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Results for “Breit-Pauli Hamiltonian”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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16 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Relativistic and Correlation Effects in CuH, AgH and AuH: Comparison of Various Relativistic Methods

The effects of relativity on the bond lengths, dissociation energies, and harmonic vibrational frequencies of the 1Epsilon(+) electronic ground states of the group IB hydrides CuH, AgH and AuH have been evaluated with a variety of ab initio methods. These properties were investigated with moderately-sized basis sets at the self-consistent field Hartree Fock (SCF HF) level and with second-order Moller-Plesset (MP2) perturbation theory for electron correlation. Comparisons were made between all-electron results using the nonrelativistic Hamiltonian, perturbation theory (PT) at first-order with only the one-electron non-fine structure terms of the Breit-Pauli Hamiltonian, the spin-free Douglas-Kroll (DK) transformed Dirac Hamiltonian and the untransformed Dirac Hamiltonian, and results using two sets of relativistic effective core potentials (RECPs). The expected trends of bond length decrease, dissociation energy increase and harmonic frequency increase with both relativity and correlation are found. Both sets of RECPs are shown to give good results, if accompanied by a reasonable basis set. The DK method is demonstrated to be an inexpensive, reliable approximation to the DHF method.

Collins, Charlene L.↗
NASA NTRS1994

An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

Dyall, Kenneth G.↗
NASA NTRS2006

Electron Impact Excitation of Forbidden and Allowed Transitions in O(II)

The B-spline R-matrix method is used to investigate the electron impact excitation of forbidden and allowed transitions in singly ionized oxygen. The relativistic effects have been incorporated in the Breit-Pauli Hamiltonian. Flexible non-orthogonal sets of radial functions are used to obtain accurate target description and to represent the scattering functions. The 47 fine-structure levels of the 2s(sup 2)2p(sup 3), 2s2p(sup 4), 2s(sup 2)2p(sup 2)3s, 2s(sup 2)2p(sup 2)3p and 2s(sup 2)2p(sup 2)3d configurations have been included in the scattering calculation. A calculation with 62 levels in the close-coupling expansion using the Breit-Pauli R-matrix (BPRM) method with orthogonal radial functions has also been carried out to check electron correlation, relativistic and channel coupling effects. The present results are in good agreement with the previous 16-level BPRM calculation by Montenegro et a1 (2006 J. Phys. B: At. Mol. Opt. Phys. 39 1863-77) for the forbidden transitions, but differ from the 21-level BPRM calculation by McLaughlin and Bell (1998 J. Phys. B: At. Mol. Opt. Phys. 31 4317-29). Our cross sections for the first forbidden (sup 4)S(sup o)-(sup 2)D(sup o)and resonance (sup 4)S(sup o)-2s(sup 2)p(sup 4) (sup 4)P transitions are in reasonably good agreement with the electron energy-loss and merged-beams experiment.

Tayal, S. S.↗
NASA NTRS1986

Oscillator strengths for Ar VII, Ca IX and Fe XV

The excitation energies and oscillator strengths are calculated for electric-dipole-allowed and intercombination transitions between 3s2 1S, 3s3p(1,3)P0, 3p2 3P, 1D, 1S and 3s3d(1,3)D states in Ar VII, Ca IX, and Fe XV ions of the magnesium sequence. These states are represented by the fairly large configuration-interaction expansions. The calculations have been carried out in both LS and intermediate coupling schemes. The relativistic corrections have been included through the Breit-Pauli Hamiltonian. The results are compared with previous theoretical calculations and with measurements.

Tayal, S. S.↗
NASA NTRS1997

Oscillator Strengths for Fine-Structure Transitions in S III

Oscillator strengths and transition probabilities for transitions among the fine-structure levels of the terms belonging to the 3s(sup 2)3p(sup 2), 3s3p(sup 3), 3s(sup 2)3p3d, 3s(sup 2)3p4s, 3s(sup 2)3p4p, and 3s(sup 2)3p4d configurations of S III are calculated using extensive configuration-interaction wave functions. The relativistic effects in intermediate coupling are incorporated by means of the Breit-Pauli Hamiltonian. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made so that the energy splittings are as close as possible to the experimental values. The present results are compared with other available calculations and experiments.

Tayal, S. S.↗
NASA NTRS1998

Oscillator Strengths of Allowed and Intercombination Transitions in Neutral Sulfur

We have calculated oscillator strengths and transition probabilities of electric-dipole allowed and intercombination transitions from fine-structure levels of the ground 3s(sup 2)3p(sup 4) configuration to the levels belonging to configurations 3s(sup 2)3p(sup 3)4s, 3s(sup 2) 3p(sup 3)5s, 3(sup 2)3p(sup 3)3d, 3s(sup 2)3p(sup 3)4d of neutral sulfur. Extensive configuration-interaction wave functions are used to represent these levels. The relativistic corrections have been included through the Breit-Pauli Hamiltonian. The results are compared with previous theoretical calculations and with measurements.

Tayal, S. S.↗
NASA NTRS1997

Interfacing Relativistic and Nonrelativistic Methods: A Systematic Sequence of Approximations

A systematic sequence of approximations for the introduction of relativistic effects into nonrelativistic molecular finite-basis set calculations is described. The theoretical basis for the approximations is the normalized elimination of the small component (ESC) within the matrix representation of the modified Dirac equation. The key features of the normalized method are the retention of the relativistic metric and the ability to define a single matrix U relating the pseudo-large and large component coefficient matrices. This matrix is used to define a modified set of one- and two-electron integrals which have the same appearance as the integrals of the Breit-Pauli Hamiltonian. The first approximation fixes the ratios of the large and pseudo-large components to their atomic values, producing an expansion in atomic 4-spinors. The second approximation defines a local fine-structure constant on each atomic centre, which has the physical value for centres considered to be relativistic and zero for nonrelativistic centres. In the latter case, the 4-spinors are the positive-energy kinetic al ly-balanced solutions of the Levy-Leblond equation, and the integrals involving pseudo-large component basis functions on these centres, are set to zero. Some results are presented for test systems to illustrate the various approximations.

Dyall, Ken↗
NASA NTRS2002

Atomic Data and Spectral Line Intensities for Ne III

A number of satellites and rockets have been launched to observe radiation from the Sun and other astrophysical objects. Line radiation is emitted when the electron impact excited levels decay to the lower levels by photon emission. From this radiation, the physical parameters such as electron temperature and density of the astrophysical plasma, elemental abundance, and opacity can be inferred. Ne III lines have been observed in H II regions, Ne-rich filaments in supernovae, and planetary nebulae. The allowed line at 489.50 Angstroms due to the transition 2s(sup 2) 2p(sup 5) (sup 3) P2 (goes to) 2s(sup 2)2p(sup 4)(sup 3)P2 has been identified in the solar spectrum by Vernazza and Reeves using Skylab observations. Other Ne III lines in the solar EUV spectrum have been reported by Thomas and Neupert based on observations from the Solar EUV Rocket Telescope and Spectrograph (SERTS) instrument. Atomic data for Ne III have been calculated by using a set of programs developed at, University College, London. The Superstructure and Distorted Wave (DW) programs have been updated over the years. In the Superstructure program, configuration interaction can be taken into account and radial functions are calculated in a modified Thomas-Fermi-Amaldi potential. This is a statistical potential and depends on parameters lambda 1 which are determined by optimizing the weighted sum of term energies. They are found to be lambda(sub 0)=1.2467, lambda(sub 1)=1.1617, and lambda(sub 2)=1.0663. The relativistic corrections are included by using the Breit-Pauli Hamiltonian as a perturbation to the nonrelativistic Hamiltonian. The same potential is used to calculate reactance matrices in the DW approximation in LS coupling. Collision strengths in intermediate coupling are obtained by using term coupling coefficients obtained from the Superstructure program. In this calculation, the configurations used are 2s(sup 2)2p(sup 4), 2s2p(sup 5), 2s(sup 2)2p(sup 3)3s, 2s(sup 2)p(sup 3)3d giving rise to 57 fine-structure levels in intermediate coupling.

Bhatia, A. K.↗
NASA NTRS2005

Measurement of absolute cross sections for excitation of the 2s(2) S-1 -> 2s2p P-1 degrees transition in O+4

Experimental cross sections are reported for the 1s(2)2s(2) S-1 -> 1s(2)2s2p P-1(o) transition in O+4 located at 19.689 eV. Use is made of the electron energy-loss method, using a merged electron-ion beam geometry. The center-of-mass interaction energies for the measurements in the S-1 -> P-1(o) transition are in the range 18 eV ( below the threshold) to 30 eV. Data are compared with other previous electron energy-loss measurements and with results of a 26 term R-matrix calculation that includes fine structure explicitly via the Breit-Pauli Hamiltonian. Clear resonance enhancement is observed in all experimental and theoretical results near the threshold for this S-1 -> P-1(o) transition.

atomic processes↗
NASA NTRS2004

Accurate Calculation of Oscillator Strengths for CI II Lines Using Non-orthogonal Wavefunctions

Non-orthogonal orbitals technique in the multiconfiguration Hartree-Fock approach is used to calculate oscillator strengths and transition probabilities for allowed and intercombination lines in Cl II. The relativistic corrections are included through the Breit-Pauli Hamiltonian. The Cl II wave functions show strong term dependence. The non-orthogonal orbitals are used to describe the term dependence of radial functions. Large sets of spectroscopic and correlation functions are chosen to describe adequately strong interactions in the 3s(sup 2)3p(sup 3)nl (sup 3)Po, (sup 1)Po and (sup 3)Do Rydberg series and to properly account for the important correlation and relaxation effects. The length and velocity forms of oscillator strength show good agreement for most transitions. The calculated radiative lifetime for the 3s3p(sup 5) (sup 3)Po state is in good agreement with experiment.

Tayal, S. S.↗
DOE OSTI2023

Scalar Breit interaction for molecular calculations

Variational treatment of the Dirac–Coulomb–Gaunt or Dirac–Coulomb–Breit two-electron interaction at the Dirac–Hartree–Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac–Coulomb–Gaunt and Dirac–Coulomb–Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac–Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin–spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Au n (n = 2–8) show that the scalar Dirac–Coulomb–Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac–Coulomb–Breit Hamiltonian. In conclusion, the scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Linearized Pair-Density Functional Theory with Spin–Orbit Coupling

Here, we include spin–orbit coupling (SOC) effects in linearized pair-density functional theory (L-PDFT), which is a multistate extension of multiconfiguration pair-density functional theory (MC-PDFT). Both 1-electron and 2-electron SOC integrals are computed using Breit-Pauli and Douglas–Kroll–Hess Hamiltonians in the atomic mean-field approximation. SO-L-PDFT removes the unphysical J-symmetry breaking observed in MC-PDFT. The accuracy of SO-L-PDFT is validated by calculations of zero-field splittings, fine-structure excitation energies, and low-energy excited-state spectra for a diverse group of atoms and molecules spanning the whole range of the periodic table, including atoms of groups 3, 11, and 13–17, the Ce 3+ and U 5+ ions, group 16 monohydrides, group 17 monoxides, lanthanide hexachlorides ([CeCl 6 ] 3− , [PrCl 6 ] 3− , and [NdCl 6 ] 3− ), actinyl ions ([UO 2 ] + , [NpO 2 ] 2+ ), and tricarbonatoactinyl complexes ([UO 2 (CO 3 ) 3 ] 5− , [NpO 2 (CO 3 ) 3 ] 4− ). We also compare the results to new spin–orbit-inclusive calculations by single-state and multistate multireference perturbation theory.

Hamiltonians↗