Douglas-Kroll and infinite order two-component transformations of Dirac-Fock operator

Area of Science:

• Quantum Chemistry
• Relativistic Calculations
• Electronic Structure Theory

Background:

• Conventional Douglas-Kroll (DK) and infinite order two-component (IOTC) methods are crucial for relativistic quantum chemistry.
• These methods face computational challenges, particularly with two-electron integrals.

Purpose of the Study:

• To extend the DK and IOTC methods to handle Fock matrices, creating extended DK (EDK) and extended IOTC (EIOTC).
• To develop an efficient approximation for small-component two-electron integrals to accelerate relativistic calculations.

Main Methods:

• Defined a strategy to partition the Dirac-Fock operator into zero- and first-order terms.
• Developed EDK and EIOTC transformations, including Foldy-Wouthuysen transformation for the zero-order term.
• Derived transformed Fock matrix, kinetic energy operator, nuclear attraction operator, and density matrix.
• Introduced the RIS-V approximation formula for small-component two-electron integrals.

Main Results:

• EDK and EIOTC methods were successfully defined and demonstrated to be accurate.
• EIOTC showed consistency with the more computationally intensive four-component approach.
• The RIS-V formula effectively approximates small-component two-electron integrals, including spin-orbit interactions.

Conclusions:

• Extended DK and IOTC methods provide accurate and reliable results for relativistic electronic structure calculations.
• The RIS-V approximation significantly accelerates four-component and extended two-component methods, making them more computationally feasible.