Three-Dimensional Rotational Averaging Using Irreducible Sets of Linearly Independent Fundamental Isotropic Cartesian...

Area of Science:

• Theoretical Chemistry
• Computational Chemistry
• Molecular Spectroscopy

Background:

• Molecular spectroscopy relies on rotational averaging of Cartesian tensors for theoretical formulation.
• This averaging process is essential for deriving rotationally invariant observables in spectroscopic studies.
• Current methods may lack efficiency for higher-rank tensors used in advanced spectroscopies.

Purpose of the Study:

• To present a mathematical and computational procedure for calculating rotational averages of Cartesian tensors of any rank (n).
• To introduce a novel heuristic computational method for identifying linearly independent Fundamental Isotropic Cartesian Tensors (FICTs).
• To demonstrate the applicability and extensibility of the proposed method for diverse molecular spectroscopy techniques.

Main Methods:

• Utilized Fundamental Isotropic Cartesian Tensors (FICTs) as the basis for tensor rotational averaging.
• Developed and implemented a heuristic computational algorithm to generate linearly independent FICTs.
• Tested the procedure for tensor ranks 2 to 12, covering a wide range of spectroscopic applications.

Main Results:

• Successfully computed rotational averages for Cartesian tensors up to rank 12 using the FICT-based method.
• The proposed heuristic method efficiently identifies the necessary sets of linearly independent FICTs.
• The computational procedure was shown to be extendable for tensor ranks greater than 12.

Conclusions:

• The developed computational procedure offers an efficient and general approach to rotational averaging of Cartesian tensors.
• This method simplifies the theoretical treatment of both linear and nonlinear molecular spectroscopies.
• The findings provide a valuable tool for researchers in computational and theoretical molecular spectroscopy.