Quantum Equation-of-Motion Method with Single, Double, and Triple Excitations

Area of Science:

• Quantum chemistry
• Computational chemistry
• Theoretical chemistry

Background:

• The quantum equation-of-motion (qEOM) method with single and double excitations (qEOM-SD) is used for excited states.
• qEOM-SD struggles with states heavily influenced by double excitations.

Purpose of the Study:

• To reformulate the qEOM method for improved accuracy in excited state calculations.
• To develop an efficient computational method that includes single, double, and triple excitations.

Main Methods:

• Reformulated qEOM within an effective Hamiltonian framework satisfying the killer condition.
• Incorporated single, double, and triple excitations with computational complexity reduced via point-group symmetry and perturbation theory.
• Applied a perturbative correction for neglected triple excitations and extended operator screening to quantum subspace expansion.

Main Results:

• Reduced computational scaling from N_o⁶N_v⁶ to N_o⁵N_v⁵.
• Achieved energy errors below 0.18 eV for challenging cases like CH⁺ and HF, with <8.2% triple excitations.
• Demonstrated efficient inclusion of selected triple excitations.

Conclusions:

• The new qEOM method effectively handles electronically excited states dominated by double excitations.
• The developed method offers a computationally efficient and accurate approach for excited-state calculations.
• The technique is extendable to other quantum chemistry methods for improved accuracy.