Visualizing the zero order basis of the spectroscopic Hamiltonian

Area of Science:

• Quantum Chemistry
• Spectroscopy
• Computational Chemistry

Background:

• Spectroscopic effective Hamiltonians are used to model molecular spectra.
• Their applicability in regions like isomerization barriers was previously uncertain.
• These Hamiltonians rely on an abstract zero-order basis (ZOB).

Purpose of the Study:

• To explain the success of effective Hamiltonians in complex spectral regions.
• To develop a method for representing the abstract ZOB in coordinate space.
• To demonstrate the adaptability of the ZOB for various potential energy surfaces.

Main Methods:

• Obtained converged eigenfunctions from variational calculations on a potential surface.
• Established a one-to-one correspondence between effective Hamiltonian and coordinate space energy eigenstates.
• Calculated a physical representation of the abstract ZOB.

Main Results:

• Successfully derived the coordinate space representation of the abstract ZOB.
• The method is effective for both generalized and standard effective Hamiltonians.
• The ZOB basis adapts its complexity based on phase space characteristics.

Conclusions:

• Spectroscopic effective Hamiltonians succeed even for systems with multiple stationary points.
• The developed method provides physical insight into the abstract ZOB.
• This work validates the use of effective Hamiltonians in previously challenging spectral regions.