How Long-Range Are Three-Body "Exchange" Interactions in Liquid Water?

We consider the random-field O($N$) spin model with long-range exchange interactions which decay with distance $r$ between spins as $r^{-d-\sigma}$ and/or random fields which correlate with distance $r$ as $r^{-d+\rho}$, and reexamine the critical phenomena near the lower critical dimension by use of the perturbative functional renormalization group. We compute the analytic fixed points in the one-loop beta functions, and study their stability. We also calculate the critical exponents at the analytical fixed points. We show that the analytic fixed point which governs the phase transition in the system with the long-range correlations of random fields can be destabilized by the nonanalytic perturbation in both cases where the exchange interactions between spins are short ranged and long ranged. For the system with the long-range exchange interactions and uncorrelated random fields, we show that the $d\to d-\sigma$ dimensional reduction at the leading order of the $d-2\sigma$ expansion holds only for $N>2(4+3{\sqrt{3}})\simeq 18.3923\cdots$. Our investigation into the system with the long-range exchange interactions and uncorrelated random fields also gives the value of the boundary between critical behaviors in systems with long-range and short-range exchange interactions, which is identical to that predicted by Sak [Phys. Rev. B {\bf{8}}, 281 (1973)]. For the system with the long-range exchange interactions and the long-range correlated random fields, we show that the $d\to d-\sigma-\rho$ dimensional reduction does not hold within the present framework, as far as $N$ is finite.

Long-range interactions in triple quantum dots (TQDs) in Kondo regime are investigated by accurately solving the three-impurity Anderson model. For the occupation configuration of (N1,N2,N3) = (1, 0, 1), a long-range antiferromagnetic exchange interaction (JAF) is demonstrated and induces a continuous phase transition from the separated Kondo singlet (KS) to the long-range spin singlet (LSS) state between edge dots. The expression of JAF is analytically derived and numerically verified, according to which JAF can be conveniently manipulated via gate control of the detuning energy. The long-range entanglement of Kondo clouds are proved to be quite robust at strong inter-dot coupling limit. Under equilibrium condition, it induces an unexpected peak in the spectral function of the middle dot whose singly occupied level keeps much higher than the Fermi level. Under nonequilibrium condition, higher inter-dot tunneling barrier induces an anomalous enhancement of current. These novel features can be observed in routine experiments.

We present a systematic approach to the calculation of finite-size (FS) effects for anO(n) field-theoretic model with both short-range (SR) and long-range (LR) exchange interactions. The LR exchange interaction decays at large distances as 1/rd+2−2α,α→0+,α→0+. Renormalization group calculations ind=du−e are performed for a system with a fully finite (block) geometry under periodic boundary conditions. We calculate the FS shift of the critical temperature and the FS renormalized coupling constant of the model to one-loop order. The universal scaling variable is obtained and the FS scaling hypothesis is verified.

Long-range corrected (LC) density functional theories (DFTs) were applied to the isomerization energy calculations of organic molecules to make clear why conventional DFTs including B3LYP have given poor isomerization reaction energies. Combining with local response dispersion (LRD) method, we performed LC-DFT calculations for the benchmark set of isomerization reactions. Consequently, we found that LC-DFT + LRD methods give accurate reaction energies equivalent to up-to-date DFTs containing many semi-empirical parameters. This result indicates that long-range exchange and intramolecular dispersion correlation interactions, which have been neglected in conventional DFTs, play prominent roles in isomerization reactions. However, we also found that these interactions are not sufficient to give accurate isomerization energies especially for cyclization reactions. Considering that Gaussian-attenuated LC-DFTs (LCgau-DFTs) give better isomerization reaction energies than LC-DFTs, we suggested that the isomerization energies will be further improved by correcting the short-range part of exchange functionals in DFT with keeping the whole long-range exchange interactions.

Low-lying excited states of planarly extended nanographenes are investigated using the long-range corrected (LC) density functional theory (DFT) and the spin-flip (SF) time-dependent density functional theory (TDDFT) by exploring the long-range exchange and double-excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long-range exchange interaction significantly improves the CC bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long-range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long-range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long-range exchange effects, the SF-TDDFT calculations show that the double-excitation correlation effects are negligible in the low-lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long-range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP-EA values. © 2017 Wiley Periodicals, Inc.

The exchange interaction governs static and dynamic magnetism. This fundamental interaction comes in two flavours-symmetric and antisymmetric. The symmetric interaction leads to ferro- and antiferromagnetism, and the antisymmetric interaction has attracted significant interest owing to its major role in promoting topologically non-trivial spin textures that promise fast, energy-efficient devices. So far, the antisymmetric exchange interaction has been found to be rather short ranged and limited to a single magnetic layer. Here we report a long-range antisymmetric interlayer exchange interaction in perpendicularly magnetized synthetic antiferromagnets with parallel and antiparallel magnetization alignments. Asymmetric hysteresis loops under an in-plane field reveal a unidirectional and chiral nature of this interaction, which results in canted magnetic structures. We explain our results by considering spin-orbit coupling combined with reduced symmetry in multilayers. Our discovery of a long-range chiral interaction provides an additional handle to engineer magnetic structures and could enable three-dimensional topological structures.

This paper contains a study of the pair and many-body interactions in cyclic water clusters: trimer, tetramer, and pentamer. Symmetry-adapted perturbation theory (SAPT) is applied to compute the pair- and three-body interactions directly and to analyze the individual electrostatic, induction, dispersion, and exchange contributions. The total interaction energies are also obtained by supermolecule coupled-cluster calculations including single, double, and noniterative triple excitations, CCSD(T). The three-body interactions contribute up to 28% of the total interaction energy in these water clusters in their equilibrium geometries and up to 50% of the barriers for different tunneling processes investigated in the trimer. The main three-body contribution is due to second- and third-order induction effects, but also three-body exchange effects are substantial. Dispersion contributions are only significant in the pair energy. The four-body effects are relatively small, and the five-body effects were found to...

The unique chemical and physical properties of liquid water are a direct result of its highly directional hydrogen-bond (HB) network structure and associated dynamics. However, despite intense experimental and theoretical scrutiny spanning more than four decades, a coherent description of this HB network remains elusive. The essential question of whether continuum or multicomponent ("intact," "broken bond," etc.) models best describe the HB interactions in liquid water has engendered particularly intense discussion. Most notably, the temperature dependence of water's Raman spectrum has long been considered to be among the strongest evidence for a multicomponent distribution. Using a combined experimental and theoretical approach, we show here that many of the features of the Raman spectrum that are considered to be hallmarks of a multistate system, including the asymmetric band profile, the isosbestic (temperature invariant) point, and van't Hoff behavior, actually result from a continuous distribution. Furthermore, the excellent agreement between our newly remeasured Raman spectra and our model system further supports the locally tetrahedral description of liquid water, which has recently been called into question.

Resolved fluorescence from the K2 43 Σ+g state to the a3 Σ+u state has been measured by the perturbation-facilitated optical–optical double resonance (PFOODR) technique. Data have been fit to an improved set of molecular constants for the a3 Σ+u state. In particular, the new Te value for this state has been determined as 4197.935±0.047 cm−1, nearly 1.8 cm−1 higher than previously reported. By combining the new results for the a3 Σ+u state and the recent results for the ground X1 Σ+g state [J. Chem. Phys. 103, 3350 (1995)], we report in this paper an improved analysis of long-range dispersion and exchange interactions between two K atoms and of the X1 Σ+g and a3 Σ+u state dissociation energies De of 4450.674±0.072 cm−1 and 252.74±0.12 cm−1, respectively.

The exchange interaction between antiferromagnetic FeMn layers across a Cu spacer is studied by employing the exchange bias as a probe in multilayers of ``NiFe∕thin $\mathrm{Fe}\mathrm{Mn}∕\mathrm{Cu}∕\text{thick}$ FeMn.'' With variation of the Cu spacer's thickness, the indirect exchange interaction, monitored through the response of the exchange bias, oscillates with a period of approximately $18--20\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, about twice that for ferromagnetic films separated by a Cu spacer. This result shows that long-range oscillatory exchange interaction is a basic and universal feature in both metallic ferromagnetic layers separated by nonmagnetic metals and metallic antiferromagnetic layers separated by a nonmagnetic metal, due to the quantum interferences induced by the spin-dependent interface reflection of Bloch waves with different oscillating periods originating from the difference in interface reflection conditions between ferromagnetic and antiferromagnetic spin ordering.

The electronic and magnetic properties of polyacenes become quite fascinating as the number of linearly conjugated benzene rings increases. Higher-order conjugated polyacenes develop radicaloid characters due to the transition of electronic structures from closed-shell to the open-shell system. Here we have investigated the role of such polyacenes as the magnetic coupler when placed between the two spin-sources based on nitroxy radicals. To do so, the magnetic exchange interactions (2J) are computed employing electronic structure theories, i.e. broken-symmetry (BS) approach within the density functional theory (DFT) as well as symmetry-adopted wave function based multi-configurational methods. In the former approach, various genre of exchange-correlation (XC) functionals such as generalized gradient approximation (GGA), meta-GGA, hybrid functional, constrained spin density (i.e. CDFT) and on-site Coulomb correlation corrected GGA+U functionals are adopted. All DFT based calculations estimate an exponential increase in 2J values with the length of the couplers, especially for the higher-order acenes. This is indeed an unexpected observation and also there is no experimental report available in support of the DFT calculations. The complexity in the electronic structure enhances with the increasing number of benzene rings due to an increase in near-degenerate or quasi-degenerate molecular orbitals (MOs) and also the reduction of the energy gap with the low-lying excited states. Consequently, it invokes a severe challenge in the computations of the magnetic exchange interactions in DFT. As an alternative approach, the wave function based multi-reference calculations, e.g. CASSCF/NEVPT2 methods are also adopted. In the later calculations, it has been realized that the π-orbitals of the couplers play a crucial role in the exchange interactions. For larger polyacenes (i.e. hexacene to decacene) such calculations become prohibitively expensive and rigorous as the number of π-orbitals increases, thus expanding the active space enormously. The limited active spaces calculations indicate quite strong ferromagnetic exchange interactions, thus in principle, reinforcing long-range magnetic exchange interactions.

The nature and importance of nonadditive three-body interactions in the ionic OH−(H2O)2 cluster have been studied by supermolecule Mo/ller–Plesset (MP) perturbation theory and coupled-cluster method, and by symmetry-adapted perturbation theory (SAPT). The convergence of the SAPT expansion was tested by comparison with the results obtained from the supermolecule Mo/ller–Plesset perturbation theory calculations through the fourth order (MP2, MP3, MP4SDQ, MP4), and the coupled-cluster calculations including single, double, and approximate triple excitations [CCSD(T)]. It is shown that the SAPT results reproduce the converged CCSD(T) results within 10%. The SAPT method has been used to analyze the three-body interactions in the clusters OH−(H2O)n, n=2,3,4,10, with water molecules located either in the first or the second solvation shell. It is shown that at the Hartree–Fock level the induction nonadditivity is dominant, but it is partly quenched by the Heitler–London and exchange-induction/deformation terms. This implies that the induction energy alone is not a reliable approximation to the Hartree–Fock nonadditive energy. At the correlated level, the most important contributions come from the induction-dispersion and the MP2 exchange energies. The exchange-dispersion and dispersion nonadditivities are much smaller, and for some geometries even negligible. This suggests that it will be difficult to approximate the three-body potential for OH−(H2O)2 by a simple analytical expression. The three-body energy represents only 4%–7% of the pair CCSD(T) intermolecular energy for the OH−(H2O)2 cluster, but can reach as much as 18% for OH−(H2O)4. Particular attention has been paid to the effect of the relaxation of the geometry of the subsystems.

The nature and importance of nonadditive three-body interactions in the (H2O)2HCl cluster have been studied by the supermolecule coupled-cluster method and by symmetry-adapted perturbation theory (SAPT). The convergence of the SAPT expansion was tested by comparison with the results obtained from the supermolecule coupled-cluster calculations including single, double, and noniterative triple excitations [CCSD(T)]. It is shown that the SAPT results reproduce the converged CCSD(T) results within 3% at worst. The SAPT method has been used to analyze the three-body interactions for various geometries of the (H2O)2HCl cluster. It is shown that the induction nonadditivity is dominant, but it is partly quenched by the first-order Heitler–London-type exchange and higher-order exchange–induction/deformation terms. This implies that the classical induction term alone is not a reliable approximation to the nonadditive energy and that it will be difficult to approximate the three-body potential for (H2O)2HCl by a simple analytical expression. The three-body energy represents as much as 21–27% of the pair CCSD(T) intermolecular energy.

The properties of localized surface states in the one-magnon spectrum of Heisenberg ferromagnets with different types of lattices and exchange interactions are considered. The systems with “isotropic” as well as “anisotropic” exchange interaction are investigated. The case of “anisotropic” exchange determined by the long-range interaction between the spins arranged along a crystallographic axis is analyzed. The dispersion relations and damping decrements of localized surface waves are obtained without using the cumbersome apparatus of Green’s functions for simple and complex ferromagnets with “isotropic” exchange between nearest neighbors. The contribution of the surface to the magnon energy distribution function is determined. Spin-wave states localized at two-dimensional defects (like a free surface, foreign plane in an infinite lattice, or the boundary between two magnetic crystals are investigted for systems with a long-range exchange interaction. The long-range interaction is found to be essential for an analysis of stability of the ferromagnetic ordering in the defect plane in the case of alternating ferro- and antiferromagnetic “anisotropic” interaction. Surface-projectable spectral densities of one-magnon states are estimated.

We investigate the valley depolarization due to the electron-hole exchange interaction in monolayer MoS$_{2}$. Both the long- and short-range parts of the intra- and inter-valley electron-hole exchange interactions are calculated. We find that both the long- and short-range exchange interactions can cause the inter- and intra-valley bright exciton transitions. With the intra-valley bright exciton transition channel nearly forbidden due to the large splitting of the valence bands, the inter-valley channel due to the exchange interaction can cause the valley depolarization efficiently by the Maialle-Silva-Sham mechanism [Phys. Rev. B {\bf 47}, 15776 (1993)]. With only the long-range exchange interaction, the calculations show good agreement with the recent valley polarization experiments, including the time-resolved valley polarization measurement, the pump-probe experiment and the steady-state PL polarization measurement. We further show that for the A-exciton with large (small) center-of-mass momentum, the long-range exchange interaction can cause the {\em fast} ({\em slow}) inter-valley exciton transition.