Expectation values of single-particle operators in the random phase approximation ground state

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Calculating molecular properties from first principles is crucial for understanding chemical behavior.
• The random phase approximation (RPA) is a method used in quantum chemistry to approximate the ground state of a system.
• Correlated RPA methods aim to improve upon standard RPA by including electron correlation effects.

Purpose of the Study:

• To develop a practical and efficient method for computing matrix elements of single-particle operators.
• To derive a simplified expression for molecular properties within the correlated random phase approximation (CRPA) framework.
• To validate the developed method by calculating molecular dipole moments.

Main Methods:

• Developed a theoretical framework for computing matrix elements in the CRPA ground state.
• Derived an explicit expression for molecular properties using CRPA amplitudes.
• Applied the method to calculate molecular dipole moments for various molecules.

Main Results:

• A computationally tractable method for calculating matrix elements in CRPA ground states was established.
• A simplified expression for molecular properties was derived, facilitating practical calculations.
• Accurate calculations of molecular dipole moments were achieved for a set of representative molecules.

Conclusions:

• The developed method provides an efficient and accurate way to compute molecular properties.
• This work offers a valuable tool for theoretical chemists and physicists.
• The CRPA approach, with this new method, shows promise for future electronic structure calculations.