The influence of electrical and mechanical anharmonicity on the vibrational transition moments of diatomic and polyatomic molecules

Geerlings, Pau̧l; Berckmans, Didier; Figeys, Hubert

doi:10.1016/0022-2860(79)80254-9

Cited by 45 publications

(18 citation statements)

References 40 publications

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“…It can be easily shown that the transition matrix elements for the dipole moment and polarizability operators in terms of anharmonic wave functions are equal to the matrix elements of contact transformed operators with wave functions of the zero order approximation [37][38][39][40][41][42]. Indeed, let and be the zero order and the anharmonic wave functions, respectively, and µ α be the effective dipole moment operator (its projection onto the axis ); the following equality then holds true:…”

Section: Methods Of Calculationmentioning

confidence: 96%

“…Since the density of the anharmonic energy spec trum sharply increases with increasing energy, anhar monic calculations of IR and Raman intensities [37][38][39][40][41][42][43] are very helpful in the interpretation of the spec trum. Because intensities can be significantly redis tributed between close resonantly coupled vibrational states, the harmonic model is insufficient and it is nec essary to take into account explicitly mixing of zero order functions.…”

Section: Methods Of Calculationmentioning

confidence: 99%

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Theoretical interpretation of the vibrational spectrum of bicyclo[1.1.0]butane in terms of an ab initio anharmonic model

et al. 2014

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The anharmonic vibrational IR and Raman spectra of the bicyclo[1.1.0]butane molecule have been calculated in the range of up to 4000 cm -1 using a numerical and analytical realization of the van Vleck second order operator perturbation theory. Cubic and quartic force constants in normal coordinates, as well as cubic surfaces of the dipole moment and polarizability, have been found by numerical differentiation of the corresponding first and second derivatives calculated by the MP2/cc pVTZ quantum mechanical method. In order to increase the prediction accuracy of vibrational transitions, corresponding harmonic frequencies have been obtained by the CCSD(T)/cc pVTZ high precision quantum mechanical method. The anhar monic intensities of the IR and Raman spectra have been calculated using canonical transformations of the operators of the dipole moment and polarizability expanded into a Taylor series around the equilibrium con figuration. The assignment of experimental vibrational bands in the IR and Raman spectra has been analyzed. It has been shown that the anharmonic calculation based on the above described procedure of combining more exact harmonic frequencies with the anharmonic force field obtained with a more economical method makes possible the reliable interpretation of the majority of spectral bands, including Fermi and DarlingDennison resonances.

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Section: Methods Of Calculationmentioning

confidence: 96%

Section: Methods Of Calculationmentioning

confidence: 99%

Theoretical interpretation of the vibrational spectrum of bicyclo[1.1.0]butane in terms of an ab initio anharmonic model

et al. 2014

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“…It is worthwhile noting that these linear combinations of the zero-order basis functions should not be confused with the wave functions of the original Hamiltonian, which can be obtained through a series of inverse canonical transformations of the zero-order ones. 13,70 The matrix representation of the polyad operator is obviously a block-diagonal matrix, so that its blocks, corresponding to a given polyad number P, are simply scalar matrices with the coefficient P on the diagonal. It is evident that the polyad operatorP commutes with the zero-order Hamilto-nianĤ 0 whose wave functions are used as the basis functions for matrix representation of the perturbed anharmonic Hamil-tonian.…”

Section: E Polyad Vector Number Operator and Commutability Of A Rementioning

confidence: 99%

Polyad quantum numbers and multiple resonances in anharmonic vibrational studies of polyatomic molecules

Krasnoshchekov

Stepanov

2013

The Journal of Chemical Physics

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In the theory of anharmonic vibrations of a polyatomic molecule, mixing the zero-order vibrational states due to cubic, quartic and higher-order terms in the potential energy expansion leads to the appearance of more-or-less isolated blocks of states (also called polyads), connected through multiple resonances. Such polyads of states can be characterized by a common secondary integer quantum number. This polyad quantum number is defined as a linear combination of the zero-order vibrational quantum numbers, attributed to normal modes, multiplied by non-negative integer polyad coefficients, which are subject to definition for any particular molecule. According to Kellman's method [J. Chem. Phys. 93, 6630 (1990)], the corresponding formalism can be conveniently described using vector algebra. In the present work, a systematic consideration of polyad quantum numbers is given in the framework of the canonical Van Vleck perturbation theory (CVPT) and its numerical-analytic operator implementation for reducing the Hamiltonian to the quasi-diagonal form, earlier developed by the authors. It is shown that CVPT provides a convenient method for the systematic identification of essential resonances and the definition of a polyad quantum number. The method presented is generally suitable for molecules of significant size and complexity, as illustrated by several examples of molecules up to six atoms. The polyad quantum number technique is very useful for assembling comprehensive basis sets for the matrix representation of the Hamiltonian after removal of all non-resonance terms by CVPT. In addition, the classification of anharmonic energy levels according to their polyad quantum numbers provides an additional means for the interpretation of observed vibrational spectra.

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“…7, the magnitude of m EA becomes 1.0 × 10 −2 D, which is comparable to m MA bend = 5.8 × 10 −3 D. It is generally accepted that for high-frequency intramolecular vibrations, anharmonic coupling is usually dominated by the mechanical anharmonicity. 9,49 In addition, the electrical anharmonicity seems to play a crucial role only in hydrogen-bonded systems 30,50,51 and other types of molecular complexes, 52 in which non-covalent interactions are involved. However, the present DFT calculations suggest that both m MA bend and m EA may contribute equally to the anharmonic coupling between the ν 1 and ν 4 modes.…”

Section: E Mechanical Vs Electrical Anharmonicity: Insight From Dft mentioning

confidence: 99%

Anharmonic coupling of the CH-stretch and CH-bend vibrations of chloroform as studied by near-infrared electroabsorption spectroscopy

Nishida

Shigeto

Yabumoto

et al. 2012

The Journal of Chemical Physics

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Combination bands that involve CH- or OH-stretch vibrations appear in the near-infrared (NIR) region (4000-10 000 cm(-1)). Because they arise from anharmonic coupling between the component fundamentals, detailed analysis of the frequency and intensity of NIR combination bands allows one to elucidate the mechanisms behind the vibrational coupling in the condensed phase in terms of mechanical and electrical anharmonicities. Nevertheless, little has been studied, in particular experimentally, on the origin of the combination band intensity. Here, we show that NIR electroabsorption (EA) spectroscopy, which directly probes the effects of an externally applied electric field on a combination band, can shed new light on anharmonic vibrational coupling through determination of the direction of the transition moment for the combination band. We studied the combination band of the CH-stretch (ν(1)) and CH-bend (ν(4)) modes of liquid chloroform. The electric-field induced absorbance change of the ν(1) + ν(4) combination band caused by reorientation of the chloroform molecule was measured at various χ angles, where χ is the angle between the direction of the applied electric field and the polarization of the incident IR light. We were able to detect an absorbance change as small as 5 × 10(-8) for the combination band. Using the NIR EA spectra of the combination band together with those of the CH-stretch and bend fundamentals, the angle between the transition moment for the combination band and the permanent dipole moment was determined experimentally for the first time to be (79 ± 14)°. The present investigation indicates that the contribution of the CH-stretch mode to the mechanical anharmonicity is minor and that the CH-bend mode plays a dominant role in the mechanical part of the vibrational coupling between the two fundamentals. Furthermore, density functional theory calculations show that both the mechanical anharmonicity of the CH-bend mode and the electrical anharmonicity may contribute equally to the anharmonic coupling.

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The influence of electrical and mechanical anharmonicity on the vibrational transition moments of diatomic and polyatomic molecules

Cited by 45 publications

References 40 publications

Theoretical interpretation of the vibrational spectrum of bicyclo[1.1.0]butane in terms of an ab initio anharmonic model

Theoretical interpretation of the vibrational spectrum of bicyclo[1.1.0]butane in terms of an ab initio anharmonic model

Polyad quantum numbers and multiple resonances in anharmonic vibrational studies of polyatomic molecules

Anharmonic coupling of the CH-stretch and CH-bend vibrations of chloroform as studied by near-infrared electroabsorption spectroscopy

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