Normal Mode Displacements Research Articles

Generalized harmonic mode scrambling

A scheme is proposed for decomposing a normal mode of a derivative molecule in terms of the normal modes of parent molecules. In the case of light and heavy isotopically labelled molecules it reduces to the harmonic mode scrambling in the usual sense. The scheme is quite general and provides a quantitative description of the normal mode displacements of one group of atoms in terms of those of another group. It is suitable for the normal mode analysis of a molecule calculated by semi-empirical or ab initio programs which perform vibrational analysis in Cartesian coordinates only.

Femtosecond photodissociation dynamics of 1,1,1-trifluoro-2The iodoethane in the Franck-Condon region

We report resonance Raman spectra of 1,1,1-trifluoro-2-iodoethane in cyclohexane taken with excitation wavelengths within the A-band absorption. The experimental A-band resonance Raman intensities and absorption spectrum were simulated using time-dependent wavepacket calculations and a simple model. The results of the time-dependent wavepacket calculations were used in conjunction with the normal mode descriptions found from normal coordinate calculations to obtain the short-time photodissociation dynamics (at 15 fs) of 1,1,1-trifluoro-2iodoethane. The short-time photodissociation dynamics of 1,1,1-trifluoro-2-iodoethane has a large amount of multidimensional character and is qualitatively consistent with an impulsive ‘semi-rigid’ radical model of the photodissociation dynamics that shows the CF3 CH2 radical going towards a more planar geometry about the CH2 carbon atom as the C–I bond is being broken. Our resonance Raman intensity analysis indicates that in the beginning stages of the photodissociation in the Franck–Condon region the C–C bond becomes longer, the CCI angle becomes smaller, the HCH and CCH angles become larger, two of the FCC angles (out of the CCI plane) become larger while the third FCC angle (in the CCI plane) becomes smaller, and there is some motion in the FCF angles and C–F bond lengths that is either positive or negative in sign, depending on the sign combination of the normal mode displacements. We also compare the photodissociation dynamics of 1,1,1-trifluoro-2-iodoethane with that of iodoethane.

Vibrational wave functions and energy levels of large anharmonic clusters: A vibrational SCF study of (Ar)13

The vibrational ground state and the fundamental excited states of (Ar)13 were studied by vibrational self-consistent field (VSCF) calculations. These calculations treat the interaction between different modes through a mean potential approximation, and incorporate anharmonicity in full. The good accuracy of VSCF for such systems was demonstrated by test calculations for (Ar)3 and other clusters. The study of (Ar)13 focused on the properties of the wave functions and the excitation energies, on the role of the coupling between the modes and on the deviation from the harmonic approximation. It was found that SCF excitation energies for the fundamental transitions differ from the harmonic values by about 25% for the softest modes, and by about 10% for the stiffest modes. Coupling between the modes, treated by SCF, was found to be much more important than the intrinsic anharmonicity of the individual modes. For the ground state, the harmonic wave function compares well with VSCF, but for the fundamental excited states appreciable differences were found. The results for a potential field expanded to fourth-order polynomial in the normal mode displacements are found to be valid, almost indentical with those for a more elaborate sixth-order polynomial expansion. The fundamental excitation frequencies computed using the Aziz–Slaman Ar–Ar pair potential are very similar, with some quantitative deviations, to the values obtained with a Lennard-Jones potential. The differences are larger for certain specific modes, and very small for the others. These calculations demonstrate the computational power of VSCF as a tool for quantum-mechanical calculations for large clusters, at the level of specific wave functions.

Vibrational wave functions and spectroscopy of (H2O)n, n=2,3,4,5: Vibrational self-consistent field with correlation corrections

Vibrational energy levels, wave functions, and ir absorption intensities are computed for (H2O)n clusters with n=2, 3, 4, and 5. The calculations were carried out by the vibrational self-consistent field (VSCF) approximation, with corrections for correlations between the modes by perturbation theory. This correlation corrected VSCF (CC-VSCF) is analogous to the familiar Möller–Plesset method in electronic structure theory. Test calculations indicate that this method is of very good accuracy also for very anharmonic systems. While the method is of highest relative accuracy for the stiffest modes, it works very well also for the soft ones. Some of the main results are (1) the frequencies calculated are in good but incomplete agreement with experimental data available for some of the intramolecular mode excitations. The deviations are attributed to the inaccuracy of the coupling between intramolecular and intermolecular modes for the potential function used. (2) Insight is gained into the pattern of blue- or redshifts from the corresponding harmonic excitation energies for the various modes. (3) Anharmonic coupling between the modes dominates in general over the intrinsic anharmonicity of individual modes in determining the spectrum. (4) The anharmonic corrections to the frequencies of some intermolecular modes (shearing, torsional) are extremely large, and exceed 100% or more in many cases. (5) An approximation of quartic potential field in the normal mode displacement is tested for the clusters. It works well for the high and intermediate frequency modes, but is in error for very soft shearing and torsional modes. (6) The relative errors of the VSCF approximation are found to decrease with the cluster size. This is extremely encouraging for calculations of large clusters, since the VSCF level is computationally simple.

Application of Time-Dependent Raman Theory to Raman Excitation Profiles of Hexamethylbenzene-Tetracyanoethylene Electron Donor-Acceptor Complex

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTApplication of Time-Dependent Raman Theory to Raman Excitation Profiles of Hexamethylbenzene-Tetracyanoethylene Electron Donor-Acceptor ComplexB. Mark Britt, Jeanne L. McHale, and Donald M. FriedrichCite this: J. Phys. Chem. 1995, 99, 17, 6347–6355Publication Date (Print):April 1, 1995Publication History Published online1 May 2002Published inissue 1 April 1995https://doi.org/10.1021/j100017a014RIGHTS & PERMISSIONSArticle Views189Altmetric-Citations57LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts

Vibrational Spectra of Diamond C(111)-(2x1) Exposed to Hydrogen and Methane: Comparison of Theory and Experiment

Optimized geometrics, energies, vibrational frequencies and normal mode displacement vectors using ab initio SCF calculations at the STO-3G and 3-21G level of theory are reported for two clusters based on the diamond lattice, isotetramantane, C[sub 22]H[sub 28], and methylisotetramantane, C[sub 23]H[sub 30]. Additionally, molecular mechanics on larger diamond clusters, [approx]C[sub 140], are also reported. The calculated vibrational spectra, together with the normal mode displacement vectors, are used to assign infrared-visible sum-frequency generation spectra of hydrogen-truncated diamond -(1 x 1) and methyl-truncated diamond -(1 x 1). 29 refs., 9 figs., 4 tabs.

Temperature dependence of the proton hyperfine interaction in HC60 and the proton-muon hyperfine anomaly.

The decrease in the proton hyperfine interaction of ${\mathrm{HC}}_{60}$ with increasing temperature is analyzed on the basis of quantum-chemical calculations of the vibrational force field of the radical. The changes of the hyperfine interaction with respect to normal-mode displacements are evaluated and used to simulate the temperature dependence. It is shown that the modulation by low-frequency A'' (${\mathit{C}}_{\mathit{s}}$ symmetry) vibrational modes of the radical that correspond to the lowest ${\mathit{h}}_{\mathit{g}}$ and ${\mathit{h}}_{\mathit{u}}$ vibrations of ${\mathrm{C}}_{60}$ dominates the observed temperature dependence. The experimentally observed negative hyperfine anomaly, vis-\`a-vis the muon coupling, is also attributed to vibrational motions, specifically to the three modes that describe hydrogen motions.

Photodissociation of alkyl iodides in solution: Substituent effects on the early-time dynamics

Resonance Raman spectra, including absolute scattering cross sections, have been measured for ethyl, isopropyl, and tert-butyl iodides in cyclohexane solution at seven to ten wavelengths between 303 and 200 nm. Spectra of fully deuterated ethyl iodide have also been obtained at five wavelengths. Spectra excited in the 300–250 nm region, on resonance with the directly dissociative A state, are dominated by long overtone progressions in the nominal C–I stretching mode near 500 cm−1. In all three molecules the fundamental of the C–I stretch is unexpectedly weak relative to the overtones when excited near the peak of the A band. This is shown to arise from interference between the A-state resonant part of the fundamental Raman amplitude and preresonant contributions from higher electronic states. In addition to the C–I stretching activity, A-state excitation generates significant intensity in fundamentals, overtones, and combination bands of modes nominally assigned as bending and CC stretching vibrations, suggesting a multidimensional character to the reaction coordinate. The absorption spectra and A-state resonant Raman intensities are modeled successfully through wave-packet propagation on a multidimensional locally harmonic potential with a preresonant contribution to the fundamental intensities included. The short-time photodissociation dynamics are then examined by using the normal-mode coefficients to convert the wave-packet motion from dimensionless normal coordinates into internal coordinates. It is found that while the dominant motion during the first 10 fs involves stretching of the C–I bond, other stretching and bending motions are also involved, although the precision of these conclusions for isopropyl and tert-butyl iodides is limited by the indeterminacy in the signs of the normal-mode displacements obtained from the intensity analysis. Comparison of the results for normal and perdeuterated ethyl iodide is used to resolve most of the sign indeterminacies for this molecule. The present results are compared and contrasted to conclusions of previous studies of energy partitioning in the vapor-phase photodissociation.

The Jahn–Teller distortion in SiH+4

The three states that correspond to the triply degenerate 2T2 state of SiH+4 at the tetrahedral configuration are studied using configuration-interaction (CI) calculations. The potential-energy surfaces for the three states of interest are modeled using a functional form of the potential that is based on normal-mode distortions from the tetrahedral configuration. It is shown that this form of the potential, which includes quadratic terms in the normal-mode displacements, is not able to correctly describe the region containing the van der Waals Cs minimum structure. However, using single-root CI calculations, the ground and excited states of the Cs, C2v, and SiH+2 +H2 structures are then studied in detail.

Potential energy surfaces of CH+4

The potential energy surfaces of the three lowest electronic states of CH+4 are calculated. CI calculations based on average natural orbitals from preliminary multireference singles and doubles CI calculations are found to provide a balanced description of the three states. The calculated points are fit to the eigenvalues of a 3×3 matrix whose elements are a power-series expansion in the normal-mode displacements from the SCF tetrahedral geometry. The equilibrium structures for the C2v, D2d, and C3v Jahn–Teller distortions are located and the vibrational frequencies for these structures are calculated. In addition, the transition state for the pseudorotation between equivalent C2v minima is located and the nature of the pseudorotation is discussed in detail.

Multidimensional Franck–Condon integrals and Duschinsky mixing effects

A general method for calculating multidimensional Franck–Condon integrals for polyatomic molecules is given. These integrals are derived by means of a multivariable generating function which incorporates both the transformation of the normal mode coordinates between initial and final electronic states and their frequency changes. The normal mode transformation or mode mixing (Duschinsky effect) scrambles the occupations of the normal modes, leading to unusual distributions, which at certain values of the angles of rotation are confined to some of the modes only or even to a single mode. Mathematically, this selectivity can be described in terms of normal mode displacements generated by the rotation matrix from the potential minima of the ground and excited states. These normal mode displacements, as well as the set of mixed frequency change parameters due to mode mixing, have no counterparts in the parallel mode approximation and are the reason that multidimensional Franck–Condon integrals are of formidable analytical complexity. This complexity is analyzed with particular attention to the symmetry of the integrals with respect to the interchange of quantum occupation numbers. Finally calculation of scattered intensities in the resonance Raman process is made, showing a strong dependence of the corresponding cross section upon the rotation angle.

Intramolecular distributions. III. N coupled modes

A previous theory of intramolecular distributions (ID) is extended to N (Duschinsky) mixed vibrational modes. For this case a multidimensional ID is derived which provides a comprehensive, complete, and unified description of vibronically assisted electronic transitions in polyatomic molecules. The multidimensional ID is introduced with the aid of a multivariable generating function. The latter quantity incorporates both the transformation of normal mode coordinates between the initial and final electronic states and its frequency changes. This normal coordinate transformation leads to the generation of additional sets of geometrical displacements which cannot be uniquely assigned to normal mode displacements as in the parallel mode approximation. It is shown that normal coordinate rotation causes the final state vibrational distribution or the spectral line shape to deviate considerably from that observed at parallel modes. A further derivable property of the multidimensional ID is its selectivity which at certain values of the rotation angles leads to specific mode selections. Similarly, the nonradiative decay probability is subject also to variations and exhibits considerable increase under certain circumstances.

Normal mode paths for hydrogen exchange in the peptide ferrichrome

Possible paths for exposure to solvent and hydrogen exchange of the amide protons of ferrichrome, a cyclic hexapeptide, are examined. The paths are obtained from calculations of the vibrational normal modes of ferrichrome and correspond to low energy atomic displacements away from the local minimum in the multidimensional conformational space of the molecule. Exposure of exchangeable groups along the normal modes was determined by using the solvent accessible surface area algorithm of Lee and Richards. Three of the exchangeable protons (Gly(1,2,3,)) are largely exposed to solvent in the x-ray structure while the remaining three exchangeable protons of the ornithines are totally shielded from solvent. A very small number of normal mode displacements are found to expose the Orn(2) and Orn(3) amide groups while the Orn(1) amide proton remains shielded from solvent for all the paths studied. The effective paths for exposure of Orn(2) and Orn(3) correspond to the lowest frequency ( approximately 18 cm(-1)) motions. The paths are characterized in terms of the magnitude and energy of atomic displacements, correlated changes in dihedral angles, and the resulting changes in exposure and hydrogen bonding of exchangeable groups.

CO2–N2 intermolecular V–T and V–V potentials via CNDO

V–T and V–V intermolecular potentials have been calculated within the CNDO approximation for the CO2 (asymmetric mode) –N2 system. The procedure followed was to compute the total energy of the CO2–N2 system for a variety of intermolecular separations, orientations, and normal mode displacements, and subtract the relevant isolated CO2 and isolated N2 total energies. The V–T and V–V intermolecular potentials were then obtained by fitting a second-order polynomial expansion in the normal mode displacements of both molecules to the total intermolecular energy for each intermolecular orientation and displacement. The resulting elastic potentials are much too deep. The inelastic potentials are highly orientation dependent, generally not well represented by a P2(ϑ) expansion in the relative angular orientation, and different for each specific V–T or V–V process.

CNDO calculation of intermolecular V-T and V-V potentials. The CO 2-N 2 system

V-T and V-V intermolecular potentials have been calculated in the CNDO approximation for the CO 2 (asymmetric mode)-N 2 system. Our procedure is to compute the CO 2-N 2 intermolecular potential for a variety of intermolecular separations, orientations, and normal mode displacements. For each intermolecular displacement and orientation, the elastic, V-T, and V-V intermolecular potentials are obtained by fitting a second-order polynomial expansion, in the normal mode displacement of both molecules, to the total intermolecular energy. Two specific orientations are considered: collinear and N 2 perpendicular to CO 2. The elastic potential is much too deep. The inelastic potentials are highly orientation dependent and different for each specific V-T or V-V process.