Frequency-dependent polarizability of open-shell atomic systems

The time-dependent variational principle is used to calculate the frequency-dependent dipole polarizabilities of 2p open-shell atomic systems. A general theory is built up to include frequency-dependent perturbations using the Roothaan–Hartree–Fock (HFR) formalism. The excitation energies corresponding to the low-lying excited states of the system are obtained from the poles of the dynamic polarizability values. A fairly accurate knowledge of transition oscillator strengths is also obtained from a knowledge of the polarizability values near the poles. The excitation energies and oscillator strengths are compared with available data.     

Frequency-dependent dielectric permittivity of salt-free charged lamellar systems

We present a new model to analyze dielectric spectroscopy measurements on charged lamellar systems, with the following improvements with respect to the hitherto available models: (i) it does not rely on the hypothesis of local electro-neutrality, and allows to treat the salt-free case; (ii) the chemical exchange governing the partition between free and bound ions is properly taken into account; (iii) a fully analytical solution is provided. The variation of the frequency-dependent dielectric permittivity with both thermodynamic and kinetic characteristics of the free-bound ion equilibrium is presented. In particular, the relative weights of both relaxation modes (exchange and transport), and their characteristic frequencies are discussed. This study opens the way to the analysis of systems for which the usual models are irrelevant, such as salt-free clay gels or membranes.     

Limitation of linear response in flow-injection systems with ion-selective electrodes

The lower limit of linear response in flow-injection systems employing membrane and second-kind ion-selective electrodes as detectors depends on the dispersion in the system and is usually much worse than in batch measurements. Below a certain value of the peak height, linearity of the electrode response is not maintained. The limiting value depends on the process causing the loss of linear response (solubility of the electrode material, contamination, or adsorption at the electrode surface), and varies from 15 to 70 mV. Chloride- iodide-, fluoride- and copper(II)-selective electrodes are discussed.     

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.     

Quantum-field theory and electrodynamics of superconducting systems

By using quantum-field theory techniques and the boson transformation method, we study systems that exhibit macroscopic ordered states. As an illustration, we apply the method to the study of superconducting systems by taking into account the quantization of the vector potential. The results of a dynamical calculation, performed in the pair approximation, are presented. The Higgs phenomenon is also discussed in the framework of a fully quantum theory.     

Frequency-dependent response properties and excitation energies from one-electron density matrix functionals

The recent formulation of the time-dependent density matrix functional theory (TD-DMFT) has opened an avenue to calculations of frequency-dependent response properties and excitation energies of atoms and molecules. In practice, the accuracy of the computed data is limited by both the errors inherent to the adiabatic approximation or its modifications and the quality of the energy functionals. The relative importance of these two factors is carefully assessed with test calculations on diatomic molecules with few electrons. The test results clearly demonstrate the superiority of an ad hoc approach that corrects the improper behavior of the adiabatic approximation at the low-frequency limit. Even more importantly, TD-DMFT convincingly removes the ambiguity in the choice of the two-electron integrals that is present in the stationary-state case. On the other hand, paralleling the previously reached conclusions pertinent to ionization potentials, the presently available BBC-type functionals are found to be insufficiently accurate to provide reliable quantitative predictions of excitation energies.     

Frequency-dependent electroosmosis

This paper presents a theory for frequency-dependent electroosmosis. It is shown that for a closed capillary the electroosmosis frequency-dependent ratio of DeltaV/DeltaP is constant with increasing frequency until inertial effects become prevalent, at which time DeltaV/DeltaP starts to decrease with increasing frequency. The frequency response of the electroosmosis coupling coefficient is shown to be dependent on the capillary radius. As the capillary radius is made smaller, inertial effects start to occur at higher frequencies. As part of this paper, frequency-dependent electroosmosis is compared to frequency-dependent streaming potentials. In this comparison it is shown that inertial effects start to become more prevalent at higher frequencies for the closed capillary frequency-dependent electroosmosis case than for the frequency-dependent streaming potential case in the same capillary. It is also shown that this difference is due to a second viscosity (transverse) wave that emanates from the velocity zero within the capillary for the electroosmosis case. The second viscosity wave superposes with the viscosity wave that emanates from wall of the capillary to effectively reduce the hydraulic radius of the capillary. Data are presented for a 0.127-mm capillary to support the findings in this paper.     

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

While an optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed-phase systems was derived by Toutounji [J. Chem. Phys. 121, 2228 (2004)], the corresponding analytical optical line shape is derived. The respective nonlinear correlation functions are also derived. Model calculations involving photon-echo, pump-probe, and hole-burning signals of model systems with both linear and quadratic coupling are provided. Hole-burning formula of Hayes-Small is compared to that of Mukamel in mixed quantum-classical systems.     

Adiabatic potentials of linear three-site mixed-valence systems

We propose a method for calculating adiabatic potentials of linear or quasi-linear threesite systems of mixed valence. The method is based on transformation of the potential energy matrix to two effective interacting modes. The adiabatic potential is calculated and its extrema are found. The electronic wave functions at the minima of the adiabatic potential correspond to complex charge distributions in a cluster. The barrier to transition of the extra electron between the terminal atoms is lower than for the transition from the terminal atom to the central atom.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 2, pp. 129–134, March–April, 1989.     

Frequency-dependent electrical detection of protein binding events

Frequency-dependent electrochemical impedance spectroscopy has been used to characterize the changes in electrical response that accompany specific binding of a protein to its substrate, using the biotin-avidin system as a model. Our results show that avidin, at concentrations in the nanomolar range, can be detected electrically in a completely label-free manner under conditions of zero average current flow and without the use of any auxiliary redox agents. Impedance measurements performed on biotin-modified surfaces of gold, glassy carbon, and silicon were obtained over a wide frequency range, from 5 mHz to 1 MHz. On each biotin-modified surface, binding of avidin is most easily detected at low frequencies, <1 Hz. Electrical circuit modeling of the interface was used to relate the frequency-dependent electrical response to the physical structure of the interface before and after avidin binding. Electrical measurements were correlated with measurements of protein binding using fluorescently labeled avidin.     

Negative linear compressibility in confined dilatating systems

The role of a matrix response to a fluid insertion is analyzed in terms of a perturbation theory and Monte Carlo simulations applied to a hard sphere fluid in a slit of fluctuating density-dependent width. It is demonstrated that a coupling of the fluid-slit repulsion, spatial confinement, and the matrix dilatation acts as an effective fluid-fluid attraction, inducing a pseudocritical state with divergent linear compressibility and noncritical density fluctuations. An appropriate combination of the dilatation rate, fluid density, and the slit size leads to the fluid states with negative linear compressibility. It is shown that the switching from positive to negative compressibility is accompanied by an abrupt change in the packing mechanism.     

Conformation transformation barriers in linear donor-acceptor systems

The PM3 semi-empirical andab initio approximations have been used to calculate the equilibrium geometry and energy levels of donor-acceptor molecules that are derivatives of conjugated amines. Chain lengthening inverts the local level of the unshared nitrogen electron pair and the delocalized level, and also changes the sign of the barrier to rotation of the dimethylamino group in the excited state. Organic Chemistry Institute, Ukrainian National Academy of Sciences, 252660 Kiev 94, ul. Murmanskaya 5, Ukraine. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 33, No. 4, pp. 224–228, July–August, 1997.     

Solitonic-like excitations in cations of linear conjugated systems

Monatshefte für Chemie - Chemical Monthly - A quantum-chemical study of the atomic charges and bond orders in the cations of the linear conjugated systems was performed. It is shown that total...     

Modelling linear reactions in inhomogeneous catalytic systems

The kinetics of linear chemical reactions in an inhomogeneous medium is modeled as an evolutionary system characterized by a fractional derivative. The corresponding mathematical model depending on one nonlocal parameter $0< \alpha <1$ is proposed. Reactions with one degree of freedom are analyzed. Solutions of the corresponding kinetic equations are shown to depend on the nonlocality parameter $\alpha $ . The concept of the critical moment of time is introduced, and the dependence of its value on the value of the relaxation coefficient is determined.     

Real-time linear response for time-dependent density-functional theory

We present a linear-response approach for time-dependent density-functional theories using time-adiabatic functionals. The resulting theory can be performed both in the time and in the frequency domain. The derivation considers an impulsive perturbation after which the Kohn-Sham orbitals develop in time autonomously. The equation describing the evolution is not strictly linear in the wave function representation. Only after going into a symplectic real-spinor representation does the linearity make itself explicit. For performing the numerical integration of the resulting equations, yielding the linear response in time, we develop a modified Chebyshev expansion approach. The frequency domain is easily accessible as well by changing the coefficients of the Chebyshev polynomial, yielding the expansion of a formal symplectic Green's operator.     

Orbital functional theory of linear response and excitation

Orbital functional theory (OFT) is based on a rule that determines a single‐determinant reference state Φ for any exact N‐electron eigenstate Ψ. An OFT model postulates an explicit correlation energy functional E_c of occupied orbital functions {?_i} and occupation numbers {n_i}. The orbital Euler–Lagrange equations are analogous to Kohn–Sham equations, but do not in general contain local potential functions. Time‐dependent Hartree–Fock theory is generalized in OFT to a formally exact linear response theory that includes electronic correlation. In the exchange‐only limit, the theory reduces to the random‐phase approximation of many‐body theory. The formalism determines excitation energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Efficient representation of the linear density-density response function

We present a thorough derivation of the mathematical foundations of the representation of the molecular linear electronic density-density response function in terms of a computationally highly efficient moment expansion. Our new representation avoids the necessities of computing and storing numerous eigenfunctions of the response kernel by means of a considerable dimensionality reduction about from 10³ to 10¹. As the scheme is applicable to any compact, self-adjoint, and positive definite linear operator, we present a general formulation, which can be transferred to other applications with little effort. We also present an explicit application, which illustrates the actual procedure for applying the moment expansion of the linear density-density response function to a water molecule that is subject to a varying external perturbation potential. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

Frequency-dependent nonlinear optical properties with explicitly correlated coupled-cluster response theory using the CCSD(R12) model

Response theory up to infinite order is combined with the explicitly correlated coupled-cluster singles and doubles model including linear-r(12) corrections, CCSD(R12). The additional terms introduced by the linear-r(12) contributions, not present in the conventional CCSD calculation, are derived and discussed with respect to the extra costs required for their evaluation. An implementation is presented up to the cubic response function for one-electron perturbations, i.e., up to frequency-dependent second hyperpolarizabilities. As first applications the authors computed the electronic polarizabilities and second hyperpolarizabilities of BH, N(2), and formaldehyde and show that the improvement in the one-electron basis set convergence known from the R12 method for ground state energies is retained for higher-order optical properties. Frequency-dependent results are presented for the second hyperpolarizability of N(2).     

Critical electron binding to linear electric quadrupole systems

Results for critical quadrupolar moments for electron binding to fixed, point-charge systems are normalized, extended, and displayed in graphical forms. The influence of rotational degrees of freedom on critical binding to quadrupolar systems is examined through calculations of critical moments for electron binding to linear electric quadrupolar rotors. The results are presented for rotors covering useful ranges of size and inertial parameters. The effect of rotational degrees of freedom on critical binding is found to be less important for quadrupolar as compared to dipolar rotors.     

Optimized linear combinations of simple exponentials for atomic systems

Hartree-Fock wave functions for the He and Be isoelectronic sequences of ions are calculated using orbitals which are linear combinations of simple exponential functions. By a full optimization of the exponents and coefficients close approximations to the HartreeFock energies were obtained. To the same order of accuracy the resulting Hartree–Fock orbitals require fewer basis functions than used previously. A number of difficulties which arise in the numerical procedures as the size of the basis set is increased are analysed in detail. Similar results are obtained for the Li sequence using the Unrestricted HartreeFock method with and without projection.