Flexible DMRG-Based Framework for Anharmonic Vibrational Calculations

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Molecular Spectroscopy

Background:

• Accurate prediction of molecular vibrational frequencies is crucial for understanding molecular properties and reactivity.
• Strongly anharmonic molecules and high-dimensional potential energy surfaces (PES) pose significant challenges for traditional computational methods.
• The vibrational density matrix renormalization group (vDMRG) is a powerful tool, but its application to general anharmonic systems is limited.

Purpose of the Study:

• To introduce a novel formulation of the vibrational density matrix renormalization group (vDMRG) algorithm.
• To extend the vDMRG framework to handle general, high-dimensional potential energy surfaces (PES) and anharmonic vibrational Hamiltonians.
• To enable efficient calculation of anharmonic transition frequencies, including excited states.

Main Methods:

• Developed the n-mode second-quantization formalism for vibrational Hamiltonians.
• Implemented an n-mode vDMRG method offering flexibility in PES functional form and single-particle basis sets.
• Combined n-mode vDMRG with an anharmonic modal basis set optimized via the vibrational self-consistent field (vSCF) algorithm.
• Incorporated excited-state-targeting algorithms for transition frequency calculations.

Main Results:

• The n-mode vDMRG method successfully handles general, high-dimensional anharmonic potential energy surfaces.
• First-time application of vDMRG using an optimized anharmonic modal basis set on an on-the-fly constructed PES.
• Demonstrated the method's capability on methyloxirane, a molecule with 24 coupled vibrational modes, calculating anharmonic transition frequencies.

Conclusions:

• The novel n-mode vDMRG framework provides a flexible and efficient approach for studying strongly anharmonic molecular vibrations.
• This method overcomes limitations of previous vDMRG formulations, enabling accurate calculations for complex molecular systems.
• The demonstrated application on methyloxirane highlights the potential of n-mode vDMRG for advancing molecular spectroscopy and computational chemistry.