Long-range Coefficients Research Articles

Quantum scattering of icosahedron fullerene C60 with noble-gas atoms

There exist multiple ways to cool neutral molecules. A front runner is the technique of buffer gas cooling, where momentum-changing collisions with abundant cold noble-gas atoms cool the molecules. This approach can, in principle, produce the most diverse samples of cold molecules. We present quantum mechanical and semiclassical calculations of the elastic scattering differential cross sections and rate coefficients of the C60 fullerene with He and Ar noble-gas atoms in order to quantify the effectiveness of buffer gas cooling for this molecule. We also develop new three-dimensional potential energy surfaces for this purpose using dispersion-corrected density functional theory (DFT) with counterpoise correction. The icosahedral anisotropy of the molecular system is reproduced by expanding the potential in terms of symmetry-allowed spherical harmonics. Long-range dispersion coefficients have been computed from frequency dependent polarizabilities of C60 and the noble-gas atoms. We find that the potential of the fullerene with He is about five times shallower than that with Ar. Anisotropic corrections are very weak for both systems and omitted in the quantum scattering calculations giving us a nearly quantitative estimate of elastic scattering observables. Finally, we have computed differential cross sections at the collision energies used in experiments by Han et al. (Chem Phys Lett 235:211, 1995), corrected for the sensitivity of their apparatus, and we find satisfactory agreement for C60 scattering with Ar.

Ab initio interaction potentials of alkali metal (M = Na and K)–rare gas (Rg = He, Ne, Ar, Kr, Xe and Rn) complexes

Spectroscopic properties and potential energy curves of alkali metal (M = Na and K) – rare gas (Rg = He, Ne, Ar, Kr, Xe and Rn) van der Waals molecules in their ground states have been studied in detail using spin-restricted open-shell coupled cluster with single and double excitations and perturbative contribution of connected triple excitations (RCCSD(T)) methods. The core-valence correlation (CV) effect was found to be crucial for M-RG molecules containing heavy rare gas atoms. The electronic energies were corrected for the basis set superposition error (BSSE) using the counterpoise method. Energies were extrapolated to the complete basis set (CBS) limit using a two-point scheme. The permanent electric dipole moments, static electric dipole polarizabilities and long-range dispersion coefficients were also calculated. The computed spectroscopic constants, vibrational levels and rotational constants were reported for M-RG and good agreement with the available experimental and theoretical values were found.

Attention guided domain alignment for conditional face image generation

Despite the great success of Generative Adversarial Network (GAN) in face image generation, it is still a challenge to generate a faithful yet high-fidelity face image given an exemplar image and a conditional input from a distinct domain (e.g., a semantic segmentation mask or an edge map). Existing methods learn image-level features to align distinct domains in an intermediate domain, which ignore the spatial relationship of the facial semantic parts and therefore lead to semantic mismatching problems. In addition, it is computationally expensive to establish dense correspondences in the intermediate domain, especially for high-resolution face images. To address these problems, we propose a novel attention guided domain alignment method for conditional face image generation, which aligns two domains directly under the guidance of the local attention learned from semantically similar face parts. In particular, we assign a dedicated index for each feature block and adopt a top-k ranking operation to correspond block-wise features in two distinct domains, which exploits the spatial relationship of facial parts and preserves the texture structure during alignment. The local attention is then learned from the retrieved blocks, which reduces computation complexity substantially and therefore enables to build alignment in a high resolution. The aligned features are finally fused with adaptive weights learned from their long-range correlation coefficients, which capture the semantic coherence of the style features between the two domains. Extensive experimental results on the CelebAMask-HQ dataset demonstrate that the proposed method is superior to the state-of-the-art methods.

Ab initio relativistic potential energy surface with analytical long-range part of benzene-Rn complex and its application to intermolecular vibrations

We study the benzene-Rn (BzRn) complex in its electronic ground state using an ab initio scalar relativistic method in the framework of the coupled-cluster level of theory with single, double, and perturbative triple excitations [CCSD(T)]. Two different approaches to treat the scalar relativistic effects have been tested — the small-core pseudopotential (PP) and the Douglas–Kroll–Hess (DKH) Hamiltonian. These methods were used with the augmented Dunning’s double zeta basis set for C and H atoms, and the augmented triple PP basis set for Rn supplemented by midbond functions. Additionally, the effects of the basis extension for C and H atoms and the extension of the correlation space to include the internal orbitals of Rn and C have been tested. The comparison of the binding energy De and the equilibrium coordinate ze found with different methods has allowed to choose the optimal one based on PP for the construction of the analytical potential energy surface (PES). The long-range part of the potential has been fitted separately and the obtained long-range coefficients have been compared to their counterparts calculated from the first principles using the CCSD polarization propagator. The vibrational energy level pattern of BzRn has been studied, and the revealed polyad structure of the complex has been compared to the previously studied benzene-Kr and benzene-Xe complexes. A Python code that yields the interaction energy at any Rn position is provided.

Classical threshold law for the formation of van der Waals molecules.

We study the role of pairwise long-range interactions in the formation of van der Waals molecules through direct three-body recombination processes A + B + B → AB + B, based on a classical trajectory method in hyperspherical coordinates developed in our earlier works [J. Pérez-Ríos et al., J. Chem. Phys. 140, 044307 (2014); M. Mirahmadi and J. Pérez-Ríos, J. Chem. Phys. 154, 034305 (2021)]. In particular, we find the effective long-range potential in hyperspherical coordinates with an exact expression in terms of dispersion coefficients of pairwise potentials. Exploiting this relation, we derive a classical threshold law for the total cross section and the three-body recombination rate yielding an analytical expression for the three-body recombination rate as a function of the pairwise long-range coefficients of the involved partners.

Highly polar molecules consisting of a copper or silver atom interacting with an alkali-metal or alkaline-earth-metal atom

We theoretically investigate the properties of highly polar diatomic molecules containing $^2S$-state transition-metal atoms. We calculate potential energy curves, permanent electric dipole moments, spectroscopic constants, and leading long-range dispersion-interaction coefficients for molecules consisting of either a Cu or Ag atom interacting with an alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atom. We use ab initio electronic structure methods, such as the coupled cluster and configuration interaction ones, with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials. We predict that the studied molecules in the ground electronic state are strongly bound with highly polarized covalent or ionic bonds resulting in very large permanent electric dipole moments. We find that highly excited vibrational levels have maximal electric dipole moments, e.g., exceeding 13$\,$debye for CsAg and 6$\,$debye for BaAg. Results for Cu$_2$, Ag$_2$, and CuAg are also reported. The studied molecules may find application in ultracold dipolar many-body physics, controlled chemistry, or precision measurement experiments.

Quasielastic Neutron Scattering and Molecular Dynamics Simulation Study on the Molecular Behaviour of Catechol in Zeolite Beta

The dynamics of catechol in zeolite Beta was studied using quesielastic neutron scattering (QENS) experiments and molecular dynamics simulations at 393 K, to understand the behaviour of phenolic monomers relevant in the catalytic conversion of lignin via metal nanoparticles supported on zeolites. Compared to previous work studying phenol, both methods observe that the presence of the second OH group in catechol can hinder mobility significantly, as explained by stronger hydrogen-bonding interactions between catechol and the Brønsted sites of the zeolite. The instrumental timescale of the QENS experiment allows us to probe rotational motion, and the catechol motions are best fit to an isotropic rotation model with a D^{rot} of 2.9 × 10^{10} s^{-1}. While this D^{rot} is within error of that measured for phenol, the fraction of molecules immobile on the instrumental timescale is found to be significantly higher for catechol. The MD simulations also exhibit this increased in ‘immobility’, showing that the long-range translational diffusion coefficients of catechol are lower than phenol by a factor of 7 in acidic zeolite Beta, and a factor of sim3 in the siliceous material, further illustrating the significance of Brønsted site H-bonding. Upon reproducing QENS observables from our simulations to probe rotational motions, a combination of two isotropic rotations was found to fit the MD-calculated EISF; one corresponds to the free rotation of catechol in the pore system of the zeolite, while the second rotation is used to approximate a restricted and rapid “rattling”, consistent with molecules anchored to the acid sites through their OH groups, the motion of which is too rapid to be observed by experiment.

Semiclassical asymptotic behavior of orthogonal polynomials

Our goal is to find asymptotic formulas for orthonormal polynomials $$P_{n}(z)$$ with the recurrence coefficients slowly stabilizing as $$n\rightarrow \infty $$ . To that end, we develop scattering theory of Jacobi operators with long-range coefficients and study the corresponding second-order difference equation. We introduce the Jost solutions $$f_{n}(z)$$ of this equation by a condition for $$n\rightarrow \infty $$ and suggest an Ansatz for them playing the role of the semiclassical Liouville–Green Ansatz for the corresponding solutions of the Schrodinger equation. This allows us to study Jacobi operators and their eigenfunctions $$P_{n}(z)$$ by traditional methods of spectral theory developed for differential equations. In particular, we express all coefficients in asymptotic formulas for $$P_{n}(z)$$ as $$\rightarrow \infty $$ in terms of the Wronskian of the solutions $$\{P_{n} (z)\}$$ and $$\{f_{n} (z)\}$$ .

Calculation of Long-Range Rapidity Correlations in the Model with String Fusion on a Transverse Lattice

By the model with the fusion of quark-gluon strings on a transverse lattice the correlations between observables from separated rapidity intervals in high-energy hadronic interactions are considered. The asymptotes of the long-range rapidity correlation coefficients between the multiplicities (n–n) and between the event-mean transverse momentum and the multiplicity of charged particles (pt–n) in these observation windows at large string density were explicitly calculated with the additional condition fixing the total number of initial strings. It is shown that this condition, which imitates in our model the fixation of the collision centrality class, has a significant impact on the behavior of the n–n and pt–n correlation coefficients for both homogeneous and inhomogeneous distribution of strings in the transverse plane.

Interactions and charge-transfer dynamics of anAl+ion immersed in ultracold Rb and Sr atoms

Atomic clocks based on an Al$^+$ ion sympathetically cooled by a laser-cooled alkaline-earth ion have achieved unprecedented accuracy. Here, we investigate theoretically interactions and charge transfer dynamics of an Al$^+$ ion immersed in an ultracold gas of Rb and Sr atoms. We calculate potential energy curves and transition electric dipole moments for the (Al+Rb)$^+$ and (Al+Sr)$^+$ ion-atom systems using coupled cluster and multireference configuration interaction methods with scalar relativistic effects included within the small-core energy-consistent pseudopotentials in Rb and Sr atoms. The long-range interaction coefficients are also reported. We use the electronic structure data to investigate cold collisions and charge transfer dynamics. Scattering of an Al$^+$ ion with alkali-metal or alkaline-earth-metal atom is governed by one potential energy curve whereas charge transfer can lead to several electronic states mixed by the relativistic spin-orbit coupling. We examine the branching ratios resulting from the interplay of the short- and long-range effects, as well as the prospects for the laser-field control and formation of molecular ions. We propose to employ the atomic clock transition in an Al$^+$ ion to monitor ion-atom scattering dynamics via quantum logic spectroscopy. The presented results pave the way for the application of atomic ions other than alkali-metal and alkaline-earth-metal ones in the field of cold hybrid ion-atom experiments.

Long-range potentials and dipole moments of the CO electronic states converging to the ground dissociation limit.

The asymptotic, R → ∞, behavior of the potential-energy and dipole-moment functions (PEFs and DMFs) for all six (1,2)Σ+, (1,2)Π, Σ-, and Δ electronic states converging to the ground C(3P) + O(3P) dissociation limit of the CO molecule are studied in the framework of long-range (LR) perturbation theory. The analytical expressions for the leading coefficients of the LR expansion, C5/R5 for PEF and d4/R4 for DMF, in terms of the atomic quadrupole constants and static dipole polarizabilities are derived. The exact relationships between the LR coefficients for the states of different spatial symmetry are established as well. The analytical results are complemented with the first-principles calculation of the PEFs and DMFs for all the above states at large distances (R = 5-20 Å). The electronic structure calculation is conducted by means of the multi-reference configuration interaction and the averaged-coupled-pair functional methods, which both implemented the aug-cc-pwCVXZ (X = T, Q, and 5) basis sets and finite-field approach. The dispersion coefficients, C5 and C6, extracted from the ab initio PEFs, are found to be very close to their present and previous theoretical counterparts. The analytically estimated d4 = -5 DÅ4 obtained for the ground X1Σ+ state perfectly agrees with the present ab initio DMF but diverges significantly from the literature data.

A new full-dimensional ab initio intermolecular potential energy surface and vibrational states for (HF)2 and (DF)2.

We present a new full-dimensional ab initio potential energy surface (PES) of a hydrogen fluoride dimer [(HF)2] using the supermolecular approach. The calculations were performed at the coupled-cluster single double triple level, with an augmented correlation-consistent polarized valence quadruple-zeta basis set plus bond functions. The basis set superposition error was corrected by a full counterpoise procedure. With the exchange symmetry of the two HF molecules, the permutation invariant polynomial neural network approach was used to fit the hypersurface with a root-mean-square-error of 0.465 cm-1 for about 110 000 points. The ab initio noise of intermolecular potential in the long range was smoothed by the long-range coefficients method. The equilibrium configuration of the complex was found to be a Cs structure located at two equivalent minima with the well depth of 1573.495 cm-1. The eigenstates were calculated by employing a symmetry-adapted Lanczos propagation algorithm in the mixed radical discrete variable representation/angular finite basis representation. The tunneling splitting for the ground state of (HF)2 is 0.665 cm-1, agreeing well with experimental value of 0.65869 cm-1. Vibrational fundamentals are also very close to the observed values. The results of vibrational states calculations demonstrate the high accuracy of our new PES.

Detrended cross-correlation patterns between North Atlantic oscillation and precipitation

In this study, the long-range relationships between North Atlantic Oscillation (NAO) and precipitation data obtained from Climate Prediction Centre (CPC) Merged Analysis of Precipitation (CMAP) from 1979 to 2016 are investigated using Detrended Fluctuation Moving Average Cross-Correlation Analysis (DMCA). In the atmosphere, teleconnections through strong convective processes sporadically affect various climatic regimes in Europe, Mediterranean basin, North Africa, Middle East, and Caucasus. The NAO is one of the teleconnection processes and results in heavy rainfall in the Mediterranean basin during its negative phase while it gives rise to rain in Europe during its positive phase. The DMCA technique shows that the NAO fluctuation series exhibit different long-range cross-correlation coefficients, ρDMCA(s) with “s” being the moving average time window length, between the precipitation values and NAO. Large ρDMCA(s) coefficients with time window(s) larger than 12 months were obtained particularly over the Mediterranean basin, near the North Pole including northern Europe. Furthermore, the ρDMCA(s) coefficients were grouped into clusters using K-mean method to distinguish the similar patterns. The 1st cluster refers to the negative phase of the NAO indicating warm-rainy conditions and dry spells, which is especially evident in the Mediterranean basin. The 2nd cluster represents the long-range cross-correlation with respect to the positive phase of NAO and precipitation values, particularly for the Western and Northern Europe. Conversely, the 3rd cluster is evaluated as power law of long-range cross-correlations between the precipitation and NAO with respect to the different time scale processes.

Highly sensitive photoassociation spectroscopy of ultracold 23Na133Cs molecular long-range states below the 3S1/2+6P1/2 limit

This article describes the preparation of ultracold heteronuclear polar excited NaCs molecules through photoassociation in a dual-species magneto-optical trap. Ten resonant positions are observed below the Na (3S1/2) + Cs (6P1/2) dissociation limit using trap-loss spectroscopy based on a highly sensitive modulation technique. We deduce the long-range molecular coefficients by fitting an improved LeRoy–Bernstein formula to our experimental data using the Levenberg–Marquardt algorithm implemented in Mathematica software, and derive the empirical potential energy curve in the long-range region; we also verify the application of the improved LeRoy–Bernstein formula to the ultracold NaCs molecule.

Dissecting reaction calculations using halo effective field theory and ab initio input

We present a description of the break-up of halo nuclei in peripheral nuclear reactions by coupling a model of the projectile motivated by Halo Effective Field Theory with a fully dynamical treatment of the reaction using the Dynamical Eikonal Approximation. Our description of the halo system reproduces its long-range properties, i.e., binding energy and asymptotic normalization coefficients of bound states and phase shifts of continuum states. As an application we consider the break-up of 11Be in collisions on Pb and C targets. Taking the input for our Halo-EFT-inspired description of 11Be from a recent ab initio calculation of that system yields a good description of the Coulomb-dominated breakup on Pb at energies up to about 2 MeV, with the result essentially independent of the short-distance part of the halo wave function. However, the nuclear dominated break-up on C is more sensitive to short-range physics. The role of spectroscopic factors and possible extensions of our approach to include additional short-range mechanisms are also discussed.

The RbSr 2Σ+ ground state investigated via spectroscopy of hot and ultracold molecules.

We report on spectroscopic studies of hot and ultracold RbSr molecules, and combine the results in an analysis that allows us to fit a potential energy curve (PEC) for the X(1)2Σ+ ground state bridging the short-to-long-range domains. The ultracold RbSr molecules are created in a μK sample of Rb and Sr atoms and probed by two-colour photoassociation spectroscopy. The data yield the long-range dispersion coefficients C6 and C8, along with the total number of supported bound levels. The hot RbSr molecules are created in a 1000 K gas mixture of Rb and Sr in a heat-pipe oven and probed by thermoluminescence and laser-induced fluorescence spectroscopy. We compare the hot molecule data with spectra we simulated using previously published PECs determined by three different ab initio theoretical methods. We identify several band heads corresponding to radiative decay from the B(2)2Σ+ state to the deepest bound levels of X(1)2Σ+. We determine a mass-scaled high-precision model for X(1)2Σ+ by fitting all data using a single fit procedure. The corresponding PEC is consistent with all data, thus spanning short-to-long internuclear distances and bridging an energy gap of about 75% of the potential well depth, still uncharted by any experiment. We benchmark previous ab initio PECs against our results, and give the PEC fit parameters for both X(1)2Σ+ and B(2)2Σ+ states. As first outcomes of our analysis, we calculate the s-wave scattering properties for all stable isotopic combinations and corroborate the locations of Fano-Feshbach resonances between alkali Rb and closed-shell Sr atoms recently observed [V. Barbéet al., Nat. Phys., 2018, 14, 881]. These results and more generally our strategy should greatly contribute to the generation of ultracold alkali-alkaline-earth dimers, whose applications range from quantum simulation to state-controlled quantum chemistry.

Benchmark CCSD-SAPT study of rare gas dimers with comparison to MP-SAPT and DFT-SAPT.

Symmetry-adapted perturbation theory (SAPT) based on coupled cluster approach with single and double excitations (CCSD) treatment of intramonomer electron correlation effects was applied to study rare gas homodimers from He2 to Kr2. The obtained benchmark CCSD-SAPT energies, including cumulant contributions to first order exchange and second-order exchange-induction terms, were then compared to their counterparts found using other methods-Møller-Plesset-SAPT based on many-body Møller-Plesset perturbation theory and DFT-SAPT based on density functional theory. The SAPT terms up to the second-order were calculated with the basis sets close to the complete basis set at the large range of interatomic distances R. It was shown that overestimation of the binding energies De found with DFT-SAPT reported in the work of Shirkov and Makarewicz [J. Chem. Phys. 142, 064102 (2015)] for Ar2 and Kr2 is mostly due to underestimation of the exchange energy Eexch(1) when comparing to the CCSD-SAPT benchmark. The CCSD-SAPT potentials were found to give the following values of the dissociation energies D0: 0.0006 cm-1 for He2, 16.71 cm-1 for Ne2, 85.03 cm-1 for Ar2, and 129.81 cm-1 for Kr2, which agree well with the values found from previously reported highly accurate ab initio supermolecular potentials and experimental data. The long-range dispersion coefficients C2n up to n = 6 that give the dispersion energy asymptotically equivalent to its SAPT counterpart were calculated from dynamic multipole polarizabilities at different levels of theory.

Asymptotic behavior of the correlation coefficients of transverse momenta in the model with string fusion

In the framework of the model with fusion of quark–gluon strings on the transverse lattice, we find the asymptotic behavior of the correlation coefficients between observables in separated rapidity intervals with a high string density in a realistic case with an inhomogeneous distribution of strings in the impact parameter plane. We calculate the asymptotic forms for three types of correlations: between the average transverse momenta of particles with rapidity in these intervals, between the average transverse momentum of particles in one rapidity interval and the multiplicity of particles in another, and also between the multiplicities of charged particles in these intervals. We show that the previously found independence of the asymptotic form of the correlation coefficient between the average transverse momenta from the variance in the number of particles produced in string fragmentation holds only in the case of a uniform distribution of strings in the transverse plane. We also show that the found general expressions for the long-range correlation coefficients in the particular case with a uniform distribution of strings in the transverse plane become the formulas previously obtained by another method applicable only in this simple case.

Explicitly-correlated coupled cluster method for long-range dispersion coefficients

A method of calculation of long-range dispersion C6 coefficients with wavefunctions, corresponding to linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] model, has been developed. Designed approach uses CCSD(F12) wave functions for the calculation of dynamic polarizabilities at complex frequencies with further utilization of Casimir-Polder formula. As a part of the algorithm, the explicitly-correlated version of the coupled-perturbed CCSD equations for the case of complex frequencies has also been implemented. Numerical tests, conducted for the set of molecules show good agreement between dispersion coefficients, calculated with developed explicitly-correlated method and corresponding complete basis set results in regular CCSD already at triple-ζ level.

Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusion

Inferring the microstructure of complex media from the diffusive motion of molecules is a challenging problem in diffusion physics. In this paper, we introduce a novel representation of diffusion MRI (dMRI) signal from tissue with spatially-varying diffusivity using a diffusion disturbance function. This disturbance function contains information about the (intra-voxel) spatial fluctuations in diffusivity due to restrictions, hindrances and tissue heterogeneity of the underlying tissue substrate. We derive the short- and long-range disturbance coefficients from this disturbance function to characterize the tissue structure and organization. Moreover, we provide an exact relation between the disturbance coefficients and the time-varying moments of the diffusion propagator, as well as their relation to specific tissue microstructural information such as the intra-axonal volume fraction and the apparent axon radius. The proposed approach is quite general and can model dMRI signal for any type of gradient sequence (rectangular, oscillating, etc.) without using the Gaussian phase approximation. The relevance of the proposed PICASO model is explored using Monte-Carlo simulations and in-vivo dMRI data. The results show that the estimated disturbance coefficients can distinguish different types of microstructural organization of axons.