Effects Of Vibrational Motion Research Articles

Theoretical Study of Dynamic Stark-Induced π-Electron Rotations in Low-Symmetry Aromatic Ring Molecules beyond the Frozen Nuclear Approximation.

The effects of vibrational motions on dynamic Stark-induced π-electron rotations in a low-symmetry aromatic ring molecule are theoretically studied in the adiabatic approximation. We adopt a simplified three-electronic state model with a few vibronic states. A pair of the lowest vibronic states in two electronic excited states is set degenerate by irradiation of two linearly polarized UV lasers. The resultant degenerate state is named the dynamic Stark-induced degenerate vibronic state (DSIDVS). The laser parameters (intensities and central frequencies) are determined under the conditions of DSIDVS formation. The aromatic ring molecules of interest are supposed to belong to the weak coupling case. The analytical expressions for the DSIDVS and coherent angular momentum LZ(t) are derived in the displaced harmonic oscillator (DHO) model. Two horizontal potential displacements (δα, δβ) between the two electronic excited states (α and β) and the ground state are the parameters in the DHO model. The LZ(t) calculated with δα = δβ is characterized by a regular sequence of the angular momentum pulses with a positive (or negative) constant. For a more general case with δα ≠ δβ, the regular sequence is broken down because of the contribution of the first excited vibronic state in each electronic state to LZ(t).

Variations in Duschinsky rotations in m-fluorotoluene and m-chlorotoluene during excitation and ionization.

We investigate Duschinsky rotation/mixing between three vibrations for both m-fluorotoluene (mFT) and m-chlorotoluene (mClT), during electronic excitation and ionization. In the case of mFT, we investigate both the S1 → S0 electronic transition and the D0 + ← S1 ionization, by two-dimensional laser-induced fluorescence (2D-LIF) and zero-electron-kinetic energy (ZEKE) spectroscopy, respectively; for mClT, only the D0 + ← S1 ionization was investigated, by ZEKE spectroscopy. The Duschinsky mixings are different in the two molecules, owing to shifts in vibrational wavenumber and variations in the form of the fundamental vibrations between the different electronic states. There is a very unusual behavior for two of the mFT vibrations, where apparently different conclusions for the identity of two S1 vibrations arise from the 2D-LIF and ZEKE spectra. We compare the experimental observations to the calculated Duschinsky matrices, finding that these successfully pick up the key geometric changes associated with each electronic transition and so are successful in qualitatively explaining the vibrational activity in the spectra. Experimental values for a number of vibrations across the S0, S1, and D0 + states are reported and found to compare well to those calculated. Assignments are made for the observed vibration-torsion ("vibtor") bands, and the effect of vibrational motion on the torsional potential is briefly discussed.

Effects of vibrational averaging on coupled cluster calculations of spin–spin coupling constants for hydrocarbons

We present vibrationally corrected nuclear spin–spin coupling constants for four hydrocarbons with different types of carbon–carbon bonds calculated with coupled cluster (CC) theory. First, we perform a systematic basis set investigation on acetylene for all of the four contributions (Fermi-contact, spin-dipole, para- and diamagnetic spin–orbit) to the spin–spin coupling constants and subsequently choose basis sets of sufficient flexibility to describe converged electronic properties. Then, in order to describe the effects of vibrational motion for the studied molecules we perform a Taylor expansion in the normal coordinates up to second order – a method that is well known for both its quality and efficiency – and rigorously estimate the resulting contribution for all types of spin–spin coupling constants. Combined, this allows us to obtain highly accurate benchmark estimates of the spin–spin coupling constants for acetylene, ethylene, ethane, and cyclopropane. This work provides one of the first systematic benchmarks of zero-point vibrational contributions to spin–spin coupling constants in poly-atomic molecules using the reliable CC theory and it is thus an important reference for further research within in-silico spin–spin coupling constant determination. We note that earlier computational estimates of zero-point vibrational effects agree well with those presented here (for acetylene, ethylene, and cyclopropane) while vibrational corrections for ethane are reported for the first time.

The effect of vibrational motion on the dynamics of shape resonant photoionization of BF3 leading to the state of

We present the results of an experimental and theoretical investigation of vibrationally resolved valence shell photoionization of BF3 leading to the state of , where vibronic coupling and shape resonances are known to be important. The experimental vibrational branching ratios for multiple quantum excitations of the symmetric stretching mode of the ion as well as for the single vibrational excitation of the asymmetric stretching mode are compared with the predictions of single-channel Schwinger variational calculations performed within the Chase adiabatic approximation to obtain vibrational-state specific cross sections. The presence of a shape resonance in the continuum of symmetry is seen to lead to significant non-Franck–Condon intrachannel vibronic coupling effects. The breakdown in the Franck–Condon approximation is due to the sensitivity to the asymmetric stretching mode of the energy of the resonance and the magnitude of the transition moment for exciting the resonance. However, there are indications that interchannel vibronic coupling effects may also be significant in this system.

Effects of vibrational motion on core-level spectra of prototype organic molecules

A computational approach is presented for prediction and interpretation of core-level spectra of complex molecules. Applications are presented for several isolated organic molecules, sampling a range of chemical bonding and structural motifs. Comparison with gas phase measurements indicates that spectral lineshapes are accurately reproduced both above and below the ionization potential, without resort to ad hoc broadening. Agreement with experiment is significantly improved upon inclusion of vibrations via molecular dynamics sampling. We isolate and characterize spectral features due to particular electronic transitions enabled by vibrations, noting that even zero-point motion is sufficient in some cases.

Vibronic Effects in Single Molecule Conductance: First-Principles Description and Application to Benzenealkanethiolates between Gold Electrodes

The effect of vibrational motion on resonant charge transport through single molecule junctions is investigated. The study is based on a combination of first-principles electronic structure calculations to characterize the system and inelastic scattering theory to calculate transport properties. The extension of the methodology to describe hole transport through occupied molecular orbitals is discussed. The methodology is applied to molecular junctions where a benzene molecule is connected via alkanethiolate bridges to two gold electrodes. The results demonstrate that, depending on the coupling between the electronic π-system of the benzene ring and the gold electrodes, vibronic coupling may have a significant influence on the transport properties of the molecular junction.

Vibrationally resolved partial cross sections and asymmetry parameters for nitrogen K-shell photoionization of the NO molecule

The vibrationally resolved partial cross sections and asymmetry parameters for the photoionization of the NO molecule producing NO+ N (1s−1) 3Π, 1Π ions in the vibrationally excited states v′ are measured for photon energies between 412 and 419 eV, across the σ* shape resonance region above the N K-shell ionization threshold. The position of the maximum of for the N (1s−1) is observed to move towards the N (1s−1) 3Π and 1Π thresholds in both channels with increasing vibrational excitation in the parent ion. The curves, on the other hand, exhibit monotonic increase in the investigated photon energy range. The major features are fairly well reproduced by ab initio vibrationally specific calculations based on the multichannel Schwinger configuration interaction (MCSCI) method for the dipole transition moments, where the effects of vibrational motion on the photoionization cross sections are included using the adiabatic approximation.

Influence of nuclear vibration on harmonic generation in molecules

The effect of vibrational motion on harmonic generation in molecules is studied within the strong-field approximation. Simple expressions are given for the cut-off energy and for the ratio of spectral intensities from two isotopes. The latter is based on electronic trajectories from the simple-man's model. The influence of vibration is given by a correlation function that is sensitive to the overlap between the initial vibrational wave packet and the wave packet after the evolution in the Born–Oppenheimer potential of the ionized molecule.

A water–water potential derived using a quantum Monte Carlo vibrational analysis

A difficulty in the generation and testing of intermolecular interaction potentials has to do with the effects of vibrational motion. For weak modes, the vibrational excursions can be and often are sizable. So, not only do model potentials have to be suitable over a considerable range, they must also be accurate with respect to experimental data that reflects the vibrational averaging (i.e., on-average structures). In this report, we present an explicit interaction potential for the water dimer that has been devised with a systematic treatment of vibrational effects by means of quantum Monte Carlo treatment of the vibrational ground state. The model potential uses intrinsic electrical properties of isolated water and four empirical parameters. An iterative procedure based on matching measured on-average rotational constants to calculated values was used to select the atom–atom Lennard-Jones (empirical) parameters. We present the results of these calculations, including zero point vibrational energies and on-average separations.

Vibrational motion effects on molecular polarizabilities. Shifts in vibrational transition frequencies and transition moments of lithium hydride from applied electrical fields

Lithium hydride has been used to provide representative information on the effects of vibrational motion on molecular polarizabilities. Dipole and quadrupole polarizability and hyperpolarizability tensors were calculated using derivative Hartree–Fock (DHF) theory. Many of the calculated tensor elements were found to be changing with internuclear separation even in the vicinity of the equilibrium. Vibrational wave functions obtained from a numerical vibrational analysis were used to vibrationally average the electrical properties (tensor elements) of the lowest four vibrational states, and this showed that the averaged polarizabilities of the states have important differences. A manifestation of these differences is that there are shifts in the vibrational transition frequencies along with changes in the transition moments of LiH from applying electrical fields and field gradients. Field gradients can augment the shifts arising from uniform axial fields. This was determined by variationally finding vibrational state energies and transition frequencies as a function of the applied electrical potential.

Influence of vibrational motion on solid state line shapes and NMR relaxation

The influence of vibrational motion on bond lengths and quadrupole constants obtained from dipolar and quadrupolar solid state line shapes is considered. It is shown that such motions average both the magnitude and the orientation of the intrinsic interaction tensor. Explicit expressions for the effective coupling constants that can be conveniently evaluated using the results of a normal mode analysis are derived. When the vibrationally averaged interaction tensor is axially symmetric, it is shown that the effect of vibrational motion on relaxation can be rigorously incorporated into an effective coupling constant which is formally identical to the one that determines the line shape. Illustrative calculations for several alkanes, in both the gas and solid phases, are presented. The relative contributions of stretching and bending vibrations and the effect of anharmonicity on the effective C–H bond lengths and deuterium quadrupole constants are examined. The influence of vibrational averaging on the magnitude of the dipolar coupling is shown to be essentially independent of the nature of the molecule and its environment and to be quite small (i.e., for C–H bonds, the coupling constant decreases by 3% and hence the effective bond length increases by 1%). Vibrational averaging of the orientation of the dipolar interaction vector, on the other hand, depends on the size of the molecule and its environment because of the predominant role played by low frequency bending and torsional modes. The implication of these results for the value of the effective internuclear distance that should be used for the interpretation of the dipolar relaxation experiments is considered.

Angular distribution in the photoelectron spectrum of the ground and first excited vibrational bands of the X 2Σg+ state in N2+ measured as a function of photon energy

Angle-resolved photoelectron spectra were taken of the first ionization state of N2 as a function of photon energy using a monochromatized beam of polarized photons from the Wisconsin Synchrotron Radiation Center. From these results the angular parameters for the first two vibrational states were determined over a range of photon energies from 17.7 to 31.0 eV. In energy ranges where resonance absorption, accompanied by autoionization, is expected to occur, β for the first excited vibrational level (v1) was frequently characterized by near zero values. In energy regions free of discrete autoionization v1 was found to have a value of β considerably larger (∼0.4 to 0.8 units) than that for the ground vibrational level (v0). This result is shown to be in accordance with recent calculations by Dehmer et al., based on the effect of vibrational motion on β in the vicinity of a shape resonance.

The effect of vibrational motion on the electron charge difference density

The effect of the internal vibrational motion on the electron difference density has been studied for the hydrogen molecular ion H + 2. The effect is quite small although there are differences between the static and dynamic densities near the nuclei.

The effect of vibrational motion on wavefunctions in momentum space

The effect of the nuclear vibrational motion on the electronic momentum density has been studied for the hydrogen molecular ion H2 +. The effect appears to be small although there are some differences at small momentum values. Similar results were obtained for the radial momentum distribution except that the effect was much smaller.