Dipole Moment Correlation Function Research Articles

Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms

Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD algorithms have focused on solving the eigenpair problem for ground, excited-state, and thermal observable estimation, there has been a lot less work in considering QSD algorithms for the problem of quantum dynamical simulation. In this work, we propose several quantum Krylov fast-forwarding (QKFF) algorithms capable of predicting long-time dynamics well beyond the coherence time of current quantum hardware. Our algorithms use real-time evolved Krylov basis states prepared on the quantum computer and a multi-reference subspace method to ensure convergence towards high-fidelity, long-time dynamics. In particular, we show that the proposed multi-reference methodology provides a systematic way of trading off circuit depth with classical post-processing complexity. We also demonstrate the efficacy of our approach through numerical implementations for several quantum chemistry problems including the calculation of the auto-correlation and dipole moment correlation functions

Computational Evidence for the Crucial Role of Dipole Cross-Correlations in Polar Glass-Forming Liquids.

In this Letter, we analyze the dipole-dipole correlations obtained from the molecular dynamics simulations for strongly and weakly polar model liquids. As a result, we find that the cross-correlations' contribution to the system's total dipole moment correlation function, which is directly measured in the dielectric spectroscopy experiment, is negligible for weakly polar liquids. In contrast, the cross-correlations' term dominates over the self-correlations' term for the examined strongly polar liquid. Consequently, our studies strongly support the interpretation of the dielectric spectra nature of glass-forming liquids recently proposed by Pabst etal.

Spectroscopy of Vibronically Coupled and Duschinskcally Rotated Polyatomic Molecules.

Electron-vibration coupling (or vibronic coupling) of polyatomic molecules in the condensed phase has received considerable attention experimentally and theoretically using linear spectroscopy and four-wave mixing techniques in an effort to probe the structure and dynamics of the system at hand. For this reason, a detailed study of vibronic coupling in harmonic polyatomic molecules featuring a greater degree of computational efficiency is presented. A full treatment of non-Condon systems whereupon linear and nonlinear Herzberg-Teller vibronic coupling and Duschinsky mixing effects in harmonic systems taking place upon electronic excitation is provided. The utilization of an exponential function to express the nuclear dependence of the electronic transition dipole moment, thereby avoiding the finite sum and eigenstate representation that is normally used in computing a non-Condon interaction, leads to a simpler electronic transition dipole moment time correlation function with rapid convergence and better numerical stability than previously reported works. A closed-form expression is obtained for the electronic transition dipole moment time correlation function of polyatomic molecules in which linear and nonlinear Herzberg-Teller vibronic coupling and Duschinsky mixing effects are accounted for. An important numerical observation regarding dealing with branch cuts, which manifest themselves as discontinuities in the function itself or its first derivative, and are often exhibited by complex-valued correlation functions, is noted and treated using the Riemann surface approach. The resultant dipole moment correlation function is in turn employed to calculate linear absorption and hole-burning signals, accounting for the aforementioned spectroscopic effects. A link between wavelets and the electronic transition dipole moment time correlation function in multidimensional harmonic systems is made in the concluding remarks.

Molecular dynamics simulation of collision-induced absorption spectra of neon-krypton mixture thin layer confined between graphite walls

Molecular dynamics (MD) simulations have been used to calculate interaction-induced absorption spectra of neon-krypton mixture confined between graphite plates. The continuous phenomenological model with parameters fitted to couple clusters (CC) quantum mechanical method has been applied to calculate collision-induced dipole moments. The collision-induced dipole moment correlation functions and its 2, 3, 4-body contributions of Ne-Kr binary mixture at three temperatures have been calculated and analyzed. The dynamics of neon and krypton atoms between graphite slabs have been investigated by the mean square displacement functions and z-profile functions. The phase separation between neon and krypton has been observed at T=100K in the direction perpendicular to the graphite surface. We have found that collision-induced absorption spectra reflect the mobility of noble gas atoms in binary mixture between graphite slabs.

Influence of hydrogen bonds and temperature on dielectric properties.

Dielectric properties are evaluated by means of molecular dynamics simulations on two model systems made up of dipolar molecules. One of them mimics methanol, whereas the other differs from the former only in the ability to form hydrogen bonds. Static dielectric properties such as the permittivity and the Kirkwood factor are evaluated, and results are analyzed by considering the distribution of relative orientations between molecular dipoles. Dipole moment-time correlation functions are also evaluated. The relevance of contributions associated with autocorrelations of molecular dipoles and with cross-correlations between dipoles belonging to different molecules has been investigated. For methanol, the Debye approximation for the overall dipole moment correlation function is not valid at room temperature. The model applies when hydrogen bonds are suppressed, but it fails upon cooling the nonassociated liquid. Important differences between relaxation times associated with dipole auto- versus cross-correlations as well as their relative relevance are at the root of the Debye model breakdown.

Effects of concentration on structure, dielectric, and dynamic properties of aqueous NaCl solutions using a polarizable model

The study of NaCl solutions in water at finite concentration, explicitly including polarization in water molecules and ions, has been carried out by molecular dynamics simulations. A comparison of the RPOL polarizable model with the rigid SPC/E potential for water has been included. Structure obtained with the two models does not show significant differences, although some deviations in the NaNa radial distribution functions at all concentrations are observed. Dielectric properties such as total and molecular dipole moment correlation functions revealed decay times of the order of 10 ps, roughly independent of concentration. The analysis of electric conductivity by means of current-current correlation functions also included the calculation of cross terms corresponding to dipole moment-current correlations, which proved to be non-neglectable at short times and especially relevant at high concentrations (m=4 mol kg(-1)). Frequency dependent dielectric constants and conductivities have been computed and the role of cross correlations has been analyzed. In all cases both concentration and cross correlations have significant influence in the results.

Casimir-Polder effect for a plane with Chern-Simons interaction

A novel formalism for the evaluation of the Casimir-Polder potential in an arbitrary gauge of vector potentials is introduced. The ground state energy of a neutral atom in the presence of an infinite two-dimensional plane with Chern-Simons interaction is derived at zero temperature. The essential feature of the result is its dependence on the antisymmetric part of a dipole moment correlation function.

Terahertz response of dipolar impurities in polar liquids: On anomalous dielectric absorption of protein solutions

A theory of radiation absorption by dielectric mixtures is presented. The coarse-grained formulation is based on the wave-vector-dependent correlation functions of molecular dipoles of the host polar liquid and a density structure factor of the solutes. A nonlinear dependence of the dielectric absorption coefficient on the solute concentration is predicted and originates from the mutual polarization of the liquid surrounding the solutes by the collective field of the solute dipoles aligned along the radiation field. The theory is applied to terahertz absorption of hydrated saccharides and proteins. While the theory gives an excellent account of the observations for saccharides, without additional assumptions and fitting parameters, experimental absorption coefficient of protein solutions significantly exceeds theoretical calculations with dipole moment of the bare protein assigned to the solute and shows a peak against the protein concentration. A substantial polarization of protein's hydration shell, resulting in a net dipole moment, is required to explain the disagreement between theory and experiment. When the correlation function of the total dipole moment of the protein with its hydration shell from numerical simulations is used in the analytical model, an absorption peak, qualitatively similar to that seen in experiment, is obtained. The existence and position of the peak are sensitive to the specifics of the protein-protein interactions. Numerical testing of the theory requires the combination of dielectric and small-angle scattering measurements. The calculations confirm that "elastic ferroelectric bag" of water shells observed in previous numerical simulations is required to explain terahertz dielectric measurements.

Structure and Mobility of Poly(ethylene terephthalate): A Molecular Dynamics Simulation Study

An accurate force-field has been parametrized for PET and is employed to simulate a long chain, consisting of 120 repeat units, over a wide temperature and pressure range, for long time scales. The force field has been validated against the experimental results for the pressure−volume−temperature properties, the characteristic ratio, the dipolar ratio, and the population of ethylene glycol bond conformer. In all cases the agreement with experiment is quite good. The glass transition temperature is calculated very accurately as a function of pressure. The local dynamics of the chain has been investigated by calculating phenylene reorientation, collective dipole moment, and individual dipole moment correlation functions. The calculated relaxation times for collective dipole moment and phenylene reorientation correlation functions show activation energies close to the corresponding experimental β-relaxation value. Local translational mobilities of phenylene groups in the backbone and end phenylene groups have also been investigated. It is concluded that the end groups have much higher mobility than the polymer backbone, and increasing the distance from the chain ends decreases the mobility dramatically. The long-time asymptotic slope of chain displacement at temperatures higher than the glass transition temperature is around 0.65 in close agreement with Rouse model. On the other hand at the glassy state, the polymer segments perform very restricted movements in the cages formed by their surrounding segments.

Dependence of low frequency spectra on solute and solvent in solutions studied by terahertz time-domain spectroscopy

This paper presents the results of measuring the frequency-dependent refractive index, the extinction coefficient, and the absorption coefficient of polar solutes (nitrobenzene, benzonitrile, and chlorobenzene) in non-polar solvents by using terahertz time-domain spectroscopy (THz-TDS) at room temperature. The intensities of the difference absorption spectra of the solution and the pure solvent show a specific peak for each particular solution. This finding demonstrates the potential application of THz-TDS in studying the microscopic details of a particular solute in solution. The low frequency spectra were analysed by using a model function for the time correlation function of the total dipole moment in order to understand the dynamics and the interactions in the systems. The picosecond exponential component was found to be less sensitive to the viscosity of the bulk solvent, and it is proposed that this component can be regarded as the result of structural relaxation in the solution. It was also found that the spectra of the benzonitrile solutions receive a large contribution from the Gaussian component, which is attributed to the librational motion. This suggests that the formation of dimers or oligomers might take place in the case of the benzonitrile solution.

Empirical relaxation function and spectral density for underdamped vibrations at low temperatures

A new relaxation function which accounts for electronic dephasing (electronic phase loss and excited state lifetime) is presented, whose applicability for underdamped motion at low temperatures is examined in detail. This new empirical relaxation function phi(t) yields linear and nonlinear spectral/temporal profiles that render accurate dephasing time in the underdamped regime. The relaxation function phi(t) is normally expressed in terms of the coupling functions M(j) (') and M(j) (") on which the time evolution of the vibrational modes in question depends. The corresponding spectral density, which is a central quantity in probing dynamics, is derived and compared to that of the multimode Brownian oscillator model. Derivation and discussion of the new position and momentum autocorrelation functions in terms of our new spectral density are presented. While the position autocorrelation function plays a key role in representing solvation structure in polar or nonpolar medium, the momentum correlation function projects out the molecular vibrational motion. The Liouville space generating function (LGF) for harmonic and anharmonic systems is expressed in terms of our new empirical phi(t) and spectral density, leading to more physical observation. Several statistical quantities are derived from the position and momentum correlation function, which in turn contribute to LGF. Model calculations reflecting the infinite population decay in the low temperature limit in linear and nonlinear spectroscopic signals are presented. The herein quantum dipole moment correlation function is compared to that derived in [M. Toutounji, J. Chem. Phys. 118, 5319 (2003)] using mixed quantum-classical dynamics framework, yielding reasonable results, in fact identical at higher temperatures. The results herein are found to be informative, useful, and consistent with experiments.

Algebraic approach to electronic spectroscopy and dynamics

Lie algebra, Zassenhaus, and parameter differentiation techniques are utilized to break up the exponential of a bilinear Hamiltonian operator into a product of noncommuting exponential operators by the virtue of the theory of Wei and Norman [J. Math. Phys. 4, 575 (1963); Proc. Am. Math. Soc., 15, 327 (1964)]. There are about three different ways to find the Zassenhaus exponents, namely, binomial expansion, Suzuki formula, and q-exponential transformation. A fourth, and most reliable method, is provided. Since linearly displaced and distorted (curvature change upon excitation/emission) Hamiltonian and spin-boson Hamiltonian may be classified as bilinear Hamiltonians, the presented algebraic algorithm (exponential operator disentanglement exploiting six-dimensional Lie algebra case) should be useful in spin-boson problems. The linearly displaced and distorted Hamiltonian exponential is only treated here. While the spin-boson model is used here only as a demonstration of the idea, the herein approach is more general and powerful than the specific example treated. The optical linear dipole moment correlation function is algebraically derived using the above mentioned methods and coherent states. Coherent states are eigenvectors of the bosonic lowering operator a and not of the raising operator a(+). While exp(a(+)) translates coherent states, exp(a(+)a(+)) operation on coherent states has always been a challenge, as a(+) has no eigenvectors. Three approaches, and the results, of that operation are provided. Linear absorption spectra are derived, calculated, and discussed. The linear dipole moment correlation function for the pure quadratic coupling case is expressed in terms of Legendre polynomials to better show the even vibronic transitions in the absorption spectrum. Comparison of the present line shapes to those calculated by other methods is provided. Franck-Condon factors for both linear and quadratic couplings are exactly accounted for by the herein calculated linear absorption spectra. This new methodology should easily pave the way to calculating the four-point correlation function, F(tau(1),tau(2),tau(3),tau(4)), of which the optical nonlinear response function may be procured, as evaluating F(tau(1),tau(2),tau(3),tau(4)) is only evaluating the optical linear dipole moment correlation function iteratively over different time intervals, which should allow calculating various optical nonlinear temporal/spectral signals.

Mixed quantum-classical description of spectroscopy of dissipative systems

Mixed quantum-classical statistical mechanics is employed to calculate dipole moment correlation function and linear absorption spectra. A quantum two-level subsystem interacting with quantum vibrations (primary oscillators) which in turn are coupled to a classical bath composed of infinite set of harmonic oscillators is used as a dissipative system. Starting with mixed quantum-classical Liouville equation for the evaluation of the mixed quantum-classical dipole moment correlation function and using coherent states and the inverse of Baker-Campbell-Hausdorf formula to evaluate the trace over the primary oscillators, whereby, a closed analytical expression for the electronic dipole moment correlation function is obtained. Illustrations of several absorption spectra at different temperatures are provided. An approximate optical four-point correlation is obtained in the high temperature limit. A strategy for deriving an exact optical four-point correlation is suggested.

Apparent phonon side-band modes in π-conjugated systems: Polymers, oligomers and crystals

The emission spectra of many π-conjugated polymers and oligomers contain side-band replicas with apparent frequencies that do not match the Raman active mode frequencies. Using a time dependent model we show that in such many mode systems, the increased damping of the time dependent transition dipole moment correlation function results in an effective elimination of the vibrational modes from the emission spectrum; subsequently causing the appearance of a regularly spaced progression at a new apparent frequency. We use this damping dependent vibrational reshaping to quantitatively account for the vibronic structure in the emission spectra of π-conjugated systems in the form of films, dilute solutions and single crystals. In particular, we show that by using the experimentally measured Raman spectrum we can account in detail for the apparent progression frequencies and their relative intensities in the emission spectrum.

Vibrational spectra from atomic fluctuations in dynamics simulations. II. Solvent-induced frequency fluctuations at femtosecond time resolution

The midinfrared (MIR) spectra of molecules in polar solvents exhibit inhomogeneously broadened bands whose spectral positions are shifted as compared to the gas phase. The shifts are caused by interactions with structured solvation shells and the broadenings by fluctuations of these interactions. The MIR spectra can be calculated from hybrid molecular dynamics (MD) simulations, which treat the solute molecule by density functional theory and the solvent by molecular mechanics by the so-called instantaneous normal mode analysis (INMA) or by Fourier transforming the time correlation function (FTTCF) of the molecular dipole moment. In Paper I of this work [M. Schmitz and P. Tavan, J. Chem. Phys. 121, 12233 (2004)] we explored an alternative method based on generalized virial (GV) frequencies noting, however, that GV systematically underestimates frequencies. As shown by us these artifacts are caused by solvent-induced fluctuations of the (i) equilibrium geometry, (ii) force constants, and (iii) normal mode directions as well as by (iv) diagonal and (v) off-diagonal anharmonicities. Here we now show, by analyzing the time scales of fluctuations and sample MD trajectories of formaldehyde in the gas phase and in water, that all these sources of computational artifacts can be made visible by a Fourier analysis of the normal coordinates. Correspondingly, the error sources (i) and (iii)-(v) can be removed by bandpass filtering, as long as the spectral signatures of the respective effects are well separated from the fundamental band. Furthermore, the artifacts arising from effect (ii) can be strongly diminished by a time-resolved version of the GV approach (TF-GV). The TF-GV method then yields for each mode j a trajectory of the vibrational frequency omega(j)(tmid R:tau) at a time resolution tau>tau(j), which is only limited by the corresponding oscillation time tau(j)=2pi/omega(j) and, thus, is in the femtosecond range. A correlation analysis of these trajectories clearly separates the librational motions from the conformational dynamics of the solvation shells and yields the inhomogeneously broadened MIR spectra, if the theory of motional narrowing is properly included. The MIR spectrum of formaldehyde in solution obtained by TF-GV agrees very well with the FTTCF result, if one applies the so-called "harmonic approximation" quantum correction factor and a temperature scaling to the FTTCF intensities. Also for INMA an excellent agreement is achieved if one disregards a slight INMA overestimate of linewidths.

Optical linear response function with linear and diagonal quadratic electron-vibration coupling in mixed quantum-classical systems.

Optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed phase systems is derived. The linear response function is derived using Kapral's formalism of statistical mechanics in mixed quantum-classical systems. Our mixed quantum-classical linear dipole moment correlation function J(t) is compared with the full quantum J(t) [Y. J. Yan and S. Mukamel, J. Chem. Phys. 85, 5908 (1986)] in the high temperature limit. Model calculations and discussion of our results are presented. Various formulas of Franck-Condon factors for both linear and quadratic coupling are discussed.

Dipolar absorption in liquid cyanoadamantane cluster—computer simulations

We have studied the dipolar absorption in the liquid phase of small cyanoadamantane C 10H 15CN cluster composed of only 19 molecules, using the molecular dynamics (MD) method. Particularly, the total dipole moment correlation functions and the dipolar absorption spectra have been studied as a function of temperature.

Thermally activated escape rate for the Brownian motion of a fixed axis rotator in a double well potential for all values of the dissipation.

The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel'nikov and Meshkov [J. Chem, Phys. 85, 1018 (1986)] is applied to the rotational Brownian motion of fixed axis rotators in a double well cosine potential. The procedure yields an expression for the Kramers escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes. This equation provides a good asymptotic estimate of the correlation time tau per pendicular of the longitudinal dipole moment correlation function calculated by solving the underlying Langevin equation using the matrix-continued fraction method. Moreover, for low barriers, where the Mel'nikov and Meshkov approach is not applicable, analytic equations for tau in the VLD and VHD limits are derived and a simple extrapolating equation that is valid for all values of the damping is proposed.

Reply to the Comment by S. Boresch and O. Steinhauser on the Letter by N. Nandi and B. Bagchi Entitled “Anomalous Dielectric Relaxation of Aqueous Protein Solution”

In their Comment about the theoretical treatment of Nandi and Bagchi (referred to as NB)1 on the dielectric relaxation of aqueous protein solution, Boresch and Steinhauser (referred to as BS)2 claimed to find several shortcomings of the theoretical treatment of NB. To put the issue in perspective, we reconcile that the observed anomalies were explained by NB assuming that the total dipole moment correlation function is composed of the self- and cross-correlations between the three dynamical species present in the solution. Major objections about this work as raised by BS are 2-fold (i) presence of a factor of (1/N) in the exact expression of dielectric function (eq 2.1 in ref 1) and (ii) interpretation of the correlation factor used in ref 1. We thank BS for their comments on our work, although we disagreewith many of their comments. Our response is given below.

Molecular Dynamics Simulations of Polar Polymer Brushes

Brushes of end-grafted, polar polymer chains in a good, nonpolar solvent are studied via molecular dynamics simulations of a bead-spring model. The monomers are connected by finitely extensible nonlinear springs. The springs connecting consecutive monomers in a chain are labeled with dipoles parallel to the chain contour. We consider the dipoles as limits of charge pairs, replacing each dipole by a pair of charges positioned at the centers of mass of two consecutive beads. Equilibrium simulations are performed, and the static and dynamic properties of the chains are related to the dipole magnitude. It was found that the electrostatic interactions lead to a shorter brush and the collapse becomes more pronounced with increasing segmental dipole moment. The dielectric relaxation of the tethered chains is studied, and the dielectric permittivity is obtained from equilibrium dipole moment correlation functions. Results on the dielectric relaxation of tethered chains from experiments conducted by Yao et al. exhibited a broader dielectric dispersion spectrum than that of free macromolecules in homogeneous solutions. These authors attributed the results to the thermodynamic confinement (to keep uniform segment density) and the spatial confinement that prohibits a chain to cross the tethering domain boundary. The simulations indicate that neither the spatial confinement nor the thermodynamic confinement lead to a broader dielectric dispersion spectrum for the tethered chains, and we attribute the discrepancies to the morphology differences between the experimental system and the simulated one. Weak electric fields parallel and perpendicular to the grafting surface are applied, and the system response is related to the equilibrium fluctuations. We also examine the structural properties of the brushes at steady state under the influence of external electric fields.