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This study introduces automatic calculation of analytic energy derivatives for coupled-cluster models. New implementations enable precise determination of nuclear electric quadrupole moments for lithium and aluminum compounds.

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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.