Improved techniques for the calculation of ab initio ion-neutral interaction potentials: application to coinage metal ions interacting with rare gas atoms

Ab initio values for the potential energy functions for ion–neutral interactions can be tested by comparison with gaseous ion transport coefficients, but only if special care is taken to compute the interaction potentials accurately over wide ranges of internuclear separation. This is illustrated here by a reanalysis of the ab initio values for the coinage metal ions interacting with rare gas atoms, precise calculations of the transport cross sections over extremely wide ranges of energy, and similarly precise calculations of the zero-field ion mobilities as functions of gas temperature and the field-dependent ion mobilities at various fixed temperatures. The calculations indicate that the mobilities for Ag⁺(¹S) moving in Ne or Ar can distinguish between the existing, very similar ab initio potentials. They also show that substantial differences exist among the mobilities of the coinage metal anions and the ground and excited states of the cations. The techniques implemented are recommended for future ab initio calculations.     

How to simulate a structural phase transition by the first-principles method?

We outline the procedure and approximations used to study the structural phase transition. The standard ab initio programs provide the Hellmann-Feynman forces, which allow, by the direct method, to describe the dispersion curves including the soft mode. The values of the anharmonic terms of the order parameter and order parameter-strain coupling terms, found from symmetry analysis, can be calculated within the ab initio total energy approach, by carring on the calculations for a variety of atom configurations. The method is used to describe the cubic-tetragonal phase transition in SrTiO₃, for which a soft mode and anharmonic coefficients have been found.     

Re-examination of the NDDO approximation and introduction of a new model beyond it

The NDDO (neglect of diatomic differential overlap) approximation, a widely used basis for many semi-empirical molecular orbital (MO) approaches, is re-examined based on non-empirical frozen-core calculations on small molecules. An improvement going beyond the NDDO approximation is proposed. Our study shows that under the NDDO approximation, when the remaining non-DDO-type two-electron repulsion integrals (TERIs) are calculated using the basis set from the Löwdin orthogonalization of the valence atomic orbitals, the resulting total energies are much higher than those from the corresponding frozen-core ab initio calculations. On the other hand, when the remaining non-DDO TERIs are calculated using non-orthogonal valence atomic orbitals (similar to the Roby model), for most of the molecules calculated, the total energies are significantly lower than those from the corresponding ab initio calculations. Furthermore, we also find that for some molecules, the total energies thus calculated are higher than the corresponding ab initio results. The nonsystematic variation of the absolute errors in the total energy calculations is due to the fact that the core-electron and the electron-electron interactions are not treated in a balanced way in the NDDO approximation. A new model, which overcomes the deficiencies in the NDDO model, is proposed. In this model, a first-order correction term is added to the electron-electron Coulomb interactions, thereby improving the balance between the core-electron and the electron-electron interactions. Non-empirical test calculations show that the total energies from the new model are consistently higher than those from the ab initio calculation but closer to the ab initio results. We expect that the proposed new model would be useful in developing new high-quality semi-empirical MO approaches.     

Non-singular descriptions of dislocation cores: a hybrid ab initio continuum approach

The core structure of straight and curved dislocations is studied by developing a hybrid approach that links the parametric dislocation dynamics method with ab initio calculations. The approach is an extension of the Peierls–Nabarro (PN) model, with the following features: (1) all three components of the displacement vector for atoms within the dislocation core are included; (2) the entire generalized stacking fault energy surface (GSFS) obtained from ab initio calculations is utilized; and (3) the method is generalized to treat curved dislocations. We combine the parametric dislocation dynamics (DD) approach for the interaction and motion of dislocations with ab initio calculations of lattice restoring forces. These forces, which are extracted from the GSFS (γ-surface), are calculated from both first-principles density functional theory (DFT) and the embedded-atom method (EAM). Dislocation core structures in aluminium and silver are determined. For straight dislocations, the results from the model are shown to be in excellent agreement with experiments for both Al and Ag. In contrast to undissociated dislocation loops in Al, it is found that the core width and the separations between partials in Ag vary along the angular direction measured with respect to the Burgers vector. It is also shown that the core-cutoff radius, which is usually employed in DD calculations to avoid singularities, must be adjusted as a function of loop size to account for the correct dislocation core energy.     

Three-body effects in hydrogen fluoride: survey of potential energy surfaces

The potential energy surface for trimers of hydrogen fluoride is examined for multiple arrangements of the three-molecule cluster. Several established approaches to model the potential energy are examined, including a strictly pairwise additive potential, an established polarizable potential model, another, strictly three-body polarizable model, and a three-body potential recently fitted to accurate ab initio calculations. These potential surfaces are compared to MP2/6-311++G** and SCF/6-311++G**ab initio calculations performed here for each configuration. In each case the overall trimer potential is examined, as well as the three-body contribution to it (obtained by subtracting the sum of the interactions taken pairwise). The effective pair potential has some correspondence to the ab initio calculations, although it generally displays a shallower minimum energy. The established polarizable model has a more repulsive core that compensates for a deeper attractive well that it has adopted to better describe phase-coexistence data. In contrast, the new three-body polarizable model shows better correspondence with the ab initio potential-energy surface.     

Significance of model Hamiltonians in energy-band theory

The results of recent ab initio calculations of energy bands are compared with interpolation schemes in order to assess the significance of the latter. When the parameters in the interpolation scheme are required to correspond to those obtainable by an ab initio calculation based on a reasonable one-electron potential, we describe the scheme as a model Hamiltonian. The analytic character of model Hamiltonians for s–p bands (pseudopotential case) or for d bands interacting with s–p bands (resonance case) is summarized. The compatibility of the results of several workers with these analyticity requirements is considered. It is shown that if the empirically-motivated adjustments of parameters are to be regarded as physically significant, these adjustments must satisfy rather strict conditions.     

Calculation of thermodynamic properties of vapor–liquid equilibria using ab initio intermolecular potential energy surfaces for dimer O2–O2

The two 5-site potentials from ab initio calculations at the theoretical level CCSD(T) with correlation consistent basis sets aug-cc-pVmZ (with m?=?4, 34) have been constructed from oxygen. The extrapolation ab initio energies were approximated by the basis sets aug-cc-pVmZ (m?=?3, 4). These two potentials were constructed by using the ab initio intermolecular energy values and a non-linear least-squares fitting method. The second virial coefficients of oxygen were determined to demonstrate the accuracy of these ab initio 5-site potentials. These ab initio potentials were employed to estimate the thermodynamic properties of the vapor–liquid equilibria by GEMC simulation. The influence of ab initio potential alone and plus 3-body interaction Axilrod-Teller potential was investigated within GEMC simulation from 80?K to 140?K. The discrepancy between them is insignificant. This showed that the two 2-body 5-site potential functions can also be used together with the 3-body interaction Axilrod-Teller potential to generate the accurate thermodynamic properties of the liquid–vapor equilibria.     

Is the Ar—Br2(X1Σ+ g ) van der Waals complex linear rather than T-shaped? A study in terms of ab initio based potential energy surfaces

The ground state Ar—Br₂ potential energy surface is predicted from ab initio calculations and from an atom—atom model using empirical ArBr potentials and the (evaluated ab initio) perturbation of the interaction between Ar and Br within Br₂. At all levels of modelling, the surface has a double-minimum topology, with wells for both the linear (L-) and T-shaped geometries. This differs from the single-minimum topology predicted by the commonly used pairwise additive Lennard-Jones potential. For both ab initio and atom—atom model surfaces, the L well is found to be significantly deeper than the T well; this relative behaviour is unchanged by zero-point vibrations. Spectroscopic parameters are predicted for the present surfaces. The final surfaces result from a scaling to reproduce the estimated bond energy of the system. Possible reflections of the surface topology in experimental observables are discussed.     

An ab initio study of the hyperfine structure in the X2 Π electronic state of HCCS–calculation of vibronically averaged components of the anizotropic hyperfine tensor

The results of ab initio calculations of the vibronically averaged components of the anisotropic magnetic hyperfine tensor in the low-lying vibronic species of the X²Π electronic state of the HCCS radical are reported. The electronically averaged hyperfine coupling constants for hydrogen, deuterium, ¹³C and ³³S are obtained as functions of two bending vibrational modes by the density functional theory method. The vibronic wave functions are calculated with the help of a variational approach which takes into account the Renner–Teller effect and spin-orbit coupling. The results of ab initio calculations are compared to the corresponding experimental findings.     

A CASSCF/MRCI study of the low-lying Rydberg states of CIO

An ab initio calculation has been performed on the lowest seven doublet and six quartet Rydberg states of CIO at the CASSCF/MRCI level and with basis sets suitable for the extended molecular orbitals of such states (aug-cc-pVTZ with up to eleven extra Gaussian functions). Calculations on the quartet states reveal the energy ordering of Rydberg orbitals to be 4sσ, 4pπ, 4pσ;, 3dδ, 3dσ and 3dπ. The calculated doublet ab initio potential curves confirm experimental assignments of the C²Σ- and F²Σ- states but require reassignments for the symmetries of the D (²Δ), E (²Π) and H (²Δ) Rydberg states. These revisions are supported by spin-orbit coupling calculations that suggest the separation between the Ω components is small. In addition, a ²Σ⁺ state has been identified as the likely upper state for two previously unassigned vibronic bands recorded in absorption studies.     

How quantum bound states bounce and the structure it reveals

We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and cold atomic few-body systems on optical lattices with sharp boundaries. We develop the general theory of elastic reflection for a composite body from a hard wall. On the numerical side we present ab initio calculations for the compression of alpha particles and universal results for two-body states. On the analytical side we derive a universal effective potential that gives the reflection scattering length for shallow two-body states.     

Some properties of electronic non-adiabatic coupling terms

Analytical expressions are obtained for the Born-Oppenheimer non-adiabatic coupling terms formed by a given distribution of conical intersections. The gauge-dependent formulae contain explicitly the boundary conditions that have to be obtained by ab initio calculations performed along a circle in the close vicinity of each conical intersection.     

Computational study of the surface properties of aluminum nanoparticles

We calculate the surface energy, surface stress, and lattice contraction of Al nanoparticles using ab initio density functional and empirical computational techniques. Ab initio calculations are carried out using the siesta pseudopotential method combined with the generalized gradient approximation. Empirical calculations are conducted using the embedded atom method. The ab initio density functional approach predicts the surface energies of Al nanoclusters to be in the range of 0.9-2.0 J/m². These values are consistent with the surface energy of bulk aluminum and are close to the surface energies of silver nanoparticles calculated in our previous study. In contrast to our previous results for Ag nanoparticles, we found a significant discrepancy between the theoretical values of surface energy and stress for Al nanoclusters. This result could be explained by a greater degree of surface reconstruction in Al clusters than in Ag clusters.     

Dependence of the H2-H2 Interaction on the Monomer Bond Lengths: Steps Toward an Accurate ab initio Estimate

We compute the vibrational coupling between two H₂ molecules from ab initio quantum chemical calculations of the H₂-H₂ potential carried out at the full configuration interaction level of theory using the atom-centered aug-cc-pVTZ basis set for hydrogen. We compare the full configuration interaction results with those obtained using two variants of coupled cluster theory and find that a fully iterative treatment of connected triples may be required to estimate the H₂-H₂ vibrational coupling accurately using coupled cluster theory.     

Ab initio potential energy curve for the helium atom pair and thermophysical properties of dilute helium gas. I. Helium–helium interatomic potential

A helium–helium interatomic potential energy curve was determined from quantum-mechanical ab initio calculations. Very large atom-centred basis sets including a newly developed d-aug-cc-pV8Z basis set supplemented with bond functions and ab initio methods up to full CI were applied. The aug-cc-pV7Z basis set of Gdanitz (J. Chem. Phys. 113, 5145 (2000)) was modified to be more consistent with the aug-cc-pV5Z and aug-cc-pV6Z basis sets. The diagonal Born–Oppenheimer corrections as well as corrections for relativistic effects were also calculated. A new analytical representation of the interatomic potential energy was fitted to the ab initio calculated values. In a following paper this potential model will be used in the framework of quantum-statistical mechanics and of the corresponding kinetic theory to calculate the most important thermophysical properties of helium governed by two-body and three-body interactions.     

Interaction potentials,spectroscopy and transport properties of RG+–He (RG=Ar–Rn)

High-level ab initio potential energy curves are calculated for the RG⁺–He complexes (RG=Ar–Rn). RCCSD(T) calculations are employed with large basis sets, and taking account of spin–orbit coupling. The calculated spectroscopic parameters are compared with experimentally determined values, with other high-level ab initio results, and with results from potentials that were obtained by fitting to experimental data. The gas-phase mobilities of RG⁺ ions in He are calculated from our potentials and compared, graphically and statistically, with the experimental mobilities as a function of E/n ₀ at several temperatures. We conclude that more precise experimental data are required in order to discriminate between potentials with more certainty. In addition, we discuss previously reported, unexpectedly large drops in experimental mobility values for RG⁺ in He at 4.35 K as E/n ₀ → 0.     

Ab initio potential energy curve for the neon atom pair and thermophysical properties of the dilute neon gas. I. Neon–neon interatomic potential and rovibrational spectra

A neon–neon interatomic potential energy curve was derived from quantum-mechanical ab initio calculations using basis sets of up to t-aug-cc-pV6Z quality supplemented with bond functions and ab initio methods up to CCSDT(Q). In addition, corrections for relativistic effects were determined. An analytical potential function was fitted to the ab initio values and utilised to calculate the rovibrational spectra. The quality of the interatomic potential function was tested by comparison of the calculated spectra with experimental ones and those derived from other potentials of the literature. In a following paper the new interatomic potential is applied in the framework of the quantum-statistical mechanics and of the corresponding kinetic theory to determine selected thermophysical properties of neon governed by two-body and three-body interactions.     

Ab initio pair potential energy curve for the argon atom pair and thermophysical properties of the dilute argon gas. I. Argon–argon interatomic potential and rovibrational spectra

An argon–argon interatomic potential energy curve was derived from quantum-mechanical ab initio calculations using basis sets of up to d-aug-cc-pV(6+d)Z quality supplemented with bond functions and ab initio methods up to CCSDT(Q). In addition, corrections for relativistic effects were determined. An analytical potential function was fitted to the ab initio values and utilised to compute the rovibrational spectrum. The quality of the interatomic potential function was tested by comparison of the calculated spectrum with experimental ones and those derived from other potentials of the literature. In a following paper the new interatomic potential is used to determine selected thermophysical properties of argon by means of quantum-statistical mechanics and the corresponding kinetic theory considering two-body and three-body interactions.     

Modelling of short-range ordering kinetics in dilute multicomponent substitutional solid solutions

ABSTRACT

Short-range ordering as the formation of couples and pairs between solutes is affected by their formation energies. This is not reflected in the standard regular solution model. Here, we present a new thermodynamic model which accounts for the dependence of the molar Gibbs energy on the concentrations of couples and pairs and their formation energies. The model treats kinetics of couples and pairs formation controlled by diffusion. This new model uses tracer diffusion coefficients of solutes and bond formation energies, which can be taken from ab initio calculations. Insofar, the current concept bridges the gap between ab initio methods and non-equilibrium thermodynamics. The reliability of the model is checked by comparison with kinetic Monte Carlo simulations. The model is applied to an Al-Mg-Si-Cu system. Finally, the configurational entropy for a binary system evaluated with the current model is compared with Bethe’s approximation, which allows estimating of applicability limits of the current model.     

Theoretical investigation of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules. 1. Variational calculation of vibronic structure in the 11Δg state of B2H2

A variational approach for the ab initio handling of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules is presented. The model Hamiltonian involves four nuclear degrees of freedom which correlate for a linear nuclear arrangement with two doubly degenerate bending modes. The bond lengths are assumed to be kept fixed at their equilibrium values and the effect of end-over-end rotations is neglected. The kinetic energy operator and the general form of the potential surfaces employed allow in principle for a treatment of large amplitude bending vibrations. However, because of restrictions implied, such as neglect of coupling between bending and stretching vibrations and interactions with other electronic states, the approach is aimed primarily at molecules bending with relatively small amplitudes around their linear equilibrium geometries. Two algorithms are developed, one for symmetric acetylene-like (A-B-B-A) molecules, the other for asymmetric (A-B-C-D) species. The approach is applied to calculate the vibronic spectrum of the lowest lying excited state, ¹Δ_g, of B₂H₂, employing ab initio computed potential energy surfaces.