Damped Dispersion Research Articles

Photo-plasmonic effect as the hot electron generation mechanism

Based on the effective Schrödinger–Poisson model a new physical mechanism for resonant hot-electron generation at irradiated half-space metal–vacuum interface of electron gas with arbitrary degree of degeneracy is proposed. The energy dispersion of undamped plasmons in the coupled Hermitian Schrödinger–Poisson system reveals an exceptional point coinciding the minimum energy of plasmon conduction band. Existence of such exceptional behavior is a well-know character of damped oscillation which in this case refers to resonant wave–particle interactions analogous to the collisionless Landau damping effect. The damped Schrödinger–Poisson system is used to model the collective electron tunneling into the vacuum. The damped plasmon energy dispersion is shown to have a full-featured exceptional point structure with variety of interesting technological applications. In the band gap of the damped collective excitation,depending on the tunneling parameter value, there is a resonant energy orbital for which the wave-like growing of collective excitations cancels the damping of the single electron tunneling wavefunction. This important feature is solely due to dual-tone wave-particle oscillations, characteristics of the collective excitations in the quantum electron system leading to a resonant photo-plasmonic effect, as a collective analog of the well-known photo-electric effect. The few nanometer wavelengths high-energy collective photo-electrons emanating from the metallic surfaces can lead to a much higher efficiency of plasmonic solar cell devices, as compared to their semiconductor counterpart of electron–hole excitations at the Fermi energy level. The photo-plasmonic effect may also be used to study the quantum electron tunneling and electron spill-out at metallic surfaces. Current findings may help to design more efficient spasers by using the feature-rich plasmonic exceptional point structure.

TO1 soft mode in Fe doped β-Ga2O3 studied by terahertz time-domain spectroscopy

The transmission spectra of terahertz (THz) waves through Fe doped β-Ga2O3 in the range of 1–6 THz by air-plasma-based THz time-domain spectroscopy (THz-TDS) at room temperature and their temperature dependence between 90 and 500 K in the range of 0.7 THz-1.8 THz have been measured. We estimated the complex dielectric constants by fitting the spectra with the classical damped oscillator dispersion model and obtained the anisotropic lowest transverse optical (TO1) phonon frequencies. The values at room temperature agreed with the reported values, and no significant temperature dependence was observed.

Supervised learning of a chemistry functional with damped dispersion

Kohn–Sham density functional theory is widely used in chemistry, but no functional can accurately predict the whole range of chemical properties, although recent progress by some doubly hybrid functionals comes close. Here, we optimized a singly hybrid functional called CF22D with higher across-the-board accuracy for chemistry than most of the existing non-doubly hybrid functionals by using a flexible functional form that combines a global hybrid meta-nonseparable gradient approximation that depends on density and occupied orbitals with a damped dispersion term that depends on geometry. We optimized this energy functional by using a large database and performance-triggered iterative supervised training. We combined several databases to create a very large, combined database whose use demonstrated the good performance of CF22D on barrier heights, isomerization energies, thermochemistry, noncovalent interactions, radical and nonradical chemistry, small and large systems, simple and complex systems and transition-metal chemistry.

Polarizable Force Field for Acetonitrile Based on the Single-Center Multipole Expansion.

A polarizable potential function describing the interaction between acetonitrile molecules is introduced. The molecules are described as rigid and linear, with three mass sites corresponding to the CH3 group (methyl, Me), the central carbon atom (C), and the nitrogen atom (N). The electrostatic interaction is represented using a single-center multipole expansion as has been done previously for H2O [Wikfeldt et al., Phys. Chem. Chem. Phys. 15, 16542 (2013)], by including multipole moments from dipole up to and including hexadecapole, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model is free of point charges. The non-electrostatic part is described in a pair-wise fashion by a Born-Mayer repulsion and damped dispersion attraction. The potential function is parameterized to fit the interaction energy of small (CH3CN)n, n = 2-6, clusters calculated using the PBE0 hybrid functional with an additional atomic many-body dispersion contribution. The parameterized potential function is found to compare well with results of the electronic structure calculations of dissociation curves for different dimer orientations and cohesive properties (the equilibrium volume, cohesive energy, and the bulk modulus) of the α-phase of acetonitrile crystal. The average value of the molecular dipole moment obtained in the α-phase is 5.53 D, corresponding to ca. 40% increase as compared to the dipole moment of an isolated acetonitrile molecule, 3.92 D. The calculated densities of solid and liquid acetonitrile turn out to be 8-10% higher than experimental values. This appears to be caused by an overestimate of the atomic many-body dispersion interaction in the density functional calculations used as input in the parametrization of the potential function.

Polarizable Water Potential Derived from a Model Electron Density.

A new empirical potential for efficient, large scale molecular dynamics simulation of water is presented. The HIPPO (Hydrogen-like Intermolecular Polarizable POtential) force field is based upon the model electron density of a hydrogen-like atom. This framework is used to derive and parametrize individual terms describing charge penetration damped permanent electrostatics, damped polarization, charge transfer, anisotropic Pauli repulsion, and damped dispersion interactions. Initial parameter values were fit to Symmetry Adapted Perturbation Theory (SAPT) energy components for ten water dimer configurations, as well as the radial and angular dependence of the canonical dimer. The SAPT-based parameters were then systematically refined to extend the treatment to water bulk phases. The final HIPPO water model provides a balanced representation of a wide variety of properties of gas phase clusters, liquid water, and ice polymorphs, across a range of temperatures and pressures. This water potential yields a rationalization of water structure, dynamics, and thermodynamics explicitly correlated with an ab initio energy decomposition, while providing a level of accuracy comparable or superior to previous polarizable atomic multipole force fields. The HIPPO water model serves as a cornerstone around which similarly detailed physics-based models can be developed for additional molecular species.

Evaluation of methods for obtaining dispersion energies used in density functional calculations of intermolecular interactions

Since semilocal density functional theory (DFT) approximations cannot recover the dispersion components of interaction energies at intermonomer separations near van der Waals minima and larger, dispersion energies computed by methods other than semilocal DFTs are often added to DFT interaction energies such dispersion energies are assessed here by comparing them to accurate dispersion energies obtained from symmetry-adapted perturbation theory on a set of molecular dimers, including variations of intermonomer separations. The evaluated methods include nonlocal DFT correlation functionals, parameterized atom–atom dispersion functions originating from the asymptotic expansion, and methods based on models of atoms in molecules. In contrast to many published comparisons of such methods focused on total interaction energies, our comparisons evaluate the performance on the actual physical quantity for which these methods have been designed. This performance is discussed in the context of the physical soundness of the methods. Our results show that atom–atom functions reproduce dispersion energies best, with a mean absolute percentage error of the order of 10%. The nonlocal correlation functionals perform much worse, with errors in the range 24–49%, far from what could be called quantitative reproduction of this quantity. The only exception is the recently proposed damped asymptotic dispersion energy functional which gave an error of 12%. The atom-in-molecule methods also gave large errors, above 29%.

A physically grounded damped dispersion model with particle mesh Ewald summation.

Accurate modeling of dispersion is critical to the goal of predictive biomolecular simulations. To achieve this accuracy, a model must be able to correctly capture both the short-range and asymptotic behavior of dispersion interactions. We present here a damped dispersion model based on the overlap of charge densities that correctly captures both regimes. The overlap damped dispersion model represents a classical physical interpretation of dispersion: the interaction between the instantaneous induced dipoles of two distinct charge distributions. This model is shown to be an excellent fit with symmetry adapted perturbation theory dispersion energy calculations, yielding an RMS error on the S101x7 database of 0.5 kcal/mol. Moreover, the damping function used in this model is wholly derived and parameterized from the electrostatic dipole-dipole interaction, making it not only physically grounded but transferable as well.

Potential energy surfaces for O + O2 collisions.

We present global potential energy surfaces for nine adiabatic electronic states of O3, namely, 1 1A', 2 1A', 1 1A″, 1 3A', 2 3A', 1 3A″, 1 5A', 2 5A', and 1 5A″. These are the states of O3 that are accessed in electronically adiabatic collisions of a ground-state triplet O2 molecule with a ground-state triplet O atom. The surfaces are based on XMS-CASPT2 electronic structure calculations with dynamically scaled external correlation. The active space has 12 active electrons distributed in the nine 2p orbitals. The adiabatic surfaces are fitted to analytic functions using a many-body expansion where the pairwise additive term is fitted to an accurate diatomic potential including a damped dispersion term, and the many-body part, without disconnected terms, is fitted with permutationally invariant polynomials in mixed exponential-Gaussians to the electronic structure data points. The selection and weighting of points for the fits are designed to produce surfaces suitable for describing energy transfer and dissociation in high-energy collisions.

An analytical formula For He-Ne Van der Waals potential without any adjustable parameters

A simple analytical formula for the entire van der Waals potential of the He-Ne dimer is derived. The short range repulsive part is essentially from the surface integral theory with the parameters calculated by a combining rule. The long range attractive potential is described by the damped asymptotic dispersion series. The potential depends only on the known dispersion coefficients and the amplitude of the asymptotic wave function and the ionization energy of the atoms. Without any adjustable parameters the HeNe potential predicted with the present formula is in excellent agreement with the accurate experimental and theoretical results around the equilibrium distance and long range distances. The same method also can be applied to other heteronuclear dimers.

Physical Molecular Mechanics Method for Damped Dispersion.

Damped dispersion can be a significant component of the interaction energy in many physical and chemical processes, for example, physisorption and noncovalent complexation. For physically interpreting and modeling such processes, it is convenient to have an analytic method to calculate damped dispersion that is readily applicable across the entire periodic table. Of the available methods to calculate damped dispersion energy for interacting systems with overlapping charge distributions, we select symmetry-adapted perturbation theory (SAPT) as providing a reasonable definition, and of the possible analytic forms, we choose the D3(BJ) method. However, the available parametrizations of D3(BJ) include not only damped dispersion energy but also corrections for errors in specific exchange-correlation functionals. Here we present a parametrization that provides a physical measure of damped dispersion without such density functional corrections. The method generalizes an earlier method of Pernal and co-workers to all elements from hydrogen to plutonium.

Numerical modeling of wave propagation for damped elbow pipes using Fourier–Legendre spectral element method in polar coordinates

Wave propagation in damped elbow pipes is investigated with the Fourier–Legendre spectral element method. The damped steady-state dispersion relationship is constructed by the frequency–wavenumber spectral decomposition of the governing wave equation, based on the strain–displacement relation of the ring coordinate. Then, the discretization formulation is obtained via the Legendre spectral element method where high-order spectral elements of polar coordinates are introduced to keep this finite element model consistent with the structures geometry. Finally, we give some dispersion curves of energy velocity and attenuation on damped elbow pipes with different curvatures in the ring wavenumber–frequency space.

Encaged molecules in external electric fields: A molecular "tug-of-war".

Response of polar molecules CH3OH and H2O2 and a non-polar molecule, CO2, as "guests" encapsulated in the dodecahedral water cage (H2O)20 "host," to an external, perturbative electric field is investigated theoretically. We employ the hybrid density-functionals M06-2X and ωB97X-D incorporating the effects of damped dispersion, in conjunction with the maug-cc-pVTZ basis set, amenable for a hydrogen bonding description. While the host cluster (cage) tends to confine the embedded guest molecule through cooperative hydrogen bonding, the applied electric field tends to rupture the cluster-composite by stretching it; these two competitive effects leading to a molecular "tug-of-war." The composite remains stable up to a maximal sustainable threshold electric field, beyond which, concomitant with the vanishing of the HOMO-LUMO gap, the field wins over and the cluster breaks down. The electric-field effects are gauged in terms of the changes in the molecular geometry of the confined species, interaction energy, molecular electrostatic potential surfaces, and frequency shifts of characteristic normal vibrations in the IR regime. Interestingly, beyond the characteristic threshold electric field, the labile, distorted host cluster fragmentizes, and the guest molecule still tethered to a remnant fragment, an effect attributed to the underlying hydrogen-bonded networks.

MN15-L: A New Local Exchange-Correlation Functional for Kohn-Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids.

Kohn-Sham density functional theory is widely used for applications of electronic structure theory in chemistry, materials science, and condensed-matter physics, but the accuracy depends on the quality of the exchange-correlation functional. Here, we present a new local exchange-correlation functional called MN15-L that predicts accurate results for a broad range of molecular and solid-state properties including main-group bond energies, transition metal bond energies, reaction barrier heights, noncovalent interactions, atomic excitation energies, ionization potentials, electron affinities, total atomic energies, hydrocarbon thermochemistry, and lattice constants of solids. The MN15-L functional has the same mathematical form as a previous meta-nonseparable gradient approximation exchange-correlation functional, MN12-L, but it is improved because we optimized it against a larger database, designated 2015A, and included smoothness restraints; the optimization has a much better representation of transition metals. The mean unsigned error on 422 chemical energies is 2.32 kcal/mol, which is the best among all tested functionals, with or without nonlocal exchange. The MN15-L functional also provides good results for test sets that are outside the training set. A key issue is that the functional is local (no nonlocal exchange or nonlocal correlation), which makes it relatively economical for treating large and complex systems and solids. Another key advantage is that medium-range correlation energy is built in so that one does not need to add damped dispersion by molecular mechanics in order to predict accurate noncovalent binding energies. We believe that the MN15-L functional should be useful for a wide variety of applications in chemistry, physics, materials science, and molecular biology.

Methanol Oxidation to Formaldehyde on VSiBEA Zeolite: A Combined DFT/vdW/Transition Path Sampling and Experimental Study

Density functional calculations have been performed applying periodic boundary conditions to investigate the oxidation of methanol on vanadium-containing SiBEA zeolite (VSiBEA). Different types of reaction configurations have been set up in conformity with the experimental conditions. Thermodynamic property calculations for T > 0 K have been performed and compared with the available experimental results. Transition path sampling was employed to unravel the reaction mechanisms for oxidation of methanol on vanadium-containing SiBEA zeolites at three temperatures (300, 415, and 523 K). Dispersion interactions were accounted for by adding a damped dispersion term to the PBE energies. The study of different reaction pathways was combined with experimental data that enabled us to shed more light on the reaction mechanism.

Non-pairwise additivity of the leading-order dispersion energy

The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained in terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is -0.11 kJ mol(-1) well(-1), which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.

Combined Density Functional Theory and Monte Carlo Analysis of Monomolecular Cracking of Light Alkanes Over H-ZSM-5

Density functional calculations applying periodic boundary conditions have been performed to investigate adsorption and cracking of light alkanes (C3–C6) on zeolite H-ZSM-5. Intrinsic energy barriers were obtained from single-point calculations by applying the revised form of the PBE functional (RPBE) to structures optimized on the PBE potential energy surface. Dispersion interactions were accounted for by adding a damped dispersion term to the PBE energies. The dependence of the adsorption enthalpy on the carbon number is in agreement with experimental observation. From intrinsic energy barriers, intrinsic rate coefficients were calculated by means of transition state theory. The dependence of the intrinsic enthalpy and entropy of activation on the carbon number is discussed and compared to experimental observations. Transition path sampling was employed to unravel qualitatively the reaction mechanism for cracking of butane. Monte Carlo simulations in the canonical ensemble were conducted to estimate the temperature dependence of the adsorption enthalpy and entropy of propane to n-hexane. These quantities are not constant, as is often assumed in the interpretation of experimental data but become less negative with increasing temperature. It is shown how the selection of adsorption parameters influences the extraction of intrinsic rate parameters from experimental rate data. Based on the present analysis, an alternative partitioning of the experimentally accessible apparent entropy of activation into contributions from adsorption and intrinsic reaction is proposed.

Structure and Dynamics of Liquid Water from ab Initio Molecular Dynamics-Comparison of BLYP, PBE, and revPBE Density Functionals with and without van der Waals Corrections.

We investigate the accuracy provided by different treatments of the exchange and correlation effects, in particular the London dispersion forces, on the properties of liquid water using ab initio molecular dynamics simulations with density functional theory. The lack of London dispersion forces in generalized gradient approximations (GGAs) is remedied by means of dispersion-corrected atom-centered potentials (DCACPs) or damped atom-pairwise dispersion corrections of the C6R(-6) form. We compare results from simulations using GGA density functionals (BLYP, PBE, and revPBE) with data from their van der Waals (vdW) corrected counterparts. As pointed out previously, all vdW-corrected BLYP simulations give rise to highly mobile water whose softened structure is closer to experimental data than the one predicted by the bare BLYP functional. Including vdW interactions in the PBE functional, on the other hand, has little influence on both structural and dynamical properties of water. Augmenting the revPBE functional with either damped atom-pairwise dispersion corrections or DCACP evokes opposite behaviors. The former further softens the already under-structured revPBE water, whereas the latter makes it more glassy. These results demonstrate the delicacy needed in describing weak interactions in molecular liquids.

Polarized Molecular Orbital Model Chemistry. II. The PMO Method.

We present a new semiempirical molecular orbital method based on neglect of diatomic differential overlap. This method differs from previous NDDO-based methods in that we include p orbitals on hydrogen atoms to provide a more realistic modeling of polarizability. As in AM1-D and PM3-D, we also include damped dispersion. The formalism is based on the original MNDO one, but in the process of parameterization we make some specific changes to some of the functional forms. The present article is a demonstration of the capability of the new approach, and it presents a successful parametrization for compounds composed only of hydrogen and oxygen atoms, including the important case of water clusters.

Quantum Chemical Modeling of Benzene Ethylation over H-ZSM-5 Approaching Chemical Accuracy: A Hybrid MP2:DFT Study

The alkylation of benzene by ethene over H-ZSM-5 is analyzed by means of a hybrid MP2:DFT scheme. Density functional calculations applying periodic boundary conditions (PBE functional) are combined with MP2 energy calculations on a series of cluster models of increasing size which allows extrapolation to the periodic MP2 limit. Basis set truncation errors are estimated by extrapolation of the MP2 energy to the complete basis set limit. Contributions from higher-order correlation effects are accounted for by CCSD(T) coupled cluster calculations. The sum of all contributions provides the "final estimates" for adsorption energies and energy barriers. Dispersion contributes significantly to the potential energy surface. As a result, the MP2:DFT potential energy profile is shifted downward compared to the PBE profile. More importantly, this shift is not the same for reactants and transition structures due to different self-interaction correction errors. The final enthalpies for ethene, benzene, and ethylbenzene adsorption on the Brønsted acid site at 298 K are -46, -78, and -110 kJ/mol, respectively. The intrinsic enthalpy barriers at 653 K are 117 and 119/94 kJ/mol for the one- and two-step alkylation, respectively. Intrinsic rate coefficients calculated by means of transition state theory are converted to apparent Arrhenius parameters by means of the multicomponent adsorption equilibrium. The simulated apparent activation energy (66 kJ/mol) agrees with experimental data (58-76 kJ/mol) within the uncertainty limit of the calculations. Adsorption energies obtained by adding a damped dispersion term to the PBE energies (PBE+D), agree within +/-7 kJ/mol, with the "final estimates", except for physisorption (pi-complex formation) and chemisorption of ethene (ethoxide formation) for which the PBE+D energies are 12.4 and 26.0 kJ/mol, respectively larger than the "final estimates". For intrinsic energy barriers, the PBE+D approach does not improve pure PBE results.

Binding energy of d10 transition metals to alkenes by wave function theory and density functional theory☆

Abstract The structures of Pd(PH 3 ) 2 and Pt(PH 3 ) 2 complexes with ethene and conjugated C n H n + 2 systems ( n = 4, 6, 8, and 10) were studied. Their binding energies were calculated using both wave function theory (WFT) and density functional theory (DFT). Previously it was reported that the binding energy of the alkene to the transition metal does not depend strongly on the size of the conjugated C n H n + 2 ligand, but that DFT methods systematically underestimate the binding energy more and more significantly as the size of the conjugated system is increased. Our results show that recently developed density functionals predict the binding energy for these systems much more accurately. New benchmark calculations carried out by the coupled cluster method based on Brueckner orbitals with double excitations and a quasiperturbative treatment of connected triple excitations (BCCD(T)) with a very large basis set agree even better with the DFT predictions than do the previous best estimates. The mean unsigned error in absolute and relative binding energies of the alkene ligands to Pd(PH 3 ) 2 is 2.5 kcal/mol for the ωB97 and M06 density functionals and 2.9 kcal/mol for the M06-L functional. Adding molecular mechanical damped dispersion yields even smaller mean unsigned errors: 1.3 kcal/mol for the M06-D functional, 1.5 kcal/mol for M06-L-D, and 1.8 kcal/mol for B97-D and ωB97X-D. The new functionals also lead to improved accuracy for the analogous Pt complexes. These results show that recently developed density functionals may be very useful for studying catalytic systems involving Pd d 10 centers and alkenes.