Local pair natural orbitals for excited states

Area of Science:

• Quantum Chemistry
• Computational Spectroscopy
• Electronic Structure Theory

Background:

• Accurate calculation of excitation energies is crucial for understanding molecular properties and reactions.
• Wavefunction-based methods, like coupled cluster, offer high accuracy but are computationally expensive due to the large number of electronic excitations.
• Local correlation methods, such as pair natural orbitals (PNOs), aim to reduce this computational cost by exploiting electron localization.

Purpose of the Study:

• To investigate the efficiency of truncated pair natural orbital (PNO) expansions for calculating excitation energies using wavefunction-based methods.
• To assess the impact of localized occupied orbitals on the accuracy and computational cost of these calculations.
• To develop a more efficient approach for electronic excitation energy calculations applicable to larger molecular systems.

Main Methods:

• Employed the CIS(D) approximation as a test model for response calculations of excitation energies.
• Utilized truncated pair natural orbital (PNO) expansions for excited state wavefunctions, generated from approximate first-order guess wavefunctions.
• Applied Pipek-Mezey localization to occupied orbitals and controlled PNO truncation error using a threshold based on generalized natural occupation numbers.

Main Results:

• Demonstrated a dramatic reduction in the number of double excitation amplitudes with minimal loss of accuracy using state-specific PNOs.
• Showed that PNO truncation error for excitation energies can be effectively controlled by a single threshold, similar to ground-state calculations.
• Achieved high accuracy (PNO truncation error < 0.01 eV) with an average of 40-80 PNOs per pair using Pipek-Mezey localized orbitals and a PNO threshold of 10(-8)-10(-7).
• Observed linear or sub-linear scaling of significant excited state PNOs with system size, depending on the delocalization of excitations.
• Confirmed that state-specific PNOs can accurately treat local, delocalized, and charge transfer excited states.

Conclusions:

• Truncated PNO expansions combined with localized occupied orbitals provide a highly efficient and accurate method for calculating excitation energies.
• This approach significantly reduces computational cost compared to traditional methods and domain-based local response approaches.
• The flexibility of state-specific PNOs ensures reliable calculations across various types of excited states, paving the way for larger system studies.