Resolution-of-the-identity approximation for complex-scaled basis functions.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Physics

Background:

• Electronic resonances are crucial in understanding molecular behavior in external fields.
• Non-Hermitian quantum mechanics uses complex-scaled wave functions to model these resonances.
• Accurate computation of electronic properties requires efficient methods for handling complex integrals.

Purpose of the Study:

• To develop and implement a novel resolution-of-the-identity (RI) approximation for two-electron integrals in non-Hermitian quantum mechanics.
• To apply this new RI approximation to Hartree-Fock (HF) and Møller-Plesset perturbation theory (MP2) methods.
• To demonstrate the efficiency and accuracy of the non-Hermitian RI methods for calculating molecular properties.

Main Methods:

• Development of a resolution-of-the-identity (RI) approximation for complex-scaled Gaussian basis functions.
• Implementation of the non-Hermitian RI approximation within Hartree-Fock (HF) and second-order Møller-Plesset perturbation (MP2) theories.
• Computational studies of orientation-dependent ionization rates for CO, C6H6, and C10H8 in static electric fields.

Main Results:

• The new RI approximation is effective for non-Hermitian quantum mechanical calculations.
• The non-Hermitian RI-MP2 method accurately captures correlation effects in electronic resonances.
• The computational cost is significantly reduced, enabling studies on medium-sized molecules.

Conclusions:

• The developed non-Hermitian RI approximation provides an efficient and accurate approach for studying molecular electronic resonances.
• This method facilitates the investigation of complex phenomena like orientation-dependent ionization rates.
• The RI-MP2 approach offers a computationally feasible way to include electron correlation in resonance calculations.