Helium configuration interaction

Fig. 13.4 Logarithm of error(Eh) in the configuration interaction energy for the ground state of the helium atom as a function of maximum orbital quantum number, L, of the one-electron basis functions. The data were obtained in an...

J.L. Sanz-Vicario, E. Lindroth, N. Brandefelt, Photodetachment of negative helium ions below and above the Is ionization threshold A complex scaled configuration-interaction approach, Phys. Rev. A 66 (2002) 052713. 

The discrepancy between theories is indicated and the maximum discrepancy ranges from 23 ppm to 30 ppm for Z = 18-26 and differences are consistent. Our measurements are at this level of uncertainty. A further indication of the uncertainty or accuracy of theory can be gained by considering the two configuration interaction (Cl) calculations of Cheng et al [6,7]. The latest calculations for mid-Z helium-like ions [7] has resulted in new values which have shifted by up to 14 ppm from the earlier calculation [6]. The difference has been attributed to the exclusion of the Latter correction to the Dirac-Kohn-Sham potentials from which the QED corrections are evaluated. The new results are considered to be more reliable [7] and are in closer agreement to the unified calculation... 

There are two ways that atoms can interact to attain noble-gas configurations. Sometimes atoms attain noble-gas configurations by transferring electrons from one atom to another. For example, lithium has one electron more than the helium configuration, and fluorine has one electron less than the neon configuration. Lithium easily loses its valence electron, and fluorine easily gains one ... 

The calculation of electron scattering on atoms whose structures can be represented by two electrons and an inert closed-shell core is an example of the general case where a configuration-interaction calculation of the target states is required. The prototype is helium, a pure two-electron target. 

Fig. 11.6 shows the noncoplanar-symmetric differential cross sections at 1200 eV for the Is state and the unresolved n=2 states, normalised to theory for the low-momentum Is points. Here the structure amplitude is calculated from the overlap of a converged configuration-interaction representation of helium (McCarthy and Mitroy, 1986) with the observed helium ion state. The distorted-wave impulse approximation describes the Is momentum profile accurately. The summed n=2 profile does not have the shape expected on the basis of the weak-coupling approximation (long-dashed curve). Its shape and magnitude are given quite well by... 

Fig. 11.6. The 1200 eV noncoplanar-symmetric momentum profiles for the ground-state (n = 1) and summed n = 2 transitions in helium (Cook et al., 1984). Curves indicated DWIA, distorted-wave impulse approximation PWIA, plane-wave impulse approximation. The curves are calculated using a converged configuration-interaction expansion (McCarthy and Mitroy, 1986) for the helium ground state. The long-dashed curve is the distorted-wave impulse approximation for the Hartree—Fock ground state. Experimental data are normalised to the Is curve at low momentum. From McCarthy and Weigold (1991).

In two previous papers [8,9] we have calculated the static polarizabilities and hyperpolarizabilities for ls3p Pj (J = 0, 2)-states of helium. The method was based on degenerate perturbation-theory expressions for these quantities. The necessary dipole matrix elements were found by using the high-precision wave function on framework of the configuration-interaction (Cl) method [10]. The perturbed wave functions are also expanded in a basis of accurate variational eigenstates [11]. These basis sets of the wave functions explicitly take account of electron correlation. To control the result we have also carried out similar calculations with Fues model potential method. 

The helium pair polarizability increment has been studied extensively [19, 29, 39, 41, 48, 56, 57, 63]. We mention in particular the most recent work by Dacre [48], which includes a careful review of previous results. Systems such as H-H in the and states may be considered as tractable examples representative of various types of real collisional pairs [6,28,54, 55,66,74,85, 144, 145, 147]. Elaborate self-consistent field (SCF) calculations, supplemented by configuration interaction (Cl) corrections are also known for the neon diatom [50]. For atom pairs with more electrons, attempts have been made to correct the SCF data in some empirical fashion for Cl effects [47, 49]. Ab initio studies of molecular systems, such as H2-H2 and N2-N2 have been communicated [16, 18]. 

The scalar spin-spin coupling has been calculated by Pecul for the helium dimer using full configuration interaction and EOM-CCSD methods. The... 

D. R. Herrick, O. Sinanoglu, Comparison of doubly-excited helium energy levels, iso-electronic series, autoionization lifetimes, and group-theoretical configuration-mixing prediction with large-configuration-interaction calculations and experimental spectra, Phys. Rev. A 11 (1975) 97. 

Johnson W R and Cheng K T 1996 Relativistic configuration-interaction calculation of the polarizabilities of helium-like ions , Phys. Rev. A 53, 1375 -8... 

In Section III.E, EOM ionization potentials and electron affinities are compared with accurate configuration interaction (Cl) results for a number of atomic and molecular systems. The same one-electron basis sets are utilized in the EOM and Cl calculations, allowing for the separation of basis set errors from errors caused by approximations made in the solution of the EOM equation. EOM results are reported for various approximations including those for the extensive EOM theory developed in Section II. Section III.F presents results of excitation energy calculations for helium and beryllium to address a number of remaining difficult questions concerning the EOM method. 

A similar expansion can be made in practical finite-basis calculations, except that limitations of the basis set preclude the possibility that the exact wavefunction lies in the space spanned by the available ( ). However, it should be clear that the formation of linear combinations of the finite number of offers a way to better approximate the exact solution. In fact, it is possible to obtain by this means a wavefunction that exactly satisfies the electronic Schrodinger equation when the assumption is made that the solution must lie in the space spanned by the -electron basis functions ( ). However, even this is usually impossible, and only a select number of the are used. The general principle of writing -electron wavefunctions as linear combinations of Slater determinants is known as configuration interaction, and the resultant improvement in the wavefunction is said to account for electron correlation. The origin of this term is easily understood. Returning to helium, an inspection of the Hartree-Fock wavefunction... 

One of the simplest van der Waals complexes is the helium dimer. The small size of the system has made it possible to evaluate the He- He spin-spin coupling constant in an accurate manner, at the full configuration interaction level The Fermi-contact term has been found to have non-negligible value of 1.3 Hz at R=5.6 a.u. (dose to the energy minimum), while the other contributions are practically zero. The coupling decreases very fast, in an exponential manner, with the intemuclear distance R. For R equal to 4 a.u. it is over 22 Hz, while for R over 7 a.u. it falls below... 

D.E. Ramaker, D.M. Schrader, Multichannel configuration-interaction theory Application to some resonances in Helium, Phys. Rev. A 9 (1980) 1974. 

If the interaction between two ground-state He atoms were strictly repulsive (as predicted by MO theory), the atoms in He gas would not attract one another at all and the gas would never liquefy. Of course, helium gas can be liquefied. Configuration-interaction calculations and direct experimental evidence from scattering experiments show that as two He atoms approach each other there is an initial weak attraction, with the potential energy reaching a minimum at 3.0 A of 0.0009 eV below the separated-atoms energy. At distances less than 3.0 A, the force becomes increasingly repulsive because of overlap of the electron probability densities. The initial attraction (called a London or dispersion force) results from instantaneous correlation between the motions of the electrons in one atom and the motions of the electrons in the second atom. Therefore, a calculation that includes electron correlation is needed to deal with dispersion attractions. 

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