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Calculating splittings between energy levels of different symmetry using path-integral methods
Edit Mátyus1, Stuart C Althorpe1
1Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
The Journal of Chemical Physics
|March 24, 2016
Summary
Path-integral methods can now calculate energy splitting patterns for multiple low-lying energy levels, not just the ground and first excited states. This generalized approach aids in computing molecular and cluster energy levels and tunnelling splittings.
Area of Science:
- Quantum mechanics
- Computational chemistry
- Spectroscopy
Background:
- Path-integral methods are established for calculating the energy difference between the ground and first excited states.
- Generalizing these methods can provide deeper insights into molecular energy landscapes.
Purpose of the Study:
- To generalize path-integral methods for calculating energy splitting patterns beyond the ground and first excited states.
- To explore the applicability of these generalized methods for various symmetry blocks.
Main Methods:
- Utilizing path-integral formulations.
- Developing generalized approaches to compute energy level splittings.
- Numerical demonstrations on two-dimensional models.
Main Results:
- The path-integral approach is successfully generalized to determine splitting patterns among multiple low-lying energy levels.
- Demonstrated the method's capability across different symmetry blocks below the first-excited totally symmetric state.
- Numerical validation on two-dimensional models confirmed the generalized method's accuracy.
Conclusions:
- The generalized path-integral method offers a powerful tool for calculating complex energy splitting patterns.
- This approach is highly promising for computing rovibrational energy levels and tunnelling splittings in floppy molecules and gas-phase clusters.
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