Born-Oppenheimer Surface Research Articles

Reactive scattering of H2 on Cu(111) at 925K: Effective Hartree potential vs sudden approximation.

We present new quantum dynamical results for the reactive scattering of hydrogen molecules from a Cu(111) surface at a surface temperature of 925K. Reaction, scattering, and diffraction probabilities are compared for results obtained using both an effective Hartree potential (EfHP) and a sudden approximation approach, implemented through the static corrugation model (SCM), to include surface temperature effects. Toward this goal, we show how the SRP48 DFT-functional and an embedded atom potential perform when used to calculate copper lattice constants and thermal expansion coefficients based on lattice dynamics calculations within the quasi-harmonic approximation. The so-calculated phonons are then used in the EfHP approach to replace the normal modes of a fictitious copper cluster used in earlier work. We find that both the EfHP and SCM approaches correctly predict the reaction probability curve broadening effect when the surface temperature is increased. Similarly, results for rovibrationally elastic scattering appear to be improved, predominantly for the SCM model. The behavior of the EfHP results appears to remain much closer to that of a Born-Oppenheimer static surface approach, which excludes any surface temperature effects. Finally, for the diffraction, we show very clear attenuation effects for the SCM approach, significantly decreasing specular diffraction probabilities at 925K surface temperature. These results demonstrate that state-of-the-art theoretical models are able to reproduce strictly quantum mechanical scattering effects with a sudden approximation model and open up interesting opportunities for further comparisons to experimental diffraction results.

Second-Order Mass-Weighting Scheme for Atom-Centered Density Matrix Propagation Molecular Dynamics.

The atom-centered density matrix propagation (ADMP) method is an extended Lagrangian approach to ab initio molecular dynamics, which includes the density matrix in an orthonormalized atom-centered Gaussian basis as additional, fictitious, electronic degrees of freedom, classically propagated along with the nuclear ones. A high adiabaticity between the nuclear and electronic subsystems is mandatory in order to keep the trajectory close to the Born-Oppenheimer (BO) surface. In this regard, the fictitious electronic mass μ, being a symmetric, nondiagonal matrix in its most general form, represents a free parameter, exploitable to optimize the propagation of the electronic density. Although mass-weighting schemes in ADMP exist, a systematic procedure to define an optimal value of the fictitious masses is not available yet. In this work, in order to rationally evaluate the electronic mass, fictitious electronic normal modes are defined through the diagonalization of the Hessian of the electronic density matrix. If the same frequency is imposed on all such modes (compatible with the chosen integration time step), then the corresponding μ matrix can be calculated and then employed for the following propagation. Analysis of several ADMP test simulations reveals that such Hessian-based mass-weighting approach is able to ensure, together with a 0.1/0.2 fs time steps, a high separation between the (real) nuclear and the (fictitious) electronic frequencies, which determines a high adiabaticity. This high, unprecedented, accuracy in the propagation leads, in turn, to low errors in the estimated nuclear vibrational frequencies, making the ADMP method totally comparable to a fully converged BO molecular dynamics simulation but more computationally efficient. This work, therefore, contributes to a further development of the ADMP ab initio molecular dynamics method, aimed at improving its accuracy through a more rational evaluation of the fictitious electronic mass parameter.

Quantum Chemical Molecular Dynamics Simulations for Methane‐Water Cages

ABSTRACTThe dynamic stability of various methane‐water clathrate‐like cages (CH4@(H2O)n, n = 16, 18, 20, 22), has been analyzed explicitly considering thermal effects by means of ab initio M06‐2X/6–31+G*/PCM calculations, which make use of Gaussian basis functions. Starting from the equilibrium filled cage structures, classical, dynamic reaction coordinate (DRC) on the Born–Oppenheimer surface, and semiclassical, Born–Oppenheimer plus harmonic zero‐point energy surface (BOMD), molecular dynamics have been carried out. Water molecules have a high tendency to orient covalent O–H bonds tangentially to the hydrophobic surface, thus clathrate‐like arrangements are an acceptable model to fully hydrate methane. If the cage size is such as to minimize core repulsion, due to electron cloud overlap, and to maximize host–guest van der Waals attractions, the clathrate‐like structures have a life‐time of two picoseconds in classical DRC simulations. The inclusion of quantum kinetic energy in BOMD simulations results in less structured cages with a reduced amount of hydrogen bond network. The preferential tangential orientation of the O‐H bonds is largely maintained, although few of them point toward the methane for a very short time in BOMD simulations. The reduced configurational space of water molecules hydrating hydrophobic moiety is highlighted, thus any satisfactory molecular modeling has to account for it.

Angular Momentum Transfer between a Molecular System and a Continuous Circularly Polarized Light Field within a Semiclassical Born-Oppenheimer Surface Hopping Framework.

We simulate semiclassically angular momentum transfer for a molecular system subject to a circularly polarized light (CPL) field either moving along a single Born-Oppenheimer (BO) surface or moving along multiple BO surfaces. Both sets of simulations are able to conserve the total angular momentum around the propagation direction of the CPL field, the former requiring a Berry force and the latter requiring a surface parametrized by both nuclear position and momentum (a so-called phase-space approach). Our results provide new insight into the nature of semiclassical nonadiabatic dynamics methods and further demonstrate the power of such methods to capture angular momentum transfer between different media, highlighting the need for accurate algorithms that conserve the total angular momentum.

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods.

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

Nonadiabatic dynamics in Rydberg gases with random atom positions

Assemblies of highly excited Rydberg atoms in an ultracold gas can be set into motion by a combination of van der Waals and resonant dipole-dipole interactions. Thereby, the collective electronic Rydberg state might change due to nonadiabatic transitions, in particular if the configuration encounters a conical intersection. For the experimentally most accessible scenario, in which the Rydberg atoms are initially randomly excited in a three-dimensional bulk gas under blockade conditions, we numerically show that nonadiabatic transitions can be common when starting from the most energetic repulsive Born-Oppenheimer surface. We outline how this state can be selectively excited using a microwave resonance, and demonstrate a regime where almost all collisional ionization of Rydberg atoms can be traced back to a prior nonadiabatic transition. Since Rydberg ionization is relatively straightforward to detect, the excitation and measurement scheme considered here renders nonadiabatic effects in Rydberg motion easier to demonstrate experimentally than in scenarios considered previously.

Mapping Quantum Chemical Dynamics Problems to Spin-Lattice Simulators.

The accurate computational determination of chemical, materials, biological, and atmospheric properties has a critical impact on a wide range of health and environmental problems, but is deeply limited by the computational scaling of quantum mechanical methods. The complexity of quantum chemical studies arises from the steep algebraic scaling of electron correlation methods and the exponential scaling in studying nuclear dynamics and molecular flexibility. To date, efforts to apply quantum hardware to such quantum chemistry problems have focused primarily on electron correlation. Here, we provide a framework that allows for the solution of quantum chemical nuclear dynamics by mapping these to quantum spin-lattice simulators. Using the example case of a short-strong hydrogen-bonded system, we construct the Hamiltonian for the nuclear degrees of freedom on a single Born-Oppenheimer surface and show how it can be transformed to a generalized Ising model Hamiltonian. We then demonstrate a method to determine the local fields and spin-spin couplings needed to identically match the molecular and spin-lattice Hamiltonians. We describe a protocol to determine the on-site and intersite coupling parameters of this Ising Hamiltonian from the Born-Oppenheimer potential and nuclear kinetic energy operator. Our approach represents a paradigm shift in the methods used to study quantum nuclear dynamics, opening the possibility to solve both electronic structure and nuclear dynamics problems using quantum computing systems.

Semiclassical Dispersion Corrections Efficiently Improve Multiconfigurational Theory with Short-Range Density-Functional Dynamic Correlation.

Multiconfigurational wave functions are known to describe the electronic structure across a Born-Oppenheimer surface qualitatively correct. However, for quantitative reaction energies, dynamic correlation originating from the many configurations involving excitations out of the restricted orbital space, the active space, must be considered. Standard procedures involve approximations that eventually limit the ultimate accuracy achievable (most prominently, multireference perturbation theory). At the same time, the computational cost increases dramatically due to the necessity to obtain higher-order reduced density matrices. It is this disproportion that leads us here to propose an MC-srDFT-D hybrid approach of semiclassical dispersion (D) corrections to cover long-range dynamic correlation in a multiconfigurational (MC) wave function theory, which includes short-range (sr) dynamic correlation by density functional theory (DFT) without double counting. We demonstrate that the reliability of this approach is very good (at negligible cost), especially when considering that standard second-order multireference perturbation theory usually overestimates dispersion interactions.

Structural and vibrational properties of lithium under ambient conditions within density functional theory

We apply a general first-principles approach to derive the phase diagram of metallic lithium at ambient pressure between 0 and 350 K, including identification of candidate phases. We use ab initio random structure searching to identify competing phases and supplement the results with calculations of vibrational properties and relevant derived neutron diffraction patterns. Strong quantum nuclear effects are present, prompting a careful treatment of vibrations. We directly map the Born-Oppenheimer surface of Li, allowing the extension of the normal quasi-harmonic treatment of vibrations to a ``quasi-anharmonic'' approach, where the effects of anharmonicity are included. The Gibbs free energies of the fcc, bcc, hcp, and 9R phases are derived using a variety of equations of state. We find that the anharmonic contribution to the Gibbs free energies of Li phases is of the same order as the differences between phases. Anharmonicity also makes a noticeable difference to the 0-K phonon dispersion of the bcc phase, with the largest difference at the $N$-point phonon. The ordering of phase transitions that we find agrees with the calculations of Ackland et al. [Science 356, 1254 (2017)], even when anharmonic effects are included, suggesting that a quasi-harmonic treatment is sufficient for correct phase behavior. We show explicitly that the martensitic phase transition from close-packed to bcc lithium upon heating is driven by entropic contributions to the phonon free energy.

Predicting a two-dimensional P2S3 monolayer: A global minimum structure

A new 2D crystal, P2S3, is found based on extensive evolutionary algorithm driven structural search. Furthermore, P2S3 is confirmed to be stable by the computed phonon spectrum and ab initio molecular dynamics simulations. This 2D crystalline phase of P2S3 corresponds to the global minimum in the Born-Oppenheimer surface of the phosphorus sulfide monolayers with 2:3 stoichiometry. It is a wide band gap (4.55 eV) semiconductor with PsbndS σ bonds. The electronic properties of P2S3 structure can be fine-tuned by stacking into multilayer P2S3 structures, forming P2S3 nanoribbons or P2S3 nanotubes, expanding its potential applications in the emerging field of 2D electronics.

Semiempirical Atom-centered Density Matrix Propagation Approach to Temperature-dependent Vibrational Spectroscopy of Irinotecan

In the present study, a molecular dynamics study of irinotecan molecule with the atom-centered density matrix propagation scheme was carried out at AM1 semiempirical level of theory, at series of different temperatures, ranging from 5 K to 300 K. Molecular dynamics simulations were performed within the NVE ensemble, initially injecting (and redistributing among the nuclei) various amounts of nuclear kinetic energies to achieve the desired target temperatures. Subsequently to initial equilibration phase of 2 ps, productive simulations were carried out for 8 ps. The accuracy of simulations and the closeness of the generated trajectory to those at the Born-Oppenheimer surface were carefully followed and analyzed. To compute the temperature-dependent rovibrational density of states spectra, the velocity-velocity autocorrelation functions were computed and Fourier-transformed. Fourier-transformed dipole moment autocorrelation functions were, on the other hand, used to calculate the temperature-dependent infrared absorption cross section spectra. The finite-temperature spectra were compared to those computed by a static approach, i.e. by diagonalization of mass-weighted Hessian matrices at the minima located on the potential energy surfaces. Thermally-induced spectral changes were analyzed and discussed. The advantages of finite-temperature statistical physics simulations based on semiempirical Hamiltonian over the static semiempirical ones in the case of complex, physiologically active molecular systems relevant to intermolecular interactions between drugs and drug carriers were pointed out and discussed.

Accurate Classical Polarization Solution with No Self-Consistent Field Iterations.

We present a new solution for classical polarization that does not require any self-consistent field iterations, the aspect of classical polarization that makes it computationally expensive. The new method builds upon our iEL/SCF Lagrangian scheme that defines a set of auxiliary induced dipoles whose original purpose was to serve as a time-reversible initial guess to the SCF solution of the set of real induced dipoles. In the new iEL/0-SCF approach the auxiliary dipoles now drive the time evolution of the real induced dipoles such that they stay close to the Born-Oppenheimer surface in order to achieve a truly SCF-less method. We show that the iEL/0-SCF exhibits no loss of simulation accuracy when analyzed across bulk water, low to high concentration salt solutions, and small solutes to large proteins in water. In addition, iEL/0-SCF offers significant computational savings over more expensive SCF calculations based on traditional 1 fs time step integration using symplectic integrators and is as fast as reversible reference system propagator algorithms with an outer 2 fs time step.

First-principles study of the dynamic Jahn-Teller distortion of the neutral vacancy in diamond

First-principles density functional theory methods are used to investigate the structure, energetics, and vibrational motions of the neutral vacancy defect in diamond. The measured optical absorption spectrum demonstrates that the tetrahedral $T_d$ point group symmetry of pristine diamond is maintained when a vacancy defect is present. This is shown to arise from the presence of a dynamic Jahn-Teller distortion that is stabilised by large vibrational anharmonicity. Our calculations further demonstrate that the dynamic Jahn-Teller-distorted structure of $T_d$ symmetry is lower in energy than the static Jahn-Teller distorted tetragonal $D_{2d}$ vacancy defect, in agreement with experimental observations. The tetrahedral vacancy structure becomes more stable with respect to the tetragonal structure by increasing temperature. The large anharmonicity arises mainly from quartic vibrations, and is associated with a saddle point of the Born-Oppenheimer surface and a minimum in the free energy. This study demonstrates that the behaviour of Jahn-Teller distortions of point defects can be calculated accurately using anharmonic vibrational methods. Our work will open the way for first-principles treatments of dynamic Jahn-Teller systems in condensed matter.

An isotopic mass effect on the intermolecular potential

The impact of isotopic variation on the electronic energy and intermolecular potentials is often suppressed when calculating isotopologue thermodynamics. Intramolecular potential energy surfaces for distinct isotopologues are in fact equivalent under the Born–Oppenheimer approximation, which is sometimes used to imply that the intermolecular interactions are independent of isotopic mass. In this communication, the intermolecular dipole–dipole interaction between hetero-nuclear diatomic molecules is considered. It is shown that the intermolecular potential contains mass-dependent terms even though each nucleus moves on a Born–Oppenheimer surface. The analysis suggests that mass dependent variations in intermolecular potentials should be included in comprehensive descriptions of isotopologue thermodynamics.

Prediction of a two-dimensional crystalline structure of nitrogen atoms

Based on first-principles density functional calculations, we predict that nitrogen atoms can form a single-layer, buckled honeycomb structure called nitrogene, which is rigid and stable even above room temperature. This 2D crystalline phase of nitrogen, which corresponds to a local minimum in the Born-Oppenheimer surface, is a nonmagnetic insulator with saturated $\ensuremath{\pi}$ bonds. When grown on a substrate like Al(111) surface and graphene, nitrogene binds weakly to substrates and hence preserves its free-standing properties, but it can easily be pealed off. Zigzag and armchair nanoribbons of nitrogene have fundamental band gaps derived from reconstructed edge states. These band gaps are tunable with size and suitable for the emerging field of 2D electronics. Nitrogene forms not only bilayer, but also 3D graphitic multilayer structures. Single-layer nitrogene can nucleate and grow on the armchair edges of hexagonal boron nitride.

The Quantum Mechanics of Nano-Confined Water: New Cooperative Effects Revealed with Neutron and X-Ray Compton Scattering

Neutron Compton scattering(NCS) measurements of the momentum distribution of light ions using the Vesuvio instrument at ISIS provide a sensitive local probe of the environment of those ions. NCS measurements of the proton momentum distribution in bulk water show only small deviations from the usual picture of water as a collection of molecules, with the protons covalently bonded to an oxygen and interacting weakly, primarily electrostatically, with nearby molecules. However, a series of measurements of the proton momentum distribution in carbon nanotubes, xerogel, and Nafion show that the proton delocalizes over distances of 0.2-0.3Å when water is confined on the scale of 20Å. This delocalization must be the result of changes in the Born-Oppenheimer surface for the protons, which would imply that there are large deviations in the electron distribution from that of a collection of weakly interacting molecules. This has been observed at Spring-8 using x-ray Compton scattering. The observed deviation in the valence electron momentum distribution from that of bulk water is more than an order of magnitude larger than the change observed in bulk water as the water is heated from just above melting to just below boiling. We conclude that the protons and electrons in nano-confined water are in a qualitatively different ground state from that of bulk water. Since the properties of this state persist at room temperature, and the confinement distance necessary to observe it is comparable to the distance between the elements of biological cells, this state presumably plays a role in the functioning of those cells.

Δ Self-Consistent Field Method for Natural Anthocyanidin Dyes.

We present an application of the Δ self-consistent field (ΔSCF) method, which we have implemented and tested in the DFT code CONQUEST, on the study of excited states of natural anthocyanidin dyes. We show that ΔSCF allows relaxation of the atomic structure for systems in excited states by following gradients on the excited Born-Oppenheimer surface. We compare the vertical excitation energies of some anthocyanidins in gas-phase to results from time-dependent density functional theory (TDDFT) and experiments. To reproduce a typical dye-sensitized solar cell interface, we adsorb cyanidin on TiO2 anatase (101), focusing on the shift of the lowest excitation energy due to the adsorption. We have found that important modifications occur in the excited state geometry of the adsorbed cyanidin.

Reactive scattering of H2 from Cu(100): Comparison of dynamics calculations based on the specific reaction parameter approach to density functional theory with experiment

We present new experimental and theoretical results for reactive scattering of dihydrogen from Cu(100). In the new experiments, the associative desorption of H(2) is studied in a velocity resolved and final rovibrational state selected manner, using time-of-flight techniques in combination with resonance-enhanced multi-photon ionization laser detection. Average desorption energies and rotational quadrupole alignment parameters were obtained in this way for a number of (v = 0, 1) rotational states, v being the vibrational quantum number. Results of quantum dynamics calculations based on a potential energy surface computed with a specific reaction parameter (SRP) density functional, which was derived earlier for dihydrogen interacting with Cu(111), are compared with the results of the new experiments and with the results of previous molecular beam experiments on sticking of H(2) and on rovibrationally elastic and inelastic scattering of H(2) and D(2) from Cu(100). The calculations use the Born-Oppenheimer and static surface approximations. With the functional derived semi-empirically for dihydrogen + Cu(111), a chemically accurate description is obtained of the molecular beam experiments on sticking of H(2) on Cu(100), and a highly accurate description is obtained of rovibrationally elastic and inelastic scattering of D(2) from Cu(100) and of the orientational dependence of the reaction of (v = 1, j = 2 - 4) H(2) on Cu(100). This suggests that a SRP density functional derived for H(2) interacting with a specific low index face of a metal will yield accurate results for H(2) reactively scattering from another low index face of the same metal, and that it may also yield accurate results for H(2) interacting with a defected (e.g., stepped) surface of that same metal, in a system of catalytic interest. However, the description that was obtained of the average desorption energies, of rovibrationally elastic and inelastic scattering of H(2) from Cu(100), and of the orientational dependence of reaction of (v = 0, j = 3 - 5, 8) H(2) on Cu(100) compares less well with the available experiments. More research is needed to establish whether more accurate SRP-density functional theory dynamics results can be obtained for these observables if surface atom motion is added to the dynamical model. The experimentally and theoretically found dependence of the rotational quadrupole alignment parameter on the rotational quantum number provides evidence for rotational enhancement of reaction at low translational energies.

First-principles molecular dynamics simulations of the H2O / Cu(111) interface

A first-principles theoretical study of the water-Cu(111) interface based on density functional calculations is reported. Using differently sized surface models: p(2 × 2), p(4 × 4) and p(4 × 5), we found out that the adsorption energy of a H(2)O monomer does not significantly change with the surface model though the adsorption geometry is sensitive to the choice of the super-cell surface and, also, to the coverage. Molecular dynamics simulations on the Born-Oppenheimer surface of liquid water on a Cu(111) surface reveal that H(2)O in the first solvent layer adsorbs O-down and that the H-bond network is weaker upon adsorption on the Cu. Furthermore, absolute electrochemical potentials are presented and compared to the potential of zero charge obtained experimentally and theoretically.

Hydrogen vibrational modes on graphene and relaxation of the C–H stretch excitation from first-principles calculations

Density functional theory (DFT) calculations are used to determine the vibrational modes of hydrogen adsorbed on graphene in the low-coverage limit. Both the calculated adsorption energy of a H atom of 0.8 eV and calculated C-H stretch vibrational frequency of 2552 cm(-1) are unusually low for hydrocarbons, but in agreement with data from electron energy loss spectroscopy on hydrogenated graphite. The clustering of two adsorbed H atoms observed in scanning tunneling microscopy images shows its fingerprint also in our calculated spectra. The energetically preferred adsorption on different sublattices correlates with a blueshift of the C-H stretch vibrational modes in H adatom clusters. The C-H bending modes are calculated to be in the 1100 cm(-1) range, resonant with the graphene phonons. Moreover, we use our previously developed methods to calculate the relaxation of the C-H stretch mode via vibration-phonon interaction, using the Born-Oppenheimer surface for all local modes as obtained from the DFT calculations. The total decay rate of the H stretch into other H vibrations, thereby creating or annihilating one graphene phonon, is determined from Fermi's golden rule. Our calculations using the matrix elements derived from DFT calculations show that the lifetime of the H stretch mode on graphene is only several picoseconds, much shorter than on other semiconductor surfaces such as Ge(001) and Si(001).