Using an internal coordinate Gaussian basis and a space-fixed Cartesian coordinate kinetic energy operator to compute...

Area of Science:

• Quantum Chemistry
• Molecular Spectroscopy
• Computational Chemistry

Background:

• Calculating molecular vibrational energy levels is crucial for understanding chemical reactions and molecular properties.
• Traditional methods often require complex derivation and numerical computation of the kinetic energy operator (KEO).

Purpose of the Study:

• To develop a method for computing vibrational energy levels without deriving or numerically computing KEO coefficients.
• To demonstrate the feasibility of solving the six-dimensional vibrational Schrödinger equation using a Gaussian basis set.

Main Methods:

• Utilizing a space-fixed KEO with numerically computed matrix elements.
• Employing basis functions dependent on curvilinear internal coordinates.
• Using a Gaussian basis set and bond coordinates for formaldehyde calculations.

Main Results:

• Achieved a mean absolute error of less than 1 cm^-1 for the zero-point energy and lowest 50 vibrational transitions of H₂CO.
• Demonstrated the first successful application of a Gaussian basis set to solve a six-dimensional vibrational Schrödinger equation.
• Attained high accuracy (most errors < 0.4 cm^-1) with a large number of collocation points and basis functions.

Conclusions:

• The proposed method enables accurate computation of vibrational energy levels without explicit KEO derivation.
• This approach offers a more efficient and accurate route to solving the vibrational Schrödinger equation for polyatomic molecules.
• The findings pave the way for more precise spectroscopic predictions and molecular dynamics simulations.