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Journal articles on the topic 'Breit-Pauli Hamiltonian'

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Published: 4 June 2021

Last updated: 16 February 2022

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1

Duan, Jun-Xin, Yun Zhou, Zhi-Zhong Xie, Tao-Lei Sun, and Jun Cao. "Incorporating spin–orbit effects into surface hopping dynamics using the diagonal representation: a linear-response time-dependent density functional theory implementation with applications to 2-thiouracil." Physical Chemistry Chemical Physics 20, no. 22 (2018): 15445–54. http://dx.doi.org/10.1039/c8cp01852a.

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2

Baretty, Reinaldo, and Carmelo Garcia. "Modified breit-pauli hamiltonian suitable for variational calculations." International Journal of Quantum Chemistry 34, S22 (March 12, 1988): 425–30. http://dx.doi.org/10.1002/qua.560340845.

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3

Singh, Jagjit, Sunny Aggarwal, A. K. Singh, and Man Mohan. "Breit–Pauli atomic structure calculations for sulphur-like titanium." Canadian Journal of Physics 90, no. 9 (September 2012): 833–47. http://dx.doi.org/10.1139/p2012-074.

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Configuration interaction calculation has been performed for excitation energies, oscillator strengths, and transition probabilities of 114 fine-structure levels of sulphur-like titanium. The relativistic effects are included in Breit–Pauli approximation by adding mass-correction, Darwin, and spin–orbit interaction terms to the nonrelativistic Hamiltonian. We have adjusted the diagonal elements of Hamiltonian matrices (fine-tuning) before the calculation of oscillator strength and transition probabilities for the electric dipole allowed transitions. Our calculated data are in close agreement with data listed in National Institute of Standards and Technology and other available results. Correct identification of some of the levels become very difficult because of strong mixing among several fine-structure levels. We predict new energy levels, oscillator strength, and transition probability data, where no other theoretical or experimental results are available, which will form the basis for future experimental work.

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4

Farazdel, Abbas, William M. Westgate, Alfredo M. Simas, Robin P. Sagar, and Vedene H. Smith. "Validity of the mass-velocity term in the Breit-Pauli hamiltonian." International Journal of Quantum Chemistry 28, S19 (June 19, 2009): 61–68. http://dx.doi.org/10.1002/qua.560280808.

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5

Karaçoban, Betül, and Leyla Özdemir. "Transition Energies of Ytterbium (Z=70)." Zeitschrift für Naturforschung A 66, no. 8-9 (September 1, 2011): 543–51. http://dx.doi.org/10.5560/zna.2011-0003.

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Abstract Transition energies of neutral ytterbium (Yb I, Z = 70, belonging to the lanthanide series), including ionization potential, excitation energies, and electron affinity are calculated by the multiconfiguration Hartree-Fock (MCHF) method within the framework of the Breit-Pauli Hamiltonian and the relativistic Hartree-Fock (HFR) method. Ionization potential and excitation energies of Yb II and Yb III are also reported. The obtained results have been compared with other works.

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6

Hibbert, Alan, Robert Glass, and Charlotte Froese Fischer. "A general program for computing angular integrals of the Breit-Pauli Hamiltonian." Computer Physics Communications 64, no. 3 (June 1991): 455–72. http://dx.doi.org/10.1016/0010-4655(91)90138-b.

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7

Özdemir, Leyla, Selda Kabakçı, and İlker Armağan. "Forbidden Transitions in the Ground State Configuration of Doubly Ionized Argon." Journal of Atomic and Molecular Physics 2014 (February 9, 2014): 1–5. http://dx.doi.org/10.1155/2014/798398.

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We have calculated forbidden transitions (M1 and E2) between fine structure levels in the ground state configuration 3s23p4 of doubly ionized argon (Ar III) using the multiconfiguration Hartree-Fock approach within the framework of the Breit-Pauli Hamiltonian. The data for the analysis of forbidden lines in the spectrum is important for the study of the plasma in astrophysical objects and fusion devices. The results obtained from this work have been compared with other results available in the literature.

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8

Özdemir, Leyla, and Sadiye Tuna. "An Investigation on the Fine Structure Levels in the Ground State Configuration for the Antimony Anion." Zeitschrift für Naturforschung A 69, no. 8-9 (September 1, 2014): 397–402. http://dx.doi.org/10.5560/zna.2014-0025.

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We have investigated the correlation, relativistic, and isotope shift effects on the fine structure levels in the ground state configuration for the antimony anion ( Sb-). Energies and radiative transition probabilities (for magnetic dipole, M1, and electric quadrupole, E2) have been obtained using the multiconfiguration Hartree-Fock method within the framework of the Breit-Pauli Hamiltonian. Therefore, the most important configuration interaction and relativistic effects have been included. Comparisons with other available works are presented. For some M1 and E2 lines the considered transition probabilities are reported for the first time

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9

Karaçoban, Betül, and Leyla Özdemir. "Energy Levels and the Landé -Factors for Singly Ionized Lanthanum." Journal of Atomic and Molecular Physics 2013 (June 5, 2013): 1–12. http://dx.doi.org/10.1155/2013/674242.

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We have calculated the energies and the Landé -factors for 5d2, 5d6s, 6s2, 4f6p, 5d7s, 5d6d, 4f2, 6p2, 6s6d, 6s7s, 4f6s, 4f5d, 5d6p, 6s6p, 4f7s, 4f6d, 5d7p, and 6s7p excited levels of singly ionized lanthanum (La II). These calculations have been carried out by using the multiconfiguration Hartree-Fock method within the framework of the Breit-Pauli Hamiltonian (MCHF+BP) and the relativistic Hartree-Fock (HFR) method. The obtained results have been compared with other works available in the literature. A discussion of these calculations for La II in this study has also been in view of the MCHF+BP and HFR methods.

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10

Zatsarinny, Oleg, and Charlotte Froese Fischer. "A general program for computing angular integrals of the Breit–Pauli Hamiltonian with non-orthogonal orbitals." Computer Physics Communications 124, no. 2-3 (February 2000): 247–89. http://dx.doi.org/10.1016/s0010-4655(99)00441-5.

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11

Buenker, Robert J. "Exponentially damped Breit-Pauli Hamiltonian for the description of positronium decay and other high energy processes." Molecular Physics 77, no. 6 (December 20, 1992): 1095–122. http://dx.doi.org/10.1080/00268979200103021.

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12

Badnell, N. R. "On the effects of the two-body non-fine-structure operators of the Breit - Pauli Hamiltonian." Journal of Physics B: Atomic, Molecular and Optical Physics 30, no. 1 (January 14, 1997): 1–11. http://dx.doi.org/10.1088/0953-4075/30/1/005.

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13

Singh, Jagjit, Sunny Aggarwal, A. K. S. Jha, A. K. Singh, and M. Mohan. "Photoionization of Al-like Si using the R-matrix method." Canadian Journal of Physics 89, no. 11 (November 2011): 1119–26. http://dx.doi.org/10.1139/p11-106.

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Relativistic calculations are made for photoionization of the ground state 3s23p ([Formula: see text]) and the lowest six excited states 3s23p ([Formula: see text]), 3s3p2 (4P1/2,3/2,5/2), and 3s3p2 (2D3/2,5/2) of Al-like Si, using the Breit–Pauli Hamiltonian within the R-matrix method. Cross sections are determined by the Rydberg series of autoionizing resonances converging to various ionic states. Relativistic effects as well as all the important physical effects like exchange, channel coupling, and short-range correlations have been considered in the present calculations. The present relativistic calculations for this ion using the lowest 20 target levels of Si III in the LSJ coupling scheme will enhance the database sufficiently for practical applications of photoionization cross sections of Si II.

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14

Havlas, Zdeněk, Mojmír Kývala, and Josef Michl. "Spin-Orbit Coupling in Biradicals. 4. Zero-Field Splitting in Triplet Nitrenes, Phosphinidenes, and Arsinidenes." Collection of Czechoslovak Chemical Communications 68, no. 12 (2003): 2335–43. http://dx.doi.org/10.1135/cccc20032335.

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The spin dipole-spin dipole and spin-orbit coupling contributions to the zero-field splitting parameter D of CH3-N, CH3-P, CH3-As, SiH3-N, SiH3-P, and SiH3-As have been calculated from CAS(12,11)/cc-pVTZ wave functions and the Breit-Pauli Hamiltonian at T1 B3LYP/cc-pVTZ optimized geometries. The spin-orbit coupling contributions represent a minor correction for the nitrenes, and bring the value computed for methylnitrene from 1.66 to 1.84 cm-1, in good agreement with experiment (1.72 cm-1). They dominate the spin-spin terms by an order of magnitude in phosphinidenes and by more than two orders of magnitude for arsinidenes. The properties of all these perfect axial biradicals follow expectations based on the simple algebraic 2-in-2 model of biradical structure.

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15

Niu, Xiang Hong, Wen Wen Shan, Shuai Wang, and De Heng Shi. "Accurate spectroscopic calculations on the X2Σ +, A2Π, and 22Σ + electronic states of the BeAr+ cation including spin-orbit coupling." Canadian Journal of Chemistry 92, no. 5 (May 2014): 397–405. http://dx.doi.org/10.1139/cjc-2014-0031.

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The complete active space self-consistent field/internally contracted multireference configuration interaction calculations with the correlation-consistent basis sets have been made to characterize all of the states of BeAr+ cation, which are attributed to the first two dissociation channels. The effect on the potential energy curves by Davidson correction, core-valence correlation, and scalar relativistic corrections is included. The spin-orbit coupling effect is taken into account by the state interaction method with the Breit–Pauli Hamiltonian. Our calculations can provide some useful guidelines for the future experimental work of band system 22[Formula: see text]+1/2-X2[Formula: see text]+1/2. For the first time, the transition properties including Franck−Condon factors and transition dipole moments have been derived for all of the Ω states. Some transition probabilities and radiative lifetimes have been estimated.

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16

Yu, Wei, Zunlue Zhu, Chuncai Cheng, and Deheng Shi. "A theoretical investigation of the S2+ cation in the gas phase." Canadian Journal of Chemistry 92, no. 11 (November 2014): 1041–52. http://dx.doi.org/10.1139/cjc-2014-0255.

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The potential energy curves (PECs) of 18 lowest energy Λ-S states of the S2+ cation have been calculated using the complete active space self-consistent field method followed by the internally contracted multireference configuration interaction approach with the Davidson modification. When spin−orbit coupling is computed using the Breit−Pauli Hamiltonian with the cc-pCVTZ basis set, the 18 Λ-S states split into 56 Ω components. To improve the quality of the PECs, core−valence correlation and scalar relativistic corrections are included. All PECs are extrapolated to the complete basis set limit. Based on the PECs obtained by the icMRCI+CV+DK+Q/(CBS-56) calculations, the spectroscopic parameters of 17 Λ-S bound states and 50 Ω bound states are obtained. The transitions (including the Franck−Condon factors and radiative lifetimes) from two low-lying states to the ground state are calculated for several low vibrational levels. Analyses show that the spectroscopic parameters reported here can be expected to be reliably predicted.

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17

Gould, M. D., and J. S. Battle. "Spin‐dependent unitary group approach to the Pauli–Breit Hamiltonian. I. First order energy level shifts due to spin–orbit interactions." Journal of Chemical Physics 98, no. 11 (June 1993): 8843–51. http://dx.doi.org/10.1063/1.464494.

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18

Gould, M. D., and J. S. Battle. "Spin‐dependent unitary group approach to the Pauli–Breit Hamiltonian. II. First order energy level shifts due to spin–spin interaction." Journal of Chemical Physics 99, no. 8 (October 15, 1993): 5983–94. http://dx.doi.org/10.1063/1.465897.

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19

Gupta, G. P., and A. Z. Msezane. "Large-scale CIV3 calculations of fine-structure energy levels and radiative rates in Al-like copper." Canadian Journal of Physics 87, no. 8 (August 2009): 895–907. http://dx.doi.org/10.1139/p09-049.

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We have performed large-scale CIV3 calculations of excitation energies from the ground state for 97 fine-structure levels as well as of oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s22s22p6)3s23p, 3s3p2, 3s23d, 3p3, 3s3p3d, 3p23d, 3s3d2, 3s24s, 3s24p, 3s24d, 3s24f, and 3s3p4s configurations of Cu XVII. These states are represented by very extensive configuration-interaction (CI) wave functions obtained with the CIV3 (Configuration-Interaction Version 3) computer code of Hibbert. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian, which consists of the nonrelativistic term plus the one-body mass correction, Darwin term, and spin–orbit, spin–other-orbit, and spin–spin operators. To keep our calculated energy splittings as close as possible to the experimental values (wherever available), we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our calculated excitation energies, including their ordering, are in excellent agreement with the available experimental results. From our radiative decay rates we have also calculated radiative lifetimes of some fine-structure levels. The mixing among several fine-structure levels is found to be so strong that the correct identification of these levels becomes very difficult. We believe that our extensive calculations will be useful to experimentalists in identifying the fine-structure levels in their future work. In this calculation we also predict new data for several fine-structure levels where no other theoretical and (or) experimental results are available.

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20

Vasilyev, Oleg A., and Viktor G. Solomonik. "FIRST-PRINCIPLES SIMULATION OF THE CERIUM TRIFLUORIDE INFRARED SPECTRUM BEYOND THE BORN–OPPENHEIMER APPROXIMATION." IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENIY KHIMIYA KHIMICHESKAYA TEKHNOLOGIYA 61, no. 3 (February 27, 2018): 31. http://dx.doi.org/10.6060/tcct.20186103.5636.

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The group-theoretical analysis was carried out to derive a spin-vibronic model Hamiltonian and a diabatic dipole moment operator for a cerium trihalide molecule, CeX3. The model comprises seven lowest-lying 4f1 electronic states coupled by six vibrational modes, (A2'' + E' + E'' + A1' + A2') × (a1' + a2'' + e' + e'), with an accounting for spin-orbit coupling. Multimode potential energy surfaces have been calculated for the CeF3 molecule at the multi-reference singles and doubles configuration interaction level of theory corrected for quadruple excitations, MRCISD+Q, and dipole moment surfaces at the MRCISD level. A hybrid approach employing a quasi-diabatization technique was utilized to determine the relevant model parameters up to forth order in power series of the Q1(a1'), Q3(e'), Q4(e') normal coordinates, and eighth order of the Q2(a2'') out-of-plane bending normal coordinate. Spin-orbit coupling was taken into account through zero-order, with the respective constants obtained from matrix elements of the Breit–Pauli operator in the basis of states generated at the MRCISD level. The spin-vibronic Hamiltonian and dipole moment operator obtained in this way has been utilized in the variational calculations to simulate the infrared absorption spectrum of CeF3. The resulting spectrum features a complex structure owing to an intricate interplay of the vibronic (Jahn–Teller and pseudo-Jahn–Teller) and spin-orbit coupling effects, and hence cannot be explained within the conventional Born–Oppenheimer (BO) approximation. The strongest absorption appearing in the simulated spectrum at about 500 cm–1, mostly associated with the Q3(e') stretching mode, is split into two bands by about 3 cm–1. This finding is in full agreement with the CeF3 matrix isolation infrared spectroscopy data. On the whole, the results of the calculations clearly indicate the vibronic rather than vibrational origin of the spectral bands, including the bands in the low-frequency region of the spectrum, and thus show the fallacy of the generally accepted assignment of the bands observed in the experiment to the fundamental vibrational transitions of the molecule made on the assumption of the admissibility of describing this within the Born–Oppenheimer approximation. The new assignment of the experimental IR spectrum of CeF3 is proposed.Forcitation:Vasilyev O.A., Solomonik V.G. First-principles simulation of the cerium trifluoride infrared spectrum beyond the Born–Oppenheimer approximation. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2018. V. 61. N 3. P. 31-44

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21

Matsushita, Toshio, Christel M. Marian, Rainer Klotz, and Sigrid D. Peyerimhoff. "Potential-energy curves, zero-field splittings, and radiative lifetimes for low-lying states of AsH." Canadian Journal of Physics 65, no. 2 (February 1, 1987): 155–64. http://dx.doi.org/10.1139/p87-026.

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Large-scale multireference configuration-interaction (MRD-CI) calculations in an atomic-orbital (AO) basis set containing up to f functions on As and d on hydrogen are employed to study the potential-energy curves of the π2(X3Σ−, a1Δ, b1Σ+), the σ → π, and the π → σ3.1Π states; a large number of σ → σ* states; and the lowest π → s,p Rydberg series. The σ → σ* states are strongly repulsive and exhibit numerous interactions with the Rydberg members causing predissociation. The probabilities for the spin-forbidden transitions from b1Σ+and a1Δ to the X3Σ−ground state as well as the zero-field splittings of theX3Σ−and A3Π states have been evaluated by employing a variational perturbation scheme in which the zero-order wave functions are MRD-CI expansions. The perturber states are determined by their spin-orbit interactions, which are calculated by employing the Breit–Pauli one- and two-electron spin-orbit operator. The radiative lifetime of the b1Σ+ state is predicted to be 0.35 ms, whereby the dominant mechanism is deactivation to the ms = ±1 component.The parallel transition is found to be much weaker. The lifetime of a1Δ is calculated to be 22 ms, whereby the process [Formula: see text] is favored. Both b–X and a–X transitions borrow their intensity primarily from the A3Π–X3Σ− transition and, furthermore, the 1Π–a1Δ and higher 3,1Π state spin-allowed transitions. The probability for the quadrupole b–a transition is evaluated to be three orders of magnitude smaller than the b–X transition. The calculated zero-field splitting of the X3Σ− ground state amounts to 101.4 cm−1, and the fine-structure splitting between the 2, 1, and 0+ components of the A3Π state evaluated to be 544.5 and 674.4 cm−1, respectively, in good accord with experimental results; whereas the calculated Λ doubling of the0+–0− fine-structure levels of the A3Π state (35.2 cm−1 vs. 44.72 cm−1) is too small in the present treatment. The dependence of spin-orbit effects and transition probabilities on AO basis sets and relativistic corrections to the zero-order Hamiltonian are discussed, and it is concluded that lifetime calculations for spin-forbidden processes in first- and second-row molecules can be extended in a fairly straightforward manner to systems with considerable spin-orbit interactions.

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22

MOROZ, ALEXANDER. "THE SINGLE-PARTICLE DENSITY OF STATES AND THE RESONANCE IN THE AHARONOV–BOHM POTENTIAL." Modern Physics Letters B 09, no. 22 (September 20, 1995): 1407–17. http://dx.doi.org/10.1142/s0217984995001406.

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The single-particle densitity of states (DOS) for the Pauli and the Schrödinger Hamiltonians in the presence of an Aharonov–Bohm potential is calculated for different values of the particle magnetic moment. The DOS is a symmetric and periodic function of the flux. The Krein–Friedel formula can be applied to this long-ranged potential when regularized with the zeta function. We have found that whenever a bound state is present in the spectrum it is always accompanied by a resonance. The shape of the resonance is not of the Breit-Wigner type. The differential scattering cross section is asymmetric if a bound state is present and gives rise to the Hall effect. As an application, propagation of electrons in a dilute vortex limit is considered and the Hall resistivity is calculated.

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23

Hata, J., D. L. Cooper, and I. P. Grant. "Inclusion of the electron anomaly in effective Hamiltonians for perturbative (Breit-Pauli) and non-perturbative approaches to fine structure." Journal of Physics B: Atomic and Molecular Physics 18, no. 10 (May 28, 1985): 1907–17. http://dx.doi.org/10.1088/0022-3700/18/10/009.

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