Tang Toennies Research Articles

Revisiting Numerical Solutions of Weakly Bound Noble Gases' Vibrational Energy Levels Modeled by the Improved Lennard-Jones Potential.

We revisit the numerical solutions of vibrational eigenstates of weakly bound homonuclear and heteronuclear noble gas pairs by applying a Fortran program based on the Numerov method. The harmonic, Lennard-Jones (LJ), Morse, Tang-Toennies (TT), and Improved Lennard-Jones (ILJ) potential models have been implemented to represent the potential energy curves (PECs). The obtained vibrational energies spectrum was tested on the experimental data and accurate ab initio calculations at CCSD(T)/CBS level. The vibrational eigenvalues and eigenfunctions can be reproduced accurately within the ILJ potential model. Moreover, considering the calculated lifetime of van der Waals (vdW) complexes, the implementation of ILJ rather than standard LJ potential model has a significant impact on the systems dynamics by providing more representative atomic trajectories when the function is incorporated in force fields for molecular dynamics (MD) simulations. Overall, the ILJ function is the best suited potential model for the representation of vibrational motions and the determination of vibrational energy levels of weakly bound systems, both at equilibrium and non-equilibrium conditions.

Mutual Intersection Points of Reduced Collision Integrals for Lennard–Jones (n-m), Hulburt–Hirschfelder, and Tang–Toennies Potential Energy Functions

We investigate the reduced collision integrals Omega ^{(ell ,s)*}(T^*) for 1 le ell le 4, ell le s le 7 and ell + s le 8 for several isotropic potential energy functions: the Lennard–Jones (n-m), the Hulburt–Hirschfelder, and Tang–Toennies potential. It is observed that for a given ell and s, Omega ^{(ell ,s)*}(T^*) shows a mutual intersection region at a reduced temperature 0.39< T^*=T^*_{ell s} < 2.22 which is nearly independent of the potential energy function used.

An accurate potential model for the a3Σu+ state of the lithium dimer.

An accurate Tang-Toennies (TT) model potential is introduced to describe the interatomic potential of the lithium dimer in the a3Σu+ state. With only one well-known parameter, the ionization energy, the new model potential compares favorably with the experimentally fitted Morse/Long-range (MLR) potential of Dattani and Le Roy [J. Mol. Spectrosc., 2011, 268, 199] and is in excellent agreement with the state-of-the-art ab initio potential of Lesiuk et al. [Phys. Rev. A, 2020, 102, 062806]. With the known dispersion coefficients and the ionization energy, the new potential requires only two experimental parameters, namely the depth of the potential well De and its location Re. The new potential can be extended to the region of zero separation by the united atom limit.

Extension of the CL&Pol Polarizable Force Field to Electrolytes, Protic Ionic Liquids, and Deep Eutectic Solvents.

The polarizable CL&Pol force field presented in our previous study, Transferable, Polarizable Force Field for Ionic Liquids (J. Chem. Theory Comput. 2019, 15, 5858, DOI: http://doi.org/10.1021/acs.jctc.9b0068910.1021/acs.jctc.9b00689), is extended to electrolytes, protic ionic liquids (PIL), deep eutectic solvents (DES), and glycols. These systems are problematic in polarizable simulations because they contain either small, highly charged ions or strong hydrogen bonds, which cause trajectory instabilities due to the pull exerted on the induced dipoles. We use a Tang-Toennies (TT) function to dampen, or smear, the interactions between charges and induced dipole at a short range involving small, highly charged atoms (such as hydrogen or lithium), thus preventing the "polarization catastrophe". The new force field gives stable trajectories and is validated through comparison with experimental data on density, viscosity, and ion diffusion coefficients of liquid systems of the above-mentioned classes. The results also shed light on the hydrogen-bonding pattern in ethylammonium nitrate, a PIL, for which the literature contains conflicting views. We describe the implementation of the TT damping function, of the temperature-grouped Nosé-Hoover thermostat for polarizable molecular dynamics (MD) and of the periodic perturbation method for viscosity evaluation from non-equilibrium trajectories in the LAMMPS MD code. The main result of this work is the wider applicability of the CL&Pol polarizable force field to new, important classes of fluids, achieving robust trajectories and a good description of equilibrium and transport properties in challenging systems. The fragment-based approach of CL&Pol will allow ready extension to a wide variety of PILs, DES, and electrolytes.

Ms2: A molecular simulation tool for thermodynamic properties, release 4.0

A new version release (4.0) of the molecular simulation tool ms2 (Deublein et al. 2011; Glass et al. 2014; Rutkai et al. 2017) is presented. Version 4.0 of ms2 features two additional potential functions to address the repulsive and dispersive interactions in a more versatile way, i.e. the Mie potential and the Tang–Toennies potential. This version further introduces Kirkwood–Buff integrals based on radial distribution functions, which allow the sampling of the thermodynamic factor of mixtures with up to four components, orientational distribution functions to elucidate mutual configurations of neighboring molecules, thermal diffusion coefficients of binary mixtures for heat, mass as well as coupled heat and mass transport, Einstein relations to sample transport properties with an alternative to the Green–Kubo formalism, dielectric constant of non-polarizable fluid models, vapor–liquid equilibria relying on the second virial coefficient and cluster criteria to identify nucleation. New version programm summaryProgram Title: ms2Program Files doi:http://dx.doi.org/10.17632/nsfj67wydx.3Licensing provisions: CC by NC 3.0Programming language: Fortran95Supplemental material: A detailed description of the parameter setup for the introduced methods, properties, functionalities etc. is given in the supplemental material. Furthermore, all molecular force field models developed by our group are provided by the MolMod Database: Stephan et al., Mol. Sim. 45 (2019) 806Journal reference of previous version: Deublein et al., Comput. Phys. Commun. 182 (2011) 2350 and Glass et al., Comput. Phys. Commun. 185 (2014) 3302 and Rutkai et al., Comput. Phys. Commun. 221 (2017) 343Does the new version supersede the previous version?: YesReasons for the new version: Introduction of new features as well as enhancement of computational efficiencySummary of revisions: Two new potential functions to address repulsive and dispersive interactions (Mie and Tang–Toennies potential), new properties (Helmholtz energy, Kirkwood–Buff integrals, thermodynamic factor, thermal diffusion coefficients, dielectric constant, mean squared displacement and non-Gaussian parameter), new functionalities (Kirkwood–Buff integration with extrapolation to the thermodynamic limit, van der Vegt correction for the radial distribution function, orientational distribution function, Einstein relations, vapor–liquid equilibria estimations, cluster criteria to identify nucleation).Nature of problem: Calculation of application-oriented thermodynamic properties: vapor–liquid equilibria of pure fluids and multi-component mixtures, thermal, caloric and entropic data as well as transport properties and data on microscopic structureSolution method: Molecular dynamics, Monte Carlo, various ensembles, Grand equilibrium method, Green–Kubo formalism, Einstein formalism, Lustig formalism, OPAS method, smooth-particle mesh Ewald summation.

A relativistic coupled-cluster interaction potential and rovibrational constants for the xenon dimer

ABSTRACT An accurate potential energy curve has been derived for the xenon dimer using state-of-the-art relativistic coupled-cluster theory up to quadruple excitations accounting for both basis set superposition and incompleteness errors. The data obtained is fitted to a computationally efficient extended Lennard-Jones potential form and to a modified Tang–Toennies potential function treating the short- and long-range part separately. The vibrational spectrum of Xe2 obtained from a numerical solution of the rovibrational Schrödinger equation and subsequently derived spectroscopic constants are in excellent agreement with experimental values. We further present solid-state calculations for xenon using a static many-body expansion up to fourth-order in the xenon interaction potential including dynamic effects within the Einstein approximation. Again we find very good agreement with the experimental (face-centred cubic) lattice constant and cohesive energy.

A combining rule calculation of the ground-state van der Waals potentials of the magnesium rare-gas complexes

ABSTRACTThe potential energy curves and spectroscopic constants of the ground-state of the Mg–Rg (Rg = He, Ne, Ar, Kr, and Xe) van der Waals complexes are generated by the Tang–Toennies potential model and a set of derived combining rules. The parameters of the model are calculated from the potentials of the homonuclear magnesium and rare-gas dimers. The predicted spectroscopic constants are comparable to other available theoretical and experimental results, except in the case of Mg–He, we note that there are large differences between various determinations. Moreover, in order to reveal relative differences between species more obviously we calculated the reduced potential of these five systems. The curves are clumped closely together, but at intermediate range the Mg–He reduced potential is clearly very different from the others.

DPotFit: A computer program to fit diatomic molecule spectral data to potential energy functions

This paper describes program dPotFit, which performs least-squares fits of diatomic molecule spectroscopic data consisting of any combination of microwave, infrared or electronic vibrational bands, fluorescence series, and tunneling predissociation level widths, involving one or more electronic states and one or more isotopologs, and for appropriate systems, second virial coefficient data, to determine analytic potential energy functions defining the observed levels and other properties of each state. Four families of analytical potential functions are available for fitting in the current version of dPotFit: the Expanded Morse Oscillator (EMO) function, the Morse/Long-Range (MLR) function, the Double-Exponential/Long-Range (DELR) function, and the ‘Generalized Potential Energy Function׳ (GPEF) of Šurkus, which incorporates a variety of polynomial functional forms. In addition, dPotFit allows sets of experimental data to be tested against predictions generated from three other families of analytic functions, namely, the ‘Hannover Polynomial’ (or “X-expansion”) function, and the ‘Tang–Toennies’ and Scoles–Aziz ‘HFD’, exponential-plus-van der Waals functions, and from interpolation-smoothed pointwise potential energies, such as those obtained from ab initio or RKR calculations. dPotFit also allows the fits to determine atomic-mass-dependent Born–Oppenheimer breakdown functions, and singlet-state Λ-doubling, or Σ2 splitting radial strength functions for one or more electronic states.dPotFit always reports both the 95% confidence limit uncertainty and the “sensitivity” of each fitted parameter; the latter indicates the number of significant digits that must be retained when rounding fitted parameters, in order to ensure that predictions remain in full agreement with experiment. It will also, if requested, apply a “sequential rounding and refitting” procedure to yield a final parameter set defined by a minimum number of significant digits, while ensuring no significant loss of accuracy in the predictions yielded by those parameters.

The van der Waals potentials of MgCa, MgSr, MgBa, CaSr, CaBa, and SrBa

Based on the facts that the potential energy curves of the homo-nuclear group 2 dimers (group IIA metal), except Be2, are conformal, and they can be described by the Tang–Toennies potential model, a set of simple combining rules are proposed for the parameters of the reduced potentials of the hetero-nuclear dimers. Together with the well-established combining rules of the range parameters of the exponential repulsion and the known dispersion coefficients, these rules enable us to determine the ground state potential energy curves of MgCa, MgSr, MgBa, CaSr, CaBa, and SrBa from those of Mg2, Ca2, Sr2, and Ba2. The determined potentials are comparable to some ab initio calculations and in excellent agreement with the experiment.

The van der Waals potentials of ZnCd, ZnHg, and CdHg

Based on the facts that the potential energy curves of the homonuclear group 12 dimers (group IIB metal) are conformal, and they can be described by the Tang–Toennies potential model, a set of combining rules are proposed for the parameters of the reduced potentials of the heteronuclear dimers. Together with the well established combining rules of the dispersion coefficients and the range parameters of the exponential repulsion, these rules enable us to determine the ground state potential energy curves of ZnCd, ZnHg, and CdHg. The determined potentials are comparable to some ab initio calculations but they are drastically different from others.

ROVIBRATIONAL BOUND STATES OF THE Ar2Ne COMPLEX

We report exact quantum dynamics calculations of the eigenstate energy levels for the bound rovibrational states of the Ar2Ne complex, across the range of J values for which such states are observed (J = 0–35). All calculations have been carried out using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space optimized discrete variable representation, optimal separable basis, and preconditioned inexact spectral transform (PIST) methods, together with an effective massive parallelization scheme. The Ar2Ne energy levels were computed using a pair-wise Aziz potential plus a three-body correction, in Jacobi co-ordinates. Effective potentials for the radial co-ordinates are constructed, which reveal important physical insight into the two distinct dissociation pathways, Ar2Ne → NeAr + Ar and Ar2Ne → Ar2 + Ne . A calculation of the bound vibrational (J = 0) levels, computed using the Tang–Toennies potential, is also performed for comparison with results from the previous literature.

Hyperspherical study of Ne2Kr and Ne2Xe systems

We have calculated the ground state energies and rotational constants for the Ne2Kr and Ne2Xe systems, as well as their corresponding isotopes using the hyperspherical method. We used B-splines as basis function to expand channel functions and make the knot distribution of B-splines characterize the behavior of the channel function precisely. As a result, the extremely slow convergence of quantum mechanic calculation for these van der Waals trimers containing heavy element is improved greatly. The convergent rotational constants and the isotope shifts are obtained and compared with other theoretical and experimental values. Our results using newly proposed Tang-Toennies (TT) pair-wise potentials are consistent with that of Ernesti and Hutson’s calculation using HFD-B potentials, and give an improved agreement with experimental data.

The van der Waals potential of mercury dimer

Both the equilibrium distance Re and the well depth De of the mercury dimer potential from a recent relativistic CCSD(T) calculation fall within the error bounds of experiment. With this set of (Re, De), the entire potential curve can be determined by the dispersion coefficients with the Tang–Toennies (TT) potential model without further fitting. The spectroscopic constants calculated from this potential are in excellent agreement with experiment. In the van der Waals well region, there is no discernible difference between the TT potential and the multi-parameter least-square fitted extented Lennard Jones potential. The TT potential has the advantage of being physically transparent and asymptotically approaching to the correct dispersion series.

The ground state van der Waals potentials of the strontium dimer and strontium rare-gas complexes

The entire ground state potential energy curve of the strontium dimer is accurately described by the Tang-Toennies potential model defined by the three dispersion coefficients and two well parameters. The predicted vibrational frequency, anharmonicity, and vibration-rotation coupling constant are in excellent agreement with experiment. The Sr(2) reduced potential is almost identical to that of Ca(2) and Hg(2), providing further evidence to the conjecture that the van der Waals dimer potentials of group IIA and group IIB elements have the same shape, which is different from that of rare-gas dimers. The potentials of Sr-RG complexes (RG=He,Ne,Ar,Kr,Xe) are generated by the same potential model with its parameters calculated with combining rules. These potentials are shown to have the same shape which is between that of the strontium and rare-gas dimers.

Elastic He + on He collision cross-sections and Monte Carlo calculation of the transport coefficients of He + ions in gaseous helium

Integral and differential cross-sections for elastic collisions of He + ions in the ground state ( 2S) with neutral He atoms are calculated, for centre-of-mass energies between 0.001 and 10 eV, using the partial waves method. The scattering phase shifts are calculated using the JWKB semi-classical approximation, with modified Tang–Toennies ion–atom (TTIA) potential energy curves, that describe spectroscopic data, dissociation energies and equilibrium internuclear distances, and the long-range interaction potentials. These cross-sections are used in a detailed three-dimensional Monte Carlo simulation model to calculate the main transport coefficients describing the ion drift through the neutral gas, as a function of the gas temperature and the reduced uniform electric field. Calculated drift velocities, ion mobilities, as well as longitudinal and transverse diffusion coefficients for He + atomic ions in gaseous He, at temperature T=293 K and reduced electric fields, E/N, in the 1 to 300 Td (1 Td=10 −17 V cm 2) range, are reported and compared with the limited experimental data available in the scientific literature. The calculated drift velocities range from 28.31 m s −1 at 1 Td to 3685.0 m s −1 at 300 Td.

The dynamical polarisability and van der Waals dimer potential of mercury

Wolfsohn's parameters for the frequency-dependent polarisability α(ω) of mercury are modified to fit the recent interferometric measurements of Goebel and Hohm [J. Phys. Chem. 100, 7710 (1996)]. The resulting α(ω) are extended to imaginary frequencies α(iω) and used to calculate the upper and lower bounds of the dipole dispersion coefficient in the long range dimer potential. The new value of C 6 = 392±4 a.u. is much greater than the generally accepted value. With the corresponding changes in the dipole–quadrupole and dipole–octopole interactions, new dispersion coefficients C 8 and C 10 are obtained. Together with the experimentally determined D e (well-depth) and R e (equilibrium distance), the Tang–Toennies model is used to predict the shape of the entire dimer potential energy curve. The new potential is found to be in excellent agreement with the ab initio calculations of Munro et al. [J. Chem. Phys. 114, 5545 (2001)] and the parameters ωe and χeωe agree with the spectroscopic measurements within the small experimental errors.

Hyperspherical coupled channel calculations for the spectra and structure parameters of rare gas trimers NeAr2 and Ne2Ar

We calculate the L=0 vibration energies and rotational constants for the van der Waals trimers 20NeAr2, 20Ne2Ar, and their corresponding isotopologues within the framework of hyperspherical coordinates. The Schrodinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B-splines and the resulting coupled hyper-radial equation is solved using the slow variable discretization method developed by Tolstikhin et al. [J. Phys. B 29, L389 (1996)]. Using the special properties of B-splines, we make the knot distributions more precisely, characterizing the behavior of channel functions. Our method improves the convergence greatly. It turns out that our numerical tool works quite well in study of rare gas trimers. Calculations are performed on two kinds of pair potentials, the HFD-B and Tang-Toennies (TT) potentials, and the resultant rotational constants and their isotope shifts are compared with the experimental results obtained from high-resolution spectroscopy. The TT pair potentials give much better agreement with the experimental values for 20Ne2Ar and 22Ne2Ar trimers, while the HFD-B pair potentials give much better agreement with the experimental values for 20NeAr2 and 22NeAr2 trimers.

Thermophysical Properties of Low-Density Pure Alkanes and Their Binary Mixtures Calculated by Means of an (n-6) Lennard-Jones Temperature-Dependent Potential

Self-consistent calculations of interaction pVT-virial coefficients B 12(T), viscosities η mix (T), and diffusion coefficients D 12(T) of binary mixtures of the alkanes C n H2n + 2 (n < 6) are presented. This study is based on the recently developed model of the (n-6) Lennard-Jones temperature-dependent potential (LJTDP) and uses already obtained potential parameters of the pure alkanes as input data. The well-known and simple Lorentz-Berthelot (LB) and the more laborate Tang-Toennies (TT) mixing rules are applied to the potential parameters of the pure alkanes in order to determine those of the mixtures. The new Hohm–Zarkova–Damyanova (HZD) mixing rule, which is an extension of the TT-mixing rule, is also considered. The HZD takes into account that for the LJTDP model, in general, the repulsive parameter is an independent variable whose value n ≠ 12. As in a recent examination of binary mixtures of globular molecules, the LB-mixing rule is superior to TT- and HZD-mixing rules when calculating equilibrium properties such as B 12(T). For the transport properties η mix (T) and D 12(T), the new mixing rule performs slightly better.

Comparison of Lorentz–Berthelot and Tang–Toennies Mixing Rules Using an Isotropic Temperature-Dependent Potential Applied to the Thermophysical Properties of Binary Gas Mixtures of CH4, CF4, SF6, and C(CH3)4with Ar, Kr, and Xe

In this paper the isotropic temperature-dependent potential (ITDP) approach and the concepts introduced in our previous papers have been used to calculate equilibrium and transport properties of low-density gas mixtures. The twelve binary mixtures considered here are: Ar–CH4, Ar–CF4, Ar–SF6, Ar–C(CH3)4, Kr–CH4, Kr–CF4, Kr–SF6, Kr–C(CH3)4, Xe–CH4, Xe–CF4, Xe–SF6 and Xe–C(CH3)4. The (n−6) Lennard–Jones potential parameters n (repulsive parameter), R m (equilibrium distance), and ɛ (potential well depth) of the pure noble gases Ar, Kr, and Xe are obtained by a minimization of the sum of squared deviations between experimental and calculated viscosity (η), and second pVT (B) and acoustic (β) virial coefficients normalized to their relative experimental error aexp. The number of included experimental points for B, β, η was N = 305, 210, and 167 for Ar, Kr, and Xe, respectively. For the pure globular gases the potential parameters were taken from previous publications. The calculations of B, η, and ρ D12 of binary mixtures were compared with experimental data by using two different mixing rules (Lorentz–Berthelot and Tang–Toennies). Recommended sets and fitting formulae for the potential parameters that can be used for the calculation of low-pressure thermophysical properties of these mixtures are provided.

Theoretical study on analytical potential function and spectroscopic parameters for CaF molecule

The equilibrium properties and potential energy curves of the ground electronic state of CaF have been calculated using the Brueckner Doubles calculation with a triples contribution added [BD(T)] and the gradient-corrected density functional theory with three-parameter exact exchange mixing (B3LYP) method, with 6-311+G*, 6-311+G(2df,2pd) and 6-311+G(3df,3pd) basis sets. All the computational PECs are fitted to analytical potential energy functions using Murrell–Sorbie, Huxley and Tang–Toennies potentials. Based on this, the spectroscopic parameters are calculated, and then compared with some other theoretical and experimental data.