Large Amplitude Bending Motion Research Articles

Stereoelectronic Effects in the Si−C Bond: A Study of the Molecular Structure and Conformation of Tetraphenylsilane by Gas-Phase Electron Diffraction and Theoretical Calculations

The molecular structure and conformation of tetraphenylsilane have been investigated by gas-phase electron diffraction and ab initio/DFT and molecular mechanics calculations. The structure of the free molecule is consistent with an S4 symmetry conformation; the calculations indicate that the twist angle τ between the plane of the phenyl group and the plane defined by the Si−C bond and the S4 axis is about 40°. Analysis of the low-frequency modes indicates that the four phenyl groups undergo large-amplitude torsional and bending vibrations about the respective Si−C bonds. The electron diffraction intensities from a previous study [Csakvari, E.; Shishkov, I. F.; Rozsondai, B.; Hargittai, I. J. Mol. Struct. 1990, 239, 291] have been reanalyzed, using constraints from the calculations. A dynamical model accounting for the large-amplitude bending motion of the phenyl groups was used in the refinement. The new analysis yields accurate values for the twist angle of the phenyl group, τ = 40 ± 2°, and the Si−Ph bo...

A Theoretical Study of Electronic Dynamics and Deformation of CO2in Intense Laser Fields

Deformations of CO2, CO2+, and CO22+ in intense laser fields (>1014 W/cm2) are investigated by using potential energy surfaces of field-following adiabatic states at various instantaneous field strengths. The adiabatic states are obtained by ab initio molecular orbital calculations. To predict tunnel ionization of multi-electron molecules, we propose a new approach based on the idea that electron transfer induced by an intense laser field charges each atom in a molecule and that ionization proceeds via the most negatively (or least positively) charged atomic site. We conclude that bond stretching in CO22+ accompanied by large amplitude bending motion is responsible for the experimentally determined geometrical structure of Coulomb explosion species CO23+, namely, that the C−O bond length is stretched to about 1.6 Å and the mean amplitude of bending is relatively large (∼40°).

Fourth-Order Rotational Corrections to the Effective Dipole Moments of Nonrigid Asymmetric Rotors

An expression for the fourth-order rotational correction terms of the effective dipole moments of nonrigid asymmetric rotors has been derived using the method of contact transformation. The treatment takes into account the large-amplitude bending motion. The correction terms have been calculated for the different bending states of the H2O molecule. A poor convergence of the rotational series for this molecule has been obtained and some different nonpolynomial forms for these series, obtained by different summation methods, have been proposed and tested.

An ab initio study on the equilibrium structure and CCC bending energy levels of carbon suboxide

The molecular parameters of carbon suboxide, C 3O 2, have been determined in large-scale ab initio calculations using the coupled-cluster method, CCSD(T), and basis sets of double- through quadruple-zeta quality. The potential energy function for the large-amplitude CCC bending motion (the ν 7 mode) was determined to be strongly anharmonic. The equilibrium structure of the molecule was found to be bent, with a barrier to linearity of only 18 cm −1. The rotation-bending energy levels were then calculated using a semirigid-bender Hamiltonian. The vibrational energy levels and effective rotational constants determined for various ν 7 states were found to be in good agreement with the experimental data.

Semiclassical study of the isomerization states of HCP

The vibrational spectrum of HCP (phosphaethyne) is studied and analyzed in terms of a 1:2 resonance effective Hamiltonian. The parameters of the model Hamiltonian are determined by fitting 361 out of the first 370 energy levels obtained from diagonalization of the full Hamiltonian, which is based on a newly calculated potential-energy surface with near spectroscopic accuracy. It is demonstrated that all features characteristic of the approach to the HCP↔CPH isomerization, such as the strong mixing between the bending and CP-stretching motions, the appearance of “isomerization states” (large amplitude bending motion) at intermediate energies, and the diagnostically significant appearance of a zig–zag pattern in the energy spacings between neighboring levels within each polyad, are quantitatively reproduced by the effective Hamiltonian. The semiclassical analysis of the model Hamiltonian for specific combinations of the HC-stretch and polyad quantum numbers explains all of the observed features of the full Hamiltonian in terms of stable and unstable periodic orbits. In particular, the birth of the isomerization states is found to be related to a saddle-node bifurcation of the classical phase space. The connection with the “polyad phase sphere” representation of quantum polyads is also discussed.

On the [formula omitted] internal conversion in the photodissociation of HNCO

We discuss a possible pathway for the S0/S1 internal conversion in the photodissociation of HNCO in the first absorption band. For this purpose, two-dimensional potential energy surfaces for the lowest two singlet states are calculated using the multi-reference configuration-interaction ab initio method; the NCO bending angle and the out-of-plane torsional angle are varied. According to our calculations, the transition from the S1 to the S0 state is likely to occur near a conical intersection at small NCO angles, which can be reached by large-amplitude NCO bending motion.

Theoretical investigation of fine-structure effects in the bending and symmetric stretching vibronic spectrum of FeH2 and FeD2

Two-dimensional potential energy surfaces were determined for the 25 spatial and spin components of the low-lying electronic 5δg, 5IIg, and 5σ+g states of iron dihydride along the bending and symmetric stretching coordinates. Spin-free electronic energies and electric dipole moments were obtained by means of an averaged coupled-pair functional employing a one-component relativistic Hamiltonian. Diagonal and oft-diagonal spin—orbit coupling matrix elements were evaluated at the ab initio level for a variation of the symmetric stretching coordinate while the dependence on the bending angle was estimated from the variation of the angular momentum matrix elements. Vibronic energy levels were calculated separately for each multiplet component; for the treatment of Renner—Teller coupling in the large amplitude bending motion an effective Hamiltonian was used in which the symmetric stretching motion is separated off and integrated over. We find that the Renner—Teller coupling is negligible in the X5δg state and that its vibronic energy level scheme is dominated by spin-orbit coupling effects. The spatial components of the excited 5IIg state, on the other hand, exhibit a considerable energy separation upon bending. Close to the 5IIA2 component we locate the 5σ+g electronic state which has large spin-orbit coupling matrix elements with both 5IIg components.

Relocalization in Floppy Free Radicals: Ab Initio Calculations of the C3H3O Isomers

Several isomers with molecular formula C3H3O may exhibit unusual properties by virtue of a configurational isomerization pathway that changes the localization of an unpaired electron. A series of ab initio calculations was undertaken at the UHF, B3LYP, MCSCF, and QCISD levels with the 6-311G(d,p) basis set to ascertain the geometries, relative energies, isomerization barriers, and relevant spectroscopic properties of the lowest energy structural and configurational C3H3O isomers. The most stable structures, with QCISD relative energies (kJ mol-l) of the stable configurations given in parentheses, are H2C2HCO (0, 8, 8), H3C3O (47), H2C3HO (87, 100), and HC2HCHO (94, 95, 101, 107). The H2C2HCO and H2C3HO structures are found to have distinct isomers connected by relocalization pathways. The H3C3O structure possesses two favorable canonical geometries, but the single optimized structure is an average of these. Potential surfaces have been calculated along two vibrational bending coordinates for H2C2HCO and H2C3HO and along a single bending coordinate for H3C3O. Extremely large amplitude bending motions are predicted for these three lowest energy structures, and at typical combustion temperatures it is likely that these molecules exist effectively as admixtures of two or more canonical structures.

An ab initio study on the equilibrium structure and HCN bending potential energy function of fulminic acid

The molecular parameters of fulminic acid, HNCO, have been determined in large-scale ab initio calculations using the coupled cluster method, CCSD(T), and basis sets of double to quadruple zeta quality. With the largest basis set employed. cc-pVQZ, the equilibrium structure of the molecule was found to be slightly bent, with the parameters r( HC) = 1.0615 A ̊ , r( CN) = 1.1648 A ̊ , r( NO) = 1.2025 A ̊ , ∠( HCN) = 165.13°, ∠( NCO) = 176.58° . The potential energy function for the large-amplitude HCN bending motion was determined to be anharmonic, with a barrier to linearity of the HCNO chain of only 7 cm −1.

Molecular Structure and Large-Amplitude Motion ofp-Diethynylbenzene from Gas-Phase Electron Diffraction and Theoretical Calculations

The molecular structure of p-diethynylbenzene has been determined by gas-phase electron diffraction and ab initio MO calculations at the HF/6-31G* and MP2/6-31G*(fc) levels. The two ethynyl groups undergo large-amplitude bending motions, making the equilibrium D2h model inadequate to describe the average structure from electron diffraction. Based on spectroscopic information on low-frequency modes, the electron diffraction data were approximated by a model consisting of a mixture of rigid conformers, differing only in the extent of the symmetric out-of-plane bending of the substituents. This gave the following geometrical parameters: ∠Cortho−Cipso−Cortho = 119.2 ± 0.2°, 〈rg(C−C)〉 = 1.402 ± 0.003 A, rg(Cring−Csp) = 1.431 ± 0.003 A, and rg(C⋮C) = 1.211 ± 0.003 A. The computed re values (MP2) are 119.2°, 1.401 A, 1.430 A, and 1.223 A, respectively, with the Cipso−Cortho bond 0.016 A longer than the central C−C bond. The HF/6-31G* geometries of ethynylbenzene and p-diethynylbenzene indicate that the interact...

Isomeric structures of the electronically excited acetylene⋅Ar complex: Spectroscopy and potential calculations

Acetylene⋅Ar complex in the S1 state has been characterized through laser fluorescence excitation spectra in the acetylene Ã←X̃, 3n0 (n=0–4) bands region. Two isomeric structures have been determined for the acetylene(Ã)⋅Ar complex from rotational band analysis, even though only one structure was known to exist for the ground state acetylene(X̃)⋅Ar. The in-plane isomer has the Ar atom situated in the molecular plane of the trans-bent acetylene, 3.77 Å from the acetylene center of mass and tilted from the H atoms. The out-of-plane isomeric structure, directly inverted from the rotational constants, has argon 3.76 Å away from the acetylene center of mass and 18° tilted from the C2 rotational axis. This structure is most likely due to large amplitude bending motions away from the equilibrium position which is along the C2 axis. Axis switching effect in the rotational band analysis for both isomers has been examined and found to be negligible. (Formulas for calculating the three-dimensional axis switching angles are detailed in the Appendix.) Three van der Waals vibrational mode frequencies have been determined from the vibrational progressions in the spectra; the stretching fundamental of the out-of-plane isomer is 28 cm−1; the in-plane bending fundamental, and the out-of-plane bending first overtone of the in-plane isomer are 11 and 17 cm−1, respectively. The isomeric structures have been compared with the results from a pairwise-atom potential calculation with parameters transferred from the ones previously derived for C2H4⋅Ar potential calculations. It was found that when the set of parameters that most closely reflects the electronic density distribution in C2H2(Ã) orbitals was used, two potential minima mimicking the two isomeric structures were generated. This potential calculation can even qualitatively reproduce the complex spectral shift induced by the ν3 mode excitation in acetylene. Combining the observed spectral shifts and previous experimental and theoretical studies of acetylene(X̃)⋅Ar, we have estimated the binding energy of the out-of-plane C2H2(Ã)⋅Ar isomer to be 179 cm−1, and that of the in-plane isomer to be 170 cm−1.

Ab initio study of the potential energy surfaces and vibrational states of the LiCN and NaCN molecules

The potential energy surfaces of the LiCN and NaCN molecules have been studied by using high-level ab initio methods. Three minimum energy structures, two linear and one T-shaped, have been found for both molecules. The most stable structure of NaCN has been found to be the T-shaped. A similar T-shaped and a linear isocyanide structure of LiCN have nearly the same energies which are very sensitive to electron correlations, so the relative stabilities of both structures could not be definitely determined. The character of the vibrational states calculated from the two-dimensional potential energy surface of LiCN has been analyzed, which allowed for a simple empirical modification of this surface yielding correct frequencies of the fundamental vibrations. The strong coupling of the large-amplitude bending motion with the stretching motion and the vibration-rotation interaction in the LiCN molecule have been investigated.

Rotational spectrum and bending potential of LiOH: A semirigid bender analysis

Some 29 microwave transitions in the millimeter region have been measured in the high-temperature vapor of LiOH, ranging up toJ=5, including lines from the isotopomers7Li16OH,7Li16OD in both ground and excited bending states, and7Li18OH in the vibrational ground state only. An analysis of these transitions, together with nine previously known radio-frequency transitions, based on the semirigid bender model of vibration-rotation interaction has been used to investigate the form of the bending potential and to measure the semirigidity parameters that show the variation in the bond lengths that accompany the large-amplitude bending motion. The molecule was found to be linear in its equilibrium configuration, with an essentially harmonic bending potential. The experimentally derived quadratic semirigidity parameter for the Li-O bond was found to agree to within less than 5% with that from an ab initio calculation at the MP3/6-311G** level.

A weak-mode representation of floppy molecules

Abstract The eigenstates of a model floppy molecule (i.e. a molecule for which large-amplitude isomerization-like deformations are possible) are variationally calculated. The Hamiltonian operator and the Hamiltonian matrix are established in following the adiabatic weak-mode approach that has been recently proposed. The model consists of a triatomic molecule with two linear isomers, roughly connected with HCN ⇌ CNH: the atomic masses are the appropriate ones, but the isomerization reaction profile does not present the shoulder that is typical of CNH, and the model potential energy surface is a simplified version of the one by Murrell et al. Indeed, the actual high-energy vibrational level distribution of both HCN and CNH turns out to be particularly complicated because of this shoulder and, in order to test new theoretical arguments for analyzing the vibrational eigenstates, using a model with no shoulder is simpler. For zero total angular momentum, the eigenvalues converge up to 20000 cm−1. An adiabatic model, based on the separation of hard (radial) and soft (angular) Jacobi coordinates, is used. The adiabatic representation (in which the analytical radial basis functions parametrically depend on the angle) is interesting from the physical viewpoint: it allows discriminating between various types of eigenstates, depending on (i) the angular distribution of the amplitude and (ii) the value of the projection of the state over the subspace corresponding to a given couple of adiabatic stretching quantum numbers. Many spectroscopic states (both energetically low- and high-lying) are localizated on one isomer side. Several other states are quantally delocalized on both sides, i.e. are linear combinations (interference pattern) of two or more contributions (at least one for each isomer), separated from each other by an angular range where the eigenfunction is very small. We call these states “composite”. Finally, high-lying states (for energies equal to or higher than well identified adiabatic isomerization barriers) are intrinsically delocalized, i.e. with noticeable amplitude almost everywhere. They are very well described within the framework of the adiabatic approach: large-amplitude bending motion of the light atom around the strongly bound diatomic core takes place. Only these states we term “floppy”. The adiabatic weak-mode description allows obtaining quasi-automatically a spectroscopic assignment (as far as it is meaningful) of the molecular states, by means of adiabatic quantum numbers, consistently from the low-lying levels (where the adiabatic quantum numbers are equivalent to standard normal-mode quantum numbers) up to the floppy states, for which normal-mode quantum numbers would be meaningless. The adiabatic quantum numbers appropriately indicate what part of the dynamics can be described as quasi-regular in the molecular states (basically the adiabatic stretching vibrations, and, in localized and floppy states, also the bending motion) and what other part (if any) can be deeply perturbed.

Structures and flexibilities of the alkali hydroxides

Analyses of the rotational transitions of cesium, rubidium and potassium hydroxide based on the semirigid bender model of vibration—rotation interaction have been used to investigate the form of the bending potential for these species, to ascertain the equilibrium structures and to measure the semirigidity parameters that show the variation in the bond lengths that accompanies the large-amplitude bending motion. The molecules were confirmed to be linear in their equilibrium configuration, with essentially harmonic bending potentials. The determined equilibrium geometries were found to be compatible with those derived by extrapolation techniques and the experimentally derived quadratic semirigidity parameter for the KO bond was found to agree well with that from an ab initio calculation at the MP3/DZ + P level. Ab initio calculations have been used to predict the semirigidity parameters of sodium hydroxide.

On the variation of bond length during large-amplitude bending from electron diffraction: the case of CaCl2

Abstract All geometrical parameters, including bond lengths, are influenced by large-amplitude vibrations. The magnitude of this effect was examined for metal dihalides performing large-amplitude bending motions, using CaCl2 as an example. By using quantum chemical calculations it was shown that the effect of bending on the bond length is very sensitive to the choice of basis set. A dynamic electron diffraction analysis, augmented with quantum chemical calculations, revealed that the effect of bending on the bond length is of moderate magnitude within experimental error. This fact contrasts with the consequences of other motions, in particular stretching, that must always be accounted for in any meaningful comparison of experimental and computed structures.

The structure of beryllium pseudohalides

The equilibrium geometries of the molecules HBeNCX and HBeXCN (XO, S) as well as HBeN 3 were calculated using second-order Møller-Plesset perturbation theory. The calculations predict linear frames for HBeNCX, HBeOCN and HBeN 3; HBeSCN is bent. New, T-shaped isomer forms are predicted for beryllium-cyanate and azide. Potential energy curves were calculated for the BeNC, BeXC and BeNN bends, which demonstrated that all these molecules are subject to large-amplitude bending motions. Harmonic vibrational frequencies and intensities were also obtained at the MP2 level.

Fourier-transform microwave spectroscopy of the HCCN radical. Determination of the hyperfine coupling constants

Two low-J transitions, N(J)=1(0)−0(1) and 1(2)−0(1), of the HCCN radical in its 3Σ− ground state have been studied by a pulsed-discharge-nozzle Fourier-transform microwave spectrometer. Spectrum with well-resolved hyperfine splittings due to hydrogen and nitrogen nuclei was observed, which enabled us to determine accurate hyperfine coupling constants for both the nuclei for the first time in the present study, as well as a much improved spin–spin coupling constant. These hyperfine coupling constants suggest that the electronic structure of the HCCN radical can be described as the one with the allenic structure to be almost twice more important than the carbenic structure. The present results seems to support a conclusion that the molecular structure of the radical is almost linear with a possibility of a large amplitude bending motion.

Infrared predissociation spectrum of the H3+ ion. II

The infrared predissociation spectrum of the H3+ ion has attracted considerable attention; theoretical models have been developed which account for many of the observed features and which make further predictions. This paper describes the results of experiments designed to test these predictions. The spectrum is recorded by bringing a mass-selected H3+ ion beam into parallel or antiparallel coincidence with a cw carbon dioxide infrared laser beam. In the earlier work, 27 000 lines were observed over the range 874–1094 cm−1, each line being recorded by detecting H+ fragment ions produced by predissociation. The spectrum varied according to the H+ kinetic energy window selected, and it was proved that many of the lines arise from metastable states of H3+ lying above the H2+H+ dissociation limit. The spectrum showed no immediately recognizable pattern, but low resolution convolutions revealed the existence of a coarse-grained structure of four main peaks. The isotopic species H2D+ and D2H+ showed similarly complex spectra which, however, differed depending on whether H+ or D+ fragments were detected. The most important conclusion from subsequent theoretical models is that the metastable states involved are in a region of classical chaos and hence cannot be simply assigned in terms of vibrational modes. However, the coarse-grained spectrum is associated with the remnants of a periodic orbit in which quasilinear H3+ undergoes a large amplitude bending motion. Rotational angular momentum barriers lead to trapping of these essentially regular states, which are embedded in a classically chaotic manifold. Semiclassical trajectory studies and three-dimensional quantum mechanical calculations are consistent with each other. Our present experimental methods are described and questions concerning reproducibility are addressed. We describe new measurements over the range 964–992 cm−1 spanning the position of one of the peaks observed earlier in the convoluted spectrum. The H3+ spectrum is recorded for a series of different H+ kinetic energy windows and the results are summarized in bar charts. Convolutions of the data recorded for H+ ions with very small center-of-mass kinetic energies are consistent with the earlier results and with theoretical predictions, but also reveal additional structure. Convolutions for large H+ kinetic energies (≥500 cm−1) reveal less evidence of characteristic structure. Measurements over the region 1025–1045 cm−1 are also described; they are only for very small H+ kinetic energy release, but the linewidths are also tabulated. Most of the metastable states of H3+ predissociate predominantly through a single channel, but examples of multiple dissociation channels have also been recorded. Direct measurements of some predissociation lifetimes are presented. Selected regions of the spectra of D2H+ and H2D+, measured by recording H+ and D+ fragments separately with kinetic energy windows from 0 to 3000 cm−1, are described. The results are in excellent agreement with theoretical predictions, as also are measurements of the background spontaneous predissociation.

The hyperfine structure of (DCCD)2

An experimental and theoretical study of the quadrupole-coupling hyperfine structure of the nonrigid (C2D2)2 dimer is carried out. This dimer exhibits a large amplitude interconversion motion which splits rotational levels into three sublevels. The quadrupole-coupling hyperfine pattern arising from the four deuterium atoms depends on the symmetry species of the tunneling sublevel. For nondegenerate sublevels, the hyperfine structure is especially interesting since the dimer behaves as if the quadrupole coupling were identical for all four deuterium atoms and the effective hyperfine Hamiltonian is completely symmetrical. The symmetry group used to classify the hyperfine levels is, therefore, the permutation group of four objects S4. For the other tunneling sublevels, which are doubly degenerate, the dimer behaves as if the two monomer units were inequivalent. Prior to the diagonalization of the hyperfine Hamiltonian, symmetry-adapted nuclear spin wave functions in S4 are set up and allow us to select hyperfine levels whose symmetry is compatible with the tunneling symmetry species. This formalism is used to analyze the hyperfine patterns of three rovibrational transitions in (C2D2)2, which were recorded under high resolution. The components of effective quadrupole-coupling tensors are thereby determined. These tensors are related to the eQq of an isolated DCCD monomer to obtain vibrationally averaged angles for large amplitude bending motions within the dimer.