1. 1 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 Mario E. Fajardo AFRL/MNME, Energetic Materials Branch, Ordnance Division, U.S. Air Force Research Laboratory, 2306 Perimeter Road, Eglin AFB, FL 32542-5910. mario.fajardo@eglin.af.mil * Data reduction: model-independent approach *Rotation-Translation Coupling (RTC) Theory *Pseudorotating Cage (PC) Model *"Center-Of-Interaction" (C.I.) for CO in pH 2 * Comparison between theory and experiment *Summary Anomalous Rotation-Translation Coupling Effects in CO Isotopomers Trapped in Solid Parahydrogen

2. 2 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 Data reduction approach Use spectroscopic assignments from CFT analysis, but abandon parameters extracted from fits. Eliminate M J dependent splittings: P(1) avg = [P(1) || + 2P(1)  ] / 3 R(0) avg = [R(0) || + 2R(0)  ] / 3 Limit analysis to J = 0, 1 states; define: B eff (pH 2 )  [R(0) avg - P(1) avg ] / 4 For gas phase 12 C 16 O: [R(0)-P(1)] / 4 = 1.9137 cm -1 (B v=0 +B v=1 ) / 2 = 1.9138 cm -1  B avg = B e +  e

3. 3 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 B eff (pH 2 ) / B avg (gas) vs.  M Rough linear correlation between matrix effect and mass asymmetry in CO molecule:  M = M O - M C ; r 2 = 0.964 for fcc, 0.966 for hcp. Correlation suggested by G. Scoles, private communication (2000). Physical interpretation?

4. 4 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 Rotation-Translation Coupling Physical assumptions: (1) Molecular "center-of-interaction" (C.I.) occupies trapping site center at equilibrium. (2) Molecular center-of-mass (C.M.) moves relative to trapping site center during rotation  another angular momentum to consider:  I 1 = Ma 2 where: M is the molecular mass, and a is the separation between C.M. and C.I. For free rotation about C.I. in a rigid cage: B eff / B = I / (I +  I 1 ) = I / (I + Ma 2 )  1 - Ma 2 /I + O (a 4 ) Isotopic substitution moves molecular C.M.; expect quadratic relation between B eff /B & a. H. Friedmann and S. Kimel, J. Chem. Phys. 43, 3925 (1965). M.T. Bowers, G.I. Kerley, and W.H. Flygare, J. Chem. Phys. 45, 3399 (1966).

5. 5 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 Pseudorotating Cage model J. Manz, J. Am. Chem. Soc. 102, 1801 (1980). T. Momose, H. Hoshina, M. Fushitani, and H. Katsuki, Vib. Spec. 34, 95 (2004). Physical assumptions: (1) Molecular rotation is coupled to synchronous pseudorotation of matrix cage atoms. Second contribution to effective molecular moment of inertia:  I 2  2  i m i  r i 2 Propose without proof: the matrix cage atom displacements,  r, depend linearly on the C.M. to C.I. separation, a. Then:  I 2  (a + k) 2, and again expect nonlinear relation between B eff /B & a.

6. 6 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 C.M. position in CO isotopomers Isotopic substitution in CO permits systematic variation of position of molecular C.M., and thus of a. Vibrational averages: I v = h / (8  2 c B v ) =  R v 2 R v = [h / (8  2 c B v  )] 1/2 isotopomerB avg (cm -1 ) R avg (Å) |C - C.M.| (Å) 12 C 16 O1.93131.13710.6497 13 C 16 O1.84621.13700.6271 12 C 18 O1.83911.13700.6822 13 C 18 O1.75401.13680.6600

7. 7 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 B eff (pH 2 ) / B avg (gas) vs. C.M. Excellent linear correlation between matrix effect and location of C.M. (plotted relative to C atom); r 2 = 0.9963 for fcc, 0.9959 for hcp. But, Rotation-Translation Coupling and Pseudorotating Cage models predict curvature in B eff /B vs. a !?! Physical significance of linear correlations?

8. 8 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 "Experimental" C.I. for CO/pH 2 Extrapolation of linear correlations back to B eff /B avg = 1 (i.e. vanishing matrix effect on rotations) yields "experimentally determined" C.I. located 0.402 Å from C atom, or 0.248 Å from C.M. of 12 C 16 O. {Co-locating C.M. and C.I. ( a = 0) would require M C = 1.828 M O ; thus, not physically realizable. Closest would be 22 C 13 O, but t 1/2 ( 22 C)  t 1/2 ( 13 O)  9 ms making a matrix isolation experiment "very challenging."}

9. 9 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 12 C 16 O - pH 2 ab-inito potential S. Moroni, M. Botti, S. DePalo, and A.R.W. McKellar, J. Chem. Phys. 122, 094314 (2005). P. Jankowski and K. Szalwicz, J. Chem. Phys. 108, 3554 (1998). pH 2 C.M. position relative to 12 C 16 O C.M. (Å) COCO

10. 10 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 "Theoretical" C.I. for CO/pH 2 P. Jankowski and K. Szalwicz, J. Chem. Phys. 108, 3554 (1998). P. Jankowski, potH2CO_V04.f, private communication (2004). * Linear pH 2 -CO-pH 2 construct. * Fix pH 2 -pH 2 separation, move CO to minimize energy. * C.I.  midpoint of pH 2 -pH 2 line. + C.I. = -0.24 Å @ R nn = 3.8 Å + C.I. = -0.27 Å @ R nn = 4.1 Å

11. 11 60th International Symposium on Molecular Spectroscopy, Talk RG04, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-171 Summary * Observed excellent (r 2 =0.996) linear correlation between B eff /B and location of C.M. in isotopically manipulated CO molecules trapped in solid pH 2. * Leading candidate theories (RTC & PC) predict non-linear correlations; more work needed here. * Extrapolation of linear fits to B eff /B vs. a data yield "experimentally determined" C.I. location 0.248 Å closer to C atom than C.M. * Theoretical estimate from ab-initio CO-pH 2 potential places C.I. 0.24-0.27 Å closer to C atom than C.M.