The A2Πu state of : Electric properties, fine and hyperfine coupling constants, and magnetic moments (g-factors). A theoretical study

Bruna, Pablo J.; Grein, Friedrich

doi:10.1016/j.jms.2008.04.013

Cited by 15 publications

(10 citation statements)

References 57 publications

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“…The situation is different for molecular Θ’s since they are not only difficult to measure experimentally , but available data are mostly rotational averages (δΘ ⊥ cannot be detected). However, there is no doubt that Π states also have two independent Θ’s since (1) all hfcc’s indicate the CDD/SDDs to be axially asymmetric around each nucleus, and the same should apply to the whole molecule, (2) the T ii , q ii , and Θ ii operators share the same rotational symmetry properties, and (3) as shown next, two other experimental processescollisions X 2 + M, and van der Waals (vdW) interactionsprovide support to our statements.…”

Section: Discussionsupporting

confidence: 76%

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Axial Asymmetry of the Charge- and Spin-Density Distributions in Π States. Molecular Quadrupole Moments and Hyperfine Coupling Constants of CH, NH, OH, CF, LiO, NO, and FO

Bruna

Grein

2009

J. Phys. Chem. A

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The axial asymmetry of the charge- and spin-density distributions in Pi states is studied via second-rank traceless tensors P(ii) (ii = xx, yy, zz), namely, quadrupole moments (Theta(ii)), electric field gradients (q(ii)), and magnetic dipolar (T(ii)) hyperfine coupling constants (hfcc's). In linear molecules, it holds that P(xx) does not = P(yy) does not = P(zz) for Pi, but P(xx) = P(yy) does not = P(zz) for Sigma, Delta, Phi,..., states. Thus, traceless P(ii) in Pi states have two independent parameters, P(parallel) = P(zz) is proportional to [r(m)(3 cos2 theta - 1] and deltaP(perpendicular) = |P(xx) - P(yy)| is proportional to [r(m) sin2 theta], with m = 2(Theta(ii)) or -3(q(ii), T(ii)). All linear states have P(parallel) does not = 0, but only Pi states exhibit deltaP(perpendicular) does not = 0, as shown by hfcc's like c = (3/2)T(zz), and d = |T(xx) - T(yy)|, as well as q0 = (-q(zz)) and |q(2)/2| = |q(xx) - q(yy)|. Little is known about Theta(zz) and deltaTheta(perpendicular) = |Theta(xx) - Theta(yy)| in Pi states since most experimental values (gas-phase) are rotational averages, and several theoretical studies have reported Theta(zz) but assumed deltaTheta(perpendicular) = 0. The diatomics studied here have X2Pi(1/2)(pi1) ground states, like CH and NO, or are of type X2Pi(3/2)(pi3), like OH, CF, LiO, and FO. The A3Pi(sigma pi3) state of NH is also included. Our P(parallel) and deltaP(perpendicular) values--calculated at the experimental R(e)'s with the B3LYP/aug-cc-pVQZ method--reproduce well the available literature data. The properties of the CF and FO radicals are not well-known so that our {c, d} and {q0, q2} values should help future experimental studies of their hyperfine spectra. Excluding OH, the complete quadrupole sets {Theta(zz), deltaTheta(perpendicular)} are new for all species discussed here. For comparison purposes, Theta(zz) of a low-lying Sigma state is also calculated for each X2Pi radical.

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Section: Discussionsupporting

confidence: 76%

“…The opposite picture holds for 2 Σ + states, where (let us say, by symmetry restraints) the only parameters are c and q 0 . For example, for N 2 + we have calculated c = 84 MHz for X 2 Σ g + , to be compared with d = 77 MHz in the A 2 Π u state …”

Section: Discussionmentioning

confidence: 99%

Axial Asymmetry of the Charge- and Spin-Density Distributions in Π States. Molecular Quadrupole Moments and Hyperfine Coupling Constants of CH, NH, OH, CF, LiO, NO, and FO

Bruna

Grein

2009

J. Phys. Chem. A

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“…Since the angular momentum matrix elements from the SOMO σ g+ state can here only couple to the higher lying π g LUMO (lowest unoccupied molecular orbital) for the components perpendicular to the axis of the molecule, this gives a negative contribution to the ∆g ⊥ as was indeed observed in the work of Garces et al [14]. Boonchun and Lambrecht estimated this ∆g ⊥ for the N 2 molecule using a tight-binding model for the N 2 molecule with parameters fitted to density functional theory (DFT) calculation and using a calculated atomic spin-orbit coupling parameter to be −2600 ppm in excellent agreement with Bruna and Grein's [16] calculation which gave a value of −2734 ppm. Both are in good agreement with the angular average of ∆g which amounts to ∼ (2/3)∆g ⊥ and experimentally is about −1900 ppm.…”

Section: Introductionsupporting

confidence: 81%

“…In some cases we also used Hubbard-U corrections to the PBE functional which can simulate the hybrid functional effects in creating an orbital dependent potential with stronger hole localization. We checked that the hybrid functional with the a Bruna and Grein [16] b Boonchun and Lambrecht [15] parameters used here, satisfy the generalized Koopmans' theorem [32][33][34][35] quite well for all of the defects considered here and at the same time provide an accurate band gap of 3.4 eV. Details about these tests are given in Supplemental Material [36].…”

Section: Methodsmentioning

confidence: 99%

Calculated electron paramagnetic resonance $g$-tensor and hyperfine parameters for zinc vacancy and N related defects in ZnO

Dabsamut,

Boonchun,

Lambrecht

2022

Preprint

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Various defects in ZnO, focused on substitutional NO and N2 in various sites, O-site, interstitial and Zn-site are studied using first-principles calculations with the goal of understanding the electron paramagnetic resonance (EPR) center reported for N2 in ZnO and substitutional N on the O-site. The g tensors are calculated using the gauge including projector augmented wave (GIPAW) method and compared with experiments. The g-tensor of the free N + 2 and N − 2 radicals and their various contributions within the GIPAW theory are analyzed first to provide a baseline reference for the accuracy of the method and for understanding the N2 behavior in ZnO. Previous controversies on the site location of N2 in ZnO for this EPR center and on the shallow or deep nature and donor or acceptor nature of this center are resolved. We find that the N2 on the Zn site is mostly zinc-vacancy like in its spin density and g-tensor, while for the O-site, a model with the N2 axis lying in-the basal plane and the singly occupied πg-orbital along the c axis provides good agreement with experiment. For the interstitial location, if the N2 is not strongly interacting with the surroundings, no levels in the gap are found and hence also no possible EPR center. The calculated g-tensors for NO and VZn are also found to be in good agreement with experiment. The effects of different functionals affecting the localization of the spin density are shown to affect the g-tensor values.

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“…Nevertheless, these measurements are possible with efficient and reliable replenishment of molecular ions in the trap. For such close detunings, our method is expected to be sensitive to the hyperfine structure of the transition [50] which is not resolved here and has, to our knowledge, not been studied experimentally yet. In this experiment, the absolute accuracy of the wavemeter used to evaluate the lattice-laser frequency was estimated to be better than 50 MHz by a repetitive measurements of the P 3/2 ← D 5/2 spectroscopic transition in Ca + during the experiment.…”

mentioning

confidence: 93%

Quantum-nondemolition state detection and spectroscopy of single trapped molecules

Sinhal

Meir

Najafian

et al. 2020

Science

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Trapped atoms and ions are among the best controlled quantum systems which find widespread applications in quantum information, sensing and metrology. For molecules, however, a similar degree of control is currently lacking owing to their complex energy-level structure. Quantum-logic protocols in which atomic ions serve as probes for molecular ions are a promising route for achieving this level of control, especially with homonuclear molecules that decouple from black-body radiation. Here, a quantum-non-demolition protocol on single trapped N + 2 molecules is demonstrated. The spin-rovibronic state of the molecule is detected with more than 99% fidelity and the position and strength of a spectroscopic transition in the molecule are determined, both without destroying the molecular quantum state. The present method lays the foundations for new approaches to molecular precision spectroscopy, for state-to-state chemistry on the single-molecule level and for the implementation of molecular qubits.The impressive advances achieved in the control of ultracold trapped atoms and ions on the quantum level are now increasingly being transferred to molecular systems. Cold, trapped molecules have been created by, e.g., binding ultracold atoms via Feshbach resonances [1] and photoassociation [2, 3], molecular-beam slowing [4], direct laser cooling [5,6] and sympathetic cooling [7,8]. The trapping of the cold molecules enables experiments with long interaction times and thus paves the way for new applications such as studies of ultracold chemistry [9] and precision spectroscopic measurements which aim, e.g., at a precise determination of fundamental physical constants [10] and their possible time variation [11,12] as well as tests of fundamental theories which reach beyond the standard model [13,14].The complex energy level structure and the absence of optical cycling transitions in most molecular systems constitute a major challenge in the state preparation, laser cooling, state detection and coherent manipulation of molecules. Molecular ions trapped in radiofrequency ion traps which are sympathetically cooled by simultaneously trapped atomic ions [7,8] have proven a promising route for overcoming these obstacles. Recently, their rotational cooling and state preparation has been achieved [15][16][17][18], precision measurements of quantum electrodynamics and fundamental constants have been performed [10,19], the first studies of dipole-forbidden spectroscopic transitions in the mid-infrared spectral domain have been reported [20] and state-and energy-controlled collisions with cold atoms have been realized [21,22]. However, in order to reach the same exquisite level of control on the quantum level for a single molecule which can be achieved with trapped atoms [23], new methodological developments are required. In this context, the most promising route for achieving ultimate quantum control of molecular ions in trap experiments is constituted by quantum-logic protocols [24] in which a cotrapped atomic ion acts as a probe for th...

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The A2Πu state of : Electric properties, fine and hyperfine coupling constants, and magnetic moments (g-factors). A theoretical study

Cited by 15 publications

References 57 publications

Axial Asymmetry of the Charge- and Spin-Density Distributions in Π States. Molecular Quadrupole Moments and Hyperfine Coupling Constants of CH, NH, OH, CF, LiO, NO, and FO

Axial Asymmetry of the Charge- and Spin-Density Distributions in Π States. Molecular Quadrupole Moments and Hyperfine Coupling Constants of CH, NH, OH, CF, LiO, NO, and FO

Calculated electron paramagnetic resonance $g$-tensor and hyperfine parameters for zinc vacancy and N related defects in ZnO

Quantum-nondemolition state detection and spectroscopy of single trapped molecules

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