Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1502.06356 · Physical Review A

Implementation of the Z -vector method in the relativistic-coupled-cluster framework to calculate first-order energy derivatives: Application to the SrF molecule

Sudip Sasmal, Himadri Pathak, Malaya Kumar Nayak, Nayana Vaval, Sourav Pal

Published Mar 30, 2015• 25 citations
arXivHTMLPDF

Abstract

The molecular dipole moment and magnetic hyperfine-structure constant demand an accurate wave function far from the nucleus and in the near nuclear region, respectively. We, therefore, employ the so-called Z-vector method in the domain of relativistic-coupled-cluster theory to calculate the first-order property of molecular systems in their open-shell ground-state configuration. The implemented method is applied to calculate the molecular dipole moment and parallel component of the magnetic hyperfine-structure constant of the SrF molecule. The results of our calculation are compared with the experimental and other available theoretically calculated values. We are successful in achieving good accordance with the experimental results. The result of our calculation of the molecular dipole moment is in the accuracy of $\ensuremath{\sim}0.5$%, which is clearly an improvement over the previous calculation based on the expectation value method in the four-component coupled-cluster framework [V. S. Prasannaa et al., Phys. Rev. A 90, 052507 (2014)]. Thus, it can be inferred that the Z-vector method can provide an accurate wave function in both the near and far nuclear region, which is evident from our calculated results.

DOI
10.1103/physreva.91.030503

Related papers

Calculation of the magnetic hyperfine structure constant of alkali metals and alkaline-earth-metal ions using the relativistic coupled-cluster method

Sudip Sasmal

The $Z$-vector method in the relativistic coupled-cluster framework is used to calculate the magnetic hyperfine structure constant (${A}_{J}$) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The $Z$-vector results are in very good agreement with the experiment. The ${A}_{J}$ values of Li, Na, K, Rb, Cs, ${\mathrm{Be}}^{+}$, ${\mathrm{Mg}}^{+}$, ${\mathrm{Ca}}^{+}$, and ${\mathrm{Sr}}^{+}$ obtained in the $Z$-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that the $Z$-vector method with the single and double approximation can produce a more precise wave function in the nuclear region than the ECC method.

arXiv:1706.09640•Physical Review A•Jul 13, 2017•9 citations

Fock-space relativistic coupled-cluster calculations of two-valence atoms

Brajesh Kumar Mani, D. Angom

We have developed an all-particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine structure constants, and electric dipole matrix elements of Sr, Ba, and Yb. Furthermore, we calculate the electric quadrupole hyperfine structure constants and the electric dipole matrix elements of ${\mathrm{Sr}}^{+}$, ${\mathrm{Ba}}^{+}$, and ${\mathrm{Yb}}^{+}$. For these we use the one-valence coupled-cluster wave functions obtained as an intermediate in the two-valence calculations. We also calculate the magnetic dipole hyperfine structure constants of ${\mathrm{Yb}}^{+}$.

arXiv:1009.2963•Physical Review A•Jan 7, 2011•27 citations

Moments-based improved quantum computation of the electric dipole moment of molecular systems

Michael A. Jones, Harish J. Vallury, Manolo C. Per +2 more

With rapid progress being made in the development of platforms for quantum computation, there has been considerable interest in whether present-day and near-term devices can be used to solve problems of relevance. A commonly cited application area is the domain of quantum chemistry. While most experimental demonstrations of quantum chemical calculations on quantum devices have focused on the ground-state electronic energy of the system, other properties of the ground state, such as the electric dipole moment, are also of interest. Here, we employ the quantum-computed-moments method, based on the Lanczos cluster expansion, to estimate the dipole moment of the water molecule on an IBM Quantum superconducting quantum device. The noise-mitigated results agree with full-configuration-interaction calculations to within 0.03 ± 0.007 D ( 2 % ± 0.5 % ), compared with direct expectation-value determination (i.e., variational quantum eigensolver, VQE) with errors of the order of 0.07 D (5%), even when the VQE calculation is performed without noise. This demonstrates that moments-based energy-estimation techniques can be adapted to noise-robust evaluation of nonenergetic ground-state properties of chemical systems. We emphasize that the dipole moment is chosen as an example of such a property, but the method applies to any property determined by one- or two-body interactions.

arXiv:2509.10758•Physical Review Applied•Mar 19, 2026•0 citations

Relativistic coupled-cluster calculation of hyperfine-structure constants of La 2+

Fang Li, Hong Ma, Yong-Bo Tang

Abstract Using the singles and doubles approximated relativistic coupled-cluster method, we calculate hyperfine-structure constant A and B of 24 low-lying states of La 2+ . The results of the lowest four states 5 d 3/2,5/2 and 4 f 5/2,7/2 are compared with recently measured values (Olmschenk et al 2017 Phys. Rev. A 96 032502). Reasonable agreement is found for hyperfine-structure constant A of 5 d 3/2 and 4 f 5/2,7/2 states, but the hyperfine-structure constant A of 5 d 5/2 and the hyperfine-structure constant B have a large deviation. To understand the role of the electron correlation effect, the intermediate results from lower-order many-body perturbation-theory and the linear version of coupled-cluster with single and double approximation are also presented. In the framework of coupled-cluster theory, the contribution trends from individual correlation effects are also investigated.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 25, 2020•10 citations

Applications of quantum annealing to magnetic dipole hyperfine structure constants: First results beyond energies for atoms

Boni Paul, Subimal Deb, Per Jönsson +2 more

We report the first results of the magnetic dipole hyperfine structure (HFS) constants of neutral $\mathrm{Li}$, Li-like $\mathrm{Be}$, neutral $\mathrm{Na}$, and Na-like $\mathrm{Mg}$ using a modified version of the Quantum Annealer Eigensolver (QAE) algorithm on D-Wave's quantum hardware. The results are benchmarked against relativistic configuration interaction with multiconfiguration Dirac Hartree-Fock (MCDHF) calculations using the General-purpose Relativistic Atomic Structure Package (GRASP), and simulated annealing. In our modified QAE, a zooming-and-sigma-annealing approach with a floating-point encoding scheme is adopted to estimate the ground-state eigenvalue and eigenvector of the relativistic Dirac-Coulomb Hamiltonian matrices ($H_{\mathrm{DC}}$) constructed from 11 or fewer configuration state functions (CSFs). For calculations with extended correlation orbital sets, we applied a CSF truncation scheme, retaining only CSFs (up to 12) that make significant contributions to the ground-state wavefunction. Our modified QAE precision is kept limited to three decimal places (up to 10 qubits). Hardware demonstrations on the D-Wave quantum processing unit (QPU) yielded results that were completely consistent with GRASP (at the chosen precision) in determining the magnetic dipole HFS constants, with accuracy varying across systems and $H_{\mathrm{DC}}$ matrix dimensions.

quant-pharXiv:2606.20166•Jun 19, 2026•0 citations

Convergence of all-order many-body methods: Coupled-cluster study for Li

Andrei Derevianko, S. G. Porsev, K. Beloy

We present and analyze results of the relativistic coupled-cluster calculation of energies, hyperfine constants, and dipole matrix elements for the $2s$, $2{p}_{1∕2}$, and $2{p}_{3∕2}$ states of Li atom. The calculations are complete through the fourth order of many-body perturbation theory for energies and through the fifth order for matrix elements and subsume certain chains of diagrams in all orders. A nearly complete many-body calculation allows us to draw conclusions on the convergence pattern of the coupled-cluster method. Our analysis suggests that the high-order many-body contributions to energies and matrix elements scale proportionally and provide a quantitative ground for semiempirical fits of ab initio matrix elements to experimental energies.

arXiv:0804.4697•Physical Review A•Jul 11, 2008•30 citations
The molecular dipole moment and magnetic hyperfine-structure constant demand an accurate wave function far from the nucleus and in the near nuclear region, respectively. We, therefore, employ the so-called Z-vector method in the domain of relativistic-coupled-cluster theory to calculate the first-order property of molecular systems in their open-shell ground-state configuration. The implemented method is applied to calculate the molecular dipole moment and parallel component of the magnetic hyperfine-structure constant of the SrF molecule. The results of our calculation are compared with the experimental and other available theoretically calculated values. We are successful in achieving good accordance with the experimental results. The result of our calculation of the molecular dipole moment is in the accuracy of \ensuremath∼0.5\ensuremath{\sim}0.5\ensuremath∼0.5%, which is clearly an improvement over the previous calculation based on the expectation value method in the four-component coupled-cluster framework [V. S. Prasannaa et al., Phys. Rev. A 90, 052507 (2014)]. Thus, it can be inferred that the Z-vector method can provide an accurate wave function in both the near and far nuclear region, which is evident from our calculated results.
The ZZZ-vector method in the relativistic coupled-cluster framework is used to calculate the magnetic hyperfine structure constant (AJ{A}_{J}AJ​) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The ZZZ-vector results are in very good agreement with the experiment. The AJ{A}_{J}AJ​ values of Li, Na, K, Rb, Cs, Be+{\mathrm{Be}}^{+}Be+, Mg+{\mathrm{Mg}}^{+}Mg+, Ca+{\mathrm{Ca}}^{+}Ca+, and Sr+{\mathrm{Sr}}^{+}Sr+ obtained in the ZZZ-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that the ZZZ-vector method with the single and double approximation can produce a more precise wave function in the nuclear region than the ECC method.
We have developed an all-particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine structure constants, and electric dipole matrix elements of Sr, Ba, and Yb. Furthermore, we calculate the electric quadrupole hyperfine structure constants and the electric dipole matrix elements of Sr+{\mathrm{Sr}}^{+}Sr+, Ba+{\mathrm{Ba}}^{+}Ba+, and Yb+{\mathrm{Yb}}^{+}Yb+. For these we use the one-valence coupled-cluster wave functions obtained as an intermediate in the two-valence calculations. We also calculate the magnetic dipole hyperfine structure constants of Yb+{\mathrm{Yb}}^{+}Yb+.
With rapid progress being made in the development of platforms for quantum computation, there has been considerable interest in whether present-day and near-term devices can be used to solve problems of relevance. A commonly cited application area is the domain of quantum chemistry. While most experimental demonstrations of quantum chemical calculations on quantum devices have focused on the ground-state electronic energy of the system, other properties of the ground state, such as the electric dipole moment, are also of interest. Here, we employ the quantum-computed-moments method, based on the Lanczos cluster expansion, to estimate the dipole moment of the water molecule on an IBM Quantum superconducting quantum device. The noise-mitigated results agree with full-configuration-interaction calculations to within 0.03 ± 0.007 D ( 2 % ± 0.5 % ), compared with direct expectation-value determination (i.e., variational quantum eigensolver, VQE) with errors of the order of 0.07 D (5%), even when the VQE calculation is performed without noise. This demonstrates that moments-based energy-estimation techniques can be adapted to noise-robust evaluation of nonenergetic ground-state properties of chemical systems. We emphasize that the dipole moment is chosen as an example of such a property, but the method applies to any property determined by one- or two-body interactions.
Abstract Using the singles and doubles approximated relativistic coupled-cluster method, we calculate hyperfine-structure constant A and B of 24 low-lying states of La 2+ . The results of the lowest four states 5 d 3/2,5/2 and 4 f 5/2,7/2 are compared with recently measured values (Olmschenk et al 2017 Phys. Rev. A 96 032502). Reasonable agreement is found for hyperfine-structure constant A of 5 d 3/2 and 4 f 5/2,7/2 states, but the hyperfine-structure constant A of 5 d 5/2 and the hyperfine-structure constant B have a large deviation. To understand the role of the electron correlation effect, the intermediate results from lower-order many-body perturbation-theory and the linear version of coupled-cluster with single and double approximation are also presented. In the framework of coupled-cluster theory, the contribution trends from individual correlation effects are also investigated.
We report the first results of the magnetic dipole hyperfine structure (HFS) constants of neutral Li\mathrm{Li}Li, Li-like Be\mathrm{Be}Be, neutral Na\mathrm{Na}Na, and Na-like Mg\mathrm{Mg}Mg using a modified version of the Quantum Annealer Eigensolver (QAE) algorithm on D-Wave's quantum hardware. The results are benchmarked against relativistic configuration interaction with multiconfiguration Dirac Hartree-Fock (MCDHF) calculations using the General-purpose Relativistic Atomic Structure Package (GRASP), and simulated annealing. In our modified QAE, a zooming-and-sigma-annealing approach with a floating-point encoding scheme is adopted to estimate the ground-state eigenvalue and eigenvector of the relativistic Dirac-Coulomb Hamiltonian matrices (HDCH_{\mathrm{DC}}HDC​) constructed from 11 or fewer configuration state functions (CSFs). For calculations with extended correlation orbital sets, we applied a CSF truncation scheme, retaining only CSFs (up to 12) that make significant contributions to the ground-state wavefunction. Our modified QAE precision is kept limited to three decimal places (up to 10 qubits). Hardware demonstrations on the D-Wave quantum processing unit (QPU) yielded results that were completely consistent with GRASP (at the chosen precision) in determining the magnetic dipole HFS constants, with accuracy varying across systems and HDCH_{\mathrm{DC}}HDC​ matrix dimensions.
We present and analyze results of the relativistic coupled-cluster calculation of energies, hyperfine constants, and dipole matrix elements for the 2s2s2s, 2p1∕22{p}_{1∕2}2p1∕2​, and 2p3∕22{p}_{3∕2}2p3∕2​ states of Li atom. The calculations are complete through the fourth order of many-body perturbation theory for energies and through the fifth order for matrix elements and subsume certain chains of diagrams in all orders. A nearly complete many-body calculation allows us to draw conclusions on the convergence pattern of the coupled-cluster method. Our analysis suggests that the high-order many-body contributions to energies and matrix elements scale proportionally and provide a quantitative ground for semiempirical fits of ab initio matrix elements to experimental energies.