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.     

Summation of Parquet diagrams as an ab initio method in nuclear structure calculations

In this work we discuss the summation of the Parquet class of diagrams within Green’s function theory as a possible framework for ab initio nuclear structure calculations. The theory is presented and some numerical details are discussed, in particular the approximations employed. We apply the Parquet method to a simple model, and compare our results with those from an exact solution. The main conclusion is that even at the level of approximation presented here, the results shows good agreement with other comparable ab initio approaches.     

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.     

Using monomer properties to obtain integrated intensities for vibrational transitions of van der Waals complexes

The integrated intensities of vibrational transitions depend on the magnitude of the derivatives of the dipole with respect to nuclear motion. Normally, the only reliable way to compute such derivatives is by tedious and expensive ab initio calculations. In this paper, we present a simplification for weakly bound complexes based on distributed schemes for describing the charge densities and polarizabilities of the monomers. Formulations based on both Cartesian and spherical harmonics are presented. The results for both these schemes agree exactly with each other, and qualitatively with full ab initio calculations for the hydrogen fluoride dimer, (HF)₂.     

Nuclear quantum effects in liquid water from path-integral simulations using an ab initio force-matching approach

We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterised by force-matching to density functional theory-based molecular dynamics simulations. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals and dispersion corrections are discussed in regards to reproducing the experimental properties of liquid water.     

An investigation of ab initio shell-model interactions derived by no-core shell model

The microscopic shell-model effective interactions are mainly based on the many-body perturbation theory (MBPT), the first work of which can be traced to Brown and Kuo’s first attempt in 1966, derived from the Hamada-Johnston nucleon-nucleon potential. However, the convergence of the MBPT is still unclear. On the other hand, ab initio theories, such as Green’s function Monte Carlo (GFMC), no-core shell model (NCSM), and coupled-cluster theory with single and double excitations (CCSD), have made many progress in recent years. However, due to the increasing demanding of computing resources, these ab initio applications are usually limited to nuclei with mass up to A = 16. Recently, people have realized the ab initio construction of valence-space effective interactions, which is obtained through a second-time renormalization, or to be more exactly, projecting the full-manybody Hamiltonian into core, one-body, and two-body cluster parts. In this paper, we present the investigation of such ab initio shell-model interactions, by the recent derived sd-shell effective interactions based on effective J-matrix Inverse Scattering Potential (JISP) and chiral effective-field theory (EFT) through NCSM. In this work, we have seen the similarity between the ab initio shellmodel interactions and the interactions obtained by MBPT or by empirical fitting. Without the inclusion of three-body (3-bd) force, the ab initio shell-model interactions still share similar defects with the microscopic interactions by MBPT, i.e., T = 1 channel is more attractive while T = 0 channel is more repulsive than empirical interactions. The progress to include more many-body correlations and 3-bd force is still badly needed, to see whether such efforts of ab initio shell-model interactions can reach similar precision as the interactions fitted to experimental data.     

Theoretical study of nonadiabatic interactions,radiative lifetimes and predissociation lifetimes of excited states of BH

Ab initio multireference configuration interaction calculations have been carried out on the lower-lying electronic states of BH and their nonadiabatic interactions. The ab initio data have been included in subsequent calculations involving solution of the complex eigenvalue Schrödinger equation to determine predissociation widths and lifetimes of vibrational-rotational levels of these states. Secondly, previously calculated ab initio data on the Rydberg states and their nonadiabatic interactions have been included in multi-state vibrational calculations on the 3p and 3d complexes in BH and BD. The results are in good agreement with the experimental analysis of the 3p and 3d spectra in BH and BD. Furthermore, interaction of the 3d states with the neighbouring 4s state is also found to be important.     

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.     

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.     

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.     

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.     

Ionic liquid structure: the conformational isomerism in 1‐butyl‐3‐methyl‐imidazolium tetrafluoroborate ([bmim][BF4])

As a probe of local structure, the vibrational properties of the 1‐butyl‐3‐methylimidazolium tetrafluoroborate [bmim][BF₄] ionic liquid were studied by infrared (IR), Raman spectroscopy, and ab initio calculations. The coexistence of at least four [bmim]⁺ conformers (GG, GA, TA, and AA) at room temperature was established through unique spectral responses. The Raman modes characteristic of the two most stable [bmim]⁺ conformers, GA and AA, according to the ab initio calculations, increase in intensity with decreasing temperature. To assess the total spectral behavior of the ionic liquid both the contributions of different [bmim]⁺ conformers and the [bmim]⁺− [BF₄]⁻ interactions to the vibrational spectra are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Theoretical and vibrational spectroscopic studies on binary mixture of o‐chlorobenzaldehyde

In this work, a combined theoretical and spectroscopic study of binary mixture of liquid o‐chlorobenzaldehyde (OCBZ) is reported using ab initio calculations, Raman and infrared (IR) spectroscopies. The purpose of this study was twofold: firstly, to describe the interaction of OCBZ in terms of bonding energies and preferred geometries; secondly, to characterize the spectroscopic effects on the vibrational modes of OCBZ in the binary mixture of different polar and nonpolar solvents. Ab initio calculations have proven to be a valuable tool for predicting relevant molecular structure and molecular parameters in the intermolecular interactions. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.     

Quantum Monte Carlo calculations of light nuclei

Quantum Monte Carlo calculations using realistic two- and three-nucleon interactions are presented for nuclei with up to ten nucleons. Our Green's function Monte Carlo calculations are accurate to ∼1-2% for the binding energy. We have constructed Hamiltonians using the Argonne v₁₈ NN interaction and reasonable three-nucleon interactions that reproduce the energies of these nuclear states with only ∼500 keV rms error. Other predictions, such as form factors, decay rates, and spectroscopic factors also agree well with data. Some of these results are presented to show that ab initio calculations of light nuclei are now well in hand. Received: 1 May 2001 / Accepted: 4 December 2001     

Ab initio NMR parameters of BrCH3 and ICH3 with relativistic and vibrational corrections

This study is focused on two effects identified when NMR parameters are calculated based on first principles. These effects are 1. vibrational correction of properties when using ab initio optimized equilibrium geometry; 2. relativistic effects and limits of using the Flygare equation. These effects have been investigated and determined for nuclear spin-rotation constants and nuclear magnetic shieldings for the CH₃Br and CH₃I molecules. The most significant result is the difference between chemical shieldings determined based on the ab initio relativistic four-component Dirac-Coulomb Hamiltonian and chemical shieldings calculated using experimental values and the Flygare equation. This difference is approximately 320 ppm and 1290 ppm for ⁷⁹Br and ¹²⁷I in the CH₃X molecule, respectively.     

Light nuclei in <Emphasis Type="Italic">ab initio</Emphasis> approach with realistic inverse scattering <Emphasis Type="Italic">NN</Emphasis>-interaction

We discuss the studies of light nuclei in ab initio No-core Full Configuration approach based on extrapolations to the infinite model space of large-scale No-core Shell Model calculations on supercomputers. The convergence at the end of p shell and beginning of the sd shell can be achieved if only reasonable soft enough NN interactions are used. In particular, good predictions are obtained with a realistic JISP16 NN interaction obtained in J-matrix inverse scattering approach and fitted to reproduce light nuclei observables without three-nucleon forces. We discuss the current status of this NN interaction and its recent development.