Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing

Area of Science:

• Quantum chemistry
• Theoretical chemistry
• Computational physics

Background:

• The Born-Oppenheimer approximation is a cornerstone of molecular quantum mechanics, simplifying calculations by separating electronic and nuclear motion.
• However, this approximation fails for systems with strong electron-vibrational coupling, limiting accuracy in many chemical processes.

Purpose of the Study:

• To develop a new theoretical and computational framework for molecular quantum mechanics that does not rely on the Born-Oppenheimer approximation.
• To represent the molecular wavefunction in a unified electronic and vibrational basis.
• To enable more accurate simulations of molecular systems where the Born-Oppenheimer approximation breaks down.

Main Methods:

• The molecular wavefunction is represented in a tensor-product space of electronic and vibrational basis functions.
• The electronic basis is specifically chosen to accurately reproduce the mean-field electronic structure across all molecular geometries.
• The molecular Hamiltonian is transformed into a fully second-quantized form using creation and annihilation operators for both electronic and vibrational quantum particles.

Main Results:

• The developed framework allows for the representation of molecular quantum mechanics beyond the Born-Oppenheimer approximation.
• The transformation to a second-quantized form opens possibilities for polynomial-scaling approximations to the tensor-product space formalism.
• A proof-of-principle application to the vibronic spectrum of C2 demonstrates the framework's potential.

Conclusions:

• The new theoretical and computational framework offers a more rigorous approach to molecular quantum mechanics.
• This method has the potential to significantly improve the accuracy of molecular simulations, particularly for systems with strong electron-vibrational coupling.
• The framework paves the way for efficient and accurate calculations of molecular properties, including vibronic spectra.