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Volume 102, Issue 11, 15 March 1995

The hybrid rotational components in the 0^{0} _{0} origin band of the ÃA‘(S _{1})←X̃A’(S _{0}) transition in acetaldehyde
View Description Hide DescriptionThe 0^{0} _{0} origin band of the S _{1}←S _{0}, electronic transition that results from n→π* electron promotion has been observed under molecular beam conditions with a pulse amplified ring laser. At low temperatures, ∼0.7 K, the spectrum consisted of 11 lines that originated from K _{ a } ^{‘}=0 and J‘=0 or 1 rotational levels. A rotational analysis revealed that the transition between the a _{1}–a _{1} torsional levels gives rise to a c‐type band, whereas the e–e levels are connected by a hybrid transition that has components along the a, b, and c principal axes. The fluorescence emission from the e levels was greatly reduced at temperatures above 3 K. The interpretation of this photophysical effect requires an intermolecular collision within the molecular beam that quenches the fluorescence from the S _{1} state.

Proton interchange tunneling and internal rotation in HSH–NH_{3}
View Description Hide DescriptionAn electric‐resonance optothermal spectrometer and phase‐locked backward‐wave oscillators are used to investigate the b type, ΔK=±1, Δm=0 spectrum of the hydrogen‐bonded HSH‐‐NH_{3} and H^{34}SH‐‐NH_{3} complexes near 300 GHz. The spectrum is characterized by nearly free internal rotation of the NH_{3} subunit against the H_{2}S, as initially concluded from Stark‐effect measurements by Herbine et al. [J. Chem. Phys. 93, 5485 (1990)]. Transitions are observed for the K=1←0, m=0, A symmetry and the K=0←±1 and K=±2←±1, m=±1, Km≳0, E‐symmetry subbands. The transitions are split into doublets with a 3:1 relative intensity ratio indicative of tunneling interchange of the two H_{2}S protons. The observed selection rules, symmetric ↔ antisymmetric in the tunneling state, indicate that the tunneling motion reverses the sign of the molecular electric dipole moment component along the b inertial axis. The most likely interchange motion consists of a partial internal rotation of the H_{2}S unit about its c inertial axis, through a bifurcated, doubly hydrogen‐bonded transition state. The proton interchange tunneling splittings of 859–864 MHz vary little between K and m states, indicating that the interchange motion is only weakly coupled to the internal rotation. The barrier to proton interchange is determined to be 510(3) cm^{−1}, which can be compared to the ∼700 cm^{−1} barrier estimated from the 57 MHz tunneling splittings associated with the H_{2}O proton interchange in the related HOH‐‐NH_{3} complex. The observation of dissociation of HSH‐‐NH_{3} following excitation of the NH_{3} umbrella mode with a line‐tunable CO_{2} laser places an upper bound of 992 cm^{−1} on the hydrogen‐bond zero‐point dissociation energy. The band origin for the umbrella vibration of 992.5(10) cm^{−1} is blueshifted by 43 cm^{−1} from the hypothetical inversion‐free band origin of uncomplexed NH_{3}. Previous studies have shown that the HOH‐‐NH_{3} binding energy is greater than 1021 cm^{−1}.

Photoabsorption of Kr^{+} _{2} in the ultraviolet: Revisited
View Description Hide DescriptionThe photoabsorptionspectrum of the Kr^{+} _{2}ground electronic state (X ^{2}Σ^{+} _{ u }) has been measured in the ultraviolet (257–355 nm) by a fluorescence suppression technique. Peak absorption is recorded at ∼330 nm and the spectral width of the observed continuum is ∼60 nm (FWHM) which is ∼25% smaller than the value predicted by theory for a Kr^{+} _{2}(X) vibrational distribution thermalized at 300 K. Similar experiments with Ar/Kr mixtures: (1) reveal weak absorption attributed to ArKr^{+} peaking at ∼280 nm, and (2) suggest that the ArKr^{+} ion is rapidly converted to Kr^{+} _{2} by a displacement reaction.

Millimeter‐wave spectroscopy of vibrationally excited ground state alkaline‐earth hydroxide radicals (X ^{2}Σ^{+})
View Description Hide DescriptionPure rotational spectra of the alkaline‐earth monohydroxides have been recorded for vibrationally excited states (0 1 0), (0 2 0), (0 3 0), and (1 0 0) of the ground electronic state (X ^{2}Σ^{+}) using millimeter‐wave absorption spectroscopy. The radicals MgOH, CaOH, SrOH, and BaOH were studied. The data for CaOH, SrOH, and BaOH were analyzed with a linear ^{2}Σ^{+} model, but with the addition of two terms to account for contamination of the v _{2}=1 ^{2}Π and v _{2}=2 ^{2}Δ vibronic levels with ^{2}Π and ^{2}Δ electronic states. The data for MgOH, however, did not fit well to this linear model and is additional evidence that this species is quasilinear.

Spectral patterns and dynamical bifurcation analysis of highly excited vibrational spectra
View Description Hide DescriptionSpectral patterns associated with recently proposed assignments of Fermi resonance systems are investigated with specific application to the 2:1 Fermi resonance fitting Hamiltonian. It is shown that the spectrum of a pair of resonant modes has characteristic patterns associated with the structure of the corresponding classical phase space. In particular, when a spectral fitting Hamiltonian has a separatrix structure in its classical phase space, the quantum Hamiltonian has an emblematic spectral pattern, a ‘‘dip’’ in the level spacings. This basic pattern is the starting point for an investigation of level patterns corresponding to the bifurcation and catastrophe map classification and associated dynamically based assignments of Fermi resonance Hamiltonians. The 2:1 Fermi resonance Hamiltonian is investigated in detail as a typical system. There are distinctive patterns for polyads from different zones of the catastrophe map classification of the 2:1 system. Conversely, when these patterns occur in an experimental spectrum, then in order to reproduce them in a reasonably behaved spectral fit, it is necessary and sufficient to invoke a resonant coupling term in the fitting Hamiltonian. Spectral fitting therefore gives reliable information about the phase space structure of a molecule. These considerations are used to address the interpretation of recent experimental and theoretical investigations of H_{2}CO and benzophenone vibrational spectra.

Mid‐infrared vibrational spectrum of CO after photodissociation from heme: Evidence for a ligand docking site in the heme pocket of hemoglobin and myoglobin
View Description Hide DescriptionTime‐resolved mid‐ir absorption spectra of CO at 283 K have been measured 100 ps after photodissociation from human hemoglobin A, horse myoglobin, and sperm whale myoglobin. The spectra reveal two vibrational features that are narrower than any reported for CO in the condensed phase near room temperature, indicating that CO becomes localized in a rotationally constrained environment. The integrated absorbance under these narrow features is 0.53±0.05 times that found for sperm whale myoglobin in low temperature glasses. A model is developed that relates this reduction of integrated absorbance to molecular motion in a rotationally constrained environment. From this model, the barrier to CO rotation is found to be 1.5±0.25 kcal/mol. The two vibrational features are tentatively assigned to CO oriented oppositely in the same site within the heme pocket. Evidently, the residues circumscribing the heme pocket in hemoglobin and myoglobin fashion a cavity near the binding site that accommodates the dissociated CO and restricts its rotational motion. This ‘‘docking’’ site mediates ligand transport to and from the active binding site and may be important to the function of ligand‐binding heme proteins.

V, Nb, and Ta hydride molecules in deuterium and rare‐gas matrices: Infrared and electron spin resonance spectra
View Description Hide DescriptionThe VH_{2} molecule was found to have S=3/2 and a ^{4}Σ ground state with a zero‐field splitting parameter ‖D‖=0.315 cm^{−1}. ^{51}V (I=7/2) hyperfine splitting was observed in the ESRspectra, but the hydrogen hyperfine was unresolved. The narrowest lines were observed for VD_{2} in solid deuterium at ∼2 K. Efforts to observe VH_{4} via ESR were not successful presumably because it could not be prepared in a high enough concentration. The infrared spectra of NbH_{2} molecules and their deuterated isotopomers were observed in solid deuterium and rare‐gas matrices. NbH_{2} was found to be bent at 130°, in accord with theoretical calculations. NbH_{2} was not observed in ESRspectra although it presumably has a ^{4} B _{1}ground state; this is attributed to a large (≳4 cm^{−1}) negative D value. NbH_{4} was observed via ESR as a tetragonally distorted (D _{2d }) tetrahedral molecule in its ^{2} B _{1} lowest state resulting from a static Jahn–Teller effect. ^{93}Nb (I=9/2) and also H hyperfine splittings were observed. A corresponding TaH_{4}spectrum was attributed to a similarly distorted tetrahedral S=1/2 molecule.

High resolution rotational analysis of the B ^{3}Π–X ^{3}Δ (1,0) band of titanium monoxide
View Description Hide DescriptionThe B ^{3}Π–X ^{3}Δ (1,0) band of titanium monoxide has been studied at sub‐Doppler resolution (0.002 cm^{−1}) by crossing a beam of TiO molecules with a cw tunable laserbeam and by collecting the laser‐induced fluorescence. The rotational structure of 42 branches belonging to the ^{3}Π–^{3}Δ transition has been analyzed up to rotational quantum numbers equal to 94. Spectroscopic data have been reduced to a set of 24 molecular constants, using a case (a) effective Hamiltonian. The rotational, spin–orbit and Λ‐doubling constants are discussed in terms of the leading configurations which give rise to the X ^{3}Δ and B ^{3}Π electronic states. It is shown that for the B state, existing ab initio calculations are not able to reproduce the second order spin–orbit effect and the Λ doubling effect.

Vibrational predissociation of HF dimer in ν_{HF}=1: Influence of initially excited intermolecular vibrations on the fragmentation dynamics
View Description Hide DescriptionTheoretical study of the influence of excited intermolecular vibrations on the total and partial decay widths of HF dimer is reported. Vibrational predissociation (VP) lifetimes and rotational state distributions of HF fragments were calculated for various quasibound states of (HF)_{2}, corresponding to combinations of the intermolecular stretching (ν_{4}) and bending (ν_{5}) vibrations with the ‘‘free’’ (ν_{1}) and ‘‘bonded’’ (ν_{2}) HF stretch fundamentals, for total angular momentumJ=1, K=0. The calculations were performed on an ab initio six‐dimensional potential energy surface of Quack and Suhm, using a quantum four‐dimensional golden rule methodology. The VP lifetimes and product rotational distributions exhibit pronounced dependence on the type of the initially excited intermolecular vibration of HF dimer. The energy deposited in the ν_{4} intermolecular stretch evolves into the translational energy of the fragments. Excitation of the ν_{5} intermolecular bending vibration, combined with the ν_{1} fundamental, is transferred to the product rotational energy. This is in good agreement with the experimental results of Bohac and Miller. We also found that in conjunction with the ν_{2} fundamental, most of the ν_{5} bending vibrational energy emerges in the translational energy of the products.

A new method for calculating the rovibrational states of polyatomics with application to water dimer
View Description Hide DescriptionA new method is developed for calculating the lowest few rovibrational states of polyatomic molecules, using the discrete variable representation (DVR). The method is an extension to the diagonalization‐truncation procedure which has been used in most DVR calculations to date. It starts with a set of functions which approximately describe the wave function at a set of DVR points, and adds corrections to them by using variation‐perturbation theory. This is done iteratively, after the manner of the recently developed iterative secular equation (ISE) method of Slee and LeRoy. This new ‘‘DVR‐ISE’’ method can be successfully applied to molecules whose dynamics involve strong coupling between all degrees of freedom. To demonstrate this it is applied to (H_{2}O)_{2} in calculations of the lowest few energy levels for intermolecular angular motion. Better convergence is obtained than was found possible in conventional finite basis calculations on the same system.

Structure of powder deuteroammonia between 2 and 180 K revisited: A refinement of the neutron diffraction pattern taking into account molecular reorientations: analysis of the diffuse intensity
View Description Hide DescriptionThe standard Rietveld profile analysis is a powerful tool for refining the structure of powder crystals. Nevertheless, in case of molecular crystals, where rigid groups undergo reorientations of large amplitude in well‐defined directions, thermal ellipsoids, even with anisotropic terms, may not be sufficient to account for the motion. That is the case for deuteroammonia for which strong librations of the ND_{3} groups are observed even at 2 K. In this paper we present a refinement of the structure of deuteroammonia using a model allowing the ND_{3} group to perform reorientations about the easy C3 axis of the cubic lattice; the adjustment of diffraction patterns measured at 2, 78, and 180 K shows the temperature dependence of the librational amplitude. The geometry of the ammonia molecule in the crystal is found to be the same as in the gas phase [r _{N–D}=1.008(4) Å] and is in excellent agreement with that determined by the analysis of the intramolecular structure factor for large momentum transfers; furthermore the molecular parameters are directly obtained from the fit, without need of rigid body corrections of bond lengths. This model assumes correlated motion of the D atoms which is confirmed by a semiquantitative analysis of the Q dependence of diffuse scattering observed under the Bragg peaks.

Dynamic level‐crossing model of antiphase electron spin polarization in spin‐correlated radical pairs
View Description Hide DescriptionThe unusual antiphase electron spin polarizations, attributed to residual spin correlations in incompletely separated radical pairs, are treated by a dynamic model in which the polarized electron spin transitions occur as the radicals diffuse through the separations where the transitions are in resonance with the microwave field. This model shows that the inter‐radical exchange interaction, and in some cases magnetic dipolar interactions as well, can produce the observed polarizations despite varying rapidly with diffusive motions of the radicals. However, the apparent fixed splitting of the emissive and absorptive components of the antiphase line is usually determined by the intrinsic width of the unpolarized electron spin resonance(ESR) line rather than by the inter‐radical interactions. Surprisingly, a static model, in which the radicals are immobile during the short ESR observation period, yields the same polarization as the dynamic model under quite general conditions.

Velocity dependent state‐to‐state differential cross sections for rotational transfer in Li_{2}–Xe using velocity selected double resonance
View Description Hide DescriptionWe describe a new and wholly spectroscopic technique in which the state‐to‐state differential scattering cross section (dcs) is determined for rotationally inelastic atom–molecule collisions. The method uses two single frequency tunable dye lasers in a sub‐Doppler double resonance experiment which has the added advantage that dependence on collision velocity may readily be determined. The method is illustrated by a determination of the dcs for rotational transfer (RT) in Li_{2} A ^{1}Σ^{+} _{ u }–Xe collisions. The dcs is obtained from the shape of the double resonance line and rotationally inelastic transitions Δj=−4 to +10 were studied. For each a range of initial relative velocities was selected and the scattering angles so obtained are differential in both angle and velocity. These are the first such measurements in atom–molecule scattering. The trends observed in scattering angle with Δj and with velocity are successfully interpreted using a hard ellipse model. We have observed significant differences in the dcs between upwards and downwards Δj transitions. The origins of these differences are discussed and emphasize the importance of the threshold velocity for a particular Δj channel.

Classical trajectories on simple model potentials for N_{2}–Kr: Comparison with relaxation and other data
View Description Hide DescriptionWe compare the ability of six N_{2}–Kr potential energy surfaces to predict experimental interaction second virial coefficients, diffusion coefficients, mixture viscosity,thermal conductivity, and nuclear magnetic resonance(NMR) rotational relaxation cross sections. These include a previously published empirical surface derived from fits to molecular beam experiments and various model potentials of the Tang and Toennies (TT) type. The TT type potentials differ in the set of dispersion coefficients employed. Two sets are obtained from published ab initio calculations, another from combining rules and one from empirical considerations. The repulsive parameters have been obtained from published results of a charge overlap combining rule. A variation of the TT model suggested by Aziz is also used to further investigate the effect of the repulsive wall anisotropy on the rotational relaxation cross sections. Forty‐five effective cross sections that determine the bulk transport and relaxation phenomena have been calculated by classical trajectories for temperatures ranging from 100 to 800 K. The sensitivity of the NMR‐derived cross sections to the various characteristics of the anisotropy of the potential (such as the anisotropy in the well depth, in the high repulsive wall, in the low repulsive wall, and at V=0) are examined. The empirical anisotropic LJ(12,6) surface of Rotzoll provides the best agreement with the diffusion,viscosity,thermal conductivity, and NMR relaxation experimental results.

Evidence for stepwise dissociation dynamics in acetone at 248 and 193 nm
View Description Hide DescriptionThe technique of molecular beam photofragment translational spectroscopy has been used to study the dissociation of acetone following S _{1}←S _{0} (248 nm) and S _{2}←S _{0} (193 nm) excitation. Excitation at 248 nm resulted in the production of CH_{3} and CH_{3}CO with 14.2±1.0 kcal/mole on average of the available energy appearing as translation of the photofragments. Comparison of the measured 〈E _{ T }〉 with values reported at 266 nm suggest that the energy partitioning is dominated by the exit barrier caused by an avoided crossing on the potential energy surface. A substantial fraction (30±4%) of the nascent acetyl radicals from the primary dissociation contain sufficient energy to undergo spontaneous secondary decomposition. From the onset of the truncation of the CH_{3}CO P(E _{ T }) a threshold of 17.8±3.0 kcal/mole for the dissociation of the acetyl radical has been determined in agreement with recent results on the photodissociation of acetyl chloride. The translational energy release in the dissociation of CH_{3}CO closely matches the experimentally determined exit barrier. At 193 nm the only observed dissociation pathway was the formation of two methyl radicals and carbon monoxide. On average ∼38% of the available energy is found in product translation suggesting that significant internal energy resides in the nascent CH_{3} fragments consistent with the results of Hall et al. [J. Chem. Phys. 94, 4182 (1991)]. We conclude that the dynamics and energy partitioning for dissociation at 193 nm is similar to that at 248 nm.

Direct calculation of time delays and eigenlifetimes for the reaction He+H^{+} _{2}■HeH^{+}+H
View Description Hide DescriptionThe Parker and Pack method for calculating accurate three‐dimensional reactive scattering information uses adiabatically adjusting, principal axes hyperspherical (APH) coordinates to reduce the three‐dimensional Schrödinger equation to a set of coupled equations in the hyperradius ρ. Solution of these coupled equations in the usual manner produces the scattering S matrix for the three‐atom system of interest. To obtain these coupled equations it is necessary to solve a series of two‐dimensional Schrödinger equations on the surface of a hypersphere defined by the hyperspherical polar and azimuthal angles θ and χ, respectively. In this paper, the computational advantages of the direct method for obtaining the energy derivatives of the S matrix are further documented using both the discrete variable representation and the analytical basis method of Pack and Parker for obtaining surface functions. Detailed studies of the title reaction are used to explore various operational criteria to assure that the predicted scattering results such as state‐to‐state transition probabilities and time delays are converged to the extent desired. It is also shown that the Hermitian property of the Smith lifetime matrix Q, which is accurately produced with the direct energy derivative method, is often not preserved when numerical energy derivatives are employed.

Geometric phase in two Kramers doublets molecular systems
View Description Hide DescriptionThe geometric phase in two Kramers doublets molecular systems is considered. We obtain the general formula for the gauge potential arising from the vibronic interaction and spin–orbit interaction between two Kramers doublet electronic levels. Simple models for the Jahn–Teller and Renner–Teller problems with spin–orbit coupling are considered. It is demonstrated that the energy spectra obtained by the Born–Oppenheimer approximation with the gauge potential agree quite well with the exact energy spectra in strong vibronic cases. It is also shown that the inclusion of the scalar gauge potential is important in order to obtain accurate zero point energy. As an application, vibronic levels of the X̃ ^{2} E ^{’} state of Cu_{3} are reexamined including spin–orbit interaction.

Ab initio study of the three lowest‐lying (X ^{1}Σ^{+,} ^{3}Σ^{+,} and ^{1}Σ^{+}) electronic states of AgF
View Description Hide DescriptionAb‐initio pseudopotential two‐configuration self‐consistent field followed by extensive variational and perturbational second order Mo/ller–Plesset multireference configuration interaction calculations using localized molecular orbitals were performed to characterize the structure and adiabatic potential energy curves of the three lowest (X ^{1}Σ^{+}, ^{3}Σ^{+}, and ^{1}Σ^{+}) purely electronic states of the AgF molecule. Spin‐orbit interactions were introduced semiempirically in a second step. The very strong coupling of the neutral Ag(4d ^{10}5s ^{1})F(2s ^{2}2p ^{5}) and ionic Ag^{+}(4d ^{9}5s ^{1})F^{−}(2s ^{2}2p ^{6}) configurations at rather short internuclear distance for both excited ^{3,1}Σ^{+} states is responsible for the appearance of very shallow minima, thus leading to a limited number of stable vibrational levels for these excited states as suggested previously for the AO ^{+} state. In contrast with the CuF molecule, where only the ionic configuration Cu^{+}(^{3,1} D)F^{−}(^{1} S) is present in the ^{3,1}Σ^{+} states, this coupling of ionic and neutral structures in AgF is explained by the relative positions of the valence orbital energies of the neutral Cu and Ag atoms with respect to the 2p level of the halogen atom. These results lead to the assignment of the observed AO ^{+}–X ^{1}Σ^{+} transition as a ^{1}Σ^{+}–^{1}Σ^{+} type transition.
The very recently observed aΩ1 and A’Ω1 states are shown to be, respectively, the Ω=O ^{−} and Ω=1 spin–orbit components of the ^{3}Σ^{+} state, which justifies the relabeling of aΩ1 into a aΩO ^{−}. The calculated spin–orbit‐induced splitting between these two components is in excellent agreement with the observed one after reconsidering spectroscopic data. For all these states the calculated spectroscopic constants are in good agreement with available experimental data. The fourth experimental state, BO ^{+}, is probably not correlated with the ^{3}Π valence state as previously suggested but it could rather correspond to a Rydberg ionic state involving the Ag^{+}(4d ^{9}5p)F^{−}(2s ^{2}2p ^{6}) structure.

A simplified released‐node quantum Monte Carlo calculation of the ground state of LiH
View Description Hide DescriptionWe report an exact ab initio calculation of the ground state of the LiH molecule using a simplified released‐node Green’s functionquantum Monte Carlo method. The energy determined for an internuclear separation of 3.015 bohr is −8.070 21±0.000 05 hartree, a value lower than that of the lowest‐energy variational calculation, more accurate than that of prior quantum Monte Carlo calculations, and in excellent agreement with the nonrelativistic energy of −8.070 21 hartree determined from experimental measurements.

Electronic structure via the auxiliary‐field Monte Carlo algorithm
View Description Hide DescriptionAuxiliary‐field Monte Carlo (AFMC) is an exact approach for calculating the ground state of a system of fermions (or bosons) interacting by pair‐potentials. The method uses the Hubbard–Stratonovich transformation to replace the exact imaginary‐time propagator by an average over an ensemble of propagators for independent particles in the presence of a varying external field, so that the calculation of the exact energy is reduced to multiple independent calculations, each of which costs essentially the same as one Hartree–Fock iteration. Here we consider the application of AFMC to calculate molecular structure, and present preliminary simulations on He and Be. We develop two simple methods to partially alleviate a ‘‘sign‐problem’’ in AFMC through restriction of the length of the imaginary‐time propagation, by either a simultaneous propagation of several initial states followed by subspace‐diagonalization or by incorporation of information from all propagated time steps. The first method is tested and found to yield significant improvement in accuracy. For the present simulations, the single‐particle orbitals are expanded in a given set of primitive orbitals. The resulting spectral‐AFMC method yields, for sufficiently converged ensembles, the full‐CI energy associated with a given basis. The developments reported here, and in particular the demonstration of subspace‐diagonalization, have however general validity independent of whether a basis set or a grid representation is used for the single‐particle orbitals (in the first case a full‐CI result is obtained in the given basis, while a converged grid representation would yield the exact result).