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Volume 102, Issue 23, 15 June 1995

Calculation of intermolecular interaction in aromatic molecular clusters from direction dependent atom‐pair potentials
View Description Hide DescriptionAn expression for the interaction potential between two anisotropic molecules is derived. This expression is suitable for describing the van der Waals interaction between two chromophores within a bichromophoric molecular cluster. For the anthracene–naphthalene cluster the calculation predicts the existence of two isomers, in agreement with experimental observations. The model is also successfully applied to other clusters yielding better results than those obtained by alternative methods which do not take into account the anisotropy of molecular polarizability.

Effects of velocity changing collisions on line shapes of HF in Ar
View Description Hide DescriptionThe generalized Hess method (GHM) gives a line shape expression which is formally equivalent to the Rautian–Sobel’man hard collision model of Dicke narrowing, but differs radically in the definition of one of the relaxation terms. The relaxation term leading to pressure broadening is the same, but the term leading to Dicke narrowing and ultimately to Dopplerline shapes at zero density differs in certain important respects: (1) in GHM it is a weighted sum of the pressure broadening coefficient and an optical diffusion coefficient and (2) there is no sharp distinction between ‘‘velocity changing’’ and ‘‘phase changing’’ collisions. The Dicke narrowing term should thus be understood as including both collision types irretrievably intermixed, with GHM providing a prescription for both relaxation terms. Applied to HFv=0→1, j→j±1 absorption spectra in a bath of Ar and using an accurate interaction potential obtained from spectra of the van der Waals complex and essentially exact close coupling scattering S matrices, GHM provides a rather good description of recently measuredline shapes.

Electronic spectra of ND_{3} in the region of 64 500–73 500 cm^{−1} and their vibronic assignments
View Description Hide DescriptionUsing a monochromatic VUV beam generated by two‐photon resonant sum frequency mixing in a Mg–Kr mixture, we have investigated the electronic transitions of ND_{3} in the 64 500–73 500 cm^{−1} region by detecting the fluorescence from the predissociation fragments of ND_{3} or by detecting the ions produced via VUV+visible resonance enhanced multiphoton ionization (REMPI). Vibronic transitions from the ground state to the 2^{ n }, n=7–12 levels of the B̃ ^{1} E‘ state are rotationally resolved and the relevant molecular constants are deduced. Two parallel progressions are observed, of which one has been analyzed previously by Douglas [Faraday Discuss. Chem. Soc. 35, 158 (1963)]. We attribute the progression observed by Douglas as transitions to the 2^{ n }3^{1} vibronic levels of the B̃ ^{1} E‘ state, the other one as transitions to the 2^{ n }3^{1}4^{1} vibronic levels of the same electronic state. Transitions to the υ_{2} ^{’}=0 vibronic level of the previously assigned D̃ ^{1} E‘ state have been rotationally resolved and the electronic symmetry of this electronic state is reassigned to E’.

Predissociative linewidths of (4pσ) M ^{2}Σ^{+} (v=1) and (3dσ,π) H ^{2}Σ^{+}, H’ ^{2}Π (v=2) Rydberg states of NO studied by the two‐color laser‐induced grating technique
View Description Hide DescriptionThe two‐color laser‐induced grating (TC‐LIG) technique has been employed to probe the predissociative Rydberg states (4pσ) M ^{2}Σ^{+} (v=1) and (3dσ,π) H ^{2}Σ^{+}, H’ ^{2}Π^{±} (v=2) and the non‐Rydberg B ^{2}Π (v=26) state of nitric oxide. The ultraviolet pump laser frequency is fixed to a specific rotational line of the A ^{2}Σ^{+} (v’=1 and 2)←X ^{2}Π_{3/2} (v‘=0) transition of NO. Interference of two pump laser beams crossing at a small angle in the gas sample forms a population grating. Then, the visible probe laser beam is diffracted off the grating as the signal beam when the probe laser frequency is resonant to a transition from the rotational level excited by the pump laser. Term values and rotational assignments of the H ^{2}Σ^{+}, H’ ^{2}Π^{±} (v=2)–B ^{2}Π_{3/2} (v=26) states have been established for the first time, resulting in the value of ∼1.77 cm^{−1} for the l‐uncoupling constant. Line broadenings due to predissociation are observed in the TC‐LIG spectra for the M ^{2}Σ^{+} (v=1) and H ^{2}Σ^{+}, H’ ^{2}Π^{+} (v=2) states. The linewidths of the M ^{2}Σ^{+} (v=1) state show no marked rotational dependence except for the N=4 level which is locally perturbed. On the other hand, the predissociative lifetimes of the H ^{2}Σ^{+} and H’ ^{2}Π^{+} (v=2) states exhibit a significant rotational dependence: The linewidth of the former state decreases with N, while the reverse tendency is seen for the latter. The mixing between the H ^{2}Σ^{+} and H’ ^{2}Π^{+} states caused by l‐uncoupling explains the observed rotational dependence successfully.

Theory and calculation of singlet excitation energy transfer in mixed molecular crystals
View Description Hide DescriptionA theoretical study of excitation energy transport among dipole–dipole interacting guests in mixed molecular crystals is carried out. To describe the temporal evolution of the excited state population, we derive a microscopic theory which treats an ensemble of dipole–dipole interacting guest molecules homogeneously distributed among two inequivalent sites of a host lattice. The theory is based on a generalized effective Hamiltonian accounting for intramolecular excited state depopulation and excitation energy transfer. The results are applied to the analysis of experimental data obtained from transient grating experiments in p‐terphenyl:pentacene mixed molecular crystals.

Phonon dynamics and relaxation processes in isotopically pure ^{35}Cl_{2} and natural crystalline chlorine
View Description Hide DescriptionWe have measured the Raman spectrum of natural and 99% isotope 35 chlorine crystal, in the lattice and in the internal mode regions, using a high resolution Raman spectrometer. We report the temperature dependence of the linewidth for both the lattice and the internal vibrational modes. The data were analyzed in terms of anharmonic interactions and contributions from the isotopic disorder. The lattice phonons are little affected by the isotopic disorder, while the internal vibrons are extremely sensitive to the presence of isotopic impurities. In the latter case the linewidths of the A _{ g } and B _{3g } internal vibrons are about one and two orders of magnitude, respectively, larger in the natural than in the isotopically pure sample. The Raman spectrum of natural chlorine in the internal region is correctly reproduced by an harmonic lattice dynamics calculation weighted over the statistical distribution of the isotopic species in the lattice.

Structure and vibrations of the phenol‐ammonia cluster
View Description Hide DescriptionThe phenol‐ammonia 1:1 complex has been investigated by mass resolved hole burning spectroscopy and ab initio methods at the HF/6‐31G(d,p) and HF/6‐31++G(d,p) levels of theory. By means of spectral hole burning four bands in the region of intermolecular vibrations could be assigned to the 1:1 complex. The ab initio computed cluster structure and its normal vibrations are reported and compared to the experimental results. Anharmonic calculations were carried out for the ammonia torsion. The results are compared to structurally related complexes.

A new time‐dependent approach to the direct calculation of reaction rates
View Description Hide DescriptionA wave packet dynamical approach to the direct calculation of the rate constant of a chemical reaction is presented. Based on the position‐flux correlation function of Miller, Schwartz, and Tromp [J. Chem. Phys. 79, 4889 (1983)] a reaction rate operator is introduced, which can be viewed as the thermal analog of the energy‐dependent reaction probability operator [J. Chem. Phys. 99, 3411 (1993)]. It is shown that this reaction rate operator has in general only a small number of eigenstates with nonvanishing eigenvalues. These eigenstates can be interpreted as the vibrational ground state and the vibrationally excited states of the activated complex. The eigenstates and eigenvalues can efficiently be computed via an iterative (Lanczos) diagonalization scheme. The number of wave packet propagations required equals approximately the number of relevant states of the activated complex, it is considerably smaller as in previous approaches to the calculation of rate constants based on wave packet dynamics. The new approach is illustrated by three examples: transmission through a one‐dimensional (Eckart) potential barrier, the collinear model of the H+H_{2}reaction, and the H+H_{2}reaction in its full dimensionality for J=0. For temperatures below 1000 K, in all examples presented, the rate constant can be calculated employing only a single wave packet. This result suggests that the approach can efficiently be applied to problems with a larger number of degrees of freedom.

Symplectic integrators for the multichannel Schrödinger equation
View Description Hide DescriptionThe multichannel radial Schrödinger equation that arises in time‐independent inelastic scatteringtheory and certain bound state problems has a classical Hamiltonian structure in which the radial coordinate plays the role of time. One consequence of this Hamiltonian structure is that the Schrödinger equation has symplectic symmetries, which lead in the context of inelastic scattering to the unitarity and symmetry of the S matrix. Another consequence is that so‐called symplectic integrators can be used to solve the radial Schrödinger equation, both for bound state and scattering problems. This idea is used here to derive a new family of symplectic integrator‐based log derivative methods for solving the multichannel radial Schrödinger equation. In addition to being simpler to write down and program, these methods are shown to be highly competitive with Johnson’s original log derivative method for several inelastic scattering and bound state test problems. An equivalent solution following version of the symplectic integrator family is also introduced and shown to have similar advantages over the DeVogelaere method. A number of more formal consequences of the classical Hamiltonian structure of the radial Schrödinger equation are also noted.

Gas phase reactions of N_{2}O_{5} with NO^{−} _{2}(H_{2}O)_{ n=0–2}, NO^{−} _{3}(H_{2}O)_{ n=1,2}, and NO^{−} _{ n=2,3}HNO_{2}
View Description Hide DescriptionThe reactions of N_{2}O_{5} with the NO^{−} _{2}(H_{2}O)_{ n=0–2}, NO^{−} _{3}(H_{2}O)_{ n=1,2}, and NO^{−} _{ n=2,3}HNO_{2} ions were studied in a flow‐tube apparatus in a He‐buffer gas at several temperatures within the range 167–298 K and at a pressure of 0.28 Torr. All these ions were observed to react quite efficiently with N_{2}O_{5}, giving rise to the main product ion NO^{−} _{3}HNO_{3}. This finding is of atmospheric interest since these reactions may occur in the atmosphere and are potentially relevant to the chemistry of reactive nitrogen species involved in ozone destruction. These results also have implications for the derivation of the HNO_{3} concentration in the upper earth’s atmosphere from ion composition measurements. The rate constants of the observed reactions were determined and mechanisms are proposed which account for the findings.

The CO:CO_{2} complex in argon matrices: Experimental evidence for two conformations with spontaneous interconversion
View Description Hide DescriptionThe CO:CO_{2} complex in argon matrices is identified near the CO absorption which appears at 2138.49 cm^{−1}, slightly shifted from the pure argon value of 2138.64 cm^{−1}, because of the presence of CO_{2}. It exhibits two features on each side of the CO frequency: a doublet at 2143.34 and 2143.01 cm^{−1} (HF A and B lines) and a narrow line at 2135.38 cm^{−1} (LF line); these small shifts indicate weakly complexed C–O stretching modes. When the temperature is raised from 5 to 12 K, the LF line decreases progressively and disappears at the benefit of the HF A and B lines, the total absorption intensity remaining unchanged. This effect is perfectly reversible and can be explained by an exchange between two different conformations of the CO:CO_{2} complex, with complexed C–O bonding shifted either towards a higher frequency (HF form), or towards a lower one (LF form). Furthermore, after a fast cooling down to any given temperature below 12 K, the intensity ratio between the two forms is time dependent; the high temperature form (HF form) converts into the LF form within a few minutes. The equilibrium value of the intensity ratio LF/HF and the rate constants for the conversion are temperature dependent. We have checked that this conversion, occurring without any temperature change, is not photoinduced.

Diffusion‐controlled reaction rate to asymmetric reactants under Coulomb interaction
View Description Hide DescriptionThe rate constant for diffusion‐controlled reactions between asymmetric reactants described by the simple model of Solc and Stockmayer under the influence of Coulomb‐type interaction is considered. Using the method of dual series relations, we calculate the rate constant with a high accuracy and obtain some approximate analytical formulas. We compare our results with an approximate analytical formula derived before by the constant‐flux approximation and with numerical calculations based on the Brownian dynamics simulation. It is shown that in the case of strong attractive potential the rate constant only slightly depends on the size of the active site and tends to the classical Debye result for isotropically reactive particles with a further increase in the Onsager length. Moreover, it is shown that for small‐sized active sites the effect of the interaction potential is to scale the rate constant for neutral reactants by a Boltzmann factor, which was first conjectured by Zhou [Biophys. J. 64, 1711 (1993)].

The F+HD→DF(HF)+H(D) reaction revisited: Quasiclassical trajectory study on an ab initio potential energy surface and comparison with molecular beam experiments
View Description Hide DescriptionThe dynamics of the F+HD reaction has been studied by means of quasiclassical trajectory calculations on an ab initiopotential energy surface (PES) at several collision energies. At the collision energy of 85.9 meV and for the DF+H isotopic channel of the reaction, there is a remarkable agreement between calculated and experimental results, in both the center of mass (c.m.) differential cross sections (DCS) and in the simulation of the laboratory (LAB) time of flight (TOF) and angular distributions (AD). The good agreement also extends to the lower collision energy of 58.6 meV for this channel of the reaction. In contrast, the simulation of the LAB angular distributions for the HF+D channel shows strong discrepancies between theory and experiment at both collision energies, which can be traced back to the absence of a forward peak in the calculated c.m. DCS for HF(v ^{’}=3). Simulations made from QCT calculations on other PES with important HF(v ^{’}=3) forward scattering contributions also fail to reproduce the overall AD. The theoretical findings and especially the roles of translational energy and initial rotational momentum on the dynamics of this reaction are discussed in terms of the topology of the PES through the analysis of individual trajectories.

The thermal energy dependence (10–20 eV) of electron impact induced fragmentation of C_{60} in molecular beams: Experiment and model calculations
View Description Hide DescriptionWe have studied the dependence of electron impact induced ionization and fragmentation of C_{60} molecules in effusive molecular beams upon the initial thermal excitation in the temperature range of 1190–1875 K, corresponding to an average vibrational energy of 10–20 eV. This is the largest energy range of parent molecule thermal excitation ever reported for electron‐impact mass‐spectrometric studies. The normalized curves of electron energy (E _{ e }) dependent ion currents of C^{+} _{60} and C^{+} _{58} were measured and analyzed for the temperatures (T _{0}) of 1190, 1435, 1570, 1695, and 1875 K. Similar measurements were done for C^{+} _{2n } (n=26–28) fragments for T _{0}=1190 and 1875 K. We have developed an expression for the dependence of C^{+} _{58} fragment ion current i _{58}(E _{ e },T _{0}), formed via the decay process C^{+} _{60}→C^{+} _{58}+C_{2}, on electron energy and initial temperature. Using this expression and the strong temperature dependence observed, we have proposed a simple experimental method for estimating the energy deposition function—the probability density of vibrational excitation ε by an ionizing electron of energyE _{ e }. The effective (apparent) value of maximum deposited energy was found to be ε_{ m }(E _{ e })=E _{ e }−E*, where E*=30±5 eV. Possible interpretations for this surprisingly low value are discussed. Comparing the experimental i _{58}(E _{ e },T _{0}) curves with the calculated ones over the range of E _{ e }=30–80 eV we find that for T _{0}≤1600 K, good agreement is obtained assuming that the C_{60} initial internal excitation is determined by the source temperature alone.
For the higher temperature range 1600 K≤T _{0}≤1900 K, we had to use a modified calculation taking into account radiative cooling and ensemble evaporative cooling processes along the molecular beam flight path. As a result, we have obtained an accurate simulation of the complete family of i _{58}(E _{ e },T _{0}) curves over all the temperature range measured, using a single set of independently measured physical quantities, and without any adjustable parameter. Uniqueness and sensitivity were thoroughly checked and demonstrated. The good agreement between experiment and calculation basically confirms our description of the underlying process and provides an additional support for the values of the independent physical parameters used. We have used maximum energy deposition parameter of E*=31 eV, an activation energy of E _{0}=4.3–4.5 eV for the neutral fragmentation channel C_{60}→C_{58}+C_{2} and E _{1}=4.0 eV for the ion fragmentation channel C^{+} _{60}→C^{+} _{58}+C_{2}, and pre‐exponential factors of A _{0}=A _{1}=2.5×10^{13} s^{−1}. These values are very close to former ones obtained by us from analysis of time‐of‐flight distributions and integrated flux decay measurements of hot C_{60} molecular beams. Correspondence with other results reported in the literature is discussed and a two‐step dissociation mechanism is proposed.

Energy relaxation of localized excitations in solid argon
View Description Hide DescriptionThe mechanisms of energy transfer from a single excited lattice particle (an energy spike) to the bulk crystal are investigated in detail. An argon matrix built up by nearly 3000 atoms serves as a model system and the molecular dynamics method is used to study the energy flow through the lattice on a femtosecond time scale. Excitation energies up to 4 eV have been used and the energy transport has been found to proceed most effectively via shock waves along 〈110〉 crystalline directions. A theoreticalmodel is employed, which confirms the shock wave character of energy transport and shows even quantitative agreement with the numerical results.

Nonadiabatic effects on the charge transfer rate constant: A numerical study of a simple model system
View Description Hide DescriptionWe use a minimal model to study the effects of the upper electronic states on the rate of a charge transferreaction. The model consists of three ions and an electron, all strung on a line. The two ions at the ends of the structure are held fixed, but the middle ion and the electron are allowed to move in one dimension, along the line joining them. The system has two bound states, one in which the electron ties the movable ion to the fixed ion at the left, and the other in which the binding takes place to the fixed ion at the right. The transition between these bound states is a charge transferreaction. We use the flux–flux correlation functiontheory to perform two calculations of the rate constant for this reaction. In one we obtain numerically the exact rate constant. In the other we calculate the exact rate constant for the case when the reaction proceeds exclusively on the ground adiabatic state. The difference between these calculations gives the magnitude of the nonadiabatic effects. We find that the nonadiabatic effects are fairly large even when the gap between the ground and the excited adiabatic state substantially exceeds the thermal energy. The rate in the nonadiabatictheory is always smaller than that of the adiabatic one. Both rate constants satisfy the Arrhenius formula. Their activation energies are very close but the nonadiabatic one is always higher. The nonadiabatic preexponential is smaller, due to the fact that the upper electronic state causes an early recrossing of the reactive flux. The description of this reaction in terms of two diabatic states, one for reactants and one for products, is not always adequate. In the limit when nonadiabaticity is small, we need to use a third diabatic state, in which the electron binds to the moving ion as the latter passes through the transition state; this is an atom transfer process. The reaction changes from an atom transfer to an electron transfer, as nonadiabaticity is increased.

Density functional calculations of lanthanide oxides
View Description Hide DescriptionDensity functional (DF) calculations have been performed on LaO, EuO, GdO, YbO and YbF. Gradient‐exchange and correlation functionals work satisfactorily in the outer valence shells of these molecules, but less well for the localized lanthanidef‐shells. Relativistic corrections to bond lengths, bond energies and vibrational frequencies are of quite different magnitudes and origins. The inner Ln 4f‐shell has a fractional electron population in several molecular states. We corroborate the assignment of the 0^{+}ground state of YbO as configuration mixed Yb^{2+}(f ^{14}/f ^{13} s)O^{2−}. The effective charge distribution of the lanthanide oxides is at best approximated by Ln^{+}O^{−}.

The structure of the CF^{−} _{4} anion and the electron affinity of the CF_{4} molecule
View Description Hide DescriptionThe electronic and geometrical structure of the CF^{−} _{4} anion and its neutral parent, CF_{4}, are calculated with the second‐order Moller–Plesset perturbation theory. Several diffuse sp shells were added to the standard 6‐31+G* basis when calculating the potential energy surface of the CF_{4}+e ^{−} system. It was found that the CF_{4} molecule does not attach an additional electron in the ground state, i.e., the molecule possesses a zero vertical electron affinity under the Born–Oppenheimer approximation. The optimized C _{3v } and C _{2v } configurations of the anion are transition states, whereas its C _{ s } configuration corresponds to a local minimum and is thermodynamically stable by 20 kcal/mol. The CF_{4} molecule has the negative adiabatic electron affinity of −1.22 eV with respect to this configuration of the anion.

Vibrational frequencies of transition metal chloride and oxo compounds using effective core potential analytic second derivatives
View Description Hide DescriptionThe application of analytic second derivative techniques to quantum chemical calculations using effective core potentials is discussed. Using a recent implementation of these techniques, the vibrational frequencies of transition metal compounds are calculated including the chlorides TiCl_{4}, ZrCl_{4}, and HfCl_{4}, the oxochlorides CrO_{2}Cl_{2}, MoO_{2}Cl_{2}, WO_{2}Cl_{2}, and VOCl_{3}, and the oxide OsO_{4}. Results are compared to previous calculations and with experimental results.

Asymmetric adiabatic correction to the rotation–vibration levels of H_{2}D^{+} and D_{2}H^{+}
View Description Hide DescriptionCalculations on H_{2}D^{+} and D_{2}H^{+} have shown that the energy levels of these asymmetric isotopomers of H_{3} ^{+} cannot be reproduced using effective potential energy surfaces with D _{3h } symmetry. It is shown that for these ions the adiabatic correction to the Born–Oppenheimer approximation has an asymmetric component which can be expressed as a mass‐independent surface multiplied by a mass factor. An expression for this function is obtained from ab initio calculations. Use of this adiabatic correction is found to resolve the discrepancy with the levels of H_{2}D^{+} and D_{2}H^{+}. The ab initio calculations reported reproduce the observed H_{2}D^{+} transitions with an average error (obs−calc) of −8 MHz for the rotational transitions, −0.06 cm^{−1} for the ν_{1} band, −0.13 cm^{−1} for ν_{2}, and −0.19 cm^{−1} for ν_{3}. These errors are nearly constant for all transitions within a vibrational band. This gives a very accurate ab initio framework for predicting unobserved transition frequencies.