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.     

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.     

Sensitivity of the electronic-interaction parameters used in molecular calculations to correlation effects

The correlation corrections to the one-center Coulomb integrals are calculated for the⁵S(1s²2s2p³) state of carbon, the⁴P(1s²2s2p⁴) state of nitrogen and the³P(1s²2s²2p⁴) state of oxygen. The calculated results are compared with semiempirical values. A satisfactory agreement is found for all three atoms.Translated from Izvestiya VUZ. Fizika, No. 3, pp. 119–122, March, 1970In conclusion the author thanks his colleagues in the Theoretical Physics Laboratory and the Optics and Spectroscopy Laboratory, Siberian Physicotechnical Institute, for many fruitful discussions of these topics.     

What atomic model should be used in internal conversion calculations?

From a measurement of the impact parameter dependence of positron production in heavy ion-atom collisions the relation between the average impact parameter and the energy transfer could be calibrated.     

K-shell polarization of O ions in ferromagnets by spin dependent electron promotion via molecular orbitals

Transient field precessions of the 6.13 MeV¹⁶O(3^-) state have been measured in polarized Fe and Ni in order to corroborate our earlier results on C ions. It is found that precessions in Fe and Ni scale with the polarized electron density of the host at v_ion = 3.0 v₀ and are comparable at v_ion = 1.5 v₀. The latter is attributed to direct K-shell polarization of the ion by spin dependent electron promotion via molecular orbitals.     

Constrained variational calculations on nuclear matter with state dependent correlations

Constrained variational calculations on the binding energy of nuclear matter have been performed employing three potentials with differing mixtures of central and tensor components. We present numerical results on the energy expectation value in two- and three-body cluster approximation as function of the separation distance at which the central and tensor correlations heal smoothly.     

Enhanced recollisions for antisymmetric molecular orbitals in intense laser fields

The peculiarities of antisymmetric molecular orbitals are investigated in very intense linearly polarized laser pulses. For this purpose, the ionization-recollision quantum dynamics is evaluated theoretically beyond the dipole approximation. As opposed to the usual situation, the laser magnetic field component is found to strongly enhance recollision probabilities for particularly oriented antisymmetric molecular orbitals. Harmonic generation and related processes are thus allowed at high laser intensities without the common limitations by the laser magnetic field.     

Role of highest occupied molecular orbitals in molecular field-free alignment by a femtosecond pulse

This paper studies the molecular rotational excitation and field-free spatial alignment in a nonresonant intense laser field numerically and analytically by using the time-dependent Schr?dinger equation. The broad rotational wave packets excited by the femtosecond pulse are defined in conjugate angle space, and their coefficients are obtained by solving a set of coupled linear equations. Both single molecule orientation angles and an ensemble of O₂ and CO molecule angular distributions are calculated in detail. The numerical results show that, for single molecule highest occupied molecular orbital (HOMO) symmetry σ tends to have a molecular orientation along the laser polarization direction and the permanent dipole moment diminishes the mean of the orientation angles; for an ensemble of molecules, angular distributions provide more complex and additional information at times where there are no revivals in the single molecule plot. In particular, at the revival peak instant, with the increase of temperature of the molecular ensemble, the anisotropic angular distributions with respect to the laser polarization direction of the π _g orbital gradually transform to the symmetrical distributions regarding the laser polarization vector and for two HOMO configurations angular distributions of all directions are confined within a smaller angle when the temperature of the molecular ensemble is higher.     

Deformed relativistic mean-field calculations on nuclei near Z = 50 with FSUGold

The ground-state properties of Sn, Te, Xe, and Ba isotopes have been systematically investigated in the framework of the deformed relativistic mean-field theory with the new parameter set FSUGold. The results show that FSUGold is as successful as NL3 ^* in reproducing the ground-state binding energies of the nuclei. The calculated two-neutron separation energies, quadrupole deformations, and root-mean-square (rms) charge radii are in good agreement with the experimental data. The parameter set FSUGold can successfully describe the shell effect of the neutron magic number N = 82 . Detailed discussions on the binding energies, two-neutron separation energies, quadrupole deformations, rms charge radii and “binding energies” of the last neutrons are given.     

Separable States can be used to distribute entanglement

We show that no entanglement is necessary to distribute entanglement; that is, two distant particles can be entangled by sending a third particle that is never entangled with the other two. Similarly, two particles can become entangled by continuous interaction with a highly mixed mediating particle that never itself becomes entangled. We also consider analogous properties of completely positive maps, in which the composition of two separable maps can create entanglement.     

First-principles electronic structure calculations with molecular dynamics made easy

The technique of quantum molecular dynamics is reviewed, and a simplified approach based on a first-principles tight-binding implementation of local density theory is discussed. Several illustrations and applications of the theory are presented. Applying it to amorphous materials, we have developed a procedure for producing amorphous Si networks with small defect concentrations. Benchmark checks are made for atomic geometries at Si(111)-(2×1) and Si(001)-(2×1), p(2×2), and c(4×2) reconstructed surfaces. A simulation of a Scanning Tunneling Microscope tip interacting with a reconstructed surface is performed, and it is shown how the tip can alter the reconstruction of the surface. Simulation of a kinked Si(001) surface step and comparison to an unkinked step are also presented.     

Atomic and molecular defects in solid He

The studies of defects formed by impurity particles (atoms, molecules, exciplexes, clusters, free electrons, and positive ions) embedded in liquid and solid ⁴He are reviewed. The properties of free electrons and neutral particles in condensed helium are described by the electron (atomic) bubble model, whereas for the positive ions a snowball structure is considered. We compare the properties of the defects in condensed helium with those of metal atoms isolated in heavier rare gas matrices.