Frequency-dependent Response Functions Research Articles

Frequency-dependent hydrodynamic finite size correction in molecular simulations reveals the long-time hydrodynamic tail.

Finite-size effects are challenging in molecular dynamics simulations because they have significant effects on computed static and dynamic properties, in particular diffusion constants, friction coefficients, and time- or frequency-dependent response functions. We investigate the influence of periodic boundary conditions on the velocity autocorrelation function and the frequency-dependent friction of a particle in a fluid, and show that the long-time behavior (starting at the picosecond timescale) is significantly affected. We develop an analytical correction allowing us to subtract the periodic boundary condition effects. By this, we unmask the power-law long-time tails of the memory kernel and the velocity autocorrelation function in liquid water and a Lennard-Jones fluid from simulations with rather small box sizes.

A new framework for frequency-dependent polarizable force fields.

A frequency-dependent extension of the polarizable force field "Atom-Condensed Kohn-Sham density functional theory approximated to the second-order" (ACKS2) [Verstraelen et al., J. Chem. Phys. 141, 194114 (2014)] is proposed, referred to as ACKS2ω. The method enables theoretical predictions of dynamical response properties of finite systems after partitioning of the frequency-dependent molecular response function. Parameters in this model are computed simply as expectation values of an electronic wavefunction, and the hardness matrix is entirely reused from ACKS2 as an adiabatic approximation is used. A numerical validation shows that accurate models can already be obtained with atomic monopoles and dipoles. Absorption spectra of 42 organic and inorganic molecular monomers are evaluated using ACKS2ω, and our results agree well with the time-dependent DFT calculations. Also for the calculation of C6 dispersion coefficients, ACKS2ω closely reproduces its TDDFT reference. When parameters for ACKS2ω are derived from a PBE/aug-cc-pVDZ ground state, it reproduces experimental values for 903 organic and inorganic intermolecular pairs with an MAPE of 3.84%. Our results confirm that ACKS2ω offers a solid connection between the quantum-mechanical description of frequency-dependent response and computationally efficient force-field models.

Chemical accuracy with σ-functionals for the Kohn-Sham correlation energy optimized for different input orbitals and eigenvalues.

Recently, a new type of orbital-dependent functional for the Kohn-Sham (KS) correlation energy, σ-functionals, was introduced. Technically, σ-functionals are closely related to the well-known direct random phase approximation (dRPA). Within the dRPA, a function of the eigenvalues σ of the frequency-dependent KS response function is integrated over purely imaginary frequencies. In σ-functionals, this function is replaced by one that is optimized with respect to reference sets of atomization, reaction, transition state, and non-covalent interaction energies. The previously introduced σ-functional uses input orbitals and eigenvalues from KS calculations with the generalized gradient approximation (GGA) exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE). Here, σ-functionals using input orbitals and eigenvalues from the meta-GGA TPSS and the hybrid-functionals PBE0 and B3LYP are presented and tested. The number of reference sets taken into account in the optimization of the σ-functionals is larger than in the first PBE based σ-functional and includes sets with 3d-transition metal compounds. Therefore, also a reparameterized PBE based σ-functional is introduced. The σ-functionals based on PBE0 and B3LYP orbitals and eigenvalues reach chemical accuracy for main group chemistry. For the 10966 reactions from the highly accurate W4-11RE reference set, the B3LYP based σ-functional exhibits a mean average deviation of 1.03 kcal/molcompared to 1.08 kcal/molfor the coupled cluster singles doubles perturbative triples method if the same valence quadruple zeta basis set is used. For 3d-transition metal chemistry, accuracies of about 2 kcal/molare reached. The computational effort for the post-self-consistent evaluation of the σ-functional is lower than that of a preceding PBE0 or B3LYP calculation for typical systems.

What do the two times in two-time correlation functions mean for interpreting tr-ARPES?

Time-resolved angle-resolved photoemission spectroscopy is one of the most powerful pump–probe measurements of materials driven far from equilibrium. Unlike the linear-response regime, where the frequency-dependent response function is independent of time, in a far-from-equilibrium experiment, the response function depends on two times in the time domain. In this work, we describe how one can use time-dependent frequency response functions and how they involve contributions from times that are near to each other. This implies that they should not be thought of as a frequency-dependent response at a single definite time. Instead, the Fourier uncertainty relations show that they involve contributions from ranges of times and must be interpreted in this light. We use this insight to help understand what time-resolved photoemission measurements actually measure.

Toward chemical accuracy at low computational cost: Density-functional theory with σ-functionals for the correlation energy.

We introduce new functionals for the Kohn-Sham correlation energy that are based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem and are named σ-functionals. Like in the well-established direct random phase approximation (dRPA), σ-functionals require as input exclusively eigenvalues σ of the frequency-dependent KS response function. In the new functionals, functions of σ replace the σ-dependent dRPA expression in the coupling-constant and frequency integrations contained in the ACFD theorem. We optimize σ-functionals with the help of reference sets for atomization, reaction, transition state, and non-covalent interaction energies. The optimized functionals are to be used in a post-self-consistent way using orbitals and eigenvalues from conventional Kohn-Sham calculations employing the exchange-correlation functional of Perdew, Burke, and Ernzerhof. The accuracy of the presented approach is much higher than that of dRPA methods and is comparable to that of high-level wave function methods. Reaction and transition state energies from σ-functionals exhibit accuracies close to 1 kcal/mol and thus approach chemical accuracy. For the 10 966 reactions of the W4-11RE reference set, the mean absolute deviation is 1.25 kcal/mol compared to 3.21 kcal/mol in the dRPA case. Non-covalent binding energies are accurate to a few tenths of a kcal/mol. The presented approach is highly efficient, and the post-self-consistent calculation of the total energy requires less computational time than a density-functional calculation with a hybrid functional and thus can be easily carried out routinely. σ-Functionals can be implemented in any existing dRPA code with negligible programming effort.

Investigation on response function of terahertz air coherent detection technique

Terahertz (THz) air coherent detection is a broadband coherent detection technique, which has been used widely in the THz science and technology. In this paper, a frequency-dependent response function of THz air coherent detection is defined based on the nonlinear polarization of gas molecules induced by the ultrashort laser pulses and the THz pulses. Calculations show that the response function of this technique has a half of Gaussian-like profile, which has a high sensitivity in the low frequency range and low sensitivity in the high frequency range of THz waves. Two fitted functions are given based on the calculated results, which can provide a good reference bandwidth when using the air coherent detection with a given probe laser pulse. The distortions of THz pulses induced by the air coherent detection in the detection process are discussed as well. This study will help to understand the response bandwidth and the limitation of detection bandwidth of the air coherent detection technique.

Systematic bottom-up theory for the viscoelastic response of worm-like chain networks

Using the frequency-dependent force-extension response functions of single worm-like chains as the only input, the linear complex viscoelastic modulus of a polymeric network with given connectivity is derived from a systematic bottom-up theory via iterative coarse-graining. Choosing a cubic connectivity and accounting for random network orientation, we find excellent agreement with experimental data for actin networks under shear over the entire frequency range with the strength of the osmotic pressure that acts within the polymeric network as the only fitting parameter. In particular, we obtain a viscoelastic plateau regime at low frequencies and a crossover to an intermediate-frequency regime characterized by a power law behavior and an inhomogeneous shear deformation field.

Nonequilibrium quantum solvation with a time-dependent Onsager cavity.

We formulate a theory of nonequilibrium quantum solvation in which parameters of the solvent are explicitly depending on time. We assume in a simplest approach a spherical molecular Onsager cavity with a time-dependent radius. We analyze the relaxation properties of a test molecular point dipole in a dielectric solvent and consider two cases: (i) a shrinking Onsager sphere and (ii) a breathing Onsager sphere. Due to the time-dependent solvent, the frequency-dependent response function of the dipole becomes time-dependent. For a shrinking Onsager sphere, the dipole relaxation is in general enhanced. This is reflected in a temporally increasing linewidth of the absorptive part of the response. Furthermore, the effective frequency-dependent response function shows two peaks in the absorptive part which are symmetrically shifted around the eigenfrequency. By contrast, a breathing sphere reduces damping as compared to the static sphere. Interestingly, we find a non-monotonous dependence of the relaxation rate on the breathing rate and a resonant suppression of damping when both rates are comparable. Moreover, the linewidth of the absorptive part of the response function is strongly reduced for times when the breathing sphere reaches its maximal extension.

A QM/MM and QM/QM/MM study of Kerr, Cotton-Mouton and Jones linear birefringences in liquid acetonitrile.

QM/MM and QM/QM/MM protocols are applied to the ab initio study of the three linear birefringences Kerr, Cotton-Mouton, and Jones, as shown by acetonitrile in the gas and pure liquid phases. The relevant first-order properties as well as linear, quadratic, and cubic frequency-dependent response functions were computed using time-dependent Kohn-Sham density-functional theory with use of the standard CAM-B3LYP functional. In the liquid phase, a series of room temperature (293.15 K) molecular dynamics snapshots were selected, for which averaged values of the observables were obtained at an optical wavelength of 632.8 nm. The birefringences were computed for electric and magnetic induction fields corresponding to the laboratory setup previously employed by T. Roth and G. L. J. A. Rikken in Phys. Rev. Lett., 2000, 85, 4478. Under these conditions, acetonitrile is shown to exhibit a weak Jones response-in fact roughly 6.5 times smaller than the limit of detection of the apparatus employed in the measurements mentioned above. A comparison is made with the corresponding gas-phase results and an assessment is made of the index of measurability, estimating the degree of overlap of the three birefringences in actual measurements. For acetonitrile, it is shown that this index is a factor of 3.6 and 6.7 larger than that of methylcyclopentadienyl-Mn-tricarbonyl and cyclohexadienyl-Fe-tricarbonyl, respectively-two compounds reported in Phys. Rev. Lett., 2000, 85, 4478 to exhibit a strong Jones signal.

Technique developments and performance analysis of chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering combustion thermometry.

This work characterizes the state of the art in the analysis of high-repetition-rate, ultrafast combustion thermometry using chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering (CPP fs-CARS). Several key aspects of the CARS spectroscopy system are described, including: (1)the ultrafast laser source, (2)use of the frequency-doubled idler versus signal from the optical parametric amplifier, (3)the geometry constraints for phase matching, and (4)spectral fitting for single-shot temperature measurements. A frequency-dependent instrument response function (IRF) for the detection system was modeled as a variable-width Gaussian and implemented through a frequency convolution of synthetic spectra. Proper accounting of the IRF increased spectral fitting performance in the high-frequency region where signal oscillations are weaker and narrower. Aggregated data from 25 system performance assessments taken over four months yielded accuracy and precision of 2.7% and ±3.5% for flame temperatures, and 9.9% and ±6.1% at room temperature, using the commonly reported method. A new processing technique, based on the statistical method of maximum likelihood, was implemented for turbulent flames where strong fluctuations in expected temperatures necessitate use of multiple temperature calibrations. Results from multiple sets of laser parameters are combined to generate an error-weighted temperature from the top-performing calibrations. A testing procedure was designed to characterize system performance when the range of expected temperatures is unknown, simulating the random temperature field of a highly turbulent flame. Accuracy error of the CPP fs-CARS system increased in this more-stressing test at all temperatures, but precision was significantly affected only at room temperature. System stability is characterized, and the contribution from shot-to-shot laser fluctuations on measurement precision is quantified. Finally, the near-adiabatic and steady assumptions for the Hencken burner calibration flame are examined in an axial scan; significant deviations from ideal behavior were observed only at heights of more than four diameters above the burner surface.

Monte Carlo simulations of measured electron energy-loss spectra of diamond and graphite: Role of dielectric-response models

In this work we compare Monte Carlo (MC) simulations of electron-transport properties with reflection electron energy-loss measurements in diamond and graphite films. We assess the impact of different approximations of the dielectric response on the observables of interest for the characterization of carbon-based materials. We calculate the frequency-dependent dielectric response and energy-loss functions of these materials in two ways: a full ab initio approach, in which we carry out time-dependent density functional simulations in linear response for different momentum transfers, and a semi-classical model, based on the Drude–Lorentz extension to finite momenta of the optical dielectric function. Ab initio calculated dielectric functions lead to better agreement with measured energy-loss spectra compared to the widely used Drude–Lorentz model. This discrepancy is particularly evident for insulators and semiconductors beyond the optical limit (q≠0), where single-particle excitations become relevant. Furthermore, we show that the behaviour of the energy-loss function obtained at different accuracy levels has a dramatic effect on other physical observables, such as the inelastic mean free path and the stopping power in the low energy (<100 eV) regime and thus on the accuracy of MC simulations.

Electronic structure, dielectric response, and surface charge distribution of RGD (1FUV) peptide.

Long and short range molecular interactions govern molecular recognition and self-assembly of biological macromolecules. Microscopic parameters in the theories of these molecular interactions are either phenomenological or need to be calculated within a microscopic theory. We report a unified methodology for the ab initio quantum mechanical (QM) calculation that yields all the microscopic parameters, namely the partial charges as well as the frequency-dependent dielectric response function, that can then be taken as input for macroscopic theories of electrostatic, polar, and van der Waals-London dispersion intermolecular forces. We apply this methodology to obtain the electronic structure of the cyclic tripeptide RGD-4C (1FUV). This ab initio unified methodology yields the relevant parameters entering the long range interactions of biological macromolecules, providing accurate data for the partial charge distribution and the frequency-dependent dielectric response function of this peptide. These microscopic parameters determine the range and strength of the intricate intermolecular interactions between potential docking sites of the RGD-4C ligand and its integrin receptor.

Impulse and Resonant Response in Systems Showing Secular and Leaky Excitations

A model consisting of a string embedded in an elastic medium and terminated by a harmonic oscillator has been studied in the frequency and time domains to elucidate the physical e ects of supersonic and subsonic leaky waves as well as that of true surface waves. A supersonic leaky wave manifests itself by a resonant maximum of the local density of states within the band of bulk waves and by an anomalous dispersion of the real part of the frequency dependent response function. The time domain impulse response then contains mainly resonant contribution from the poles of the response function in analogy to ordinary resonances. True surface waves show generally analogous behaviour. Here, however, the phenomenon is governed by dissipation mechanisms di erent from the radiation into the bulk. An important di erence is that the impulse response contains equilibrated contributions due to the poles and due to the stop frequency gap in the case of true surface waves. The main manifestation of a subsonic leaky wave, i.e. a surface resonance with the frequency situated in the stop gap, is a sharp peak of the real part of the frequency-dependent response function just at the bottom of the bulk waves band. This is in certain analogy with a large reactive power in electric circuits. A strong destructive interference of the resonant part of the impulse response with the part due to the gap makes the time domain response fast attenuated.

Dissipative electro-elastic network model of protein electrostatics

We propose a dissipative electro-elastic network model to describe the dynamics and statistics of electrostatic fluctuations at active sites of proteins. The model combines the harmonic network of residue beads with overdamped dynamics of the normal modes of the network characterized by two friction coefficients. The electrostatic component is introduced to the model through atomic charges of the protein force field. The overall effect of the electrostatic fluctuations of the network is recorded through the frequency-dependent response functions of the electrostatic potential and electric field at the protein active site. We also consider the dynamics of displacements of individual residues in the network and the dynamics of distances between pairs of residues. The model is tested against loss spectra of residue displacements and the electrostatic potential and electric field at the heme's iron from all-atom molecular dynamics simulations of three hydrated globular proteins.

Improving accuracy and efficiency of calculations of photoemission spectra within the many-body perturbation theory

We present an approach to evaluate quasiparticle energies within many-body perturbation theory that substantially improves both the computational efficiency and numerical accuracy of existing techniques. We use the eigenvectors of the static dielectric matrix as a basis for the frequency-dependent density-density response function, and density functional perturbation theory to avoid the explicit calculation of empty electronic states, and storage and inversion of large dielectric matrices. The numerical accuracy of our approach is controlled by a single parameter that can be systematically varied to test the convergence of the computed quasiparticle energies. We discuss the advantages of the technique by presenting the calculations of the vertical ionization potential and electron affinity of several molecules and clusters, including benzene and diamondoids.

Microstructure, transport, and acoustic properties of open-cell foam samples: Experiments and three-dimensional numerical simulations

This article explores the applicability of numerical homogenization techniques for analyzing transport properties in real foam samples, mostly open-cell, to understand long-wavelength acoustics of rigid-frame air-saturated porous media on the basis of microstructural parameters. Experimental characterization of porosity and permeability of real foam samples are used to provide the scaling of a polyhedral unit-cell. The Stokes, Laplace, and diffusion-controlled reaction equations are numerically solved in such media by a finite element method in three-dimensions; an estimation of the materials’ transport parameters is derived from these solution fields. The frequency-dependent visco-inertial and thermal response functions governing the long-wavelength acoustic wave propagation in rigid-frame porous materials are then determined from generic approximate but robust models and compared to standing wave tube measurements. With no adjustable constant, the predicted quantities were found to be in acceptable agreement with multi-scale experimental data and further analyzed in light of scanning electron micrograph observations and critical path considerations.

Strongly correlating liquids and their isomorphs

This paper summarizes the properties of strongly correlating liquids, i.e., liquids for which the virial/potential energy correlation coefficient is above 0.9 for equilibrium fluctuations in the NVT ensemble. The definition and properties of strongly correlating liquids' isomorphs are given, and various isomorph invariants are discussed. The cause of strong virial/potential energy correlations is also discussed, and it is argued that strongly correlating liquids are not merely to be thought of as approximate inverse power-law liquids. The experimental predictions for strongly correlating glass-forming liquids include: i) density scaling; ii) isochronal superposition; iii) that there is a single function of frequency from which all frequency-dependent viscoelastic response functions may be calculated; iv) that strongly correlating liquids are approximately single-parameter liquids with close to unity Prigogine–Defay ratio; v) that the fictive temperature initially decreases for an isobaric temperature up jump. The paper also briefly discusses the “isomorph filter”, which provides a necessary condition for universality of theories for the non-Arrhenius temperature dependence of the relaxation time.

A combined measurement of thermal and mechanical relaxation

In order to describe relaxation the thermodynamic coefficient 1 β S = ( ∂ V ∂ S ) p can be generalized into a complex frequency-dependent cross response function. We explore theoretically the possibility of measuring 1 β S ( ω ) for a supercooled liquid near the glass transition. This is done by placing a thermistor in the middle of the liquid which itself is contained in a spherical piezoelectric shell. The piezoelectric voltage response to a thermal power generated in the thermistor is found to be proportional to 1 β S ( ω ) but factors pertaining to heat diffusion and adiabatic compressibility κ S ( ω) do also intervene. We estimate a measurable piezoelectric voltage of 1 mV to be generated at 1 Hz for a heating power of 0.3 mW. Together with κ S ( ω) and the longitudinal specific heat c l ( ω) which may also be found in the same setup a complete triple of thermoviscoelastic response functions may be determined when supplemented with shear modulus data.

INTERFEROMETRIC DETECTION OF GRAVITATIONAL WAVES: THE DEFINITIVE TEST FOR GENERAL RELATIVITY

Even though Einstein's general relativity has achieved great success and passed a lot of experimental tests, it has also shown some shortcomings and flaws which today prompt theorists to ask if it is the definitive theory of gravity. In this essay we show that if advanced projects on the detection of gravitational waves (GWs) improve their sensitivity, allowing us to perform a GW astronomy then accurate angle- and frequency-dependent response functions of interferometers for GWs arising from various theories of gravity, i.e. general relativity and extended theories of gravity, will be the definitive test for general relativity. The papers mentioned in this essay were the world's most-cited in 2007 of the Astroparticle Publication Review of ASPERA with 13 citations.

Blindness of the Exact Density Response Function to Certain Types of Electronic Excitations: Implications for Time-Dependent Density-Functional Theory

Examples of electronic excitations are presented and discussed that do not contribute to the sum-over-state expression of the frequency-dependent density-density response function and thus do not lead to poles of the latter. As a consequence, these excitations principally cannot be described by time-dependent density-functional theory (TDDFT) response methods or any other method relying on the poles of the density-density response function. For these excitations, the DFT response approach commonly used in molecular physics or quantum chemistry is shown to not properly represent a DFT method and to yield differences of Kohn-Sham eigenvalues as excitation energies. The discussed examples are simple valence-valence excitations in the neon atom and the nitrogen molecule.