Tests of accuracy for computed magnetic properties via off-diagonal hypervirial relations

Area of Science:

• Quantum Chemistry
• Computational Magnetism
• Theoretical Chemistry

Background:

• Current methods for molecular magnetic response, like magnetizability and shielding, often yield inaccurate electronic current density maps.
• These inaccuracies stem from a lack of guaranteed conservation, leading to unphysical results in computational models.

Purpose of the Study:

• To generalize existing theoretical frameworks for molecular magnetic response calculations.
• To develop a more accurate and computationally efficient method for computing electronic current densities.
• To address the issue of unphysical features in current density maps.

Main Methods:

• Proving a novel off-diagonal hypervirial relationship connecting functions of position and their derivatives.
• Applying this relationship to generalize the work of Epstein and Sambe.
• Demonstrating how Sambe's conservation check equations arise as special cases of the new theorem.

Main Results:

• A generalized off-diagonal hypervirial relationship has been established.
• The new theorem provides a more computationally efficient method for calculating electronic current densities.
• The proposed method ensures better conservation, leading to more physically realistic current density maps.

Conclusions:

• The generalized hypervirial relationship offers a significant improvement for calculating molecular magnetic responses.
• This approach enhances the accuracy and reliability of electronic current density computations.
• The findings pave the way for future advancements in computational quantum chemistry and magnetism.