Computational analysis of nematic liquid crystal reorientation under weak anchoring: Variational minimization, perturbation theory, and asymptotic approximations

Enhanced Intersystem Crossing (EISC) is an important mechanism that allows for formally forbidden population transfer from the singlet to triplet manifold in chromophore-radical (C-R) systems. We use first order perturbation theory to estimate the likelihood of EISC in various organic C-R molecules. The first order mixing coefficient κ between the states involved in EISC depends on the difference in pairwise exchange interactions between photoexcited chromophore electrons and the radical. Exchange coupling constants were calculated with the Heisenberg-Dirac-Van Vleck Hamiltonian using excited state wave functions and energies obtained from the CASSCF/QD-NEVPT2 calculations. The predictions derived using this framework are in a good agreement with the available experimental data on EISC observed with transient absorption spectroscopy.

Three-body interactions in water play a crucial role in accurately modeling its structural and thermodynamic properties. These interactions consist of a polarization term that decays as an inverse power of the intermolecular separations Rab and a term that is usually assumed to describe exchange interactions and decay exponentially. Due to the complexity of fitting the latter term at large Rab, it is often damped or truncated beyond a certain distance, also because the computational cost of including three-body effects in molecular simulations scales as N3 with the number of molecules, compared to the N2 scaling of two-body interactions. Here, investigations of the impact of long-range three-body exchange interactions on the results of such simulations have been performed by systematically extending the average Rab of trimers included. It is demonstrated that these long-range effects are important for accurately describing the density of liquid water, ρ(T), as a function of temperature, but are essentially negligible for several other properties of water. The effects of three-body damping onset on ρ(T) are larger than they would have been with an exponential decay; however, it is shown here that the decay is dominated by exponential components only at fairly small Rab, while for large Rab, the nonpolarization three-body effects decay as 1/Rabn. These findings are rationalized by calculations with the symmetry-adapted perturbation theory. Another reason for the importance of three-body effects is their N3 scaling. Clearly, long-range three-body exchange interactions should be included in high-accuracy water models. It is shown that the reason these interactions have such large effects on ρ(T) is their extreme anisotropy affecting the structure of liquid water. Our work also sheds light on discrepancies between the theory and experiment for ρ(T).

Singlet fission is a photophysical process in organic molecules that generates two triplet electronic states from an excited singlet electronic state. Molecules exhibiting singlet fission can multiply charge carriers and thus have the potential to enhance the performance of solar cells beyond the Shockley-Queisser limit by reducing thermalization losses. However, in order to implement singlet fission for applications in photovoltaics, it is essential to understand how charge or energy can be harvested from triplet excitons. In this work, we investigate these processes in a prototypical donor-acceptor complex consisting of a bis(diazadiborine)-based chromophore as a singlet fission-active donor and tetracyanoquinodimethane as an acceptor molecule. Using a combined approach of high-level ab initio multireference perturbation theory techniques and quantum dynamical simulations, we show the existence of intermolecular singlet fission, charge and energy transfer following intramolecular singlet fission, and energy loss decay channels to low-lying states as the three competing charge and energy transfer mechanisms from the donor to the acceptor molecule. We analyze the role of the different electronic states, specific vibrational modes, and vibronic couplings in these processes. The results provide insights into the rational design of donor-acceptor systems with efficient singlet fission-based charge and energy transfer.

Lead-free double perovskites are actively explored as environmentally benign alternatives to lead-based halide perovskites for optoelectronic applications. In this work, the influence of halide substitution (X = I, Br, Cl) on the structural, mechanical, electronic, and optical properties of cubic K2AgSbX6 double perovskites is systematically investigated. Halide replacement induces a monotonic reduction in lattice parameters and a widening of the electronic band gap, increasing from the iodide to the chloride compound. Hybrid-functional calculations predict indirect band gaps ranging from 0.60 eV for K2AgSbI6 to 1.73 eV for K2AgSbCl6. Mechanical analysis reveals ductile behavior for the iodide and bromide phases, while the chloride phase is significantly stiffer and brittle. Optical calculations indicate strong absorption across the visible range, with K2AgSbBr6 exhibiting an optimal balance between band gap, absorption strength, and mechanical flexibility, making it particularly promising for optoelectronic and photovoltaic applications. First-principles density functional theory calculations were performed using the CASTEP code. Structural optimization and ground-state properties were obtained using the rSCAN meta-GGA functional, while electronic band structures were refined using the HSE06 hybrid functional. Ultrasoft pseudopotentials generated within the on-the-fly scheme were employed with a plane-wave cutoff energy of 500 eV and a Γ-centered 4 × 4 × 4 Monkhorst-Pack k-point mesh. Elastic properties were evaluated via the Voigt-Reuss-Hill approach, phonon dispersions were calculated using density-functional perturbation theory, and frequency-dependent optical properties were derived from the complex dielectric function.

Abstract Light-cone perturbation theory is a powerful tool for calculating high-energy scattering amplitudes, particularly for quantum particles such as electrons, photons, or protons scattering off heavy nuclei, a process analogous to potential scattering. Central to these computations are the light-cone wave functions of incoming and outgoing particles, representing the projection of dressed initial and final states onto partonic Fock states. The dressed states are obtained by applying an evolution operator in the Dirac picture to bare partonic states, which may be interpreted physically as a time evolution from preparation to interaction. In standard approaches, a non-unitary operator is used, and proper normalization is imposed a posteriori. Here, we systematically develop perturbation theory from a perturbatively unitary evolution operator, using adiabatic switching to regularize the infinite-time limits. This provides a theoretically coherent framework for organizing calculations, reproducing known results entirely diagrammatically without enforcing unitarity by hand. We illustrate the method with a simple quantum mechanical model, enabling calculations to arbitrary perturbative orders, and then evaluate wave functions in field theories quantized on the light cone, focusing on a massive scalar theory with cubic interaction at one-loop accuracy.

Vibration-based energy indicators have been widely studied for structural damage identification, offering an advantage over traditional methods by avoiding reliance on modal parameters. However, their accuracy is highly sensitive to the selection of appropriate frequency bands. Conventional techniques typically require prior knowledge of damage states to determine the optimal frequency range, limiting their applicability in unsupervised damage identification. To overcome this limitation, this article proposes a structural damage identification method based on the energy intensity ratio of specific frequency band components. By analyzing the regularities of frequency band information changes caused by damage base on modal parameter perturbation theory, a damage information entropy function is constructed to accurately select sensitive bands without supervision. Using the optimally selected frequency bands, equivalent energy features related to acceleration, velocity, and displacement are constructed. The precise identification of damage is then achieved using the energy intensity ratio indicator. The feasibility, accuracy, and robustness of the proposed method are validated through numerical simulations of high-rise building and two typical experimental cases of frame structures. The comparative analysis and detection results indicate that, compared to traditional full-band energy indicators, the proposed method significantly improves the accuracy of damage localization and the sensitivity to damage degree changes, demonstrating promising prospects for engineering applications.

The quantum spin Hall insulator with intrinsic piezoelectric response has attracted much attention due to its potential applications in topological electronic states and piezoelectric electric coupling fields. Motivated by the comparable chemical properties of Br and I, we construct Janus Bi4BrxI4−x (x = 1, 2, 3) monolayers by tuning the I concentration and systematically investigate their electronic, topological, and piezoelectric properties. First-principles calculations demonstrate that all three Janus structures are dynamically stable, wide-bandgap quantum spin Hall insulators, with nontrivial bandgaps of ∼0.26 eV. Density functional perturbation theory calculations confirm that non-centrosymmetric Bi4Br3I1 and Bi4Br1I3 possess significant in-plane piezoelectric effects, with Bi4Br3I1 exhibiting a notably large piezoelectric strain coefficient of |d11| = 7.092 pm/V. Notably, Bi4BrxI4−x (x = 1, 2, 3) structures have already been synthesized and their properties experimentally verified, underscoring their practical feasibility. These findings establish Janus Bi4BrxI4−x (x = 1, 2, 3) monolayers as a promising platform, enabling the coexistence of nontrivial topological states and strong piezoelectricity, paving the way for next-generation multifunctional quantum devices.

The effective Flory-Huggins parameter χ e is one of the most important characteristics of any multicomponent polymer system. This parameter characterizes the free energy of interaction between monomers of different types and controls the phase behavior of polymer mixtures. In this work, we developed a perturbation theory and derived how χ e depends on the details of an arbitrary coarse-grained polymer model. After defining χ e in this way, we found that the models of symmetric polymer blends and diblock copolymer melts behaved universally: Their phase transition points, free energies, and mesoscopic invariant structure factors depended solely on the chain architecture, the invariant chain length N ¯ , and the interaction parameter χ e N . To parametrize our perturbative expression for χ e , only the effective coordination number distribution in a reference homogeneous system needs to be measured. This distribution, in turn, can be directly mapped onto coarse-grained model parameters set prior to simulation, which clarifies how model construction influences χ e . Our definition of χ e enables straightforward quantitative comparison of models with each other and with experiments, which will facilitate the computational design of multicomponent polymer materials.

Abstract The computation of gravitational wave scattering on black hole spacetimes is an extremely hard problem, typically requiring approximation schemes that either treat the black hole perturbatively or are only amenable to numerical techniques. In this paper, we consider linearised gravitational waves (or gravitons) scattering on the self-dual analogue of a black hole: namely, the self-dual Taub-NUT (SDTN) metric. Using the hidden integrability of the self-dual sector, we solve the linearised Einstein equations on these self-dual black hole backgrounds exactly in terms of simple, explicit quasi-momentum eigenstates. Using a description of the SDTN metric and its gravitons in terms of twistor theory, we obtain an explicit formula, exact in the background, for the tree-level maximal helicity violating (MHV) graviton scattering amplitude at arbitrary multiplicity, with and without spin. This is obtained from the description of the MHV amplitudes in terms of the perturbation theory of a chiral sigma model whose target is the twistor space of the background. The incorporation of spin effects on these backgrounds is a straightforward application of the Newman–Janis shift. We also demonstrate that the holomorphic collinear splitting functions in the self-dual background are equal to those in flat space so that the celestial symmetry algebra is undeformed.

A theoretical study of the dielectric permittivity tensor for the plasmonic metals (Au, Ag, and Cu) nanofilms of different thicknesses in the THz-ultraviolet frequency range was conducted. Using DFT calculation data, the models for calculating longitudinal and transverse to nanofilm surface components ɛ‖(ω, h) and ɛ⊥(ω, h) for the metal nanofilms of any thickness h are proposed. The model for the ɛ‖(ω, h) calculation uses a sum of the interband contribution of the bulk metal obtained from density functional perturbation theory, the Drude contribution of intraband excitations, and the Lorentz model to account for the film surface influence. The model for the ɛ⊥(ω, h) calculation uses, in addition to the interband term, the contribution of the electron's motion perpendicular to the film surface, described as its motion in a 1D infinitely deep potential well. This contribution is calculated using transient perturbation theory and Fermi's golden rule. Based on both of these models, a Python program has been written that allows one to calculate in seconds longitudinal and transverse permittivity components in the THz-ultraviolet range for nanofilms of these metals with surface indices (001), (110), or (111) and any film thickness h. Using Bruggeman's effective medium theory, the effective permittivities ɛeff(ω, h) of several thin gold films were calculated and shown to be in good agreement with the available experimental data.

Eleven feasible stationary points have been located on the potential energy surface of the ground electronic state of (CO)2 with shapes H, I , T, V, X, and Z. The global minimum has a planar, slipped, antiparallel arrangement of the atoms with a CC contact. There is a secondary minimum with an OO contact. The first-order transition state connecting the two minima has a CO contact. The remaining feasible stationary points are higher-order transition states. At intermediate levels of electronic structure theory, one can easily become lost in the web of polytopism. The relative energies of the most important stationary points were determined with the help of the focal-point analysis scheme. The relative energies are based on calculations up to the CCSDT(Q) level of electronic structure theory, basis sets up to aug-cc-pV6Z, and the inclusion of so-called ‘small’ corrections due to core-core and core-valence correlation, relativistic effects, and the diagonal Born–Oppenheimer correction. The electronic interaction energy of the global minimum is − ( hc ) 136.8 ( 15 ) cm − 1 , while the electronic energy difference between the global and local minima is (hc)17.1(25) cm − 1 . A detailed interaction energy analysis via symmetry-adapted perturbation theory suggests that the bonding in the dimer arises primarily from dispersion rather than electrostatics.

UGA-SSMRPT2, the spin-free perturbative analogue of Mukerjee's State-Specific Multireference Coupled Cluster Theory (MkMRCC), is known to be successful for size-extensive and intruder-free construction of dissociation curves. This work demonstrates that UGA-SSMRPT2 is also an accurate and computationally inexpensive framework for computing the excitation energies. The method achieves near-chemical accuracy for the vast majority of π → π*, n → π*, charge-transfer, valence-Rydberg, and Rydberg excited states commonly used for benchmarking electronic structure theories for excited states. Our results demonstrate that UGA-SSMRPT2 excitation energies lie within 0.20 eV of EOM-CCSD and/or well-established theoretical best estimates, often surpassing the popular MRPT2 approaches like NEVPT2, CASPT2, and MCQDPT while typically requiring smaller active spaces. Its state-specific formulation circumvents the well-known intruder-state problem and eliminates the need for empirical parameters, such as IPEA shifts in CASPT2. This work proposes UGA-SSMRPT2 as a robust and scalable approach for modeling challenging electronically excited states.

An adjoint-based, depletion perturbation theory (DPT) sensitivity analysis methodology has been implemented in OpenMC and is tested using a complex, 252Cf production activation chain. The DPT methodology has been improved from previous iterations, providing higher-fidelity sensitivity coefficients with improved computational performance for more intensive problems. The method shows good agreement with reference direct perturbation results, though some disagreement is observed for several sensitivity coefficients, possibly due to limitations in the DPT numerical integration implementation. Significant computational speedups were obtained for the DPT numerical integration, showing that increasing the number of DPT substeps appears to increase the accuracy for some of the sensitivity coefficients.

Abstract Metric reconstruction is the general problem of parameterizing GR in terms of its two “true degrees of freedom” e.g., by a complex scalar “potential”—in practice mostly with the aim of simplifying the Einstein equation (EE) within perturbative approaches. In this paper, we re-analyze the metric reconstruction procedure by Green, Hollands, and Zimmerman (GHZ) [Class. Quant. Grav. 37, 075001 (2020)], which is a generalization of the Chrzanowski-Cohen-Kegeles (CCK) approach. Contrary to the CCK method, that by GHZ is applicable not only to the vacuum, but also to the sourced linearized Einstein equation (EE) on Kerr. Our main innovation is a version of the GHZ integration scheme that is suitable for the initial value problem of the sourced linear EE. By iteration, our scheme gives the metric to as high an order in perturbation theory as one might wish, in principle. At each order, the metric perturbation is a sum of a corrector, obtained by solving a triangular system of transport equations, a reconstructed piece, obtained from a Hertz potential as in the CCK approach, and an algebraically special perturbation, determined by the ADM quantities. As a byproduct, we determine the precise relations between the asymptotic tail of the Hertz potential in the GHZ and CCK schemes, and the quantities relevant for gravitational radiation, namely, the energy flux, news- and memory tensors, and their associated BMS-supertranslations. We also discuss ways of transforming the metric perturbation to Lorenz gauge.

Starting from the interaction picture in quantum mechanics it is shown that perturbation theory for a weak static coupling of two subsystems in a natural way can be reformulated through integrals over products of imaginary time cross correlation functions. This leads to an expression for the London dispersion energy contribution of intermolecular interactions offering new ways to its numerical computation. The frequency-dependent charge susceptibility functions at imaginary frequencies appearing in the Casimir-Polder expression for the dispersion energy and the imaginary time density fluctuation cross correlation functions occuring in the equivalent alternative formula turn out to be Fourier cosine transform pairs.

In this paper, we study the Cauchy problem for the nonlinear Hartree equation associated with Dunkl Laplace operator: { i ∂ t u ( t , x ) + Δ k u ( t , x ) = ( | x | − β ∗ D | u ( t , x ) | 2 ) ⋅ u ( t , x ) , u ( 0 , x ) = φ ( x ) ∈ L k 2 ( R d ) , where Δ k is the Dunkl Laplace operator, and ∗ D denotes the Dunkl convolution. For 0 < β < min { 2 , d + 2 γ } , we establish both local and global well-posedness in L k 2 ( R d ) in the mass-subcritical regime by combining Strichartz estimates with convolution estimates in the Dunkl setting. In the mass-critical case β = 2 , we prove the local theory, and obtain a global solution when the initial value is sufficiently small in L k 2 ( R d ) . Moreover, we establish the scattering behavior in the critical case, and show that if blow-up occurs in finite time, then the H k s -norm necessarily diverges for all s>0. Finally, we develop a long-time perturbation theory which ensures that approximate solutions remain close to exact solutions under control of the critical norm.

Context. Magnetic fields affect stellar oscillations through eigenmode mixing. If the contribution of a magnetic field to the stellar oscillation frequency is weak, this mode coupling can be determined using perturbation theory. The general matrix element between two modes quantifies their coupling strength. Aims. This study revises the calculation of the direct effect of a subsurface toroidal magnetic field on solar-like stellar oscillations and provides corrected expressions for the general matrix element and the corresponding angular kernels. Methods. We perturbed a non-magnetic, non-rotating equilibrium stellar model using a superposition of toroidal magnetic fields. Applying quasi-degenerate perturbation theory and generalised spherical harmonics, we derived the general matrix element and computed the shifts and splitting of the multiplet frequencies. We identified selection rules for mode coupling by analysing the symmetries of the angular kernels. Results. Previous studies underestimated the direct effect of a toroidal magnetic field by neglecting non-zero contributions in integrals over products of scalar generalised spherical harmonics. We have developed an analytical method to calculate these integrals. For a strong toroidal field located at the base of the solar convection zone, the frequency shift due to the direct effect can reach 14 nHz, which is twice as large as previously reported. Modes couple through the toroidal field only if their azimuthal orders are equal and the sum of the harmonic degrees of the modes and the magnetic field components is even. The toroidal field only partially lifts the degeneracy of multiplet frequencies, leaving modes with the same absolute azimuthal order m within a multiplet degenerate. Conclusions. We confirm that deep toroidal magnetic fields are not responsible for the observed frequency shifts between the maximum and minimum of the solar cycle. However, although their detection is strongly impeded by the much stronger effects of near-surface fields, their existence cannot be ruled out.

Fluorine-activated and -directed allene cycloadditions with nitrile oxide: Exploration of selectivities, reactivities, energetic aspects, and molecular mechanism.

We derive the energy-differential cross section and energy loss rate for dissipative self-interacting dark matter (dSIDM) models within the Born regime using perturbative quantum field theory. Six dissipative scenarios are considered, incorporating the emission of particles that may be either massless or possess a kinematically allowed light mass. Both short-range and long-range force-mediated dSIDM interactions are examined. In the non-relativistic regime, we obtain closed-form expressions of the energy-differential cross sections by a controlled expansion in the initial relative dark matter velocity. Up to trivial factors, the leading-order squared emission amplitude is model-independent for massless emissions. Model dependence arises for massive particle emission and at the next-to-leading order. The latter reduces to three distinct cases. The derived analytical expressions exhibit excellent agreement with numerical computations, providing simple, ready-to-use formulas. Furthermore, we analyze the behavior of these processes in the soft emission limit. Our results show that additional corrections are necessary when applying factorization at the next-to-leading order in a velocity expansion to ensure consistency between the soft energy-differential cross section and the full counterparts across a broad energy range. Finally, we investigate the regime of perturbative validity in terms of the model parameters, identifying the conditions under which our results are applicable.