A general nuclear motion Hamiltonian and non-internal curvilinear coordinates

Area of Science:

• Quantum Chemistry
• Molecular Spectroscopy
• Computational Chemistry

Background:

• Accurate molecular vibrational analysis requires precise Hamiltonians.
• Existing Hamiltonians are often limited to specific coordinate systems (rectilinear or internal).
• General curvilinear coordinates offer greater flexibility but are computationally challenging.

Purpose of the Study:

• To derive a general, exact Hamiltonian for nuclear motion in curvilinear coordinates.
• To demonstrate its transformation into established Hamiltonians (Wilson-Howard, Meyer-Guenthard).
• To provide a practical formulation for non-internal curvilinear coordinates.

Main Methods:

• Derivation of an exact nuclear motion Hamiltonian in general curvilinear coordinates.
• Coordinate transformation analysis to connect with existing models.
• Application to a water molecule model potential using diverse coordinate systems.

Main Results:

• The general Hamiltonian successfully reduces to known forms under specific coordinate constraints.
• A simplified expression for non-internal curvilinear coordinates was achieved.
• Vibrational spectra from rectilinear, internal, and non-internal coordinates showed excellent agreement.

Conclusions:

• The derived general Hamiltonian is applicable and accurate for molecular vibrational analysis.
• It unifies various coordinate systems, simplifying computational approaches.
• This work enhances the utility of curvilinear coordinates in computational chemistry.