Non-empirical pseudo-potentials for molecular calculations

Our non-empirical pseudo-potential method is tested on the molecules ScH₃, TiH₃F, MnO₄ ^-, Zn(CH₃)₂ and Pd(CO)₄. The calculations are performed with the PSIBMOL algorithm, described in paper I (Molec. Phys., 1977, 33, 159) at the independent particle restricted Hartree-Fock level with minimal and double-zeta basis sets of Slater orbitals expanded in gaussian functions. The agreement between pseudo-potential and all-electron calculations for these molecules is as good as for non-transition element compounds as concerns valence molecular orbital energies and expectation values of various one-electron operators. The general conclusion of this series (papers I, II and III) is that our non-empirical pseudo-potential method can now be used as a routine tool to predict efficiently the ground-state valence electronic properties of molecules containing any atom of the Periodic Table as far as relativistic effects remain unimportant.     

Binding energy calculations for metal aggregates

Within the framework of the local density functional formalism the binding energies of atoms in metallic aggregates are computed. The calculations are based on the following approach: The total charge density is approximated by the superposition of the charge densities of the respective free atoms. The kinetic energy is obtained by a modified Thomas-Fermi-Weizsäcker expression, and the exchange/correlation energy is determined by theX -approximation. As a first example of application we have calculated the adsorption energies of Cu and Pd on tungsten and the formation energy of a vacancy in pure copper and in copper with Ge impurities. The results are in fair agreement with the respective experimental data.     

Configuration interactions constrained by energy density functionals

A new method for constructing a Hamiltonian for configuration interaction calculations with constraints to energies of spherical configurations obtained with energy-density-functional (EDF) methods is presented. This results in a unified model that reproduced the EDF binding-energy in the limit of single-Slater determinants, but can also be used for obtaining energy spectra and correlation energies with renormalized nucleon–nucleon interactions. The three-body and/or density-dependent terms that are necessary for good nuclear saturation properties are contained in the EDF. Applications to binding-energies and spectra of nuclei in the region above ²⁰⁸Pb are given.     

Constrained minima of nonlocal free energy functionals

We consider variational problems involving nonlocal free energy functionals that arise from Gibbs measures with Kac potentials and are related to the characterization of the optimal (i.e., typical) shape of an interface under given constraints on the magnetization profile.     

Semiempirical molecular orbital calculations for ketene dimers

The semiempirical molecular orbital method known as symmetrically orthogonalised intermediate neglect of differential overlap (sindo) has been employed to determine the geometry, bonding, binding energy, ionisation potential, dipole moment and net charges of diketene and cyclobutane-1,3-dione molecules. Results obtained have been compared with available experimental data.     

Variationally optimized numerical orbitals for molecular calculations

The problem of variational optimization of the atomic orbitals used in molecular calculations is investigated. It is shown that the variational principle leads to an equation similar to the radial Schrodinger equation but containing an inhomogeneous term. As an example, the equations are solved for the minimum basis set orbitals for the methane molecule. The results show a substantial improvement over those of a previous calculation optimizing in a minimum basis of Slater orbitals.     

Quantum-mechanical molecular orbital calculations

The theory of generalized combined orbitals is outlined. This is a development of the theory put forward by Löwdin [3]. Certain spectral characteristics of benzene, diphenyl, and nitrobenzene are calculated and the results are compared with the theory.In conclusion the author wishes to thank N. A. Prilezhaevaya, V, I. Danilova and O. A. Ponomarev for many discussions and also L. G. Turovets for carrying out the calculations.     

Nuclear energy density functionals constrained by low-energy QCD

A microscopic framework of nuclear energy density functionals is reviewed, which establishes a direct relation between low-energy QCD and nuclear structure, synthesizing effective field theory methods and principles of density functional theory. Guided by two closely related features of QCD in the low-energy limit: a) in-medium changes of vacuum condensates, and b) spontaneous breaking of chiral symmetry; a relativistic energy density functional is developed and applied in studies of ground-state properties of spherical and deformed nuclei.     

Discrepancies in ICC calculations for low energy transitions

Systematic comparison of theK-M ₅ subshell ICC of Hager and Seltzer with calculations of this paper was performed forZ=50, 60, 80, 100, and forE1-E4 andM1-M4 multipolarities and for conversion electron energies ranging from 1 to 1500keV. In most cases, the two sets of ICC agree within a few per cent; for high multipolarities and very low conversion electron energies, however, discrepancies as large as 20 per cent were observed.     

A soft-core Thomas-Fermi pseudopotential for total energy calculations

We present a modification of the “Thomas-Fermi pseudopotential” developed by Chelikowsky for the calculation of cohesive energies of solids. In the original work, the pseudopotential was singular at the origin, owing to a cusp in the pseudowavefunction. We derive here a “Thomas-Fermi pseudopotential” based on the form of pseudowavefunction introduced by Kerker, which is smooth and nonvanishing at the origin. This pseudopotential was tested in cellular calculations of the total binding energy and equilibrium cell size of bcc Na, both of which were in excellent agreement with experiment. The precision of the variationally determined charge density n(r) was checked by calculating the corresponding chemical potential μ(r), which was virtually uniform except in a small neighborhood of the origin. An LCAO parametrization of the charge density is outlined that would be appropriate for 3D problems such as a point defect.     

Optimum atomic orbitals for molecular calculations A review

This review is intended to give a broad outline of the many techniques used in the calculation of atomic structure and the methods of using the information gained from this work in molecular calculations. Consequently, no topic is considered in full depth and only selected examples from the literature are used to illustrate the main points. Extensive tabulatios of atomic and molecular properties are already available in the literature, and these serve as additional sources of examples. Only methods within the Hartree-Fock framework, where a single Slater determinant (or in some cases a linear combination of Slater determinants) and the variation principle form the basis of the model, are considered in detail. Extensions of the independent particle model to include correlation have been considered briefly and smaller corrections, such as magnetic and relativistic effects are omitted.

We describe, in the first part of the review, the partical requirements of the functional form of the basis set and consider examples of the types of functions available in the literature. These include exponential- and Gaussian type-functions and many others. For' chemical accuracy' the total energy of the electronic system should be estimated to within one kilocalorie or better, requiring at least Hartree-Fock accuracy for the isolated atoms and optimization or augmentation of the bases in the molecule. Smaller, less accurate basis sets for the atoms are still useful, however, in the prediction of certain atomic and molecular properties, and in supplying simple orbital pictures of interest to chemists, although producing poorer representations of the total wave function.

In order to produce good wave functions there are certain criteria that they may satisfy. These, when coupled with the independent particle model, produce many methods of obtaining wave functions of varying accuracy depending in the size and type of functions comprising the basis set. Some of the criteria considered include the minimal energy principle, the best approximation to operators other than the Hamiltonian and other less known, and perhaps less practical, methods.

The quality of the atomic wave functions, produced from Hartree-Fock equations, using different types of basis functions, may be investigated with the aid of many operators, and in particular the position operators, <rⁿ >, and tested in the prediction of such quantities as the electron-electron interaction operators. The atomic <rⁿ > values are extremely useful in choosing a basis for the calculation of a particular molecular property that depends heavily on the same region of space.

In order to allow for the polarization of an atom in a molecular environment, and hence achieve better molecular properties, one may either reoptimize or augment the existing basis. If large basis sets are used initially for the atom, then they may be contracted without appreciable loss of ‘chemical accuracy’ before being used in the molecular calculations. These points are illustrated, using different basis sets produced by several methods, for the molecules HF, H₂O, NH₃ and HCN. Rules for orbital exponents (non-linear parameters of the basis set) for atoms and molecules are also discussed.     

Total cross-section calculations for electrons colliding with molecular nitrogen over an extensive energy range from meV to keV

We report a comprehensive study of the electron impact total cross-sections for molecular nitrogen for impact energies from 0.01?eV to 2000?eV. Ab initio calculations are performed using the R-matrix formalism at low impact energies (up to ～15?eV), while the Spherical Complex Optical Potential formalism is utilised beyond this range. The two methods are consistent at the transition energy, which enables us to provide data for such an extensive range. The results obtained show overall good agreement with the available data.