Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 The Ground State Four Dimensional Morphed Potentials of HBr and HI Dimers Collaborator: J. W.

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Presentation transcript:

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 The Ground State Four Dimensional Morphed Potentials of HBr and HI Dimers Collaborator: J. W. Bevan, TAMU Funding: National Science Foundation Robert R. Lucchese Department of Chemistry Texas A&M University

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Morphing of Intermolecular Potentials Compute a full potential energy surface (PES) using a quantum chemistry model Morph potential to obtain best possible agreement with experiment

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Morphing Functions

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Interpolation of PES The V ab initio must be interpolated onto a fine grid Interpolation is done using reproducing kernel Hilbert space (RKHS) fitting functions of Ho and Rabitz Interpolate the transformed function for correct behavior at large and small R

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Regularized Non-Linear Least Squares Function to be minimized The C 0 ,i correspond to no morphing The regularization parameter  reduces the linear dependence among the parameters C ,i One obtains the best fit of the experiment that is also as close as possible to the original ab initio potential

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Regularized Non-Linear Least Squares The quality of the fit is characterized by the root- mean-square deviation from the experiment  (∞) gives the quality of the ab initio potential  (0) gives the quality of an unconstrained fit

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Types of Experimental Data Used in Morphing Rotation constants ( B 0 ), value of R 0 Distortion constants ( D J ), curvature in R direction, curvature in  direction D , coupling between R and  directions Intermolecular bending and stretching vibrational transition frequencies D and H isotopes Second virial coefficients, well depth

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 (HX) 2 Interaction Potential Two identical isomers Tunneling splitting is very sensitive to the shape of the barrier Potential is a function of four intermolecular coordinates

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Data Used in (HBr) 2 Fit, (v 5, K) ObservableIsotopomerFitExp. kk B(0,0) cm -1 H 79 Br:H 81 Br a B(1,0) cm -1 H 79 Br:H 81 Br a B(0,0) cm -1 H 79 Br:D 81 Br b B(0,1) cm -1 H 79 Br:H 81 Br c B(0,2) cm -1 H 79 Br:H 81 Br c B(1,1) cm -1 H 79 Br:H 81 Br c D(0,0) cm -1 H 79 Br:H 81 Br a 0.01 D(1,0)10 -8 cm -1 H 79 Br:H 81 Br a 0.01 D(0,0) cm -1 H 79 Br:D 81 Br b 0.01

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 More Data Used in (HBr) 2 Fit, (v 5, K) Observable Isotopomer FitExp. kk P 2 (cos  ) (H 79 Br)(0,0) H 79 Br:H 81 Br P 2 (cos  ) (H 81 Br)(0,0) H 79 Br:H 81 Br P 2 (cos  ) (H 79 Br)(1,0) H 79 Br:H 81 Br P 2 (cos  ) (H 81 Br)(1,0) H 79 Br:H 81 Br P 2 (cos  ) (H 79 Br)(0,0) H 79 Br:D 81 Br P 2 (cos  ) (D 81 Br)(0,0) H 79 Br:D 81 Br cm -1 H 79 Br:H 81 Br A( 5 =0) cm -1 H 79 Br:H 81 Br

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Still More Data Used in (HBr) 2 Fit, (v 5, K) ObservableIsotopomerFitExp. kk B(T=231.9 K) m 3 mol -1 H 79 Br:H 79 Br B(T=333.4 K) m 3 mol -1 H 79 Br:H 79 Br B(T=444.5 K) m 3 mol -1 H 79 Br:H 79 Br G2.73

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Morphed (HBr) 2 PES,  2 vs  1 Low barrier between the two equivalent structures

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Morphed (HBr) 2 PES, R vs  Near the equilibrium structure

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Morphed (HBr) 2 PES, R vs  At the top of the barrier

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 (HBr) 2 Wave Functions  E = cm –1

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Features of the Morphed (HBr) 2 PES

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 (HBr) 2 Potential Ab initio potential computed using a large TZV(3d,3f) basis set with MP2 and BSSE The use of the log( V ) interpolation with RKHS fitting functions is dramatically better that a direct fit of V.  (  )/  (10)~15.4, with 7 fitting parameters and 20 experimental observations.

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Data Used in (HI) 2 Fit,  = 2.91 ModelExp.Uncer. B(v 4 =0,v 5 =0,K=0) cm B(v 4 =1,v 5 =0,K=0) cm B(v 4 =0,v 5 =1,K=0) cm B(v 4 =0,v 5 =0,K=1) cm D(v 4 =0,v 5 =0,K=0) cm D(v 4 =1,v 5 =0,K=0) cm D(v 4 =0,v 5 =1,K=0) cm D(v 4 =0,v 5 =1,K=1) cm (B-C) (v 4 =0,v 5 =1,K=1) cm P 2 (cos  ) (v 4 =0,v 5 =0,K=0) P 2 (cos  ) (v 4 =0,v 5 =1,K=0) E(v 4 =1,v 5 =0,K=0)-E (v 4 =0,v 5 =0,K=1) cm E(v 4 =0,v 5 =1,K=0)-E (v 4 =0,v 5 =0,K=0) cm

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Morphed (HI) 2 PES,  2 vs  1

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 (HI) 2 Wave Functions  E = cm –1

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 (HI) 2 Potential Ab initio potential computed using a aug-cc-pvtz basis set with CCSD(T) and BSSE and an ECP for I.  = 2.91, with 6 fitting parameters and 13 experimental observations. The state seems to be very weakly tunneling in the geared motion, with a significant probability at the symmetric geometry. Further refinements of the potential are in progress.

Int. Symp. Molecular Spectroscopy Ohio State Univ., 2005 Conclusions Potential morphing can lead to accurate representations in the regions of the potential which have been experimentally interrogated. Morphed potentials have estimated errors that increase only slowly away from the experimental region. Morphed potentials have yielded accurate predictions of unmeasured spectroscopic constants. Goal is to develop general morphing parameters that can be used to adjust a given level of ab initio theory for accurate predictions of intermolecular interactions.