Vibrational Basis Research Articles

Calculating energy levels of isomerizing tetra-atomic molecules. I. The rovibrational bound states of Ar2HF

A general, six-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the Ar2HF van der Waals trimer is presented in which the HF intramolecular stretching coordinate is separated out adiabatically and is not treated explicitly. Vibrational term values up to about 100 cm−1 with absolute convergence to better than 0.1 cm−1 are reported. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than hitherto. States that sample Ar–Ar–HF linear configurations and approach Ar–HF–Ar linear configurations are characterized for the first time. Results for total angular momentum J=0 and 1 provide the first accurate calculations of rotational constants for this system. The rotational constants for the HF bending states of Ar2HF in the ground and first vibrationally excited states of the HF monomer are in good agreement with experiment, confirming the accuracy of the potential used in this work.

Inelastic processses from vibrationally excited states in slowH++H2andH+H2+collisions. II. Dissociation

We present a detailed quantum-mechanical study for dissociation of vibrationally excited molecular diatomic target, of ${\mathrm{H}}_{2}({\ensuremath{\nu}}_{i})$ by proton impact and ${\mathrm{H}}_{2}^{+}({\ensuremath{\nu}}_{i})$ by hydrogen-atom impact, in the range of center-of-mass collision energies from threshold to 9.5 eV. The dominant dissociation mechanisms in this three-atomic collision system are identified and their effectiveness analyzed for different collision geometries. The cross section calculations for direct and charge-transfer dissociation are performed by solving the Schr\odinger equation for the nuclear and electronic motions on the two lowest diabatic electronic surfaces of ${\mathrm{H}}_{3}^{+},$ and by using an expansion of nuclear wave function in a vibrational basis containing all discrete ${\mathrm{H}}_{2}$ and ${\mathrm{H}}_{2}^{+}$ states and a large number of pseudostates from each of the corresponding discretized continua. The energy and angular spectra of the fragments are also calculated and analyzed.

Elastic processes involving vibrationally excited molecules in cold hydrogenplasmas

We describe here a comprehensive quantum mechanical study of elastic scatteringof protons by vibrationally excited hydrogen molecules and of hydrogen atoms byvibrationally excited hydrogen molecular ions, in the range of collisionenergies from a fraction of an eV to 6 eV. The problem was solved withina treatment considering all inelastic processes between the vibrationalstates, including excitation, charge transfer and dissociation. This wasrealized by expanding the problem in vibrational bases of H2 and H2+which, in addition to all bound states, contained a large number of discretizedvibrational continuum states, and solving the resulting set of coupled channelequations. The sudden approximation was applied with regard to rotations of thetarget molecule, and particular attention has been paid to convergence of theelastic cross sections with the number of partial waves of the projectile. Importantplasma transport related moments of the elastic scattering cross section, themomentum transfer and viscosity cross sections, are also reported here andcompared with inelastic cross sections for various vibrationally excited states.

Inelastic processes from vibrationally excited states in slowH++H2andH+H2+collisions: Excitations and charge transfer

A comprehensive study is presented of the scattering of protons on ${\mathrm{H}}_{2}({\ensuremath{\nu}}_{i})$ and of hydrogen atoms on ${\mathrm{H}}_{2}^{+}({\ensuremath{\nu}}_{i}),$ where ${\ensuremath{\nu}}_{i}$ is any vibrationally excited state of the relevant molecules. Cross sections for charge transfer and excitation have been calculated in the range of center-of-mass energies 0.6--9.5 eV using a fully quantal, coupled-channel approach. An extensive vibrational basis set, defined in a large configuration space of the reactants, is used, including a large number of discretized vibrational continua. A detailed picture is produced of all inelastic processes that involve two lowest, nonadiabatically coupled electronic surfaces of the ${\mathrm{H}}_{3}^{+}$ molecule. The rotational dynamics of ${\mathrm{H}}_{2}$ and ${\mathrm{H}}_{2}^{+}$ are treated within the sudden approximation. The cross sections obtained are compared with the sparse data available from literature.

Breakdown of the spectator model for the OH bonds in studying the H+H2O reaction.

The time-dependent wave packet method is used to study the exchange and abstraction processes for the H+H2O reaction with both OH bonds in the H2O reactant treated as reactive bonds in full dimension. The calculation clearly shows that it is necessary to treat both OH bonds in this way in order to accurately investigate the exchange process. However, for the abstraction process, the spectator model works very well. Nonreactive treatment of one OH bond by using a few vibrational basis functions or even freezing the bond can yield very accurate abstraction reaction probability.

Quantum-mechanical calculations on termolecular association reactions XY+Z+M→XYZ+M: Application to ozone formation

We present a quantum-mechanical model for termolecular association reactions XY+Z+M→XYZ+M involving the formation of a long-lived complex XYZ*. The rotation of the molecule XYZ is treated in the infinite order sudden approximation (IOS) and its vibrations are treated by the coupled-channel method (VCC). Resonances featuring the XYZ* long-lived complex formation are first computed by means of the stabilization method and are then included in the vibrational basis functions used for the inelastic VCC-IOS scattering calculation. The method yields rate constants for the association process selected in resonance and bound states of XYZ. We apply the method to the formation of ozone and investigate isotope effects. Calculations of energy transfer and collision-induced recombination of O+O2 in collision with Ar are reported for a range of ozone isotopomers. The bending mode of O3 is not treated explicitly in these computations. The results establish a strong selectivity in vibrational state-to-state cross sections for the deactivation of O3 during the collisional energy transfer process with Ar. The present calculations also account for the high sensitivity of rate constants with respect to the isotopic composition of ozone molecules but not in the same proportion as experiments. The energy transfer from selected initial vibrational states is also calculated as a function of the initial relative kinetic energy.

Phonons in isostructural compounds CuxM1−x(HCOO)2·2H2O (M = Mn, Co, Ni, Zn, and Cd): a Raman scattering study

AbstractThe Raman spectra of isostructural compounds CuxM1−x(HCOO)2·2H2O (M = Mn, Co, Ni, Zn, and Cd) at room temperature are presented. The phonons observed were assigned on the basis of formate and water group vibrations and correlations with previous data reported for other formates. The influence of metal–guest ion substitution is discussed in the system Cu0.53Mn0.47(HCOO)2·2H2O when Mn is replaced by Cd. Copyright © 2002 John Wiley & Sons, Ltd.

Studies on the mechanism of hypoxic selectivity in copper bis(thiosemicarbazone) radiopharmaceuticals.

Copper diacetyl-bis(N4-methylthiosemicarbazone), Cu(II)ATSM, is a promising agent for imaging hypoxic tissue. Here we present results that provide insight into the chemical and electronic properties underlying previously observed structure-activity relationships. Density functional theory (DFT) calculations on the electronic structures and molecular orbitals of a series of 13 Cu(II)bis(thiosemicarbazone) analogues with different alkylation patterns and with fixed geometries based on the known structure of Cu(II)PTSM showed that the LUMO and the next lowest orbital were very close in energy, and their energy order was strikingly dependent on the ligand alkylation pattern in a way that correlated with hypoxia-selectivity and redox potentials. The LUMOs of Cu(II)ATSM and other hypoxia-selective analogues were predominantly metal-based (leading to a singlet reduced species) while the LUMOs of Cu(II)PTSM and other nonselective analogues were predominantly ligand-based (leading to a triplet reduced species). Upon relaxation of the geometric constraint and full optimization in both Cu(II)ATSM and Cu(II)GTS, the metal-based orbital became the LUMO, and the singlet was the thermodynamically preferred form of the reduced species. Chemical and electrochemical investigation showed that all Cu(II) complexes were reducible, but Cu(I)PTSM and other nonselective analogues dissociated immediately upon reduction with release of ligand (detected by UV-vis) while Cu(I)ATSM and other hypoxia-selective analogues did not. Instead they were rapidly re-oxidized to the Cu(II) complex by molecular oxygen. The reversible electrochemical reduction of nonselective complexes Cu(II)PTSM and Cu(II)GTS became irreversible in the presence of weak acid, whereas that of Cu(II)ATSM was unaffected. In light of these results we present a model to explain the structure-activity relationships on the basis of electronic structure and molecular vibrations.

Charge Transfer Processes in Slow Collisions of Protons with Vibrationally Excited Hydrogen Molecules

We report on a comprehensive study of scattering of hydrogen ions on vibrationally excited hydrogen molecules in the range of center of mass energies 0.6–9.5 eV. The reported charge transfer processes, including nuclear particle exchange, have been calculated using a fully-quantal, coupled-channel approach. An extensive vibrational basis set on the relevant two-state electronic surfaces was employed, with inclusion of vibrational continua, while the rotational dynamics of H2 was treated within the sudden approximation.

Complex symmeterized analysis of benzene vibrations

AbstractThe aim of this work is to introduce specific complex coordinates and wave functions (Hamiltonian eigenfunctions) for the description of vibrational motion in benzene. When suitably chosen, these complex functions are shown to possess interesting transformation behavior under the symmetry operations of the molecular symmetrical top point group D6. This behavior is analyzed and classified as “complex symmetry types” (CSTs). CSTs can be defined for all symmetrical top point groups. The description in terms of complex symmeterized coordinates and wave functions allows for the construction of a separable symmeterized vibrational basis set for benzene. New results from calculations on vibrational energies and redeterminations of harmonic force constants in benzene, obtained using the CST description, are presented. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Orbit bifurcations and the scarring of wave functions

Orbit bifurcations and the scarring of wave functions

The NO(X2Π)–Ne complex. II. Investigation of the lower bound states based on new potential energy surfaces

High-quality ab initio potential energy surfaces were calculated and subsequently used to predict the positions of the lowest bend-stretch vibrational states of the NO(X2Π,v=0)–Ne complex. The vibrational wavefunctions and basis set expansion coefficients, determined within the adiabatic bender model, were then used to simulate the observed spectrum for excitation of the NO(X2Π,v=2)–Ne complex. The overall position and rotational substructure matches well the experimental results for this system, which are presented in the preceding article [Y. Kim, J. Fleniken and H. Meyer, J. Chem. Phys. 114, 5577 (2001)]. A heuristic Hamiltonian, which includes the most important couplings and splittings, is used to improve the fit to experiment.

Smart Fluid Damping: Shaping the Force/Velocity Response through Feedback Control

It is now well known that smart fluids [electrorheological (ER) and magnetorheological (MR)] can form the basis of controllable vibration damping devices. With both types of fluid, however, the force/velocity characteristic of the resulting damper is significantly non-linear, possessing the general form associated with a Bingham plastic. In a previous paper the authors showed that by using a linear feedback control strategy it is possible to produce the equivalent of a viscous damper with a continuously variable damping coefficient. In the present paper the authors illustrate an extension of the technique, by showing how the shape of the force/velocity characteristic can be controlled through feedback control. This is achieved by using a polynomial function to generate a set point based upon the damper velocity. The response is investigated for polynomial functions of zero, 1st and 2nd order. It is shown how the damper can accurately track higher order polynomial shaping functions, while the zero-order function is particularly useful in illustrating the dynamics of the closed-loop system.

Electronic and Vibrational Coherence in the Core Light-Harvesting Antenna of Rhodopseudomonas viridis

In this paper we explain the wavelength-dependent oscillatory features in the pump−probe kinetics of the core LH1 antenna of Rhodopseudomonas viridis (Monshouwer, R.; Baltuška, A.; van Mourik, F.; van Grondelle, R. J. Phys. Chem. A 1998, 102, 4360). A quantitative fit of the data was obtained using the doorway−window representation of the nonlinear optical response in the vibrational eigenstate basis. In contrast to LH1/LH2 complexes from the BChl a-containing species, the LH1 antenna of Rps. viridis is characterized by a strong coupling of the excitonic states with two underdamped low-frequency modes (58 and 110 cm-1 at 77 K). Following a short femtosecond excitation pulse, this gives rise to the intense oscillations observed in the pump−probe traces, including their time and excitation/detection wavelength dependence. Furthermore, it leads to a pronounced and specific heterogeneity of the major absorption band due to the combined effects of the exciton splitting, disorder, and the presence of vibrational sidebands. The sharp maxima in the second derivative of the low-temperature absorption spectrum (Monshouwer, R.; Visschers, R. W.; van Mourik, F.; Freiberg, A.; van Grondelle, R. Biochim. Biophys. Acta 1995, 1229, 373) were assigned to the lowest exciton−vibrational transitions. The wavelength dependence of the experimentally observed oscillatory pattern suggests a different vibrational coherence decay for the ground- and excited-state wave packets. This can be explained by assuming the (incoherent) migration of the delocalized exciton (polaron) around the ringlike antenna with a characteristic time constant of 0.9−1.5 ps at 77K.

Temperature-Dependent Raman Study of CaCu(HCOO)4 and Ca2Cu(HCOO)6 Crystals

Unpolarized Raman spectra of policrystalline samples of calcium (II)–copper (II) formate [CaCu(HCOO)4] and dicalcium (II)–copper (II) formate [Ca2Cu(HCOO)6] were recorded and analyzed in the temperature range from 30 to 300 K. The observed modes at 300 K were assigned on the basis of formate group vibrations and correlations with previous data reported for other formate compounds. The splitting of the internal HCOO modes agrees with the group theory predictions. No changes either in the wavenumber or intensity of Raman modes were observed when the temperature of the samples was cooled to 30 K. This indicates that these compounds do no exhibit any phase transformation in the temperature range investigated.

Decoding the dynamical information embedded in highly mixed quantum states.

The standard description of the vibrational and rotational motion of polyatomic molecules, as expressed by the distortable rotor/harmonic oscillator approximation, provides an adequate description of the molecular quantum states only in regions of low total state density. When the total state density is large, exceeding 100 states/cm(-1), the vibrational dynamics are "dissipative" and the fundamental process of intramolecular vibrational energy redistribution is operative. The presence of intramolecular vibrational energy redistribution leads to molecular quantum states of a qualitatively different nature. With respect to a normal-mode vibrational basis, these quantum states are "highly mixed" in their vibrational character and represent nuclear motion that is a combination of all the normal-mode motions. This review describes frequency domain spectroscopy techniques designed to probe the vibrational, rotational, and structural composition of these eigenstates. Recent work that investigates spectroscopy between highly mixed states is also reviewed.

Vibrational study of cytotoxic bis(1-ethylimidazole)l(−)malatoplatinum(II)

In this work, we present the FT-Raman and FT-IR spectra (4000–100cm−1) of the newly synthesized cytotoxic platinum complex, bis(1-ethylimidazole)l(−)malatoplatinum(II), (abbr.: I) and reference substances: l(−)malic acid, silver l(−)malate and 1-ethylimidazole. Assignment of the bands was done on the basis of characteristic group vibrations, in comparison with the spectra of I with reference compounds as well as using the literature and our previous data. Using water solution and deuterated samples of I and of l-malic acid was helpful in making an assignment. The spectral analysis confirmed the chelated structure of I and indicated that in contrast to references containing l(−)malate ion, the l(−)malatoplatinum complex I does not form intramolecular hydrogen-bonded cyclic structures in solid state. The intermolecular hydrogen bonding is, however, possible. The characteristic vibrations at the Pt2+ centre was observed below 600cm−1, the ν(Pt–N) and ν(Pt–O) in the range 600–430cm–1, whereas the δ skeletal, δ(N–Pt–N), δ(N–Pt–O) and δ(O–Pt–O), appeared in the lowest part of the observed spectra. In the spectra of reference compounds, the most important are assignments of the band at 323cm−1 of silver malate as ν(Ag–O), as well as the bands at 743cm−1 of l-malic acid and at 801cm−1 of silver malate, as intramolecular hydrogen bonded cyclic structures. Both bands are the most intense in their Raman spectra and might be used as analytical bands.

Tritium diffusive transport parameters and trapping effects in the reduced activating martensitic steel OPTIFER-IVb

A time-dependent gas-phase isovolumetric desorption technique has been used to obtain the hydrogen isotopes transport parameters between 423 and 892 K and driving pressures ranging from 4×10 4 to 1×10 5 Pa. For protium and deuterium the properties diffusivity ( D), Sieverts’ constant ( K s), permeability ( Φ), trapping energy ( E t) and the trap sites concentration ( N t) are given. On the basis of ideal harmonic vibration of the hydrogen isotope atoms in a unique type of solution site, the values derived for the characteristic protium oscillation temperatures are: θ=1884 K, θ *=2387 K. These values lead to the following extrapolated tritium transport parameters: D ( m 2 s −1)=4.166×10 −8 exp (−12 027/RT), K s ( mol m −3 Pa −1/2)=0.271 exp (−27 905/RT) , Φ ( mol m −1 Pa −1/2 s −1)=1.127×10 −8 exp (−39 933/RT), E t ( J/ mol)=55 554, and N t ( sites/ m 3)=0.79×10 24 . The dynamics of the hydrogen isotopes transport and the origin of the trapping phenomenon are discussed in connection with the OPTIFER-IVb microstructure.

Properties of random state manifolds with applications to intramolecular vibrational redistribution

We investigate spectral properties of random manifolds, which consist of a bright state coupled to mutually uncoupled dark states for an equal but otherwise arbitrary distribution of the couplings. Both Poisson and Wigner distributions of the energy spacings of the dark states are taken into account. The Poisson spacing model is solved exactly. The average spectrum is Lorentzian. The average dilution factor comes out to be a function alone of the mean coupling strength normalized to the mean neighbor spacing of the dark states. A simple expression for the explored fraction of the available phase space is obtained. Numerical studies indicate that the normalized coupling even controls the whole distribution of the dilution factor for the Poisson model. For weak mean coupling strength a secondary peak occurs in this distribution for both the Poisson and the Wigner model. A perturbational analysis shows that this peak leads back to accidental resonances of the bright state with single dark states. A simple tier model is suggested for treating the intermixing of vibrational dark basis states in molecules. Results are compared with experimental data.

A joint theoretical–experimental investigation of the lower bound states of the NO(X 2Π)–Ar complex

In an extension of recent work [Y. Kim, K. Patton, J. Fleniken, and H. Meyer, Chem. Phys. Lett. 318, 522 (2000)], overtone pumping followed by resonantly enhanced multiphoton ionization (REMPI) detection is used to record spectra corresponding to excitation of the lowest five bend–stretch vibrational levels of the NO(X 2Π,v=2)–Ar complex. High-quality ab initio potential energy surfaces, coupled-electron-pair (CEPA) and coupled cluster single double triple [CCSD(T)], are used to predict the positions of these same five states, but in the NO(X 2Π,v=0)–Ar complex. The vibrational wave functions and basis set expansion coefficients, determined within the adiabatic bender model, are then used to simulate the observed spectrum for excitation of the NO(X 2Π, v=2)–Ar complex. The overall position and rotational substructure matches the experiment extremely well, particularly when the simulation is based on the presumably more accurate CCSD(T) potential energy surfaces.