Adiabatic Connection without Coupling Constant Integration.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Many-body perturbation theory (MBPT) is crucial for accurate electronic structure calculations.
• The Random Phase Approximation (RPA) and its renormalized version (RPAr) are common MBPT methods.
• Accurate calculation of correlation energy remains a challenge in electronic structure theory.

Purpose of the Study:

• To develop a "higher-order terms" (HOT) approximation for correlation energy.
• To improve the accuracy of MBPT methods for electronic structure calculations.
• To investigate the computational efficiency and applicability of the new HOT approximation.

Main Methods:

• Utilized a second-order approximation to the renormalized Random Phase Approximation (RPAr) for the density-density response function.
• Developed the higher-order terms (HOT) approximation by incorporating first-order RPAr corrections.
• Applied the HOT approximation to various periodic solids and molecular systems.

Main Results:

• The HOT approximation achieves high accuracy for correlation energy, with errors typically 1% or less.
• The method faithfully captures infinite-order correlation effects for a given exchange-correlation kernel.
• For exchange-like kernels, the HOT approximation eliminates the need for coupling-strength integration, reducing computational cost.
• Accurate correlation energy reproduction leads to accurate predictions of structural properties and energy differences.

Conclusions:

• The HOT approximation offers a significant advancement in accurately calculating correlation energy within MBPT.
• This method demonstrates broad applicability for predicting properties of solids and molecules.
• While highly accurate for many properties, energy differences involving fragmentation present a challenge due to error cancellation issues.