Two-component Calculations Research Articles

Does δD from fluid inclusion in quartz reflect the original hydrothermal fluid?

Hydrogen isotope investigations on hydrothermal quartz reveal two H-reservoirs: (i) trapped fluid inclusions, and (ii) structurally bound water in homogenously distributed small clusters or bubbles. Varying mixing ratios of the two reservoirs are sampled by means of mechanical and thermal decrepitation applied to different grain size fractions. A two-component mixing calculation results in an isotopic characterisation of the two H-reservoirs, which fractionate hydrogen isotopes close to the known MOH–H 2O system, with water being enriched in deuterium. Temperature controls both the internal fractionation as well as the abundance ratio of inclusion water to bonded water. At high temperatures, fractionation is small but bound water becomes more abundant, comprising a significant amount of water from both thermal and mechanical extraction techniques. Hence, the isotope composition of the extracted water does not reflect the original hydrogen isotope composition of the hydrothermal fluid especially at temperatures higher than 200°C. Previously reported δD data of fluid inclusion, which were used to elucidate the origin of the hydrothermal fluid, tend to be too low.

Two-component coupled-cluster calculations for the hydride of element 111: on the performance of relativistic effective core potentials

We have calculated bond lengths, harmonic vibrational frequencies, and dissociation energies for (1 1 1)H using relativistic effective core potentials (RECP) including one-electron spin–orbit operators at the Hartree–Fock and coupled-cluster levels of theory. The spectroscopic constants calculated using shape-consistent RECPs compare favorably with available four-component results, but energy-consistent RECPs are found to underestimate the spin–orbit effects. The best computed(estimated) spectroscopic constants of (1 1 1)H are 1.512(1.524) A ̊ , 2668(2647) cm −1 , and 2.87(2.77) eV for R e, ω e, and D e, respectively. The calculated spin–orbit effects (+0.009 A ̊ ,−113 cm −1 , and −0.64 eV) are modest, although the molecule has a closed-shell electronic structure.

Small-core multiconfiguration-Dirac–Hartree–Fock-adjusted pseudopotentials for post- d main group elements: Application to PbH and PbO

Relativistic pseudopotentials (PPs) of the energy-consistent variety have been generated for the post-d group 13–15 elements, by adjustment to multiconfiguration Dirac–Hartree–Fock data based on the Dirac–Coulomb–Breit Hamiltonian. The outer-core (n−1)spd shells are explicitly treated together with the nsp valence shell, with these PPs, and the implications of the small-core choice are discussed by comparison to a corresponding large-core PP, in the case of Pb. Results from valence ab initio one- and two-component calculations using both PPs are presented for the fine-structure splitting of the ns2np2 ground-state configuration of the Pb atom, and for spectroscopic constants of PbH (X 2Π1/2, 2Π3/2) and PbO (X 1Σ+). In addition, a combination of small-core and large-core PPs has been explored in spin-free-state shifted calculations for the above molecules.

On the consistent definition of spin–orbit effects calculated by relativistic effective core potentials with one-electron spin–orbit operators: Comparison of spin–orbit effects for Tl, TlH, TlH3, PbH2, and PbH4

The spin–orbit effects for Tl, TlH, TlH3, PbH2, and PbH4 are evaluated by two-component calculations using several relativistic effective core potentials (RECP) with one-electron spin–orbit operators. The used RECPs are shape-consistent RECPs derived by Wildman et al. [J. Chem. Phys. 107, 9975 (1997)] and three sets of energy-consistent (or adjusted) RECPs published by Schwerdtfeger et al. [Phys. Scr. 36, 453 (1987); J. Chem. Phys. 90, 762 (1989)], Küchle et al. [Mol. Phys. 74, 1245 (1991)], and Leininger et al. [Chem. Phys. 217, 19 (1997)]. The shape-consistent RECP results are in very good agreement with the Küchle et al. energy-consistent RECP results for all the molecules studied here and all-electron results for TlH. The RECPs of Schwerdtfeger et al. and Leininger et al. seem to provide qualitatively different spin–orbit effects. If one defines spin-free RECP as the potential average of the corresponding two-component RECP, all RECPs give very similar spin–orbit effects for all the cases. Most of the discrepancies of molecular spin–orbit effects among various RECPs reported in the literature may originate from different definitions of RECPs with or without a spin–orbit term and not from the inherent difference in spin–orbit operators.

Two-component calculations for the molecules containing superheavy elements: Spin–orbit effects for (117)H, (113)H, and (113)F

We have calculated bond lengths, harmonic vibrational frequencies, and dissociation energies for (117)H, (113)H, and (113)F using relativistic effective core potentials (RECPs) with one-electron spin–orbit operators at the two-component coupled-cluster levels of theory. It is shown that any reasonable theoretical descriptions of the electronic structures of molecules containing superheavy elements require consideration of relativistic interactions and electron correlations. Comparisons with available all-electron Dirac–Fock (DF) based results indicate that our two-component approaches are very promising tools in the calculations for the molecules containing superheavy elements. The spin–orbit effects calculated from one- and two-component RECPs are in good agreement with those from all-electron Douglas–Kroll and DF results, implying that the potential average scheme is useful for obtaining one-component RECPs even for superheavy elements. Spin–orbit and electron correlation effects are not additive for molecular properties of (117)H, (113)H, and (113)F, but spin–orbit effects are qualitatively similar at all levels of theory considered. Spin–orbit effects contract Re and increase ωe for (113)H and (113)F, whereas they expand Re and decrease ωe for (117)H. Spin–orbit effects decrease De for all molecules considered, but the amount of decrease for (113)H and (117)H is substantially smaller than that estimated from the atomic splittings. For (117)H, our best calculations yield 1.983 Å (Re), 1403 cm−1(ωe), and 1.60 eV (De).

Low-lying states of Tl2 calculated by the configuration interaction methods based upon relativistic effective core potentials and two-component spinors

We have modified a Dirac–Fock program package, MOLFDIR [L. Visscher et al., Comput. Phys. Commun. 81, 120 (1994)], to perform two-component molecular spinor calculations based upon the relativistic effective core potentials (REPs) incorporating effective spin–orbit operators. The modified MOLFDIR can be used to perform two-component REP calculations instead of four-component all-electron calculations at various levels of theory including the configuration interaction (CI) level. As a test case for the multireference CI methods, the low-lying states of Tl2 are calculated with the two-component CI method and the more conventional spin–orbit CI method. Results indicate that the two-component method has some advantages in describing the ground state of Tl2 while excited states are similarly described by both methods.

Spin-orbit effects in the PtH +2 ion

The five low-lying doublet states of PtH + 2 have been studied by all-electron one- and two-component variational calculations using the Douglas–Kroll operator in a RASCI formalism. CASSCF calculations are performed in order to optimize orbitals for the subsequent RASCI calculations. Spin-orbit effects are introduced on the CI level both as a perturbation based on the spin-free CI states and variational in spin-orbit RASCI calculation. The influence of the spin-orbit effects are studied on geometries, excitation energies, reaction barrier and dissociation energies.

Growth of the normal-flow instability of a vortex array in two-component HeII

It has been known for some time that there is a hydrodynamic instability in rotating vortex-permeated superfluid HeII. This instability sets in at a critical relative velocity of the two components (normal and superfluid). The first theoretical treatment assumed a uniform constant velocity of the normal component, thus limiting the dynamics to the superfluid. Growth rates were found. A little later, it was shown that the critical velocity for the onset of the instability so obtained survived a more rigorous two-component calculation. However, growth rates obtained from the one fluid model are a different story and remain questionable (the original calculation is inconsistent with an expansion in the ratio of the two densities). Here the problem is solved by considering the two-component model. Generally speaking, growth rates are somewhat different from those hitherto used. This is important in view of recent experiments in which the superfluid matches the vorticity of the normal fluid.

Spin-orbit and correlation effects in platinum hydride (PtH)

The low-lying electronic states of PtH were studied by all-electron one- and two-component variational calculations on the multireference CI levels. The orbital optimization is performed within a one-component formalism, whereas the further refinement of the wave functions follows two different schemes: The most demanding approach introduces spin–orbit coupling in the CI optimization step, giving a simultaneous treatment of electron correlation and spin–orbit coupling. The second, considerably less demanding approach, corresponds almost to a perturbational treatment, introducing spin–orbit coupling as a final step after the CI optimization by diagonalizing the resulting Hamiltonian matrix over CI states. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 53–64, 1998

Two-component density-functional calculations for positrons trapped by defects in solids

We present results of two-component density-functional calculations for electron systems with a localized positron. The theory is implemented into several electronic-structure calculation methods. For example, positron states at vacancies in semiconductors have been calculated in the pseudopotential plane-wave framework. The ionic relaxations, including the positron induced relaxation, have been determined in this scheme by first-principles molecular-dynamics methods. Positron states localized at vacancies in metals have been calculated using the tight-binding linear muffin-tin-orbital method within the atomic-spheres approximation as well as using the full-potential linear muffin-tin-orbital method. Calculations have been performed for positron lifetimes, core annihilation lineshapes and two-dimensional angular correlation maps. The results are compared with experiment.

Symmetric group approach to relativistic CI. IV. Representations of one-electron spin operators and their products in a symmetric group-adapted basis ofN-electron spin functions

A detailed study on representations of one-electron spin operators and of their products in an N-electron SN-adapted spin space is presented. Some conclusions relevant for their evaluation and implementation in relativistic two-component SGA-CI calculations are derived. © 1997 John Wiley & Sons, Inc.

Symmetric group approach to relativistic CI. IV. Representations of one‐electron spin operators and their products in a symmetric group‐adapted basis of N‐electron spin functions

A detailed study on representations of one-electron spin operators and of their products in an N-electron SN-adapted spin space is presented. Some conclusions relevant for their evaluation and implementation in relativistic two-component SGA-CI calculations are derived. © 1997 John Wiley & Sons, Inc.

Crust-mantle interaction in continental arcs: inferences from the Mesozoic arc in the southwestern United States

Arc magmas ranging in composition from basaltic andesites to rhyolites and intrusive equivalents were emplaced into the western margin of the North American craton starting in Late Triassic time giving way to rift0related sedimentation in the Late Jurassic. The region of this study cuts across Proterozoic basements of contrasting Nd model ages, 1.7–1.8 Ga (average ɛNd∼−11) in eastern Arizona and 2.0 to 2.3 GA (average ɛNd∼−18) in western Arizona and eastern California (Bennett and DePaolo 1987). The Mesozoic rocks have initial ɛNd of -3.4 to-6.4 in the eastern part of the study area and -7.1 to -9.2 in the western part. All of the rocks have elevated 87Sr/87Sr initial ratios (>0.706). Trends in initial ɛNd values of Mesozoic arc rocks are directly correlated with the Nd model ages of the basement through which they passed. Simple two-component mixing calculations indicate that recycled continental crust in the arc magmas represents on average about 65%. A minimum of 35% mantle input into continental arc magmas, as recent as the Mesozoic, represents a significant contribution to the growth of the continental crust, in the absence of a return flow of continental material into the mantle of similar magnitude. In a detailed study in the Santa Rita Mountains. Arizona, there is a pattern of increase of ɛNd with time: early basaltic andesites have more negative ɛNd than later felsic rocks. A correlated pattern of depletion with time is also observed with trace element and major element data. We attribute this either to progressive hybridization of the lower crust by repeated injection of mantle magmas, or the progressive thinning of the continental crust during prolonged arc magmatism. The present data do not allow distinction between the two models. Progressive decrease in crustal contribution to arc magmas with time may be an important feature of continental arc evolution. Hybridization of the lower crust due to repeated injection of mantle melts during arc magmatism may help contribute to small-scale heterogeneities in lower crust inferred from seismic and xenolith data. Similarly, whether there is a well defined MOHO or sharp crust-mantle boundary in any given segment of the continental crust may in part depend on the extent of crust modification as a result of continental arc magmatism.

Carrier capture in quantum wells and its importance for ambipolar transport

The transmission, reflection, and capture probabilities of carriers in a quantum well heterostructure are calculated including the decrease of the current density across the well and the decay of phase coherence, which reduces the resonant structure of the transmission probability. These probabilities connect the carrier distribution functions on both sides of the well. We introduce “interface velocities”, which serve as boundary conditions for the diffusion equation. The velocities of electrons and holes are, in general, quite different. Analogous to the ambipolar diffusion coefficient ambipolar interface velocities are calculated from the quantities for both carrier types. For typical sample dimensions and carrier densities the ambipolar calculation is in very good agreement with a two-component calculation. In very small samples at low densities, however, the results differ. It is demonstrated that a unique determination of the diffusion coefficient and the interface parameters requires measurements at different transport distances.

Regular Two-Component Pauli-Like Effective Hamiltonians in Dirac Theory

The standard Pauli Hamiltonian is highly singular for Coulomb potentials near the nuclei of the atoms. It is shown that the theory of effective Hamiltonians allows the determination of Pauli-like Hamiltonians that are regular enough to be used in variational calculations. A numerical illustration is given for hydrogenic atoms with atomic number varying from Z = 1 to Z = 86. These calculations yield relativistic correction potentials which are used for studying the series of neutral rare gas atoms. Our approach opens the way for accurate two-component calculations for molecules.