Geometry optimizations in the zero order regular approximation for relativistic effects

Geometry optimizations in the zero order regular approximation for relativistic effects

1999 | van Lenthe, E.; Ehlers, A.W.; Baerends, E.J.
This paper presents a detailed analysis of geometry optimizations using the zeroth order regular approximation (ZORA) for relativistic effects. The authors derive analytical expressions for energy gradients in the ZORA method, which is a scalar relativistic approach based on the Dirac equation. They compare ZORA with the quasirelativistic Pauli method, highlighting the limitations of the latter, such as its lack of lower bound and gauge dependence issues. The ZORA method is shown to be more stable and accurate, especially when using the electrostatic shift approximation (ESA) to avoid gauge dependence. The paper discusses the application of ZORA to calculate bond dissociation energies and geometries for transition metal complexes such as W(CO)6, Os(CO)5, and Pt(CO)4. The authors investigate the effects of different basis sets on the accuracy of these calculations. They also compare ZORA results with those obtained using the quasirelativistic Pauli method, emphasizing the advantages of ZORA in terms of numerical stability and accuracy. The paper addresses the implementation of ZORA in the Amsterdam Density Functional (ADF) program, including the calculation of analytical energy gradients. The authors also discuss the importance of using appropriate basis sets and the frozen core approximation to ensure accurate and efficient calculations. They highlight the need for careful selection of core orthogonalization functions to avoid variational collapse and ensure numerical stability. The results of geometry optimizations for small molecules, such as diatomics, are presented and compared with pointwise calculations. The authors show that the ZORA method, when combined with appropriate basis sets and the ESA approximation, provides accurate and reliable results. They also discuss the limitations of the quasirelativistic Pauli method, particularly in terms of variational stability and gauge dependence. In conclusion, the paper demonstrates that the ZORA method, especially when used with the ESA approximation and appropriate basis sets, is a robust and accurate approach for geometry optimizations in relativistic quantum chemistry. The authors emphasize the importance of careful implementation and basis set selection to achieve high accuracy and numerical stability in relativistic calculations.This paper presents a detailed analysis of geometry optimizations using the zeroth order regular approximation (ZORA) for relativistic effects. The authors derive analytical expressions for energy gradients in the ZORA method, which is a scalar relativistic approach based on the Dirac equation. They compare ZORA with the quasirelativistic Pauli method, highlighting the limitations of the latter, such as its lack of lower bound and gauge dependence issues. The ZORA method is shown to be more stable and accurate, especially when using the electrostatic shift approximation (ESA) to avoid gauge dependence. The paper discusses the application of ZORA to calculate bond dissociation energies and geometries for transition metal complexes such as W(CO)6, Os(CO)5, and Pt(CO)4. The authors investigate the effects of different basis sets on the accuracy of these calculations. They also compare ZORA results with those obtained using the quasirelativistic Pauli method, emphasizing the advantages of ZORA in terms of numerical stability and accuracy. The paper addresses the implementation of ZORA in the Amsterdam Density Functional (ADF) program, including the calculation of analytical energy gradients. The authors also discuss the importance of using appropriate basis sets and the frozen core approximation to ensure accurate and efficient calculations. They highlight the need for careful selection of core orthogonalization functions to avoid variational collapse and ensure numerical stability. The results of geometry optimizations for small molecules, such as diatomics, are presented and compared with pointwise calculations. The authors show that the ZORA method, when combined with appropriate basis sets and the ESA approximation, provides accurate and reliable results. They also discuss the limitations of the quasirelativistic Pauli method, particularly in terms of variational stability and gauge dependence. In conclusion, the paper demonstrates that the ZORA method, especially when used with the ESA approximation and appropriate basis sets, is a robust and accurate approach for geometry optimizations in relativistic quantum chemistry. The authors emphasize the importance of careful implementation and basis set selection to achieve high accuracy and numerical stability in relativistic calculations.
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