Computation of Harmonic and Anharmonic Vibrational Spectra

BO approximation + motion separation: - purely vibrational Hamiltonian

The Harmonic Approximation !

The Harmonic Approximation

The Harmonic Approximation mass weighted coordinates

The Harmonic Approximation mass weighted coordinates normal mode coordinates

The Harmonic Approximation

The Harmonic Approximation mass weighted coordinates normal mode coordinates

Spectral intensities

Spectral intensities

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

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

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

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

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) 3632.502 3471.790 0.48654719 0.58330320 2(1) 3237.247 3097.389 0.55008107 0.56423762 Overtones --------- Mode(n) E(harm) E(anharm) RA(anharm) 1(2) 7265.003 6795.777 0.00042922 2(2) 6474.493 6201.735 0.00030375 Combination Bands Mode(n) Mode(n) E(harm) E(anharm) RA(anharm) 2(1) 1(1) 6869.748 6579.779 0.00001961 3(1) 1(1) 6845.714 6561.405 0.00002336 S4.doc, gahtables …

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

S4 program higher order terms can be added

Difficult implementation of intensities …..

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