Subject: Clarification on Phase Consistency and Directionality of TDM in Different Coordinate Systems

Dear Theoretical Chemists,

I am currently exploring transition dipole moment (TDM) calculations for identical molecules positioned in different coordinate systems using quantum chemistry software (Orca, Gaussian). In these computations, I've observed that TDMs sometimes emerge with opposite signs despite representing the same physical transition in identically structured molecules. My hypothesis attributes this phenomenon to differences in phase conventions used by different computational methods, which is evident from the orbital visualizations.

This phase variation seems to alter the sign of the TDM vector calculated, potentially leading to misinterpretation of the directionality which should physically be from the 'hole' to the 'particle' as indicated by the transition density difference. The output from Orca and Gaussian suggests a fixed sign for the TDM vector that might not consistently align with the physical direction from electron depletion to electron accumulation regions. I ma using TDA-DFT, b3lyp/def2tzvp Orca/Gaussian.

Given this context, I seek clarification on the following:

Your insights into these questions would be invaluable in helping to standardize and interpret TDM calculations accurately across different computational frameworks.

Thank you for your time and expertise.

Best regards,

Alexander, Technion