Highly Accurate Expectation Values Using High-Order Relativistic Coupled Cluster Theory

Area of Science:

• Computational chemistry
• Quantum chemistry
• Relativistic molecular calculations

Background:

• Coupled-cluster (CC) methods are essential for accurate molecular electronic structure.
• Analytic energy derivatives are crucial for calculating molecular properties.
• Relativistic effects are important for heavy elements and precise calculations.

Purpose of the Study:

• To implement automatic generation of analytic first derivatives of the energy for general coupled-cluster (CC) models.
• To report the first implementation of expectation values for coupled cluster with triple and quadruple excitations (CCSDT and CCSDTQ) within the DIRAC program package.
• To compute nuclear electric quadrupole moments for lithium and aluminum compounds.

Main Methods:

• Utilized the tenpi toolchain for automatic generation of analytic derivatives.
• Implemented CCSDT and CCSDTQ expectation values in the DIRAC program.
• Calculated electric field gradients (EFGs) at Li and Al nuclei in various compounds.

Main Results:

• Successfully computed corrections for triple and quadruple excitations for the EFG.
• Determined the nuclear electric quadrupole moment for Aluminum-27 (Q(27Al)) as 0.146598 ± 0.000001 b, showing excellent agreement with recommended values.
• Obtained the nuclear electric quadrupole moment for Lithium-7 (Q(7Li)) as -0.038624 ± 0.000292 b, which is lower than the current recommended value, suggesting further research.

Conclusions:

• The developed methods provide accurate calculations of nuclear electric quadrupole moments.
• The new implementation facilitates high-level coupled-cluster calculations for relativistic systems.
• The obtained Q(7Li) value indicates a potential need for re-evaluation of current experimental or theoretical recommendations.