C6 Coefficients Research Articles

Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer.

We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H10) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H2, LiH, H2O, OH-, and NH3, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the C6 coefficients of H2, LiH, H2O, OH-, and NH3.

The significance of fluctuating charges for molecular polarizability and dispersion coefficients.

The influence of fluctuating charges or charge flow on the dynamic linear response properties of isolated molecules from the TS42 database is evaluated, with particular emphasis on dipole polarizability and C6 dispersion coefficients. Two new descriptors are defined to quantify the charge-flow contribution to response properties, making use of the recoupled dipole polarizability to separate isotropic and anisotropic components. Molecular polarizabilities are calculated using the "frequency-dependent atom-condensed Kohn-Sham density functional theory approximated to second order," i.e., the ACKS2ω model. With ACKS2ω, the charge-flow contribution can be constructed in two conceptually distinct ways that appear to yield compatible results. The charge-flow contribution is significantly affected by molecular geometry and the presence of polarizable bonds, in line with previous studies. We show that the charge-flow contribution qualitatively reproduces the polarizability anisotropy. The contribution to the anisotropic C6 coefficients is less pronounced but cannot be neglected. The effect of fluctuating charges is only negligible for small molecules with at most one non-hydrogen atom. They become important and sometimes dominant for larger molecules or when highly polarizable bonds are present, such as conjugated, double, or triple bonds. Charge flow contributions cannot be explained in terms of individual atomic properties because they are affected by non-local features such as chemical bonding and geometry. Therefore, polarizable force fields and dispersion models can benefit from the explicit modeling of charge flow.

Effect of Repeated Application of Switching Electric Field on Al/Ba<sub>0.9</sub>Sr<sub>0.1</sub>TiO<sub>3</sub>/Pt/Si and Al/Ba<sub>0.3</sub>Sr<sub>0.7</sub>TiO<sub>3</sub>/Pt/Si Thin Films

Repeated application of switching the electric field on the electrical properties of the films, such as variation of capacitance with voltage and leakage current, were studied on thin films of Al/Ba0.9Sr0.1TiO3/Pt/Si (BST-0.9) and Al/Ba0.3Sr0.7TiO3/Pt/Si (BST-0.3) prepared by sol-gel method. The ferroelectric BST-0.9 films that exhibited degradation by applying a switching electric field showed hysteresis. Paraelectric BST-0.3 films did not show any degradation on repeated application of switching electric field. The resistivity, breakdown field, and Devonshire thermodynamic coefficient C3 were calculated for all the films. These physical properties are essential in choosing a film for particular applications such as memory, dynamic random access memory, tunable phase shifter, photodiodes in light sensors, etc.

Analysis of Corneal Biomechanical Properties in Different Keratotopographic Patterns of Keratoconus.

To analyze the frequency of main keratotopographic patterns at the 1st, 2nd, and 3rd stages of keratoconus and investigate corneal biomechanical properties across different patterns. The study comprised two stages. The first stage was computational-experimental, where we utilized COMSOL Multiphysics® software (COMSOL AB, Stockholm, Sweden) to mathematically model corneal mechanical behavior under intraocular pressure and pulsed air jet action in both normal and keratoconic conditions. The second stage was the clinical phase, during which we retrospectively analyzed the examination results of both healthy subjects and patients with keratoconus. In total, the study included 256 eyes (256 subjects). Among them, 174 eyes (174 healthy individuals) had normal corneas with different refractions, and 82 eyes (82 individuals) had stages 1, 2, and 3 of keratoconus based on Amsler-Krumeich classification. The keratotopographic characteristics of the participants were assessed using Sirius (Schwind, Germany) and Pentacam AXL (OCULUS Optikgeräte GmbH, Germany) keratotomographs, while the corneal biomechanical properties were studied using noncontact tonometry with the Corvis ST device (OCULUS Optikgeräte GmbH, Germany). The study focused on evaluating corneal stiffness index values in the central optical zone under various keratotopographic patterns. In addition, it compared the elastic coefficient values c1, c2, and c3 for the model of hyperelastic behavior of corneal material outside the keratoconus zone. Furthermore, the study examined the values of reduced stiffness zone characteristics, including the stiffness reduction factor ψmax, effective radius Rk, and the ratio of maximum and minimum strain intensity in keratoconus of different stages. The mean age of the patients in the study was 30.16 ± 8.31 years, with 166 men and 90 women participating. The study revealed typical keratotopographic patterns in the examined keratoconus stages, as well as their occurrence frequency. In the 1st stage of keratoconus, the pattern of asymmetric astigmatism was noted more frequently (in 75% of cases). In the 2nd stage, the pattern with an ectasia zone in the lower cornea was observed in 80% of cases, and in the 3rd stage, a centrally located keratotopographic ectasia pattern was found in 42% of cases. Comparative analysis showed that the greatest decrease in stiffness parameter (SpA1) and stress-strain index occurred in the central pattern (by 64% and 46%, respectively), while the least decrease was observed in local corneal radius reduction in the lower cornea (by 42% and 33%, respectively). The decrease in strength properties in keratoconus occurs in a local area, the size and degree of which are determined by the disease stage. The indicated biomechanical parameters are consistent regardless of the shape and localization of keratotopographic patterns but are relevant to diagnostic specifications using the Corvis ST pneumotonometer, which assesses corneal properties in the apical zone.

Nonperturbative Corrections to Adler Function and Hypothesis of Vacuum Dominance

We check the range of values of four-quark condensate, relying on the processing of experimental data on e+e− annihilation into even number of pions (BaBar, CMD-2, OLYA) and extracting from them the values of the nonperturbative corrections. According to the hypothesis of vacuum dominance, the vacuum average of the four-quark condensate is expressed in terms of quark condensate while only vacuum intermediate states contribution is taken into account. However, assuming a possible non-zero effect of non-vacuum intermediate states, we check its influence on the four-quark condensate, or coefficient C6 in operator product expansion. Moreover, we explore how other nonperturbative corrections, C2 (operator with dimension 2), and C4 (which includes gluon condensate), are changed when assuming this effect. It is shown that values of four-quark condensate, or coefficient C6, can vary not more than 15-20%. Other parameters (C2 and C4) take values close to the currently available ones.

Interaction Potential for NaCs for Ultracold Scattering and Spectroscopy.

We obtain the interaction potential for NaCs by fitting to experiments on ultracold scattering and spectroscopy in optical tweezers. The central region of the potential has been accurately determined from Fourier transform spectroscopy at higher temperatures, so we focus on adjusting the long-range and short-range parts. We use coupled-channel calculations of binding energies and wave functions to understand the nature of the molecular states observed in ultracold spectroscopy and of the state that causes the Feshbach resonance used to create ultracold NaCs molecules. We elucidate the relationships between the experimental quantities and features of the interaction potential. We establish the combinations of experimental quantities that determine particular features of the potential. We find that the long-range dispersion coefficient C6 must be increased by about 0.9% to 3256(1)Eha06 to fit the experimental results. We use coupled-channel calculations on the final potential to predict bound-state energies and resonance positions.

Deformation Modeling and Simulation of a Novel Bionic Software Robotics Gripping Terminal Driven by Negative Pressure Based on Classical Differential Algorithm.

A general pneumatic soft gripper is proposed in this paper. Combined with the torque balance theory, the mathematical theoretical model of bending deformation of soft gripper is established based on Yeoh constitutive model and classical differential geometry. Assuming that the pressure in each inner cavity is evenly distributed, the input gas is in an ideal state, which is approximately treated as an isothermal condition, and all orifices experience blocked flow. In addition, compared with the mechanical work of gas, the energy related to gas flow and heat transfer is negligible. The nonlinear mechanical properties of silicone rubber are studied. It is regarded as isotropic and incompressible material, which is characterized by strain energy per unit volume. The material constant coefficients C10 and C20 are determined through the uniaxial tensile test, and the software gripper is simulated on the ABAQUS platform. The bending deformation models of grippers with three different force-bearing cavity structures are analyzed and compared, and the software clamping structure with the bending deformation most in line with the application conditions is selected. The limit input air pressure of the gripper and the situation of enveloping the clamping target object are analyzed. Through the bending deformation experiment, the maximum deformation angle is 72.4°. The relative error between the simulation analysis data and the prediction results of the mathematical model is no more than 3.5%, which verifies the effectiveness of the simulation and the correctness of the mathematical theoretical model of bending deformation. The soft manipulator proposed in this paper has good adaptability to grasping objects of different shapes and sizes. The minimum diameter of the target object that can be clamped is 0.1 mm. It can clamp the object weighing up to 1 kg. It has compact size, light weight, high ductility, and flexibility.

Long-Range Interactions for Hydrogen Atoms in Excited D States

Pressure shifts inside an atomic beam are among the more theoretically challenging effects in high-precision measurements of atomic transitions. A crucial element in their theoretical analysis is the understanding of long-range interatomic interactions inside the beam. For excited reference states, the presence of quasi-degenerate states leads to additional challenges, due to the necessity to diagonalize large matrices in the quasi-degenerate hyperfine manifolds. Here, we focus on the interactions of hydrogen atoms in reference states composed of an excited nD state (atom A), and in the metastable 2S state (atom B). We devote special attention to the cases n=3 and n=8. For n=3, the main effect is generated by quasi-degenerate virtual P states from both atoms A and B and leads to experimentally relevant second-order long-range (van-der-Waals) interactions proportional to the sixth inverse power of the interatomic distance. For n=8, in addition to virtual states with two states of P symmetry, one needs to take into account combined virtual P and F states from atoms A and B. The numerical value of the so-called C6 coefficients multiplying the interaction energy was found to grow with the principal quantum number of the reference D state; it was found to be of the order of 1011 in atomic units. The result allows for the calculation of the pressure shift inside atomic beams while driving transitions to nD states.

The ground state van der Waals potentials of Cd-RG systems

Assuming that the corresponding states principle is valid for the hetero-nuclear dimers formed from group 12 and rare gas atoms, that is, the reduced potentials of Cd-RG and Hg-RG systems are conformal, together with the dispersion coefficients C6, C8, and C10 calculated from the combining rules with the parameters of Cd-Cd and RG-RG, the van der Waals potentials of Cd-RG can be described by the TT potential. According to the present potential curves of Cd-RG, the spectroscopic constants of these dimers can be obtained. The present results of Cd-RG are compared with available experimental and theoretical results of other studies.

New atoms-in-molecules dispersion models for use in ab initio derived force fields.

Recently, substantial research efforts have gone into bridging the accuracy-efficiency gap between parameterized force field models and quantum chemical calculations by extracting molecule-specific force fields directly from ab initio data in a robust and automated manner. One of the challenging aspects is deriving localized atomic polarizabilities for pairwise distributed dispersion models. The Tkatchenko-Scheffler model is based upon correcting free-atom C6 coefficients according to the square of the ratio of the atom-in-molecule volume to the free-atom volume. However, it has recently been shown that a more accurate relationship can be found if static atomic polarizabilities are also taken into account. Using this relationship, we develop two modified Tkatchenko-Scheffler dispersion models and benchmark their performance against SAPT2+3 reference data and other commonly used dispersion models.

Size-dependent polarizabilities and van der Waals dispersion coefficients of fullerenes from large-scale complex polarization propagator calculations.

While the anomalous non-additive size-dependencies of static dipole polarizabilities and van der Waals C6 dispersion coefficients of carbon fullerenes are well established, the widespread reported scalings for the latter (ranging from N2.2 to N2.8) call for a comprehensive first-principles investigation. With a highly efficient implementation of the linear complex polarization propagator, we have performed Hartree-Fock and Kohn-Sham density functional theory calculations of the frequency-dependent polarizabilities for fullerenes consisting of up to 540 carbon atoms. Our results for the static polarizabilities and C6 coefficients show scalings of N1.2 and N2.2, respectively, thereby deviating significantly from the previously reported values obtained with the use of semi-classical/empirical methods. Arguably, our reported values are the most accurate to date as they represent the first ab initio or first-principles treatment of fullerenes up to a convincing system size.

Dipole oscillator strength distributions, sum rules, mean excitation energies, and isotropic van der Waals coefficients for benzene, pyridazine, pyrimidine, pyrazine, s-triazine, toluene, hexafluorobenzene, and nitrobenzene

Experimental, theoretical, and additive-model photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and the high-energy behavior of the dipole oscillator strength density are used to construct dipole oscillator strength distributions for benzene, pyridazine (1,2-diazine), pyrimidine (1,3-diazine), pyrazine (1,4-diazine), s-triazine (1,3,5-triazine), toluene (methylbenzene), hexafluorobenzene, and nitrobenzene. The distributions are used to predict dipole sum rules S(k) for -6 ≤ k ≤ 2, mean excitation energies I(k) for -2 ≤ k ≤ 2, and isotropic van der Waals C6 coefficients. A popular combination rule for estimating C6 coefficients for unlike interactions from the C6 coefficients of the like interactions is found to be accurate to better than 1% for 606 of 628 cases (96.4%) in the test set.

An accurate semiempirical potential energy curve for the a3Σ+-state of KRb.

A semiempirical potential energy curve for the a3Σ+-state of the KRb molecule with only five parameters is reported. The potential is continuous over the entire range of internuclear distances and has the correct long-range attractive dispersion potential from established theory. The potential provides an equally good fit of the laser induced fluorescence Fourier transform spectroscopic data of Pashov et al. [Phys. Rev. A 76, 022511 (2007)] as their multi-parameter potential. The new potential is supported by the good agreement of the well parameters De, Re and the harmonic vibrational constant ωe with combining-rule estimates. The scattering lengths for all six isotopologues are also in excellent agreement with experiment with a 0.2% adjustment within theoretical uncertainty of the leading dispersion coefficient C6. An analysis of the harmonic vibrational constant ωe and the constant ωexe of the potential of Pashov et al. reveals a significant difference to the present potential which turned out to be due to an oscillatory deviation in their potential in the vicinity of the potential minimum. The new potential is, thus, the best available because its simplicity is ideal for further applications.

Investigation of Interaction of Cs Atoms with Sapphire Surface by Means of an Ultrathin Cell and the Second-Derivative Spectrometry of Vapor Absorption

The influence of interaction of Cs atoms with a dielectric surface on position and shape of the hyperfine components of the D2 line in the case of nanometer-scale distance between the atom and the surface is investigated. Using a wedged nanocell enabled investigating the dependence of shift of all hyperfine components of the D2 line corresponding to Fg = 3 → Fe = 2, 3, 4 and Fg = 4 → Fe = 3, 4, 5 transitions on distance L between the atoms and the surface of a sapphire window in the interval from 50 to 400 nm. At L smaller than 100 nm, atomic transitions experience strong broadening due to van der Waals interaction and shift to lower frequencies (the red shift). Calculation of the second derivative (SD) of the absorption spectra of vapors in a nanocell allows spectrally resolving the hyperfine components of an atomic transition down to L ~ 50 nm and determining the van der Waals interaction coefficient C3. It is demonstrated that the spectrum experiences an additional red shift with increase in the density of atoms at L < 100 nm. In contrast, a blue shift occurs with increase in the density of atoms at relatively large distances between the atoms and the surface (L ~ 400 nm). The above results are important for development of miniature submicron-size devices containing alkali metals.

Many‐body response of benzene at monolayer MoS2: Van der Waals interactions and spectral broadening

AbstractModels of surface enhancement of molecular electronic response properties are challenging for two reasons: (a) molecule‐surface interactions require a simultaneous solution of the molecular and the surface dynamic response (a daunting task), and (b) when solving for the electronic structure of the combined molecule + surface system, it is not trivial to single out the particular physical effects responsible for enhancement. To tackle this problem, in this work, we apply a formally exact decomposition of the system's response function into subsystem contributions by using subsystem density functional theory (DFT), which grants access to dynamic polarizabilities and optical spectra. In order to access information about the interactions between the subsystems, we extend a previously developed subsystem‐based adiabatic connection fluctuation‐dissipation theorem of DFT to separate the additive from the nonadditive correlation energy and identify the nonadditive correlation as the van der Waals interactions. As an example, we choose benzene adsorbed on monolayer MoS2. We isolate the contributions to benzene's dynamic response arising from the interaction with the surface, and for the first time, we evaluate the enhancements to the effectiveness of C6 coefficients as a function of benzene‐MoS2 distance and adsorption site. We also quantify the spectral broadening of the benzene's electronic excited states due to their interaction with the surface. We find that the broadening has a similar decay law with the molecule‐surface distance as the leading van der Waals interactions (ie, R−6) and that the surface enhancement of dispersion interactions between benzene molecules is less than 5% but is still large enough (0.5 kcal/mol) to likely play a role in the prediction of interface morphologies.

Calculations of long-range three-body interactions for Li(2 2S )-Li(22 S )-Li+(1 1S)

SynopsisUsing perturbation theory for energies, we evaluate the additive and nonadditive interaction co-efficients C4, C6 , C7 , C8 and C9 for the Li(22S)-Li(22S)-Li+(11S) system. The obtained coefficients Cn are evaluated with highly accurate variationally-generated nonrelativistic wave functions in Hylleraas coordinates. The nonadditive interaction coefficients depend on the geometrical configurations of this three-body system and on the different position of the ion for each configuration. Our calculations may be of interest for the study of three-body recombination and for constructing precise potential energy surfaces.

Anisotropic interactions in electric field polarized ultracold Rydberg gases

We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective C3 dipole–dipole and C6 van der Waals coefficients. We compare the C3 and C6 with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole–dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in states in the blockade regime. For internuclear distances close to the blockade radius, Rbl ≈ 4–6 μm, molecular calculations are in much better agreement with experimental results than those based on the properties of single atoms and independent calculations of C3 and C6 which were used to analyze the original experiment. We find that the calculated C6 coefficient is within 8% of the experimental value while the C3 coefficient is within 20% of the experimental value.

Selective reflection from a potassium atomic layer with a thickness as small as λ/13

We demonstrate that a method using the derivative of the selective reflection (SR) signal from a nanocell is a convenient and robust tool for atomic laser spectroscopy, achieving a nearly Doppler-free spectral resolution. The recorded linewidth of the signal from a potassium-filled cell, whose thickness ℓ lies in the range 350–500 nm, is 18 times smaller than the Doppler linewidth (∼900 MHz full width at half maximum) of potassium atoms. We also show experimentally a sign oscillation of the reflected signal’s derivative with a periodicity of λ/2 when ℓ varies from 190 to 1200 nm confirming the theoretical prediction. We report the first measurement of the van der Waals atom-surface interaction coefficient C3 = 1.9 ± 0.3 kHz × μm3 of potassium transitions with the nanocell’s sapphire windows, demonstrating the usefulness and convenience of the derivative of SR technique for cell thicknesses in the range 60–120 nm.

Study on the composite mechanism of large Rubber-Sleeved Stud connector

Abstract The Ordinary Headed Stud (OHS) connector whose diameter is 25 mm or larger is regarded as the large OHS connector, which possesses greater shear stiffness and ultimate capacity. Therefore, it is expected that the required number of OHS connectors can be reduced by applying the large OHS connectors in the steel-concrete interface, which have its construction advantages over smaller ones. However, the great stiffness could also cause the shear force of the large OHS connector at the interface edge exceeding the design allowable value. Hence, the large Rubber-sleeved Stud (RSS) connector was proposed by wrapping rubber sleeve at the root of large OHS connector to decrease its stiffness, making the shear force in the steel-concrete interface more evenly distributed. In this study, push-out tests and numerical simulation were carried out to reveal the composite mechanism of the large RSS connector. Based on the verified modeling method, parametric analysis was performed to investigate the influence of different parameters on the shear stiffness of RSS connectors. The results show that the shear stiffness of large RSS connector is decreased to 41.5% of the large OHS connector. RSS connectors exhibit better deformation recovery and accumulation compared with OHS connectors under cyclic loading. Furthermore, the maximum principal tensile stress of concrete could be decreased and concrete damaged areas are reduced when the large OHS connectors are wrapped with rubber sleeves. The shear stiffness of RSS connector is positively related to the rubber shearing coefficient C10 and concrete compressive strength fcm while negatively related to the rubber sleeve thickness tr, rubber sleeve height hr and rubber compressibility coefficient D1.

Computation of Dynamic Polarizabilities and van der Waals Coefficients from Path-Integral Monte Carlo.

We demonstrate computation of total dynamic multipole polarizabilities using path-integral Monte Carlo method (PIMC). The PIMC approach enables accurate thermal and nonadiabatic mixing of electronic, rotational, and vibrational degrees of freedom. Therefore, we can study the thermal effects, or lack thereof, in the full multipole spectra of the chosen one- and two-electron systems: H, Ps, He, Ps2, H2, and HD+. We first compute multipole-multipole correlation functions up to octupole order in imaginary time. The real-domain spectral function is then obtained by analytical continuation with the maximum entropy method. In general, sharpness of the active spectra is limited, but the obtained off-resonant polarizabilities are in good agreement with the existing literature. Several weak and strong thermal effects are observed. Furthermore, the polarizabilities of Ps2 and some higher multipole and higher frequency data have not been published before. In addition, we compute isotropic dispersion coefficients C6, C8, and C10 between pairs of species using the simplified Casimir-Polder formulas.