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Molecular Modeling: Molecular Vibrations

Molecular Modeling: Molecular Vibrations. C372 Introduction to Cheminformatics II Kelsey Forsythe. Next Time . Modeling Nuclear Motion (Vibrations) Harmonic Oscillator Hamiltonian. Modeling Potential energy (1-D). 0. 0 at minimum. Modeling Potential energy (1-D).

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Molecular Modeling: Molecular Vibrations

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  1. Molecular Modeling:Molecular Vibrations C372 Introduction to Cheminformatics II Kelsey Forsythe

  2. Next Time

  3. Modeling Nuclear Motion (Vibrations)Harmonic Oscillator Hamiltonian

  4. Modeling Potential energy (1-D)

  5. 0 0 at minimum Modeling Potential energy (1-D)

  6. Assumptions:Harmonic Approximation Determining k?

  7. Assumptions:Harmonic Approximation E(.65)=3.22E-20J E(.83)=2.13E-20J Dx=.091

  8. Assumptions:Harmonic Approximation

  9. Assumptions:Harmonic Approximation

  10. Modeling Potential energy (N-D)

  11. 0 0 at minimum Modeling Potential energy (N-D) Coordinate Coupling Spoils!!!

  12. CoordinatesDegrees of Freedom? • For N points in space • 3*N degrees of freedom exist • Cartesian to Center of Mass system • All points related by center/centroid of mass • COM ia origin

  13. CoordinatesCenter of Mass System • 3*N degrees of freedom exist DOF = itranslation + jrotation + kvibration • Linear: • 3N=3 + 2 + k, k=3N-5 • Non-linear • 3N=3+3+k, k=3N-6

  14. CoordinatesDegrees of Freedom? • Hydrogen Molecule • Cartesianr1=x1,y1,z1r2=x2,y2,z2 • COM-translational degrees of freedomx=(m1x1+m2x2)/MTy=(m1y1+m2y2)/MTz=(m1z1+m2z2)/MT • COM-rotational degrees of freedomr,q - required • 3(2)-5 = 1 (stretch of hydrogen molecule)

  15. Normal Modes • Decouples motion into orthogonal coordinates • All motions can be represented in terms of combinations of these coordinates or modes of motion • These normal modes are typically/naturally those of bond stretching and angle bending

  16. Normal Modes • Problem

  17. Normal Modes • Solutionr  q

  18. Normal Modes • Solutionr  q Eigenvalue Problem

  19. Normal Modes • Solutionr  q Eigenvalue Problem Normal modes

  20. Normal ModesHydrogen • N=#atoms=2 • # normal modes = ? • Linear • 3N-5=1

  21. Normal ModesAcetylene • N=#atoms=4 • # normal modes = ? • Linear • 3N-5=7

  22. QM Harmonic oscillator Modeling • Need to solve Schrodinger Equation for harmonic oscillator

  23. QM Harmonic oscillator Modeling • Solutions are Hermite Polynomicals

  24. QM Harmonic oscillator Modeling • Energies • NON-CLASSICAL EFFECTS • Quantization • Emin NOT zero

  25. QM Harmonic oscillator ERRORS • Molecular Mechanics • Error a parameterization • Semi-Empirical • SAM1>PM3>AM1 • HF • Frequencies too high • Harmonic approximation • No electron correlation • Correction • Multiply .9wout • DFT - typically better than semi-empirical and HF

  26. IR-SpectraDiatomic Molecule

  27. ApplicationBioMolecules

  28. Application-Thermodynamics/Statistical Mechanics • Equipartition Theorem • Heat capacities • Enthalpy, Entropy and Free Energy

  29. Anharmonic Effects? • Must calculate higher order derivatives • More computational time required

  30. Summary

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