Harnessing molecular excited states with Lanczos chains

Area of Science:

• Quantum mechanics
• Computational chemistry
• Spectroscopy

Background:

• The Haydock, Heine, and Kelly recursion method efficiently computes diagonal matrix elements of quantum-mechanical Hamiltonians using continued fractions.
• Extending this method to off-diagonal elements and general operators is crucial for advanced spectral simulations.

Purpose of the Study:

• To generalize the recursion method for calculating off-diagonal matrix elements of general operators.
• To apply the extended method to simulate molecular optical absorption and photoemission spectra.
• To validate the approach using the caffeine molecule.

Main Methods:

• Extension of the Haydock, Heine, and Kelly recursion method to handle off-diagonal matrix elements.
• Application of the generalized method within time-dependent density-functional theory (TD-DFT) for optical absorption.
• Utilization of the method within many-body perturbation theory (MBPT) for photoemission spectra.
• Simulation of spectra for the caffeine molecule as a case study.

Main Results:

• Successful extension of the recursion method to off-diagonal matrix elements of general operators.
• Accurate simulation of optical absorption spectra using TD-DFT.
• Accurate simulation of photoemission spectra using MBPT.
• Demonstration of the method's applicability with spectral calculations for caffeine.

Conclusions:

• The generalized recursion method provides a powerful and versatile tool for spectral simulations.
• This approach enhances the capability to study molecular electronic properties.
• The method is effective for both Hermitian and non-Hermitian operators in quantum systems.