Infrared-induced coherent vibration of a hydrogen-bonded system: Effects of mechanical and electrical anharmonic couplings

Journal of Chemical Physics

Volumn 131, Issue 4, 2009, Pages

  Ishii, Kunihiko ^a   Takeuchi, Satoshi ^a   Tahara, Tahei ^a  

^a RIKEN   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ABSORPTION INTENSITY; ANHARMONIC COUPLINGS; ANHARMONICITIES; BONDED MOLECULE; COHERENT VIBRATIONS; COMBINATION BANDS; HYDROGEN BONDED SYSTEMS; HYDROGEN-BOND; LOW FREQUENCY; LOW-FREQUENCY MODES; MECHANICAL ANHARMONICITY; PROBE SPECTROSCOPY; QUINIZARIN; STRETCHING MODES; TIME RESOLUTION; TRANSITION MOMENTS; VIBRATIONAL ANALYSIS; VIBRATIONAL COHERENCES;

DENSITY FUNCTIONAL THEORY; HYDROGEN; PROBABILITY DENSITY FUNCTION;

VIBRATIONS (MECHANICAL);

1,4-DIHYDROXYANTHRAQUINONE; ANTHRAQUINONE DERIVATIVE; QUINIZARIN;

ARTICLE; CHEMICAL STRUCTURE; CHEMISTRY; HYDROGEN BOND; INFRARED RADIATION; INFRARED SPECTROPHOTOMETRY; QUANTUM THEORY; VIBRATION;

ANTHRAQUINONES; HYDROGEN BONDING; INFRARED RAYS; MOLECULAR STRUCTURE; QUANTUM THEORY; SPECTROPHOTOMETRY, INFRARED; VIBRATION;

EID: 68249113077     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3181777     Document Type: Article

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40. The displacement of the potential between vOH =0 and vOH =1 levels is readily explained as follows. Taking account of the mechanical anharmonic coupling shown in Eq., the two-dimensional vibrational Hamiltonian is represented as H= Tlow + (1/2) klow Q low 2 + TOH + (1/2) k OH 0 Q OH 2 + (1/2) ( kOH / Qlow) Qlow Q OH 2 = Tlow + (1/2) klow Q low 2 + TOH + (1/2) kOH [Qlow] Q OH 2. Thus, the force constant kOH becomes Qlow -dependent (kOH [Qlow] = k OH 0 + kOH / Qlow × Qlow) if the kOH / Qlow factor is nonzero. Because the vibration of the OH-stretching mode is much faster than the low-frequency mode, we can take the partial average of H with respect to only QOH, 〈 vOH H vOH 〉 = Tlow + (1/2) klow Q low 2 + (vOH + (1/2)) kOH [Qlow] = Tlow + (1/2) klow Q low 2 + (vOH + (1/2)) (k OH 0 + ( kOH / Qlow) Qlow). Here, vOH is the quantum number of the OH-stretching vibration. Note that k=h in the current coordinate system [Eq.]. The remaining part of H contains only Qlow. Then, the Hamiltonian of Qlow for vOH =0 and vOH =1 levels can be obtained as Hv (OH) =0 [Qlow] = Tlow + (1/2) klow Q low 2 + (1/2) (k OH 0 + ( kOH / Qlow) Qlow) = Tlow + (1/2) klow (Qlow + (1/2 klow) ( kOH / Qlow)) 2 + (1/2) k OH 0-(1/8 klow) ( kOH / Qlow) 2, Hv (OH) =1 [Qlow] = Tlow +(1/2) klow Q low 2 +(3/2) (k OH 0 +( kOH / Qlow) Qlow) = Tlow +(1/2) klow (Qlow + (3/2 klow) ( kOH / Qlow)) 2 +(3/2) k OH 0 -(9/8 klow) ( kOH / Qlow) 2. These expressions clearly show that the potential curves of vOH =1 is displaced from that of vOH =0 by -1/ klow × kOH / Qlow.
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