Computation of Harmonic and Anharmonic Vibrational Spectra

Prezentace na téma: "Computation of Harmonic and Anharmonic Vibrational Spectra"— Transkript prezentace:

1 Computation of Harmonic and Anharmonic Vibrational Spectra

2 BO approximation + motion separation:
- purely vibrational Hamiltonian

3 The Harmonic Approximation
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4 The Harmonic Approximation

5 The Harmonic Approximation
mass weighted coordinates

6 The Harmonic Approximation
mass weighted coordinates normal mode coordinates

7 The Harmonic Approximation

8 The Harmonic Approximation
mass weighted coordinates normal mode coordinates

9 Spectral intensities

10 Spectral intensities

11 … “double-harmonic” approximation
Spectral intensities X X … “double-harmonic” approximation

12 The Harmonic Approximation
formally works for any molecule exact solution of the vibrational part of Schrödinger equation Gaussian: FREQ (VCD, Raman, ROA) flexible motions (CH3 rot) unusable bond stretching – large error combination modes, overtones – not appropriate

13 Typical spectrum overtones combinations Harmonic “anharmonic”
CH, NH anharmonic - low

14 G16: AH Raman, ROA Freq=(ROA, Anharm)

15 S4.doc, gahtables … ## MEASUREMENT INFORMATION: SCP(90)z ##
Units: Transition energies (E) in cm^-1 Raman activity (RA) in Ang^6 Fundamental Bands Mode(n) E(harm) E(anharm) RA(harm) RA(anharm) 1(1) 2(1) Overtones Mode(n) E(harm) E(anharm) RA(anharm) 1(2) 2(2) Combination Bands Mode(n) Mode(n) E(harm) E(anharm) RA(anharm) 2(1) (1) 3(1) (1) S4.doc, gahtables …

16

17

18 S4 program PT2 as in Gaussian VCI
VCI is more numerically stable than PT2, but diagonalization of a huge matrix (~106 x 106) needed

19 S4 program higher order terms can be added

20 Difficult implementation of intensities
…..

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