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Hydrogen formation is a key process for the physics and the chemistry of interstellar clouds. Molecular hydrogen is believed to form on the carbonaceous surface of dust grains, and several mechanisms have been invoked to explain its abundance in different regions of space, from cold interstellar clouds to warm photon-dominated regions. Here, we investigate direct (Eley-Rideal) recombination including lattice dynamics, surface corrugation, and competing H-dimers formation by means of ab initio molecular dynamics. We find that Eley-Rideal reaction dominates at energies relevant for the interstellar medium and alone may explain observations if the possibility of facile sticking at special sites (edges, point defects, etc.) on the surface of the dust grains is taken into account. [ABSTRACT FROM AUTHOR]

The exothermic, collinearly-dominated Eley–Rideal hydrogen formation on graphite is studied with electronic structure and quantum dynamical means. In particular, the focus is on the importance of the model used to describe the graphitic substrate, in light of the marked discrepancies present in available literature results. To this end, the collinear reaction is considered and the potential energy surface is computed for a number of different graphitic surface models using Density Functional Theory (DFT) for different dynamical regimes. Quantum dynamics is performed with wavepacket techniques down to the cold collision energies relevant for the chemistry of the interstellar medium. Results show that the reactivity at moderate-to-high collision energies sensitively depends on the shape of the PES in the entrance channel, which in turn is related to the adopted surface model. At low energies we rule out the presence of any barrier to reaction, thereby highlighting the importance of quantum reflection in limiting the reaction efficiency. [ABSTRACT FROM AUTHOR]

Abstract: A recently developed effective-mode representation is employed to characterize the influence of a multi-dimensional environment on the S 2–S 1 conical intersection in pyrazine, taken as a paradigm case of high-dimensional dynamics at a conical intersection. We consider a simplified model by which four modes are strongly coupled to the electronic subsystem while a number of weakly coupled tuning modes, inducing energy gap fluctuations, are sampled from a spectral density. The latter is approximated by a series of simplified spectral densities which can be cast into a continued-fraction form, as previously demonstrated in Hughes et al. (K.H. Hughes, C.D. Christ, I. Burghardt, J. Chem. Phys. 131 (2009) 124108). In the time domain, the hierarchy of spectral densities translates to truncated effective-mode chains with a Markovian or quasi-Markovian (Rubin type) closure. A sequential deconvolution procedure is employed to generate this chain representation. The implications for the ultrafast dynamics and its representation in terms of reduced-dimensional models are discussed. [ABSTRACT FROM AUTHOR]

[Display omitted] • Neural network (NN) potentials for quantum dynamics of cis–trans photoisomerization. • Multiplicative NNs adapted to regularized diabatic states at a conical intersection. • NN potentials match a sum-of-products form required by MCTDH wavefunction propagation. • Good agreement found for highly correlated dynamics with up to 13 degrees of freedom. Neural-network (NN) potentials are employed in conjunction with the Multiconfiguration Time-Dependent Hartree (MCTDH) method in order to simulate an ultrafast photoinduced cis–trans type isomerization process induced by a conical intersection. To this end, NN potentials are fitted to a diabatic potential of regularized diabatic states type [Köppel et al., J. Chem. Phys. 115, 2377 (2001)], which entirely relies on adiabatic potential information. Multiplicative NNs are employed which match the sum-of-products form of the multiconfigurational MCTDH wavefunction. Good agreement with the reference dynamics is obtained for simulations of the highly correlated dynamics with up to 13 degrees of freedom. This study contributes to developing NN methodologies suitable for photochemical dynamics at complex excited-state topologies. [ABSTRACT FROM AUTHOR]

Geometric phases play a crucial role in diverse fields. In molecules, they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wave function experiences quantum-mechanical interference effects. This intriguing effect, closely resembling the magnetic Aharonov-Bohm effect, crucially relies on the adiabatic description of the dynamics, and it is an open issue whether and how it persists in an exact quantum dynamical framework. Recent works suggest that the molecular geometric phase is an artifact of the adiabatic approximation, thereby challenging the entire concept. Here, building upon a recent investigation (Martinazzo, R.; Burghardt, I. Phys. Rev. Lett. 2024 , 132 , 243002), we address this issue using the exact factorization of the total wave function. We introduce instantaneous gauge-invariant phases separately for the electrons and nuclei and use them to monitor the phase difference between the trailing edges of a wavepacket encircling a conical intersection between adiabatic surfaces. The transition from the time-dependent open-path phase differences to the closed-path limit is examined, revealing how the phase differences in the electronic and nuclear subspaces compensate for each other upon path closure. In this way, we unambiguously demonstrate the role of the geometric phase in the interference process and shed light on its persistence beyond the adiabatic approximation.

We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton methods, and classical molecular dynamics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunneling-dominated regime is identified at low friction. At low temperatures, incoherent tunneling dominates most of Kramer's curve, except at very low friction, when coherent tunneling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (or decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviors. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

The fate of the molecular geometric phase in an exact dynamical framework is investigated with the help of the exact factorization of the wave function and a recently proposed quantum hydrodynamical description of its dynamics. An instantaneous, gauge-invariant phase is introduced for arbitrary paths in nuclear configuration space in terms of hydrodynamical variables, and shown to reduce to the adiabatic geometric phase when the state is adiabatic and the path is closed. The evolution of the closed-path phase over time is shown to adhere to a Maxwell-Faraday induction law, with nonconservative forces arising from the electron dynamics that play the role of electromotive forces. We identify the pivotal forces that are able to change the value of the phase, thereby challenging any topological argument. Nonetheless, negligible changes in the phase occur when the local dynamics along the probe loop is approximately adiabatic. That is, the geometric phase effects that arise in an adiabatic limiting situation remain suitable to effectively describe certain dynamic observables.

Understanding how to catalytically break the C-H bond of aromatic molecules, such as polycyclic aromatic hydrocarbons (PAHs), is currently a big challenge and a subject of study in catalysis, astrochemistry, and planetary science. In the latter, the study of the breakdown reaction of PAHs on mineral surfaces is important to understand if PAHs are linked to prebiotic molecules in regions of star and planet formation. In this work, we employed a periodic density functional theory along with Grimme's D4 (DFT-D4) approach for studying the adsorption of a sample of PAHs (naphthalene, anthracene, fluoranthene, pyrene, coronene, and benzocoronene) and fullerene on the [010] forsterite surface and its defective surfaces (Fe-doped and Ni-doped surfaces and a MgO-Schottky vacancy) for their implications in catalysis and astrochemistry. On the basis of structural and binding energy analysis, large PAHs and fullerene present stronger adsorption on the pristine, Fe-doped, and Ni-doped forsterite surfaces than small PAHs. On a MgO-Schottky vacancy, parallel adsorption of the PAH leads to the chemisorption process (C-Si and/or C-O bonds), whereas perpendicular orientation of the PAH leads to the catalytic breaking of the aromatic C-H bond via a barrierless reaction. Spin density and charge analysis show that C-H dissociation is promoted by electron donation from the vacancy to the PAH. As a result of the undercoordinated Si and O atoms, the vacancy acts as a Frustrated Lewis Pair (FLP) catalyst. Therefore, a MgO-Schottky vacancy [010] forsterite surface proved to have potential catalytic activity for the activation of C-H bond in aromatic molecules., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

A recently developed lower bound theory for Coulombic problems (E. Pollak, R. Martinazzo, J. Chem. Theory Comput. 2021 , 17 , 1535) is further developed and applied to the highly accurate calculation of the ground-state energy of two- (He, Li + , and H - ) and three- (Li) electron atoms. The method has been implemented with explicitly correlated many-particle basis sets of Gaussian type, on the basis of the highly accurate (Ritz) upper bounds they can provide with relatively small numbers of functions. The use of explicitly correlated Gaussians is developed further for computing the variances, and the necessary modifications are here discussed. The computed lower bounds are of submilli-Hartree (parts per million relative) precision and for Li represent the best lower bounds ever obtained. Although not yet as accurate as the corresponding (Ritz) upper bounds, the computed bounds are orders of magnitude tighter than those obtained with other lower bound methods, thereby demonstrating that the proposed method is viable for lower bound calculations in quantum chemistry applications. Among several aspects, the optimization of the wave function is shown to play a key role for both the optimal solution of the lower bound problem and the internal check of the theory., Competing Interests: The authors declare no competing financial interest., (© 2021 The Authors. Published by American Chemical Society.)

Ritz eigenvalues only provide upper bounds for the energy levels, while obtaining lower bounds requires at least the calculation of the variances associated with these eigenvalues. The well-known Weinstein and Temple lower bounds based on the eigenvalues and variances converge very slowly and their quality is considerably worse than that of the Ritz upper bounds. Lehmann presented a method that in principle optimizes Temple's lower bounds with significantly improved results. We have recently formulated a Self-Consistent Lower Bound Theory (SCLBT), which improves upon Temple's results. In this paper, we further improve the SCLBT and compare its quality with Lehmann's theory. The Lánczos algorithm for constructing the Hamiltonian matrix simplifies Lehmann's theory and is essential for the SCLBT method. Using two lattice Hamiltonians, we compared the improved SCLBT (iSCLBT) with its previous implementation as well as with Lehmann's lower bound theory. The novel iSCLBT exhibits a significant improvement over the previous version. Both Lehmann's theory and the SCLBT variants provide significantly better lower bounds than those obtained from Weinstein's and Temple's methods. Compared to each other, the Lehmann and iSCLBT theories exhibit similar performance in terms of the quality and convergence of the lower bounds. By increasing the number of states included in the calculations, the lower bounds are tighter and their quality becomes comparable with that of the Ritz upper bounds. Both methods are suitable for providing lower bounds for low-lying excited states as well. Compared to Lehmann's theory, one of the advantages of the iSCLBT method is that it does not necessarily require the Weinstein lower bound for its initial input, but Ritz eigenvalue estimates can also be used. Especially owing to this property the iSCLBT method sometimes exhibits improved convergence compared to that of Lehmann's lower bounds., (© 2021. The Author(s).)

Density functional theory (DFT) has provided deep atomic-level insights into the adsorption behavior of aromatic molecules on solid surfaces. However, modeling the surface phenomena of large molecules on mineral surfaces with accurate plane wave methods (PW) can be orders of magnitude more computationally expensive than localized atomic orbitals (LCAO) methods. In the present work, we propose a less costly approach based on the DFT-D4 method (PBE-D4), using LCAO, to study the interactions of aromatic molecules with the {010} forsterite (Mg 2 SiO 4 ) surface for their relevance in astrochemistry. We studied the interaction of benzene with the pristine {010} forsterite surface and with transition-metal cations (Fe 2+ and Ni 2+ ) using PBE-D4 and a vdW-inclusive density functional (Dion, Rydberg, Schröder, Langreth, and Lundqvist (DRSLL)) with LCAO methods. PBE-D4 shows good agreement with coupled-cluster methods (CCSD(T)) for the binding energy trend of cation complexes and with PW methods for the binding energy of benzene on the forsterite surface with a difference of about 0.03 eV. The basis set superposition error (BSSE) correction is shown to be essential to ensure a correct estimation of the binding energies even when large basis sets are employed for single-point calculations of the optimized structures with smaller basis sets. We also studied the interaction of naphthalene and benzocoronene on pristine and transition-metal-doped {010} forsterite surfaces as a test case for PBE-D4. Yielding results that are in good agreement with the plane wave methods with a difference of about 0.02-0.17 eV, the PBE-D4 method is demonstrated to be effective in unraveling the binding structures and the energetic trends of aromatic molecules on pristine and transition-metal-doped forsterite mineral surfaces. Furthermore, PBE-D4 results are in good agreement with its predecessor PBE-D3(BJM) and with the vdW-inclusive density functionals, as long as transition metals are not involved. Hence, PBE-D4/CP-DZP has been proven to be a robust theory level to study the interaction of aromatic molecules on mineral surfaces.

The Ritz upper bound to eigenvalues of Hermitian operators is essential for many applications in science. It is a staple of quantum chemistry and physics computations. The lower bound devised by Temple in 1928 [G. Temple, Proc. R. Soc. A Math. Phys. Eng. Sci. 119, 276-293 (1928)] is not, since it converges too slowly. The need for a good lower-bound theorem and algorithm cannot be overstated, since an upper bound alone is not sufficient for determining differences between eigenvalues such as tunneling splittings and spectral features. In this paper, after 90 y, we derive a generalization and improvement of Temple's lower bound. Numerical examples based on implementation of the Lanczos tridiagonalization are provided for nontrivial lattice model Hamiltonians, exemplifying convergence over a range of 13 orders of magnitude. This lower bound is typically at least one order of magnitude better than Temple's result. Its rate of convergence is comparable to that of the Ritz upper bound. It is not limited to ground states. These results complement Ritz's upper bound and may turn the computation of lower bounds into a staple of eigenvalue and spectral problems in physics and chemistry., Competing Interests: The authors declare no competing interest.

The dynamics of the Eley-Rideal abstraction reaction of hydrogen atoms on a movable graphitic surface is investigated for the first time in a numerically exact fully quantum setting. A system-bath strategy was applied where the two recombining H atoms and a substrate C atom form a relevant subsystem, while the rest of the lattice takes the form of an independent oscillator bath. High-dimensional wavepacket simulations were performed in the collision energy range 0.2-1.0 eV with the help of the multi-layer multi-configuration time-dependent Hartree method, focusing on the collinear reaction on a zero-temperature surface. Results show that the dynamics is close to a sudden limit in which the reaction is much faster than the substrate motion. Unpuckering of the surface is fast (some tens of fs) but starts only after the formation of H 2 is completed, thereby determining a considerable substrate heating (∼0.8 eV per reactive event). Energy partitioning in the product molecule favors translational over vibrational energy, and H 2 molecules are vibrationally hot (∼1.5 eV) though to a lesser extent than previously predicted.