Efficient Solution of the Electronic Eigenvalue Problem Using Wavepacket Propagation.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Electronic structure theory

Background:

• Traditional methods for solving the electronic eigenvalue problem include iterative subspace diagonalization schemes.
• Methods like Davidson and Lanczos are commonly used but can be computationally intensive.
• A need exists for more efficient computational approaches in quantum dynamics.

Purpose of the Study:

• To present imaginary time wavepacket propagation as an efficient method for calculating the lowest-lying eigenstates of the electronic Hamiltonian.
• To introduce an extended short iterative Lanczos wavepacket propagation scheme to enhance computational efficiency.
• To demonstrate the computational competitiveness of the relaxation method against established algorithms.

Main Methods:

• Imaginary time wavepacket propagation (relaxation method)
• Extended short iterative Lanczos wavepacket propagation scheme
• Calculation of lowest-lying eigenstates of the electronic Hamiltonian

Main Results:

• The relaxation method offers a fundamentally different approach to solving the electronic eigenvalue problem.
• The proposed extended short iterative Lanczos scheme makes the relaxation method computationally competitive.
• In tested cases, the relaxation method demonstrated comparable or superior computational efficiency to the block Davidson-Liu algorithm.

Conclusions:

• Imaginary time wavepacket propagation is an efficient technique for electronic structure calculations.
• The developed Lanczos-based propagation scheme enhances the practicality of the relaxation method.
• This method presents a viable and potentially more efficient alternative to traditional diagonalization techniques.