On the fluctuation theory for the liquid—vapor interface

Using the statistical mechanical formulation of Triezenberg and Zwanzig, we argue that the “intrinsic” or “bare” width of the liquid—vapor interface in the Buff—Lovett—Stillinger capillary model may be identified as the interfacial width described by the “van der Waals-like” theories.     

Correlation and response functions with non-Markovian dissipation: a reduced Liouville-space theory

Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime.     

On Koopmans' theorem in density functional theory

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms.     

On the connection between Gaussian statistics and excited-state linear response for time-dependent fluorescence

Time-dependent fluorescence (TDF) of a chromophore in a polar or nonpolar solvent is frequently simulated using linear-response approximations. It is shown that one such linear-response-type approximation for the TDF Stokes shift derived by Carter and Hynes [J. Chem. Phys. 94, 5961 (1991)] that is based on excited-state dynamics gives the same result as that obtained by assuming Gaussian statistics for the energy gap. The derivation provides insight into the much discussed relationship between linear response and Gaussian statistics. In particular, subtle but important differences between the two approximations are illuminated that suggest that the result is likely more generally applicable than suggested by the usual linearization procedure. In addition, the assumption of Gaussian statistics directly points to straightforward checks of the validity of the approximation with essentially no additional computational effort.     

Extending the fluctuation theorem to describe reaction coordinates

The fluctuation theorem describes the distribution of work done on small systems which have been pushed out of equilibrium in response to an external field. The theorem has recently been a subject of much interest for describing single-molecule experiments and simulations. In this communication, it is shown how the fluctuation theorem can be extended to describe fluctuations not only in the work done on a system, but also in a reaction coordinate. The extension explored in this work allows for a generalized derivation of Hummer and Szabo's expression (G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. 98, 3658 (2001)) for reconstructing the potential of mean force from nonequilibrium trajectories. The derivation demonstrates how implementation of this expression can be more easily facilitated. Atomistic simulations of a biomolecular system are presented which support these results.     

On the connection between the alternant molecular orbital method and the separated-pair theory

It is shown that the alternant molecular orbital method can be entirely fitted into the separated-pair theory. The total wave function can be taken as a linear combination of antisymmetrized product functions constructed of strongly orthogonal geminals. In the single parameter case, however, these strongly orthogonal geminals cannot be uniquely defined by the criterion of minimum energy alone. The separated-pair formalism may prove more favorable when the one-electron basis is to be extended in order to include, e. g., vertical correlation effects.

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Zusammenfassung Es wird gezeigt, daß die AMO-Methode einen Sonderfall der Methode der Elektronenpaare darstellt, denn die zugehörige Wellenfunktion kann in eine Linearkombination antisymmetrischer Geminalprodukte umgeformt werden. Diese im starken Sinn orthogonalen Geminale sind jedoch bei nur einem freien Parameter im AMO-Ansatz durch die Bedingung minimaler Energie nicht vollständig bestimmt. Der Geminalformalismus könnte dann Vorteile bieten, wenn die Einelektronenbasis erweitert werden soll.

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Résumé On montre que la méthode des orbitales moléculaires alternantes peut être comprise dans la théorie des paires séparées. La fonction d'onde totale s'écrit comme combinaison linéaire de produits antisymétrisés de géminales fortement orthogonales. Cependant, au cas d'un seul paramètre, ces géminales ne sont pas définies uniquement par le critère d'énergie minimum. Le formalisme pourrait se montrer avantageux si la base des fonctions monoélectroniques est étendue pour comprendre, par exemple, la corrélation verticale.

     

A critical transition rule for broadening exponent of fluctuation and its effect on dissipation in chemical reaction-heat conduction coupling systems

A stochastic model of chemical reaction-heat conduction-diffusion for a one-dimensional gaseous system under Dirichlet or zero-fluxes boundary conditions is proposed in this paper. Based on this model,we extend the theory of the broadening exponent of critical fluctuations to cover the chemical reaction-heat conduction coupling systems as an asymptotic property of the corresponding Markovian master equation (ME),and establish a valid stochastic thermodynamics for such systems. As an illustration,the non-iso...     

On the equivalence of ring-coupled cluster and adiabatic connection fluctuation-dissipation theorem random phase approximation correlation energy expressions

The correlation energy in the direct random phase approximation (dRPA) can be written, among other possibilities, either in terms of the interaction strength averaged correlation density matrix, or in terms of the coupled cluster doubles amplitudes obtained in the direct ring approximation (drCCD). Although the corresponding dRPA correlation density matrix on the one hand, and the drCCD amplitude matrix on the other hand, differ significantly, they yield identical energies. Similarly, the analogous RPA and rCCD correlation energies calculated from antisymmetrized two-electron integrals are identical to each other despite very different underlying working equations. In the present communication, a direct correspondence between amplitudes and densities is established and investigated with perturbation theory arguments. Our analysis also sheds some light on the properties of recently proposed RPA/rCCD variants which use antisymmetrized integrals in part of the equations and nonantisymmetrized integrals in others.     

Non-equilibrium spin-boson model: counting statistics and the heat exchange fluctuation theorem

We focus on the non-equilibrium two-bath spin-boson model, a toy model for examining quantum thermal transport in many-body open systems. Describing the dynamics within the noninteracting-blip approximation equations, applicable, e.g., in the strong system-bath coupling limit and/or at high temperatures, we derive expressions for the cumulant generating function in both the Markovian and non-Markovian limits by energy-resolving the quantum master equation of the subsystem. For a Markovian bath, we readily demonstrate the validity of a steady-state heat exchange fluctuation theorem. In the non-Markovian limit a "weaker" symmetry relation generally holds, a general outcome of microreversibility. We discuss the reduction of this symmetry relation to the universal steady-state fluctuation theorem. Using the cumulant generating function, an analytic expression for the heat current is obtained. Our results establish the validity of the steady-state heat exchange fluctuation theorem in quantum systems with strong system-bath interactions. From the practical point of view, this study provides tools for exploring transport characteristics of the two-bath spin-boson model, a prototype for a nonlinear thermal conductor.     

A fluctuation theory analysis of the salting-out effect

An analysis of the salting-out, or Sechenow, effect is given in terms of Kirkwood-Buff, or fluctuation, integrals. The analysis is formally exact but cannot easily be applied in its original form. When the solute that is being salted out is sparingly soluble, simplifications arise and the theory can be used to compute one of the Kirkwood-Buff integrals which is otherwise difficult to obtain.     

On the applying of fluctuation theorems to the theory of slow discharge in galvanostatic regime

Expressions for the equation of slow discharge in galvanostatic regime are drawn, as power expansion with respect to overvoltage, in terms of the Bochkov-Kuzovlev and Jarzynski fluctuation theorems combined with the Stratonovich relations for nonlinear nonequilibrium thermodynamics. Coefficients of the expansion are linear functions of the intensities of cumulant correlation functions that characterize the electrode potential fluctuations.     

Unified theory of the exciplex formation/dissipation

The natural extension and reformulation of the unified theory (UT) proposed here makes it integro-differential and capable of describing the distant quenching of excitation by electron transfer, accompanied with contact but reversible exciplex formation. The numerical solution of the new UT equations allows specifying the kinetics of the fluorescence quenching and exciplex association/dissociation as well as those reactions' quantum yields. It was demonstrated that the distant electron transfer in either the normal or inverted Marcus regions screens the contact reaction of exciplex formation, especially at slow diffusion.     

Applications of a time correlation function theory for the fifth-order Raman response function I: atomic liquids

Multidimensional spectroscopy has the ability to provide great insight into the complex dynamics and time-resolved structure of liquids. Theoretically describing these experiments requires calculating the nonlinear-response function, which is a combination of quantum-mechanical time correlation functions R5(t1,t2) was expressed with a two-time, computationally tractable, classical TCF. Writing the response function in terms of classical TCFs brings the full power of atomistically detailed molecular dynamics to the problem. In this paper, the new TCF theory is employed to calculate the fifth-order Raman response function for liquid xenon and investigate several of the polarization conditions for which experiments can be performed on an isotropic system. The theory is shown to reproduce line-shape characteristics predicted by earlier theoretical work.     

On the area of feasible solutions and its reduction by the complementarity theorem

Multivariate curve resolution techniques in chemometrics allow to uncover the pure component information of mixed spectroscopic data. However, the so-called rotational ambiguity is a difficult hurdle in solving this factorization problem. The aim of this paper is to combine two powerful methodological approaches in order to solve the factorization problem successfully. The first approach is the simultaneous representation of all feasible nonnegative solutions in the area of feasible solutions (AFS) and the second approach is the complementarity theorem. This theorem allows to formulate serious restrictions on the factors under partial knowledge of certain pure component spectra or pure component concentration profiles.     

Application of the dissipation theorem to turbulent flow and mass transfer in a pipe

The dissipation theorem is applied to turbulent pipe flow. The eddy-viscosity profiles can be made to agree with some in the literature in the sense that the eddy viscosity starts at zero on the solid pipe wall, rises to a maximum, and declines again toward the center line. A relationship between the volumetric dissipation and the eddy viscosity is derived by means of an energy balance on a core of fluid of radius r. The question of what exponent to use on the radius in another governing equation is clarified, thereby giving better agreement with experimental data than other values tried. Negative values of the eddy viscosity can be obtained in some regions of the flow field, such as near the center line, and it is suggested that these can be eliminated by slight modification of the decay term. Better agreement with the shapes of friction-factor and mass-transfer curves could be achieved by further (empirical) modification of the stress dependence of parameters in the model.     

Benchmarking two-photon absorption with CC3 quadratic response theory, and comparison with density-functional response theory

We present a detailed study of the effects of electron correlation on two-photon absorption calculated by coupled cluster quadratic response theory. The hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3 has been used to investigate the effects of electron correlation on the two-photon absorption cross sections of formaldehyde (CH2O), diacetylene (C4H2), and water (H2O). In particular, the effects of triple excitations on two-photon transition cross sections are determined for the first time. In addition, we present a detailed comparison of the coupled cluster results with those obtained from Hartree-Fock and density-functional response theories. We have investigated the local-density approximation, the pure Becke-Lee-Yang-Parr (BLYP) functional, the hybrid Becke-3-parameter-Lee-Yang-Parr (B3LYP), and the Coulomb-attenuated B3LYP (CAM-B3LYP) functionals. Our results show that the CAM-B3LYP functional, when used in conjuction with a one-particle basis-set containing diffuse functions, has much promise; however, care must still be exercised for diffuse Rydberg-type states.     

Spin virial theorem in the density functional theory

The spin virial theorem is derived in the density functional theory. The theorem establishes a relation between the differences of spin-up and -down kinetic and potential energies. The theorem is useful for checking the accuracy of spin orbitals. As an illustration, the example of the Xα method is studied. © 1994 John Wiley & Sons, Inc.     

Extended Koopmans' theorem at the second-order perturbation theory

The extended Koopmans' theorem (EKT), when combined with the second-order Møller−Plesset (MP2) perturbation theory through the relaxed density matrix approach [J. Cioslowski, P. Piskorz, and G. Liu, J. Chem. Phys. 1997, 107, 6,804], provides a straightforward way to calculate the ionization potentials (IPs) as an one electron quantity. However, such an EKT-MP2 method often suffers from the negative occupation problem, failing to provide the complete IP spectra for a system of interest. Here a small positive number scheme is proposed to cure this problem so as to remove the associated unphysical results. In order to obtain an in-depth physical interpretation of the EKT-MP2 method, we introduce a Koopmans-type quantity, named KT-MP2, based on which the respective contribution from the relaxation and the correlation parts in the EKT-MP2 results are recognized. Furthermore, the close relationship between the EKT-MP2 method and the derivative approach of the MP2 energy with respect to the orbital occupation numbers [N. Q. Su and X. Xu, J. Chem. Theory Comput. 2015, 11, 4,677] is revealed. When these MP2-based methods are applied to a set of atoms and molecules, new insights are gained on the role played by the relaxation and the correlation effects in the electron ionization processes.     

The linked-cluster theorem in the open-shell coupled-cluster theory for incomplete model spaces

The linked-cluster theorem (LCT) holds good in open-shell coupled-cluster theory for incomplete model spaces provided the intermediate normalization condition (IN) for the eigenfunctions is abandoned. The crucial requirement for proving the LCT is the valence universality of the wave operator Ω. Thus Ω contains not only m-valence operators S̃^(m) for an m-valence problem but also all the lower-valence S̃S^(k) operators to correlate k <m valence problems. LCT is proved using a particular scheme for choosing the S̃S^(k) operators for which IN does not hold good.     

On the evaluation of the characteristic polynomial via symmetric function theory

The use of power sum symmetric functions leads to Newton's identities, which relate the traces of various powers ofA, the adjacency matrix of a graph, and the coefficients of the characteristic polynomials. While it is possible to solve Newton's identities and generate the coefficients by recursion or, alternatively, to derive them by sequential manipulations (yielding the explicit formulas), we show how the results can be expressed using a combinatorial approach and relate the evaluation of the coefficients to selected Young diagrams.