A simple theoretical model for the van der Waals potential at intermediate distances. II. Anisotropic potentials of He–H2and Ne–H2

Accurate Adiabatic and Diabatic Potential Energy Surfaces for the Reaction of He + H2

The accurate adiabatic and diabatic potential energy surfaces, which are for the two lowest states of He + H₂, are presented in this study. The Molpro 2012 software package is used, and the large basis sets (aug-cc-pV5Z) are selected. The high-level MCSCF/MRCI method is employed to calculate the adiabatic potential energy points of the title reaction system. The triatomic reaction system is described by Jacobi coordinates, and the adiabatic potential energy surfaces are fitted accurately using the B-spline method. The equilibrium structures and electronic energies for the H₂ are provided, and the corresponding different levels of vibrational energies of the ground state are deduced. To better express the diabatic process of the whole reaction, avoid crossing points being calculated and conical intersection also being optimized. Meanwhile, the diabatic potential energy surfaces of the reaction process are constructed. This study will be helpful for the analysis of histopathology and for the study in biological and medical mechanisms.

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 a³Σ_u⁺ 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 D_e and its location R_e. The new potential can be extended to the region of zero separation by the united atom limit.

Accurate semiempirical potential energy curves for the a3Σ+-state of NaCs, KCs, and RbCs

A five parameter semiempirical Tang-Toennies type model is used to describe the potential curves of the a³Σ⁺-state of the heteronuclear polar molecules NaCs, KCs, and RbCs. These molecules are of current interest in experiments at ultra-cold conditions to explore the effects of the strong dipole-dipole forces on the collective many-body quantum behavior. New quantum phenomena are also anticipated in systems consisting of atomic species with different fermion/boson statistics. The model parameters are obtained by simultaneously fitting all five of the parameters to the extensive LIF-Fourier transform spectroscopy published by Tiemann and collaborators [e.g., Docenko et al. J. Phys. B: At., Mol. Opt. Phys. 39, S929-S943 (2006)], who also report best fit potential curves. Although the new potentials are in good agreement with the earlier potentials, they have the advantage that they are continuous over the entire range of internuclear distances and have the correct long-range behavior. The scattering lengths for all isotope combinations show good agreement with dedicated experiments where available. The new potentials are also in excellent agreement with combining rules based on the potentials of the homonuclear systems.

The development of a full range analytical interatomic potential

A chronological account is given to the development of a full range interatomic potential. Starting with a simple phenomenological model, the terms in the model are gradually modified, so that they can carry some definite physical meaning. To gain insight, a systematic, order by order interaction potential theory is developed. Conversely, this theory suggests the functional form for the potential model. At present, we have a simple interaction model that is capable of describing the van der Waals potentials of many systems from R = 0 to R→∞.

van der Waals Function for Molecular Mechanics

van der Waals (vdW) interaction has been described with a Lennard-Jones potential for decades in molecular mechanics. Here, we report a new potential function Exp-PE from quantum mechanical derivation for vdW interactions for molecular mechanic simulation. High-order ab initio calculations and experimental atomic force microscopy measurements have been used to test its feasibility, and the results suggest that this formula is simple, accurate, and transferable. This new potential function is capable of upgrading the traditional force fields especially for the applications involving vdW interactions.

An accurate potential model for the a3Σu+ state of the alkali dimers Na2, K2, Rb2, and Cs2

A modified semi-empirical Tang-Toennies potential model is used to describe the a³Σ_u⁺ potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth D_e, well location R_e, and the harmonic vibrational frequency ω_e of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na₂, K₂, Rb₂, and Cs₂, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li₂ and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li₂ less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.

Calculation of inelastic helium atom scattering from H2/NaCl(001)

The one-phonon inelastic low energy helium atom scattering theory is adapted to cases where the target monolayer is a p(1 × 1) commensurate square lattice. Experimental data for para-H(2)/NaCl(001) are re-analyzed and the relative intensities of energy loss peaks in the range 6 to 9 meV are determined. The case of the H(2)/NaCl(001) monolayer for 26 meV scattering energy is computationally challenging and difficult because it has a much more corrugated surface than those in the previous applications for triangular lattices. This requires a large number of coupled channels for convergence in the wave-packet-scattering calculation and a long series of Fourier amplitudes to represent the helium-target potential energy surface. A modified series is constructed in which a truncated Fourier expansion of the potential is constrained to give the exact value of the potential at some key points and which mimics the potential with fewer Fourier amplitudes. The shear horizontal phonon mode is again accessed by the helium scattering for small misalignment of the scattering plane relative to symmetry axes of the monolayer. For 1° misalignment, the calculated intensity of the longitudinal acoustic phonon mode frequently is higher than that of the shear horizontal phonon mode in contrast to what was found at scattering energies near 10 meV for triangular lattices of Ar, Kr, and Xe on Pt(111).

Density functional method including weak interactions: Dispersion coefficients based on the local response approximation

A new method to calculate the atom-atom dispersion coefficients in a molecule is proposed for the use in density functional theory with dispersion (DFT-D) correction. The method is based on the local response approximation due to Dobson and Dinte [Phys. Rev. Lett. 76, 1780 (1996)], with modified dielectric model recently proposed by Vydrov and van Voorhis [J. Chem. Phys. 130, 104105 (2009)]. The local response model is used to calculate the distributed multipole polarizabilities of atoms in a molecule, from which the dispersion coefficients are obtained by an explicit frequency integral of the Casimir-Polder type. Thus obtained atomic polarizabilities are also used in the damping function for the short-range singularity. Unlike empirical DFT-D methods, the local response dispersion (LRD) method is able to calculate the dispersion energy from the ground-state electron density only. It is applicable to any geometry, free from physical constants such as van der Waals radii or atomic polarizabilities, and computationally very efficient. The LRD method combined with the long-range corrected DFT functional (LC-BOP) is applied to calculations of S22 weakly bound complex set [Phys. Chem. Chem. Phys. 8, 1985 (2006)]. Binding energies obtained by the LC-BOP+LRD agree remarkably well with ab initio references.

Low-temperature inelastic collisions between hydrogen molecules and helium atoms

Inelastic H(2):He collisions are studied from the experimental and theoretical points of view between 22 and 180 K. State-to-state cross sections and rates are calculated at the converged close-coupling level employing recent potential energy surfaces (PES): The MR-PES [J. Chem. Phys. 100, 4336 (1994)], and the MMR-PES and BMP-PESs [J. Chem. Phys. 119, 3187 (2003)]. The fundamental rates k(2-->0) and k(3-->1) for H(2):He collisions are assessed experimentally on the basis of a master equation describing the time evolution of rotational populations of H(2) in the vibrational ground state. These populations are measured in the paraxial region of supersonic jets of H(2)+He mixtures by means of high-sensitivity and high spatial resolution Raman spectroscopy. Good agreement between theory and experiment is found for the k(2-->0) rate derived from the MR-PES, but not for the BMP-PES. For the k(3-->1) rate, which is about one-third to one-half of k(2-->0), the result is less conclusive. The experimental k(3-->1) rate is compatible within experimental error with the values calculated from both PESs. In spite of this uncertainty, the global consistence of experiment and theory in the framework of Boltzmann equation supports the MR-PES and MMR-PESs, and the set of gas-dynamic equations employed to describe the paraxial region of the jet at a molecular level.

A quasiclassical trajectory study of collisional energy transfer and dissociation in He + H2(v,j) using a new potential energy surface

Quasiclassical trajectories for He + H2 were carried out using the recent ab initio potential of Boothroyd, Martin, and Peterson (J. Chem. Phys. 2003, 119, 3187) and results for the 348 (v, j) states of H2 are compared to those of earlier calculations that used the potential of Wilson, Kapral, and Burns (Chem. Phys. Lett. 1974, 24, 4884). Examined are the cross sections for energy transfer and dissociation, the extent of threshold elevation, and the interconversion of vibrational and rotational energy. Implications for modeling the interstellar medium are discussed.

A reliable new three-dimensional potential energy surface for H2–Kr

An improved three-dimensional potential energy surface for the H(2)-Kr system is determined from a direct fit of new infrared spectroscopic data for H(2)-Kr and D(2)-Kr to a potential energy function form based on the exchange-Coulomb model for the intermolecular interaction energy. These fits require repetitive, highly accurate simulations of the observed spectra, and both the strength of the potential energy anisotropy and the accuracy of the new data make the "secular equation perturbation theory" method used in previous analyses of H(2)-(rare gas) spectra inadequate for the present work. To address this problem, an extended version of the "iterative secular equation" method was developed which implements direct Hellmann-Feynman theorem calculation of the partial derivatives of eigenvalues with respect to parameters of the Hamiltonian which are required for the fits.

Intermolecular interaction in an open-shell π-bound cationic complex: IR spectrum and coupled cluster calculations for C2H2+-Ar

The intermolecular potential energy surface (PES) of Ar interacting with the acetylene cation in its (2)Pi(u) ground electronic state is characterized by infrared photodissociation (IRPD) spectroscopy and quantum chemical calculations. In agreement with the theoretical predictions, the rovibrational analysis of the IRPD spectrum of C(2)H(2) (+)-Ar recorded in the vicinity of the antisymmetric CH stretching fundamental (nu(3)) is consistent with a vibrationally averaged T-shaped structure and a ground-state center-of-mass separation of R(c.m.) = 2.86 +/- 0.09 A. The nu(3) band experiences a blueshift of 16.7 cm(-1) upon complexation, indicating that vibrational excitation slightly reduces the interaction strength. The two-dimensional intermolecular PES of C(2)H(2) (+)-Ar, obtained from coupled cluster calculations with a large basis set, features strong angular-radial coupling and supports in addition to a global pi-bound minimum also two shallow side wells with linear H-bound geometries. Bound state rovibrational energy level calculations are carried out for rotational angular momentum J = 0-10 (both parities) employing a discrete variable representation-distributed Gaussian basis method. Effective spectroscopic constants are determined for the vibrational ground state by fitting the calculated rotational energies to the standard Watson A-type Hamiltonian for a slightly asymmetric prolate top.