Eckart-Sayvetz conditions revisited

Area of Science:

• Molecular Spectroscopy
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The Eckart-Sayvetz conditions are crucial for defining molecular vibrational and rotational motions.
• Standard methods for transforming molecular coordinates between states or isotopologues can be complex.

Purpose of the Study:

• To demonstrate a method for constructing vibrational displacements that satisfy the Eckart-Sayvetz conditions.
• To explore the implications of this construction for molecular coordinate transformations and Hamiltonian derivations.

Main Methods:

• Projection of unconstrained displacements to satisfy Eckart-Sayvetz conditions.
• Linear transformation of normal coordinates between different molecular states or isotopologues.
• Derivation of the rotational-vibrational Hamiltonian using curvilinear internal coordinates.

Main Results:

• A method to construct Eckart-Sayvetz satisfying displacements from unconstrained ones.
• Normal coordinates transform linearly and non-orthogonally between electronic states or isotopologues.
• Enhanced separation of rotational and vibrational motions is achievable.
• A simplified derivation of the rotational-vibrational Hamiltonian is presented.

Conclusions:

• The projection method offers a robust way to handle molecular vibrations under Eckart-Sayvetz conditions.
• This approach provides new insights into axis switching and coordinate transformations.
• It facilitates a more effective separation of rotational and vibrational dynamics.
• The method simplifies the derivation of the molecular Hamiltonian, particularly in curvilinear coordinates.