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.

Quantum rates in dissipative systems with spatially varying friction.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Full quantum dynamical investigation of the Eley-Rideal reaction forming H2 on a movable graphitic substrate at T = 0 K.

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 H2 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 H2 molecules are vibrationally hot (∼1.5 eV) though to a lesser extent than previously predicted.

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.

Inherently Chiral Spider-Like Oligothiophenes.

The racemate of an inherently chiral "spider-like" octathiophene monomer T83 , in which chirality is generated by torsion in its backbone, was synthesized. The racemate was resolved into configurationally stable antipodes by HPLC on a chiral stationary phase. Electrooxidation of the enantiomers resulted in materials displaying high enantiorecognition ability towards the antipodes of some chiral probes. Moreover, the T83 racemate demonstrated great aptitude to stimulate formation of 3D rigid architectures if used as a cross-linking monomer for molecular imprinting. This feature was exploited to devise a molecularly imprinted polymer-based chemosensor selective for a thymine-adenine oligonucleotide.

Quantum dynamical investigation of the isotope effect in H2 formation on graphite at cold collision energies.

The Eley-Rideal abstraction of hydrogen atoms on graphitic surfaces at cold collision energies was investigated using a time-dependent wave packet method within the rigid-flat surface approximation, with a focus on hydrogen-deuterium isotopic substitutions. It is found that the marked isotope effect of collinear collisions disappears when the full dimensionality of the problem is taken into account, thereby suggesting that abstraction is less direct than commonly believed and proceeds through glancing rather than head-on collisions. In contrast, a clear isotope effect is observed for "hot-atom" formation, which appears to be strongly favored for heavy projectiles because of their higher density of physisorbed states. Overall, the dynamics is essentially classical and reasonably well described by quasi-classical trajectory methods at all but the lowest energies (≲10 meV). A comparison of the results obtained in the (substrate) adiabatic and diabatic limits suggests that the reaction is only marginally affected by the lattice dynamics, but highlights the importance of including energy dissipation processes in order to accurately describe the internal excitation of the product molecules.

Hydrogen on silicene: like or unlike graphene?

Hydrogenation of free-standing silicene, the two-dimensional allotrope of silicon, is investigated in detail using first-principles methods and compared with the adsorption of H atoms on graphene. Similarly to graphene, chemisorption of a single H atom on silicene induces the formation of a semilocalized state around the adatom, a sharp peak in the density of states at the Fermi level which acts as a strong resonant scatterer for charge carriers. This state hosts an unpaired electron, the itinerant electron of the resonating valence bond picture which primarily resides on the "majority" sublattice and biases the reactivity towards specific lattice positions. Contrary to graphene, sticking of hydrogen atoms is barrierless, on both the pristine and the hydrogenated surface. As a consequence, hydrogen adsorption on silicene is expected to proceed randomly under typical laboratory conditions, and preferential binding to form balanced dimers (or clusters) only occurs when thermodynamic equilibrium conditions prevail. The absence of clustering can be experimentally confirmed using scanning tunneling microscopy techniques since simulated imaging shows that the investigated structures provide distinguishable features that should allow their easy identification, if present on the surface. Overall, our findings can be rationalized by the fact that in silicene π bonds are weaker and the lattice is softer than in graphene and suggest that in silicene adatoms may severely limit carrier mobility.

Insights into H2 formation in space from ab initio molecular dynamics.

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.

Electron transport in carbon wires in contact with Ag electrodes: a detailed first principles investigation.

The structure and electronic properties of carbon atom chains Cn in contact with Ag electrodes are investigated in detail with first principles means. The ideal Ag(100) surface is used as a model for binding, and electron transport through the chains is studied as a function of their length, applied bias voltage, presence of capping atoms (Si, S) and adsorption site. It is found that the metal-molecule bond largely influences electronic coupling to the leads. Without capping atoms the quality of the electric contact improves when increasing the carbon atom coordination number to the metal (1, 2 and 4 for adsorption on a top, bridge and hollow position, respectively) and this finding translates almost unchanged in more realistic tip-like contacts which present one, two or four metal atoms at the contact. Current-voltage characteristics show Ohmic behaviour over a wide range of bias voltages and the resulting conductances change only weakly when increasing the wire length. The effect of a capping species is typically drastic, and either largely reduces (S) or largely increases (Si) the coupling of the wire to the electrodes. Comparison of our findings with recent experimental results highlights the limits of the adopted approach, which can be traced back to the known gap problem of density-functional-theory.