Ground State Research Articles

Finite point blowup for the critical generalized Korteweg-de Vries equation

In the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de Vries equation, including the determination of sufficient conditions for blowup, the stability of blowup in a refined topology and the classification of minimal mass blowup. Exotic blow-up solutions with a continuum of blow-up rates and multi-point blow-up solutions were also constructed. However, all these results, as well as numerical simulations, involve the bubbling of a solitary wave going at infinity at the blow-up time, which means that the blow-up dynamics and the residue are eventually uncoupled. Even at the formal level, there was no indication whether blowup at a finite point could occur for this equation. In this article, we answer this question by constructing solutions that blow up in finite time under the form of a single-bubble concentrating the ground state at a finite point with an unforeseen blow-up rate. Finding a blow-up rate intermediate between the self-similar rate and other rates previously known also reopens the question of which blow-up rates are actually possible for this equation.

3,4-Dimethylenecyclobutene: A Building Block for Design of Macrocycles with Excited State Aromatic Low-Lying High-Spin States.

3,4-Dimethylenecyclobutene (DMCB) is an unusual isomer of benzene. Motivated by recent synthetic progress to substituted derivatives of this scaffold, we carried out a theoretical and computational analysis with a particular focus on the extent of (anti)aromatic character in the lowest excited states of different multiplicities. We found that the parent DMCB is non-aromatic in its singlet ground state (S0), lowest triplet state (T1), and lowest singlet excited state (S1), while it is aromatic in its lowest quintet state (Q1) as this state is represented by a triplet multiplicity cyclobutadiene (CBD) ring and two uncoupled same-spin methylene radicals. Interestingly, the Q1 state, despite having four unpaired electrons, is placed merely 4.8 eV above S0, and there is a corresponding singlet tetraradical 0.16 eV above. The DMCB is potentially a highly useful structural motif for the design of larger molecular entities with interesting optoelectronic properties. Here, we designed macrocycles composed of fused DMCB units, and according to our computations, two of these have low-lying nonet states (i. e., octaradical states) at energies merely 2.40 and 0.37 eV above their S0 states as a result of local Hückel- and Baird-aromatic character of individual 6π- and 4π-electron monocycles.

Solvation effects on the excitation dynamics, structural and photorelaxation, quantum chemical investigation, and photophysical properties of 2D p-expanded quinoidal terthiophene (2DQTTs): Outlook from Ab-initio calculations

All dyes have different degrees of absorption. The present study delves into the intricate interplay between solvation and the photophysical behaviors of 2D p-expanded quinoidal terthiophene (2DQTT) dye compounds represented as A3, A4, and A5. In this study, a comprehensive investigation is presented, elucidating how solvation impacts excitation dynamics, ground and excited state geometry, photophysical characteristics. and photorelaxation dynamics of 2DQTTs. The energy gap data shows that the energies of the compounds increased in polar mediums and were greater for compound A3 which had ΔE values of 3.5227 eV in water, and 3.5225 eV in DMSO while compound A5 had the highest ΔE in all phases, with a ΔE value of 3.5453 eV in EtOH. Relaxation of the compounds leads to changes in the bonds and structural conformation of the 2D P-expanded quinoidal terthiophene (2DQTT) compounds as the compounds de-excite back to a lower energy level, and the photon causes a change in structural bonding (Stokes shift) in the heteroatoms which was taken into consideration. This manuscript not only advances our fundamental understanding of the interactions between solvation and molecular structure but also provides valuable insights into optimizing the performance of 2DQTT in optoelectronic devices as the compounds display a high absorption band in all phases, especially in water medial with compound A3, A4 and A5 recording absorbances of 785.32 nm, 787.13 nm, and 786.78 nm respectively, a high light harvesting efficiency LHE, great electron exciton energy and an injecting capacity (ΔGinject) greater than 0.20 eV in all phases. This work contributes significantly to the design and application of novel materials for next-generation optoelectronic technologies hence we hope that experimental research tests the studied compound towards the mentioned application.

Precise Modulation of Circularly Polarized Luminescence via Polymer Chiral Co-assembly and Contactless Dynamic Chiral Communication.

Circularly polarized luminescence (CPL) plays a pivotal role in cutting-edge display and information technologies. Currently achieving precise color control and dynamic signal regulation in CPL still remains challenging due to the elusory relationship between fluorescence and chirality. Inspired by the natural mechanisms governing color formation and chiral interaction, we proposed an addition-subtraction principle theory to address this issue. Three fluorene-based polymers synthesized by Suzuki polycondensation with different electron-deficient monomers exhibit similar structures and UV/Vis absorption, but distinct fluorescence emissions due to intramolecular charge transfer. Based on this, precise-color CPL-active films are obtained through quantitative supramolecular co-assembly directed by addition principle. Particularly, an ideal white-emitting CPL film (CIE coordinates: (0.33, 0.33)) is facilely fabricated with a high quantum yield of 80.8 % and a dissymmetry factor (glum) of 1.4×10-2. Structural analysis reveals that the ordered stacking orientation favors higher glum. Furthermore, to address the dynamically regulated challenge, the comparable subtraction principle is proposed, involving a contactless chiral communication between excited and ground states. The representative system consisting of as-prepared fluorene-based polymers and chirality-selective absorption azobenzene (Azo)-containing polymers is constructed, achieving CPL weakening, reversal, and enhancement. Finally, a switchable quick response code is realized based on trans-cis isomerization of Azo moiety.

Precise Modulation of Circularly Polarized Luminescence via Polymer Chiral Co‐assembly and Contactless Dynamic Chiral Communication

AbstractCircularly polarized luminescence (CPL) plays a pivotal role in cutting‐edge display and information technologies. Currently achieving precise color control and dynamic signal regulation in CPL still remains challenging due to the elusory relationship between fluorescence and chirality. Inspired by the natural mechanisms governing color formation and chiral interaction, we proposed an addition‐subtraction principle theory to address this issue. Three fluorene‐based polymers synthesized by Suzuki polycondensation with different electron‐deficient monomers exhibit similar structures and UV/Vis absorption, but distinct fluorescence emissions due to intramolecular charge transfer. Based on this, precise‐color CPL‐active films are obtained through quantitative supramolecular co‐assembly directed by addition principle. Particularly, an ideal white‐emitting CPL film (CIE coordinates: (0.33, 0.33)) is facilely fabricated with a high quantum yield of 80.8 % and a dissymmetry factor (glum) of 1.4×10−2. Structural analysis reveals that the ordered stacking orientation favors higher glum. Furthermore, to address the dynamically regulated challenge, the comparable subtraction principle is proposed, involving a contactless chiral communication between excited and ground states. The representative system consisting of as‐prepared fluorene‐based polymers and chirality‐selective absorption azobenzene (Azo)‐containing polymers is constructed, achieving CPL weakening, reversal, and enhancement. Finally, a switchable quick response code is realized based on trans‐cis isomerization of Azo moiety.

Magneto-Structural Correlation of Five-Coordinate Trigonal Bipyramidal High Spin Cobalt(II) Complexes.

Here, we combined magnetometry, multi-frequency electronic paramagnetic resonance, and wave function based ab initio calculations to investigate magnetic properties of two high spin Co(II) complexes Co(BDPRP) (BDPRP=2,6-bis((2-(S)-di(4-R)phenylhydroxylmethyl-1-pyrrolidi-nyl)methyl)pyridine, R=H for 8; R=tBu for 9). Complexes 8 and 9 featuring effective D3h symmetry were found to possess D=24.0 and 32.0 cm-1, respectively, in their S=3/2 ground states of . Ligand field analyses revealed that the low-lying d-d excited states make either positive or vanishing contributions to D. Hence, total positive D values were measured for 8 and 9, as well as related D3h high spin Co(II) complexes. In contrast, negative D values are usually observed for C3v congeners. In-depth analyses suggested that lowering symmetry from D3h to C3v induces orbital mixing between and and admixes excited state into the ground state. Both factors turn the total D value progressively negative with the increasing distance (δ) of the Co(II) center out of the equatorial plane. Therefore, δ determines the sign and magnitude of final D values of five-coordinate trigonal bipyramidal S=3/2 Co(II) complexes as measured for a series of such species with varying δ.

THE STUDY OF ELECTRIC QUADRUPOLE TRANSITION (E2) IN 58Ce AND 60Nd NUCLEI

Transition strengths 2w.u. M(E2) for gamma transition from first excited 21+statesto the ground states that produced by pure electric quadrupole emission in even –even nuclei of 58Ce and 60Nd have been calculated as a function of neutron number(N). The life times for 21+ excited states together with the intensities of γ0- transitionsmeasurements are used in calculations. The results thus obtained have shown that;the nuclei with magic neutron number such as 58Ce140 and 60Nd142 have minimumvalue for 2w.u. M(E2) . The reduced transition probabilities B(E2) are alsocalculated and compared with the experimental data and other theoretical models.PACS:- 27.60-j, 23.20-g, 23.20.Ck, 23.20.Gq

Aufbau Suppressed Coupled Cluster Theory for Electronically Excited States.

We introduce an approach to improve single-reference coupled cluster theory in settings where the Aufbau determinant is absent from or plays only a small role in the true wave function. Using a de-excitation operator that can be efficiently hidden within a similarity transform, we create a coupled cluster wave function in which de-excitations work to suppress the Aufbau determinant and produce wave functions dominated by other determinants. Thanks to an invertible and fully exponential form, the approach is systematically improvable, size consistent, size extensive, and, interestingly, size intensive in a granular way that should make the adoption of some ground state techniques, such as local correlation, relatively straightforward. In this initial study, we apply the general formalism to create a state-specific method for orbital-relaxed, singly excited states. We find that this approach matches the accuracy of similar-cost equation-of-motion methods in valence excitations while offering improved accuracy for charge transfer states. We also find the approach to be more accurate than excited-state-specific perturbation theory in both types of states.

Recent Developments of Nontraditional Single-Molecule Toroics.

Single-molecule toroics (SMTs), defined as a type of molecules with toroidal arrangement of magnetic moment associated with bi-stable non-magnetic ground states, are promising candidates for high-density information storage and the development of molecule based multiferroic materials with linear magneto-electric coupling and multiferroic behavior. The design and synthesis of SMTs by arranging the magnetic anisotropy axis in a circular pattern at the molecular level have been of great interest to scientists for last two decades since the first detection of the SMT behavior in the seminal Dy3 molecules. DyIII ion has long been the ideal candidate for constructing SMTs due to its Kramer ion nature as well as high anisotropy. Nevertheless, other LnIII ions such as TbIII and HoIII ions, as well as some paramagnetic transition metal ions, have also been used to construct many nontraditional SMTs. Therefore, we review the progress in the studies of SMTs based on the nontraditional perspective, ranging from the 3D topological to 1D&2D&3D polymeric SMTs, and 3d-4f to non Dy-based SMTs. We hope the understanding we provide about nontraditional SMTs will be helpful in designing novel SMTs.

Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation.

In this work, we utilize the framework of many-body expansion (MBE) to decompose electronic structures into fragments by incrementing virtual orbitals, aiming to accurately solve the ground and excited state energies of each fragment using the variational quantum eigensolver and deflation algorithms. While our approach is primarily based on unitary coupled cluster singles and doubles (UCCSD) and its generalization, we also introduce modifications and approximations to conserve quantum resources in MBE by partially generalizing the UCCSD operator and neglecting the relaxation of the reference states. As a proof of concept, we investigate the potential energy surfaces for the bond-breaking processes of the ground state of two molecules (H2O and N2) and calculate the ground and excited state energies of three molecules (LiH, CH+, and H2O). The results demonstrate that our approach can, in principle, provide reliable descriptions in all the tests including strongly correlated systems when appropriate approximations are chosen. Additionally, we perform model simulations to investigate the impact of shot noise on the total MBE energy and show that precise energy estimation is crucial for lower-order MBE fragments.

Cluster perturbation theory IX: Perturbation series for the coupled cluster singles and doubles ground state energy.

In this paper, we develop and analyze a number of perturbation series that target the coupled cluster singles and doubles (CCSD) ground state energy. We show how classical Møller-Plesset perturbation theory series can be restructured to target the CCSD energy based on a reference CCS calculation and how the corresponding cluster perturbation series differs from the classical Møller-Plesset perturbation series. Subsequently, we reformulate these series using the coupled cluster Lagrangian framework to obtain series, where fourth and fifth order energies are determined only using parameters through second order. To test the methods, we perform a series of test calculations on molecular photoswitches of both total energies and reaction energies. We find that the fifth order reaction energies are of CCSD quality and that they are of comparable accuracy to state-of-the-art approximations to the CCSD energy based on local pair natural orbitals. The advantage of the present approach over local correlation methods is the absence of user defined threshold parameters for neglecting or approximating contributions to the correlation energy. Fixed threshold parameters lead to discontinuous energy surfaces, although this effect is often small enough to be ignored, but the present approach has a differentiable energy that will facilitate derivation and implementation of gradients and higher derivatives. A further advantage is that the calculation of the perturbation correction is non-iterative and can, therefore, be calculated in parallel, leading to a short time-to-solution.

Ta+ and Nb+ + CO2: intersystem crossing in ion-molecule reactions.

The reactions of Ta+ and Nb+ with CO2 proceed only by a highly efficient oxygen atom transfer reaction to the respective oxide at room temperature in the gas phase. Although the product spin states are not determined, thermochemistry dictates that they must be different from ground state quintet Ta+ and Nb+, implying that intersystem crossing (ISC) has occurred. Recent reactive scattering experiments found dominant indirect dynamics for the reaction with Ta+ hinting at a bottleneck along the reaction path. The question on the nature of the bottleneck, whether it involves a crossing point or a transition state, could not be finally answered because theory located both close to each other. Here, we aim at shedding further light onto the impact of intersystem crossing on the reaction dynamics and ultimately the reactivity of transition metal ion reactions in the gas phase. We employ a combination of thermal kinetics for Ta+ and Nb+ with CO2 using a selected-ion flow tube (SIFT) apparatus and differential scattering cross sections for Nb+ + CO2 from crossed-beam velocity map imaging. The reaction with niobium again shows dominant indirect dynamics and in general very similar dynamics compared to Ta+ + CO2. At thermal energies, both reactions show sub-collisional rate constants with small negative temperature dependencies. Experiments are complemented by high level quantum chemical calculations of the minimum energy pathway. Statistical modelling well-reproduces the experimental thermal rate constants, and suggests that the Nb+ reaction is rate-limited by the intersystem crossing at thermal energies.

Benchmarking calculations of level energies, transition parameters and electron impact excitation cross sections of S-like Xe38+

Atomic structure parameters for levels corresponding to 2s22p63s23p4, 2s22p63s3p5, 2s22p63s23p23d2, 2s22p63s3p43d and 2s22p63s23p33d configurations of S-like Xe38+ are calculated using the fully relativistic multiconfiguration Dirac-Hatree-Fock (MCDHF) method followed by the subsequent relativistic configuration interaction (RCI) calculations. The parameters evaluated include energies of the lowest 75 levels and E1, M1, E2, and M2 transition parameters among these levels. The effect of the choice of virtual orbitals for generating the wavefunctions is discussed. The accuracy of our line strengths is established through the rigorous calculations of their associated uncertainties using three different methods. Another set of calculations using the many-body perturbation theory (MBPT) to validate the present MCDHF-RCI energies is carried out. Further, the electron impact excitation cross-sections using the relativistic distorted wave (RDW) theory are determined for all transitions from the ground and metastable states in the incident electron energy range from the excitation threshold to 10 keV. For plasma physics applications, the fitting parameters for these cross sections employing two distinct equations tailored for low and high-energy regimes are reported. Moreover, the rate coefficients are determined in the electron temperatures range of 15 eV to 100 eV by taking into account the Maxwellian electron energy distribution function and our computed cross-sections. In addition to addressing the atomic data gap in highly charged Xe ions, the present results are of good accuracy and can serve as benchmark tests for other theoretical evaluations. Moreover, they can also assist in line identification of the complex spectra of highly charged sulphur-like xenon ions.

Derivation of the Schrödinger equation from QED

The Schrödinger equation relates the emergent quantities of wavefunction and electric potential and is postulated as a principle of quantum physics or obtained heuristically. However, physical consistency requires that the Schrödinger equation is a low-energy dynamical condition we can derive from the foundations of quantum electrodynamics. Due to the small value of the electromagnetic coupling constant, we show that the electric potential accurately represents the contributions of intermediate low-energy photon exchanges. Then, from the total nonrelativistic energy relation, we see that the dominant term of the electron wavefunction is a superposition of plane waves that satisfies the Schrödinger equation. Our derivation shows that the Schrödinger equation is not an energy conservation relation because its middle term does not represent the electron kinetic energy as assumed. We analyze the physical content of the Schrödinger equation and verify our assessments by calculating and evaluating the physical quantities in the ground state of the hydrogen atom. Furthermore, we explain why nonrelativistic quantum dynamics differs from classical dynamics. Undergraduate students can follow the derivation because it involves fundamental physical concepts and mathematical expressions, and we explain every step.

Necessary and sufficient conditions for ground state solutions to planar Kirchhoff-type equations

In this paper, we are concerned with the ground states of the following planar Kirchhoff-type problem: \[ -\left(1+b\displaystyle\int_{\mathbb{R}^2}|\nabla u|^2\,{\rm d}x\right)\Delta u+\omega u=|u|^{p-2}u, \quad x\in\mathbb{R}^2. \] where $b,\, \omega >0$ are constants, $p>2$ . Based on variational methods, regularity theory and Schwarz symmetrization, the equivalence of ground state solutions for the above problem with the minimizers for some minimization problems is obtained. In particular, a new scale technique, together with Lagrange multipliers, is delicately employed to overcome some intrinsic difficulties.

Entanglement-enabled symmetry-breaking orders

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wavefunction of some few-body clusters; some standard examples include the simplest ferromagnets and valence bond solids. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any such tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.

Quantum criticality in chains of planar rotors with dipolar interactions.

In this work, we perform a density matrix renormalization group study of chains of planar rotors interacting via dipolar interactions. By exploring the ground state from weakly to strongly interacting rotors, we find the occurrence of a quantum phase transition between a disordered and a dipole-ordered quantum state. We show that the nature of the ordered state changes from ferroelectric to antiferroelectric when the relative orientation of the rotor planes varies and that this change requires no modification of the overall symmetry. The observed quantum phase transitions are characterized by critical exponents and central charges, which reveal different universality classes ranging from that of the (1 + 1)D Ising model to the 2D classical XY model.

Single crystal of barium bis para-nitrophenolate para-nitrophenol tetrahydrate for NLO applications: crystal growth and DFT analysis

Abstract Single crystals of barium bis para-Nitrophenolate para-Nitrophenol tetrahydrate (BBPNT) were grown via the slow evaporation technique. The crystal dimensions were measured to be 15 mm × 10 mm × 6 mm. The BBPNT crystal was analyzed using X-ray diffraction, FTIR spectrum, UV–vis spectrum, dielectric studies, thermo-gravimetric (TG) differential thermal analyses (DTA), Vickers microhardness test, second-harmonic generation efficiency, Z-scan technique, PL spectra, and laser damage threshold studies. These findings were previously published in our paper. In the current situation, the theoretical methods include analyzing several aspects, such as the molecular structure determined using X-ray experimentation at its lowest energy state. This analysis is then contrasted by means of density functional theory (DFT) with a suitable set of basic functions. The first-order hyperpolarizability may also be determined via the use of Density Functional Theory (DFT) methods. The molecule’s stability, resulting from hyper conjugative interactions, was examined using the natural bond orbital approach to analyses its nonlinear optical activity and charge delocalization. The magnitude of the HOMO–LUMO energy gap indicates the potential for charge transfer inside the molecule. The investigation of donor-acceptor interactions was conducted using NBO analysis based on optimized ground state geometries.

Production of positronium chloride: A study of the charge exchange reaction between Ps and Cl.

We present cross sections for the formation of positronium chloride (PsCl) in its ground state from the charge exchange between positronium (Ps) and chloride (Cl-) in the range of 10 meV-100eV Ps energy. We have used theoretical models based on the first Born approximation in its three-body formulation. We simulated the collisions between Ps and Cl- using abinitio binding energies and positronic wave functions at both the mean-field and correlated levels extrapolated to the complete basis set limit. The accuracy of these abinitio data was benchmarked on the PsF system with the existing highly accurate results, including the very recent quantum Monte Carlo results. We have investigated Ps excited states up to n = 4. The results suggest that the channel Ps(n = 2) is of particular interest for the production of PsCl in the ground state and shows that an accurate treatment of correlation effects (i.e., electron-electron and electron-positron correlations) leads to a significant change in the magnitude of the PsCl production cross section with respect to the mean-field level.

The Resorcinarene Hexameric Capsule as a Supramolecular Photoacid to Trigger Olefin Hydroarylation in Confined Space.

The self-assembled resorcinarene capsule C6 shows remarkable photoacidity upon light irradiation, which is here exploited to catalyze olefin hydroarylation reactions in confined space. An experimental pKa* value range of -3.3--2.8 was estimated for the photo-excited hexameric capsule C6 *, and consequently an increase in acidity of 8.8 log units was observed with respect to its ground state (pKa=5.5-6.0). This makes the hexameric capsule the first example of a self-assembled supramolecular photoacid. The photoacid C6 * can catalyze hydroarylation reaction of olefins with aromatic substrates inside its cavity, while no reaction occurred between them in the absence of irradiation and/or capsule. DFT calculations corroborated a mechanism in which the photoacidity of C6 * plays a crucial role in the protonation step of the aromatic substrate. A further proton transfer to olefin with a concomitant C-C bond formation and a final deprotonation step lead to product releasing.