Molecular eigensolution symmetry analysis and fine structure

International Journal of Molecular Sciences

Volumn 14, Issue 1, 2013, Pages 714-806

  Harter, William G ^a   Mitchell, Justin C ^b  

^a UNIVERSITY OF ARKANSAS   (United States)

^b INTEL CORPORATION   (United States)

Author keywords

Level clusters; Molecular dynamics; Symmetry; Tunneling

Indexed keywords

CALCULATION; CLUSTER ANALYSIS; EIGENSOLUTION SYMMETRY ANALYSIS; FOURIER TRANSFORMATION; GEOMETRY; MATHEMATICAL COMPUTING; MOLECULAR PHYSICS; PROBABILITY; QUANTUM THEORY; REVIEW; STATISTICAL ANALYSIS; STATISTICAL MODEL; STRUCTURE ANALYSIS; VARIANCE; ALGORITHM; CHEMICAL MODEL; CHEMICAL STRUCTURE; COMPUTER SIMULATION; KINETICS;

ALGORITHMS; COMPUTER SIMULATION; KINETICS; MODELS, CHEMICAL; MODELS, MOLECULAR; QUANTUM THEORY;

EID: 84872174249     PISSN: 16616596     EISSN: 14220067     Source Type: Journal    
DOI: 10.3390/ijms14010714     Document Type: Review

References (41)

1. Boudon, V.; Champion, J.; Gabard, T.; Loete, M.; Rotger, M.; Wenger, C. Spherical top theory and molecular spectra. Wiley Handb. High Resolut. Spectrosc. 2011, 1, 301.
2. 4. Mol. Phys. 2012, 58, 391-400.
3. Bowman, J.M. Beyond born-oppenheimer. Science 2008, 319, 40-41.
4. +2 photoelectron imaging. Science 2008, 319, 72-75.
5. Tsukerblat, B.; Palii, A.; Clemente-Juan, J.M.; Gaita-Arino, A.; Coronado, E. A symmetry adapted approach to the dynamic jahn-teller problem: Application to mixed-valence polyoxometalate clusters with keggin structure. Int. J. Quantum Chem. 2012, 112, 2957-2964.
6. Schnalle, R.; Schnack, J. Calculating the energy spectra of magnetic molecules: Application of real and spin-space symmetries. Int. Rev. Phys. Chem. 2010, 29, 403-452.
7. Harel, E.; Engel, G. Quantum coherence spectroscopy reveals complex dynamics in bacterial light harvesting complex 2 (LH2). Proc. Nat. Acad. Sci. 2012, 109, 706-711.
8. Harter, W.G. Theory of hyperfine and superfine levels in symmetric polyatomic molecules. II. Elementary cases in octahedral hexaflouride molecules. Phys. Rev. A 1981, 24, 192-263.
9. 3. Phys. Chem. Chem. Phys. 2005, 7, 573-582.
10. 2 molecules (X = Bi, P, and Sb). J. Mol. Spectrosc. 2009, 256, 119-127.
11. 4. Eur. Phys. J. D 2001, 17, 13.
12. Crogman, H.T.; Boudon, V.; Sadovskii, D.A. Local modes of silane within the framework of stretching vibrational polyads. Eur. Phys. J. D 2007, 42, 61-72.
13. 6 based on the classical interpretation of the effective rotation-vibration hamiltonian. J. Mol. Spectrosc. 2000, 201, 95-108.
14. Harter, W.G.; Patterson, C.W. Asymptotic eigensolutions of fourth and sixth rank octahedral tensor operators. J. Math. Phys. 1979, 20, 1453-1459.
15. Harter, W.G.; Weeks, D.E. Rotation-vibration spectra of icosahedral molecules. I. Icosahedral symmetry analysis and fine structure. J. Chem. Phys. 1988, 90, 4727.
16. Harter, W.G.; Weeks, D.E. Rovibrational spectral fine structure of icosahedral molecules. Chem. Phys. Lett. 1986, 132, 387.
17. Ortigoso, J.; Hougen, J.T. Rotational energy surfaces of molecules exhibiting internal rotation. J. Chem. Phys. 1994, 101, 2710-2719.
18. Crogman, H.T.; Boudon, V.; Harter, W.G.; Mitchell, J. Deformation of sulfer hexaflouride and floppiness of triflouromethyl sulfer pentaflouride. Mol. Phys. 2006, 104, 2781-2790.
19. Harter, W.G. Reply to comment on RES and high-J eigenvalue structure of polyatomic molecules. J. Chem. Phys. 1986, 84, 5218-5219.
20. Lea, K.R.; Leask, M.J.M.; Wolf, W.P. Crystal field splitting and level degeneracy. J. Chem. Phys. Solids 1962, 23, 1381-1386.
21. d molecules. J. Mol. Spectrosc. 1972, 42, 135-148.
22. 6 rotational spectra. I. Qualitative features of high J levels. J. Chem. Phys. 1977, 66, 4872.
23. 6. Phys. Rev. Lett. 1977, 8, 1-4.
24. 4 molecules: Part I. Theory of spherical top molecules. J. Mol. Spectrosc. 1961, 5, 355-389.
25. Harter, W.G. Computer graphical and semiclassical approaches to molecular rotations and vibrations. Comput. Phys. Rep. 1988, 8, 319-394.
26. Gulacsi, M.; Gulasci, Z.; Tosa, V. The eigenvalue spectra of octahedral invariant tensor operator combinations up to eighth rank. J. Mol. Spectrosc. 1986, 118, 424-433.
27. Heine, V. Group Theory in Quantum Mechanics; Number 9 in International Series of Monographs in Pure and Applied Mathematics, The MacMilliam Company: New York, NY, USA, 1960.
28. Kroto, H.W. Molecular Rotation Spectra; Dover Publications, Inc: New York, NY, USA, 1992.
29. Papousek, D.; Aliev, M. Molecular Vibrational-Rotational Spectra; Number 17 in Studies in Physical and Theoretical Chemistry, Elsevier Scientific Publishing Company: Amsterdam, The Netherlands, 1982.
30. Bright, E.; Wilson, J.; Decius, J.C.; Cross, P.C. Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra; McGraw-Hill Book Company: New York, NY, USA, 1955.
31. Bunker, P.R.; Jensen, P. Molecular Symmetry and Spectroscopy, 2nd ed.; NRC Research Press: Ottawa, Canada, 1998.
32. Harter, W.G. Principles of Symmetry, Dynamics, and Spectroscopy;Wiley Interscience: New York, NY, USA, 1993.
33. Frost, A.A.; Musulin, B. A mnemonic device for molecular orbital energies. J. Chem. Phys. 1953, 21, 572-573.
34. Bright, E.;Wilson, J. Symmetry considerations concerning the splitting of vibration-rotation levels in polyatomic molecules. J. Chem. Phys. 1935, 3, 818.
35. + 3. J. Mol. Spectrosc. 1987, 123, 197-227.
36. Hougen, J.T. The Calculation of Rotational Energy Levels Using Tunneling Hamiltonians. In Proceedings of the International Symposium on Molecular Spectroscopy, Ohio State University, Columbus, OH, USA, 2009; Volume 64.
37. 6. J. Mol. Spectrosc. 1979, 76, 322-340.
38. ν2) vibration rotation spectrum of spherical top molecules. J. Chem. Phys. 1978, 69, 4888.
39. ν3) rovibrational bands in spherical top molecules. J. Chem. Phys. 1978, 69, 4896.
40. 3 type combination bands of tetrahedral molecules. J. Mol. Spectrosc. 1979, 77, 457-473.
41. Harter, W.G. Molecular Symmetry. In Handbook of Atomic, Molecular and Optical Physics; Drake, G., Walther, H., Eds.; Springer: Berlin/Heidelberg, Germany, 2006; Chapter 32, p. 501.