N-representability violations in truncated equation-of-motion coupled-cluster methods

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• One-electron reduced density matrices (1RDMs) are fundamental to describing electronic states in quantum mechanics.
• The N-representability of a 1RDM ensures it corresponds to a valid N-electron quantum state.
• Equation-of-motion coupled-cluster (EOM-CC) methods are widely used for electronic structure calculations.

Purpose of the Study:

• To analyze the N-representability of 1RDMs obtained from equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD) calculations.
• To identify conditions under which EOM-CCSD 1RDMs may not correspond to physical N-electron states.
• To investigate the implications for time-dependent EOM-CC simulations.

Main Methods:

• Analysis of one-electron reduced density matrices (1RDMs) derived from EOM-CCSD stationary states.
• Assessment of N-representability using ensemble-state and pure-state (generalized Pauli constraints) conditions.
• Examination of 1RDMs during time-dependent EOM-CC simulations under external fields.

Main Results:

• Identified EOM-CCSD stationary states with 1RDMs violating N-representability conditions (ensemble and pure-state).
• Demonstrated that these unphysical 1RDMs do not represent any valid N-electron quantum state.
• Observed violations of ensemble-state N-representability for time-dependent states in EOM-CC simulations.

Conclusions:

• EOM-CCSD calculations can produce 1RDMs that are not physically realizable.
• Unphysical 1RDMs can arise even from stationary states and during time-dependent evolutions.
• These findings highlight potential challenges in interpreting results from time-dependent EOM-CCSD simulations.