Dynamics of the Molecular Geometric Phase.

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.

Adsorption of Polycyclic Aromatic Hydrocarbons and C60 onto Forsterite: C-H Bond Activation by the Schottky Vacancy.

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.

Signatures of coherent vibronic exciton dynamics and conformational control in the two-dimensional electronic spectroscopy of conjugated polymers.

Two-dimensional electronic spectroscopy (2DES) signals for homo-oligomer J-aggregates are computed, with a focus on the role of structural change induced by low-frequency torsional modes, along with quasi-stationary trapping effects induced by high-frequency polaronic modes. To this end, a model system is derived from an ab initio parametrized site-based Hamiltonian for oligothiophenes [Binder et al., Phys. Rev. Lett., 2018, 120, 227401]. To obtain a compact representation, we introduce a collective lattice mode whose vibronic coupling depends nonlinearly on the exciton density. As a result, an N-site model with a single polaronic mode and a single torsional mode is obtained. Furthermore, a quantum-classical treatment is employed where the torsional mode is treated within a mean-field Ehrenfest/Langevin approximation. 2D electronic spectra are computed using the equation-of-motion phase-matching approach (EOM-PMA) within a wavefunction description. It is seen that the spectra combine the vibronic fine structure, due to the polaronic mode, and a dynamic Stokes shift, due to torsional relaxation. The signatures of the coherent effects and adiabatic evolution in the 2DES signals are discussed.

Quantum Dynamics with Electronic Friction.

A theory of electronic friction is developed using the exact factorization of the electronic-nuclear wave function. No assumption is made regarding the electronic bath, which can be made of independent or interacting electrons, and the nuclei are treated quantally. The ensuing equation of motion for the nuclear wave function is a nonlinear Schrödinger equation including a friction term. The resulting friction kernel agrees with a previously derived mixed quantum-classical result by Dou et al., [Phys. Rev. Lett. 119, 046001 (2017)]PRLTAO0031-900710.1103/PhysRevLett.119.046001, except for a pseudomagnetic contribution in the latter that is here removed. More specifically, it is shown that the electron dynamics generally washes out the gauge fields appearing in the adiabatic dynamics. However, these are fully re-established in the typical situation where the electrons respond rapidly on the slow time scale of the nuclear dynamics (Markov limit). Hence, we predict Berry's phase effects to be observable also in the presence of electronic friction. Application to a model vibrational relaxation problem proves that the proposed approach represents a viable way to account for electronic friction in a fully quantum setting for the nuclear dynamics.

Lower Bounds for Nonrelativistic Atomic Energies.

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.

Comparison of an improved self-consistent lower bound theory with Lehmann's method for low-lying eigenvalues.

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.

The Different Story of π Bonds.

We revisit "classical" issues in multiply bonded systems between main groups elements, namely the structural distortions that may occur at the multiple bonds and that lead, e.g., to trans-bent and bond-length alternated structures. The focus is on the role that orbital hybridization and electron correlation play in this context, here analyzed with the help of simple models for σ- and π-bonds, numerically exact solutions of Hubbard Hamiltonians and first principles (density functional theory) investigations of an extended set of systems.

Interaction of Aromatic Molecules with Forsterite: Accuracy of the Periodic DFT-D4 Method.

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 (Mg2SiO4) surface for their relevance in astrochemistry. We studied the interaction of benzene with the pristine {010} forsterite surface and with transition-metal cations (Fe2+ and Ni2+) 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.

Lower Bounds for Coulombic Systems.

As of the writing of this paper, lower bounds are not a staple of quantum chemistry computations and for good reason. All previous attempts at applying lower bound theory to Coulombic systems led to lower bounds whose quality was inferior to the Ritz upper bounds so that their added value was minimal. Even our recent improvements upon Temple's lower bound theory were limited to Lanczos basis sets and these are not available to atoms and molecules due to the Coulomb singularity. In the present paper, we overcome these problems by deriving a rather simple eigenvalue equation whose roots, under appropriate conditions, give lower bounds which are competitive with the Ritz upper bounds. The input for the theory is the Ritz eigenvalues and their variances; there is no need to compute the full matrix of the squared Hamiltonian. Along the way, we present a Cauchy-Schwartz inequality which underlies many aspects of lower bound theory. We also show that within the matrix Hamiltonian theory used here, the methods of Lehmann and our recent self-consistent lower bound theory (J. Chem. Phys. 2020, 115, 244110) are identical. Examples include implementation to the hydrogen and helium atoms.

Self-consistent theory of lower bounds for eigenvalues.

A rigorous practically applicable theory is presented for obtaining lower bounds to eigenvalues of Hermitian operators, whether the ground state or excited states. Algorithms are presented for computing "residual energies" whose magnitude is essential for the computation of the eigenvalues. Their practical application is possible due to the usage of the Lanczos method for creating a tridiagonal representation of the operator under study. The theory is self-consistent, in the sense that a lower bound for one state may be used to improve the lower bounds for others, and this is then used self-consistently until convergence. The theory is exemplified for a toy model of a quartic oscillator, where with only five states the relative error in the lower bound for the ground state is reduced to 6 · 10-6, which is the same as the relative error of the least upper bound obtained with the same basis functions. The lower bound method presented in this paper suggests that lower bounds may become a staple of eigenvalue computations.

Lower bounds to eigenvalues of the Schrödinger equation by solution of a 90-y challenge.

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.

Local-in-Time Error in Variational Quantum Dynamics.

The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrödinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact expressions are provided for this error, which are then evaluated in illustrative cases, notably the widely used mean-field approach and the adiabatic quantum molecular dynamics. Based on these findings, we demonstrate the rigorous formulation of an adaptive scheme that resizes on the fly the underlying variational manifold and, hence, optimizes the overall computational cost of a quantum dynamical simulation. Such adaptive schemes are a crucial requirement for devising and applying direct quantum dynamical methods to molecular and condensed-phase problems.

Effective Enantiodiscrimination in Electroanalysis Based on a New Inherently Chiral 1,1'-binaphthyl Selector Directly Synthesizable in Enantiopure Form.

Enantioselective electroanalysis, which aims to discriminate the enantiomers of electroactive chiral probes in terms of potential difference, is a very attractive goal. To achieve this, its implementation is being studied for various "inherently chiral" selectors, either at the electrode surface or in the medium, yielding outstanding performance. In this context, the new inherently chiral monomer Naph2T4 is introduced, based on a biaromatic atropisomeric core, which is advantageously obtainable in enantiopure form without HPLC separation steps by a synthetic route hinging on enantiopure 2,2'-dibromo-1,1'-binaphthalenes. The antipodes of the new inherently chiral monomer can be easily electrooligomerized, yielding inherently chiral electrode surfaces that perform well in both cyclic voltammetry (CV) enantiodiscrimination tests with pharmaceutically interesting molecules and in magnetoelectrochemistry experiments.

Superhydrogenation of pentacene: the reactivity of zigzag-edges.

Investigating the hydrogenation of carbonaceous materials is of interest in a wide range of research areas including electronic device development, hydrogen storage, and, in particular, astrocatalytic formation of molecular hydrogen in the universe. Polycyclic Aromatic Hydrocarbons (PAHs) are ubiquitous in space, locking up close to 15% of the elementary carbon. We have used thermal desorption measurements to study the hydrogenation sequence of pentacene from adding one additional H to the fully hydrogenated pentacene species. The experiments reveal that hydrogenated species with an even number of excess H atoms are highly preferred over hydrogenated species with an odd number of H atoms. In addition, the experiments show that specific hydrogenation states of pentacene with 2, 4, 6, 10, 16 and 22 extra H atoms are preferred over other even numbers. We have investigated the structural stability and activation energy barriers for the superhydrogenation of pentacene using Density Functional Theory. The results reveal a preferential hydrogenation pattern set by the activation energy barriers of the hydrogenation steps. Based on these studies, we formulate simple concepts governing the hydrogenation that apply equally well for different PAHs.

To bend or not to bend, the dilemma of multiple bonds.

Beyond the second row of the periodic table, the nature of the multiple bonds between the elements of the main groups remains yet elusive, and "non-classical" bonding schemes are often invoked for their description. Here, focusing on group 14, we have performed an accurate modeling of the Si-Si and C-C double bonds, including electron correlation effects. We have shown that Si[double bond, length as m-dash]Si bonds are "classical" and closely resemble C[double bond, length as m-dash]C ones, being similarly subjected to a sort of tug of war in which the σ bond favors distortion and the π bond opposes it. The essential difference between Si and C boils down to the sizes of their valence shells, which determine the π-bending stiffness. In carbon, such a stiffness is large because, upon bending, the atomic s orbitals interfere destructively with the p ones. In silicon, the s shell is smaller than the p one, the bending stiffness is reduced and the π bonds typically succumb, distort, and weaken. Electron correlation plays a major role in this context, since π bonds are far from their molecular orbital limit. Hence, we have further shown that upon weakening the effective repulsion between π electrons one may remove any structural instability, strengthen the π bonds and turn Si into a closer relative of C than it used to be.

Vibronic coupling models for donor-acceptor aggregates using an effective-mode scheme: Application to mixed Frenkel and charge-transfer excitons in oligothiophene aggregates.

A reduced-dimensional effective-mode representation is developed in order to efficiently describe excited-state dynamics of multichromophoric donor-acceptor aggregates within a linear vibronic coupling model. Specifically, we consider systems where vibrational modes pertaining to a given molecular fragment couple both to local excitations of Frenkel type and delocalized states of charge transfer exciton type. A hierarchical chain representation is constructed which is suitable to describe correlated fluctuations, leading to a set of correlated spectral densities. An application is shown for a first-principles parameterized model of an oligothiophene H-type aggregate whose properties are modified due to the presence of charge transfer excitons. Within a pentamer model comprising 13 electronic states and 195 normal modes, good convergence of the effective-mode representation of the spectral densities is achieved at the eighth order of the hierarchy with 104 modes, and a qualitatively correct picture is obtained at the sixth order with 78 modes.

Dual-Route Hydrogenation of the Graphene/Ni Interface.

Nanostructured architectures based on graphene/metal interfaces might be efficiently exploited in hydrogen storage due to the attractive capability to provide adsorption sites both at the top side of graphene and at the metal substrate after intercalation. We combined in situ high-resolution X-ray photoelectron spectroscopy and scanning tunneling microscopy with theoretical calculations to determine the arrangement of hydrogen atoms at the graphene/Ni(111) interface at room temperature. Our results show that at low coverage H atoms predominantly adsorb as monomers and that chemisorption saturates when ∼25% of the surface is hydrogenated. In parallel, with a much lower rate, H atoms intercalate below graphene and bind to Ni surface sites. Intercalation progressively destabilizes the C-H bonds and triggers the release of the hydrogen chemisorbed on graphene. Valence band and near-edge absorption spectroscopy demonstrate that the graphene layer is fully lifted when the Ni surface is saturated with H. Thermal programmed desorption was used to determine the stability of the hydrogenated interface. Whereas the H atoms chemisorbed on graphene remain unperturbed over a wide temperature range, the intercalated phase abruptly desorbs 50-100 K above room temperature.

Magnetic Moments and Electron Transport through Chromium-Based Antiferromagnetic Nanojunctions.

We report the electronic, magnetic and transport properties of a prototypical antiferromagnetic (AFM) spintronic device. We chose Cr as the active layer because it is the only room-temperature AFM elemental metal. We sandwiched Cr between two non-magnetic metals (Pt or Au) with large spin-orbit coupling. We also inserted a buffer layer of insulating MgO to mimic the structure and finite resistivity of a real device. We found that, while spin-orbit has a negligible effect on the current flowing through the device, the MgO layer plays a crucial role. Its effect is to decouple the Cr magnetic moment from Pt (or Au) and to develop an overall spin magnetization. We have also calculated the spin-polarized ballistic conductance of the device within the Büttiker⁻Landauer framework, and we have found that for small applied bias our Pt/Cr/MgO/Pt device presents a spin polarization of the current amounting to ≃25%.

Sticking of atomic hydrogen on graphene.

Recent years have witnessed an ever growing interest in the interactions between hydrogen atoms and a graphene sheet. Largely motivated by the possibility of modulating the electric, optical and magnetic properties of graphene, a huge number of studies have appeared recently that added to and enlarged earlier investigations on graphite and other carbon materials. In this review we give a glimpse of the many facets of this adsorption process, as they emerged from these studies. The focus is on those issues that have been addressed in detail, under carefully controlled conditions, with an emphasis on the interplay between the adatom structures, their formation dynamics and the electric, magnetic and chemical properties of the carbon sheet.

Multi-configurational Ehrenfest simulations of ultrafast nonadiabatic dynamics in a charge-transfer complex.

Multi-configurational Ehrenfest (MCE) approaches, which are intended to remedy the lack of correlations in the standard mean-field Ehrenfest method, have been proposed as coherent-state based ansätze for quantum propagation [D. V. Shalashilin, J. Chem. Phys. 130, 244101 (2009)] and also as the classical limit of the variational Gaussian-based multiconfiguration time dependent Hartree (G-MCTDH) method [S. Römer and I. Burghardt, Mol. Phys. 111, 3618 (2013)]. In the present paper, we establish the formal connection between these schemes and assess the performance of MCE for a coherent-state representation of the classical-limit subsystem. As a representative model system, we address the ultrafast, coherent charge transfer dynamics in an oligothiophene-fullerene donor-acceptor complex described by a two-state linear vibronic coupling model. MCE calculations are compared with reference calculations performed with the MCTDH method, for 10-40 vibrational modes. Beyond a dimensionality of 10 modes, it is shown that the correct representation of electronic coherence depends crucially on the sampling of initially unoccupied Gaussians.