insight - Computational Chemistry - # Relativistic and electron-correlation effects on static dipole polarizabilities of group 11 elements

Accurate Determination of Static Dipole Polarizabilities for Group 11 Elements Using Relativistic Coupled-Cluster Methods

Q: How do the relativistic and electron-correlation effects on dipole polarizabilities vary across the periodic table?

The relativistic and electron-correlation effects on dipole polarizabilities exhibit significant variation across the periodic table, primarily influenced by the atomic number and the electron configuration of the elements. As one moves down a group in the periodic table, the relativistic effects become more pronounced due to the increasing nuclear charge, which leads to greater electron velocities and consequently stronger relativistic corrections. For instance, in group 11 elements such as copper (Cu), silver (Ag), and gold (Au), the study indicates that scalar-relativistic effects are the dominant contribution to the dipole polarizabilities, while spin-orbit coupling (SOC) effects are relatively negligible. In lighter elements, the dipole polarizabilities are primarily influenced by non-relativistic electron correlation effects, which are significant due to the lower nuclear charge and electron density distribution. However, as the atomic number increases, the importance of relativistic effects, particularly scalar-relativistic corrections, grows, leading to a more complex interplay between these effects. The study highlights that while electron correlation remains crucial for accurate calculations, the relativistic contributions must also be carefully considered, especially for heavier elements where they can significantly alter the predicted values of dipole polarizabilities.

Q: What are the potential implications of the improved accuracy in dipole polarizabilities for the development of higher-precision atomic clocks?

The improved accuracy in dipole polarizabilities has profound implications for the development of higher-precision atomic clocks. Accurate dipole polarizability measurements are essential for understanding the black-body radiation (BBR) shift, which affects the frequency standards used in atomic clocks. The leading-order shifts in atomic clock frequencies are proportional to the differential polarizability between the two clock states. Therefore, enhanced precision in dipole polarizability directly translates to improved accuracy in the frequency measurements of atomic transitions. Moreover, the study's findings provide crucial benchmarks for theoretical methods, such as density-functional theory, which are employed in the design and optimization of atomic clocks. The refined values of dipole polarizabilities for elements like Cu, Ag, and Au can lead to better predictions of clock performance and stability, ultimately contributing to advancements in global timekeeping standards and navigation systems like GPS. Additionally, the ability to explore new physics, such as variations in fundamental constants, is facilitated by the precise knowledge of atomic dipole polarizabilities, making them a critical factor in the ongoing development of next-generation atomic clocks.

Q: What other atomic properties could be investigated using the computational approach employed in this study to gain further insights into the interplay between relativistic and electron-correlation effects?

The computational approach employed in this study, particularly the relativistic coupled-cluster method with single, double, and perturbative triple excitations (CCSD(T)), can be applied to investigate a variety of other atomic properties that are sensitive to relativistic and electron-correlation effects. Some of these properties include: Quadrupole Polarizabilities: Similar to dipole polarizabilities, quadrupole polarizabilities can provide insights into the electron density distribution and its response to external electric fields, revealing additional details about the atomic structure and interactions. Hyperpolarizabilities: The study of hyperpolarizabilities, which describe the response of a system to higher-order electric fields, can enhance understanding of non-linear optical properties and their applications in photonics and materials science. Ionization Energies and Electron Affinities: Investigating these properties can shed light on the stability and reactivity of atoms, particularly in the context of chemical bonding and molecular interactions. Excitation Energies: The approach can be extended to calculate excitation energies, which are crucial for understanding electronic transitions and spectra, particularly in heavy elements where relativistic effects are significant. Magnetic Properties: Properties such as magnetic susceptibility and g-factors can also be explored, as they are influenced by both relativistic effects and electron correlation, providing insights into the magnetic behavior of atoms and their compounds. By applying the same rigorous computational methods, researchers can gain a deeper understanding of how relativistic and electron-correlation effects influence these various atomic properties, ultimately contributing to the broader field of atomic and molecular physics.

Core Concepts

Highly accurate static dipole polarizabilities for Cu, Ag, and Au are computed using relativistic coupled-cluster methods, with a detailed analysis of the impact of relativistic effects and electron correlation.

Abstract

The study presents a comprehensive investigation of the static dipole polarizabilities of group 11 elements (Cu, Ag, and Au) using relativistic coupled-cluster methods. The key highlights and insights are:

Relativistic effects, including scalar-relativistic, spin-orbit coupling (SOC), and fully relativistic Dirac-Coulomb contributions, are systematically analyzed. The results show that scalar-relativistic effects are the dominant relativistic contribution, while SOC effects are negligible for these elements.
Electron-correlation effects are found to play a significant role in accurately determining the dipole polarizabilities across all relativistic regimes. The influence of electron correlation increases with atomic number, with the maximum contribution observed for Ag.
The final recommended dipole polarizability values, including uncertainties, are 46.91 ± 1.30 for Cu, 50.97 ± 1.88 for Ag, and 36.68 ± 0.62 for Au. These values are in good agreement with the previously recommended values, with reduced uncertainties for Ag and Au.
The analysis provides important insights into the interplay between relativistic and electron-correlation effects on atomic properties, which is crucial for the development of accurate computational methods and the interpretation of experimental data.

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Stats

The static dipole polarizability (α) of Cu is 46.91 ± 1.30 a.u.
The static dipole polarizability (α) of Ag is 50.97 ± 1.88 a.u.
The static dipole polarizability (α) of Au is 36.68 ± 0.62 a.u.

Quotes

"Scalar-relativistic effects are the dominant relativistic contribution for these elements, while SOC effects are negligible."
"Electron-correlation effects are found to play a significant role in accurately determining the dipole polarizabilities across all relativistic regimes."
"The final recommended dipole polarizability values, including uncertainties, are 46.91 ± 1.30 for Cu, 50.97 ± 1.88 for Ag, and 36.68 ± 0.62 for Au."

Key Insights Distilled From

Relativistic and electron-correlation effects in static dipole polarizabilities for group 11 elements

by YingXing Che... at arxiv.org 10-03-2024

https://arxiv.org/pdf/2410.01493.pdf

Relativistic and electron-correlation effects in static dipole polarizabilities for group 11 elements

Deeper Inquiries

How do the relativistic and electron-correlation effects on dipole polarizabilities vary across the periodic table?

The relativistic and electron-correlation effects on dipole polarizabilities exhibit significant variation across the periodic table, primarily influenced by the atomic number and the electron configuration of the elements. As one moves down a group in the periodic table, the relativistic effects become more pronounced due to the increasing nuclear charge, which leads to greater electron velocities and consequently stronger relativistic corrections. For instance, in group 11 elements such as copper (Cu), silver (Ag), and gold (Au), the study indicates that scalar-relativistic effects are the dominant contribution to the dipole polarizabilities, while spin-orbit coupling (SOC) effects are relatively negligible.
In lighter elements, the dipole polarizabilities are primarily influenced by non-relativistic electron correlation effects, which are significant due to the lower nuclear charge and electron density distribution. However, as the atomic number increases, the importance of relativistic effects, particularly scalar-relativistic corrections, grows, leading to a more complex interplay between these effects. The study highlights that while electron correlation remains crucial for accurate calculations, the relativistic contributions must also be carefully considered, especially for heavier elements where they can significantly alter the predicted values of dipole polarizabilities.

What are the potential implications of the improved accuracy in dipole polarizabilities for the development of higher-precision atomic clocks?

The improved accuracy in dipole polarizabilities has profound implications for the development of higher-precision atomic clocks. Accurate dipole polarizability measurements are essential for understanding the black-body radiation (BBR) shift, which affects the frequency standards used in atomic clocks. The leading-order shifts in atomic clock frequencies are proportional to the differential polarizability between the two clock states. Therefore, enhanced precision in dipole polarizability directly translates to improved accuracy in the frequency measurements of atomic transitions.
Moreover, the study's findings provide crucial benchmarks for theoretical methods, such as density-functional theory, which are employed in the design and optimization of atomic clocks. The refined values of dipole polarizabilities for elements like Cu, Ag, and Au can lead to better predictions of clock performance and stability, ultimately contributing to advancements in global timekeeping standards and navigation systems like GPS. Additionally, the ability to explore new physics, such as variations in fundamental constants, is facilitated by the precise knowledge of atomic dipole polarizabilities, making them a critical factor in the ongoing development of next-generation atomic clocks.

What other atomic properties could be investigated using the computational approach employed in this study to gain further insights into the interplay between relativistic and electron-correlation effects?

The computational approach employed in this study, particularly the relativistic coupled-cluster method with single, double, and perturbative triple excitations (CCSD(T)), can be applied to investigate a variety of other atomic properties that are sensitive to relativistic and electron-correlation effects. Some of these properties include:

Quadrupole Polarizabilities: Similar to dipole polarizabilities, quadrupole polarizabilities can provide insights into the electron density distribution and its response to external electric fields, revealing additional details about the atomic structure and interactions.

Hyperpolarizabilities: The study of hyperpolarizabilities, which describe the response of a system to higher-order electric fields, can enhance understanding of non-linear optical properties and their applications in photonics and materials science.

Ionization Energies and Electron Affinities: Investigating these properties can shed light on the stability and reactivity of atoms, particularly in the context of chemical bonding and molecular interactions.

Excitation Energies: The approach can be extended to calculate excitation energies, which are crucial for understanding electronic transitions and spectra, particularly in heavy elements where relativistic effects are significant.

Magnetic Properties: Properties such as magnetic susceptibility and g-factors can also be explored, as they are influenced by both relativistic effects and electron correlation, providing insights into the magnetic behavior of atoms and their compounds.

By applying the same rigorous computational methods, researchers can gain a deeper understanding of how relativistic and electron-correlation effects influence these various atomic properties, ultimately contributing to the broader field of atomic and molecular physics.