproduce the dissociation time of the compound. Keeping the aim of gaining physical insight, it is demonstrated that, in order to make accurate predictions, the models evidence empirical rules that are, today, part of the common chemical knowledge. This opens the way for conceptual breakthroughs in chemistry where machine analysis would provide a source of inspiration to humans.

*J Chem Phys ; 149(9): 094108, 2018 Sep 07.*

##### RESUMO

An algorithm is described for quantum dynamics where an Ehrenfest potential is combined with fully quantum nuclear motion (Quantum-Ehrenfest, Qu-Eh). The method is related to the single-set variational multi-configuration Gaussian approach (vMCG) but has the advantage that only a single quantum chemistry computation is required at each time step since there is only a single time-dependent potential surface. Also shown is the close relationship to the "exact factorization method." The quantum Ehrenfest method is compared with vMCG for study of electron dynamics in a modified bismethylene-adamantane cation system. Illustrative examples of electron-nuclear dynamics are presented for a distorted allene system and for HCCI+ where one has a degenerate Π system.

*Chem Rev ; 118(15): 6927-6974, 2018 08 08.*

##### RESUMO

Bioluminescence is a phenomenon that has fascinated mankind for centuries. Today the phenomenon and its sibling, chemiluminescence, have impacted society with a number of useful applications in fields like analytical chemistry and medicine, just to mention two. In this review, a molecular-orbital perspective is adopted to explain the chemistry behind chemiexcitation in both chemi- and bioluminescence. First, the uncatalyzed thermal dissociation of 1,2-dioxetane is presented and analyzed to explain, for example, the preference for triplet excited product states and increased yield with larger nonreactive substituents. The catalyzed fragmentation reaction and related details are then exemplified with substituted 1,2-dioxetanone species. In particular, the preference for singlet excited product states in that case is explained. The review also examines the diversity of specific solutions both in Nature and in artificial systems and the difficulties in identifying the emitting species and unraveling the color modulation process. The related subject of excited-state chemistry without light absorption is finally discussed. The content of this review should be an inspiration to human design of new molecular systems expressing unique light-emitting properties. An appendix describing the state-of-the-art experimental and theoretical methods used to study the phenomena serves as a complement.