Index of content:
Volume 106, Issue 7, 15 February 1997

The microwave spectrum of the NH_{2} radical: The hyperfine structure of the ^{2} B _{1} ground electronic state
View Description Hide DescriptionThe pure rotational spectrum of the NH_{2} radical in its X̃ ^{2}B_{1} ground electronic state was measured in the frequency region of 230–470 GHz by microwave spectroscopy. The radical was generated in a free space cell by dcglow discharge of NH_{3}. Seventy nine fine and hyperfine components of four rotational transitions were measured, and were analyzed by least squares methods. The hyperfine coupling constants for both the nitrogen and hydrogen nuclei were redetermined with higher precision than those of the previous analysis for microwave optical double resonance (MODR) data. The nuclear spin–rotation constants for the hydrogen nucleus as well as the nitrogen nucleus were found to be anomalously large. The anomalous constant of C_{aa} (H) is interpreted by the same reason for the anomalous large value for C_{aa} (N) originating from the large A constant and the relatively lowlying Ã ^{2}A_{1} electronic state.

Twodimensional Raman spectroscopy of the intermolecular modes of liquid CS_{2}
View Description Hide DescriptionThe twodimensional response of the intermolecular modes of CS_{2} has been measured using nonresonant fifth order Raman spectroscopy. Whereas third order Raman spectroscopies only observe the spatially averaged spectrum of solvent motions, the fifth order experiment allows the microscopic composition of this spectral density to be probed. Within the limitations of the theory, the results confirm a picture of the liquid CS_{2} in which dynamics are dictated by a distribution of fixed structures at short times (<300 fs), and by spatially uniform structural relaxation at long times (>700 fs). The data suggest that the microscopic dynamics show highly damped oscillatory behavior at intermediate times. The full sensitivity to the details of the molecular dynamics is obtained by virtue of the full twodimensional response. The ability to make such observations has important general implications for understanding the broad range of time scales in the study of dynamics in complex condensed phases.

Infrared spectra of vaporized Pt and Pt+H_{2} in raregas matrices: Unique phonon effects
View Description Hide DescriptionLaservaporized platinummetal, trapped in solid Ne, Ar, Kr, Xe (and Ar, Kr mixture) produced a progression of absorption bands with a spacing of ∼200 cm^{−1} beginning at 1942 cm^{−1} in Ne and shifting successively to 1579 cm^{−1} in Xe. In contrast with the specimen in Ne, strong patterns of similar sidebands appeared in the spectra in the heavier matrices. This matrix effect is considered in some detail in attempting to assign the trapped molecule and to explain the source and structure of the sidebands. The conclusion is that the absorptionspectrum is the previously unobserved transition of Pt_{2} (inferred from Balasubramanian’s calculation) but with unique phonon interactions in the heavier matrices. When hydrogen was present in the matrix gases, Pt hydride bands were observed but not prominently, in contrast to Ni+H_{2} matrices.

On the coherent vibrational phase in polarization sensitive resonance CARS spectroscopy of copper tetraphenylporphyrin
View Description Hide DescriptionPolarization sensitive multiplex spectroscopy of resonancecoherent antiStokes Raman scattering(CARS) of copper(II)tetraphenylporphyrin in solution (CH_{2}Cl_{2}) is reported. The measurements were performed in the Q band range of the porphyrin electronic absorption. Four polarized CARS spectra were resolved in 1300–1650 cm^{−1} Raman range and were simultaneously fitted with a single set of vibrational parameters (band positions, bandwidths, amplitudes, depolarization ratios, and phases). The obtained coherent vibrational phases of A_{1g} , A_{2g} , and B_{1g} skeletal modes of the porphyrin macrocycle appeared to correlate strongly with the mode vibrational symmetry. The origin of such correlation is analyzed within a model of the thirdorder nonlinear electric susceptibility χ^{(3)}. The proposed model is based on multidimensional displaced harmonic oscillator in the Herzberg–Teller expansion of Raman polarizability. The coherent vibrational phases of modes of different symmetry classes are directly affected by the symmetry dependent vibronic couplings between the pairs of Q_{x} , Q_{y} and B_{x} , B_{y} electronic transitions of the porphyrin. The phase contrast between the modes of various symmetries is most pronounced near the Q _{00}resonance.

Semiclassical theory of multichannel curve crossing problems: LandauZener case
View Description Hide DescriptionA twobytwo diabatic propagation method is developed to deal with general onedimensional multichannel curve crossing problems. Each crossing is treated within the newly completed twostate semiclassical theory in the diabatic representation and is represented by a nonadiabatic transition matrix (Imatrix). A product of all the Imatrices yields the reduced scattering matrix for the entire system. This theory can handle the multichannel curve crossing problems as simply as a twostate problem. An analysis of the complex crossing points in the momentum space can provide a comprehensive illustrative criterion of this method. A detailed severe numerical test is made by taking a sevenstate system with 6 and 12 nonzero diabatic couplings. It is demonstrated that dominant processes among the statetostate transitions are well reproduced by the present semiclassical theory.

Theoretical study of vibronic spectra and photodissociation pathways of methane
View Description Hide DescriptionPotential energy surfaces for the first singlet and triplet excited states of methane have been studied using multireference configuration interaction (MRCI) and equationofmotion coupled cluster (EOMCCSD) ab initio molecular orbital calculations. The vertical excitation energies for the ^{1} T _{2} and ^{3} T _{2} states are computed to be 10.64–10.66 and 10.25–10.30 eV, respectively. Two minima are found on the first excited singlet surface,1 (∼C_{3v} ) and 2 (C_{2v}), with adiabatic excitation energies of 9.16–9.25 and 8.39–8.52 eV, respectively. No minima is located on the triplet surface. Vibronic spectra, calculated based on the geometries, vibrational frequencies, and normal modes of the ground and excited states, reproduce well the experimental results. The spectra due to the 3s(C_{2v})←1t_{2} transition start at ∼8.63 eV and form a broad underlying continuum. The 3s(C_{3v})←1t_{2} transition is shown to be responsible for the minor fine structure observed in the experimental absorption spectra between 9.5 and 10.6 eV. Dissociation pathways leading to various photofragmentation products are discussed on the basis of the calculated minimal energy pathways of H and H_{2} elimination. Production of and fast hydrogen atoms, the major channel observed experimentally, is speculated to occur either via the S_{0}←S_{1} internal conversion or, more likely, via the S_{1}(^{1}A″)→T_{1}(^{3}A) intersystem crossing followed by fast dissociation in the triplet state. Spin–orbit coupling between S _{1} and T _{1} has been calculated to be about 45 cm^{−1}.

A perturbation molecular orbital theory of electrontransfer rates
View Description Hide DescriptionPerturbation molecular orbital (PMO) theory is used to approximate the electronic matrix element in the semiclassical expression for the rate of nonadiabaticelectron transfer(ET). The resulting expression gives a satisfactory account of the intramolecular ET rate data reported by Closs, Miller, and coworkers. We develop the idea of electrontransfer efficiency for the contribution of electron transfer to the observed kinetics of ion–molecule collisions followed by electron transfer.Electrontransfer efficiency comes from the calculated ET rate divided by the maximum calculated ET rate. Electrontransfer efficiency values are also obtained by dividing the observed reaction rate by the collision rate, calculated by the PMO treatment of ion–molecule collision rates. We applied this approach to data on electron transfer from sulfurhexafluoride or perfluoromethylcyclohexane anions to aromatic acceptors. The structural reorganization energies, λ _{s} , for these reactions were 0.016 and 0.046 eV, respectively. The vibrational reorganization energies, λ _{v} , for the reactions were 1.01 and 1.00 eV, respectively. Electron transfer from either of the donor anions to fluoranil occurs in the inverted region.

Reactivity induced by complex formation: The reaction of O(^{3} P) with HCl dimers
View Description Hide DescriptionThe reaction of O(^{3} P) with HCl⋅M (M=HCl, Ar) complexes has been studied. While the monomer HCl, in its ground vibrational state, reacts extremely slow with O(^{3} P), it is shown here that the van der Waals complexes react with an efficiency of about 3 orders of magnitude larger than that of the monomer. The reactivity of DCl, on the other hand, is not enhanced by the complex formation. Molecular dynamics simulation indicates that the collision complex lifetime increases by several orders of magnitude due to the existence of the “third body” in the cluster. A model for explaining the complex induced enhancement of reactivity is presented and is supported by ab initio calculations.

Real time study of bimolecular interactions: Direct detection of internal conversion involving Br(^{2} P _{1/2})+I_{2} initiated from a van der Waals dimer
View Description Hide DescriptionA reaction complex is formed from a van der Waals dimer precursor, HBr⋅I_{2}, and is monitored with picosecond time resolution using standard pump–probe spectroscopy. The reaction is initiated in a slightly attractive region of an excited electronic state with insufficient energy to fragment and will eventually undergo an internal conversion to a lower electronic state via electronic to vibration energy transfer. A resulting product, highly vibrationally excited molecular I_{2}, is monitored by resonance enhanced multiphoton ionization (REMPI) combined with time of flight mass spectroscopy. The HBr constituent of the precursor HBr⋅I_{2} is photodissociated at 220 nm. The Hatom departs instantaneously, allowing the remaining electronically excited Br(^{2} P _{1/2}) to form a collision complex, (BrI_{2})^{*}, in a restricted region along the Br+I_{2}reaction coordinate determined by the precursor geometry. The evolution of this complex is probed in real time by tuning the probe to the REMPI line of the I atom: 298 nm. The resulting transients include I_{2} ^{+} and I^{+}, with lifetimes of 55(±5) and 40(±5) ps, respectively. Similar results are obtained for initiation from DBr⋅I_{2}, with risetimes of 43(±5) and 29(±5) ps measured for the I_{2} ^{+} and I^{+} transients, respectively. The originally formed (BrI_{2})^{*} does not have enough internal energy to dissociate directly, but must undergo an internal conversion to a lower electronic state in order to continue to reactants or products. An isotope effect is also detected and explained with a simple kinetics model that is consistent with mechanism described above. Temporal discrepancies in the risetimes of I_{2} ^{+} and I^{+} imply that either the ground state process is also being observed or that differing vibrational states of the I_{2} product are formed at differing rates and detected with differing efficiencies.

A multiconfigurational timedependent Hartree approach to the direct calculation of thermal rate constants
View Description Hide DescriptionA method employing the multiconfigurational timedependent (MCTDH) approach for the direct calculation of the thermal rate constant is presented. It is based on the fluxposition correlation function of Miller et al. [J. Chem. Phys. 79, 4889 (1983)]. Eigenvalues of the thermal flux operator are calculated employing an iterative diagonalization scheme suitable for the MCTDH approach. F̂_{T} has only a few significant eigenvalues, which can be interpreted as contributions of the ground and excited vibrational states of the activated complex. The rate constant is calculated by propagating the eigenfunctions of F̂_{T} in time. As an example, the H+H_{2}reaction is studied. Exact results for vanishing total angular momentum (J=0) are given. The total thermal rate constant is calculated by a J shifting scheme which takes the linear geometry of the transition state into account.

On the transition from nonadiabatic to adiabatic rate kernel: Schwinger’s stationary variational principle and Padé approximation
View Description Hide DescriptionFor a two state system coupled to each other by a nonzero matrix element Δ and to the bath arbitrarily, the generalized master equation is derived by applying the wellknown projection operator techniques to the quantum Liouville equation. The timedependent rate kernel is expressed by an infinite summation of the perturbative terms in Fourier–Laplace space. The Schwinger’s stationary variation principle in Hilbert space is extended to Liouville space and then applied to the resummation of the rate kernel. The Cini–Fubinitype trial state vector in Liouville space is used to calculate the variational parameters. It is found that the resulting stationary value for the rate kernel in Fourier–Laplace space is given by the [N,N−1]–Padé approximants, in the Ndimensional subspace constructed by the N perturbatively expanded Liouville space vectors. The (firstorder) simplest approximation satisfying the variational principle turns out to be equal to the [1,0] Padé approximant instead of the secondorder Fermi golden rule expression. Two wellknown approximations, the noninteracting blip approximation (NIBA) and nonadiabatic approximation, are discussed in the context of the [1,0] Padé approximants, based on the variational principle. A higherorder approximation, [2,1] Padé approximant, is also briefly discussed.

Hopping reactions of charged particles
View Description Hide DescriptionThe hoppingtheory of transfer reactions is essentially generalized to account for the electrostatic interaction between reactants. An application is made for a solvated electron that may be trapped by ions in the course of a random walk in liquid solutions. The hoppingreaction constant differs essentially from the diffusional constant but exhibits a similar dependence on the Onsager radius: reactions with anions are strongly suppressed while reactions with cations are significantly accelerated.

Prediction of the temperature dependence of Kchanging rotational collisional processes in CH_{3}Cl
View Description Hide DescriptionThe complexity of rotational energy transfer (RET) in polyatomic molecules has in general precluded prediction of nontrivial temperature and energy related effects. In this paper, experimental measurements of ΔK=3n RET in CH_{3}Cl between 200 K and 400 K are successfully compared with predictions of an earlier model.

Hybrid schemes combining the Hartree–Fock method and densityfunctional theory: Underlying formalism and properties of correlation functionals
View Description Hide DescriptionHybrid schemes that combine elements of the Hartree–Fock and the Kohn–Sham procedures are shown here to have a rigorous formal basis within exact densityfunctional theory.Properties of the exact correlation energy and its functional derivative, corresponding to each hybrid scheme, are introduced and the correlation energy is expressed by a coupling constant integral. The coupling constant expansions of hybrid correlation energies are considered.

Perturbation theory for coupled anharmonic oscillators
View Description Hide DescriptionPerturbation theory is applied to a pair of coupled oscillators with cubic anharmonicity. Largeorder perturbation theory is shown to be more efficient computationally than numerical diagonalization of the Hamiltonian. Quadratic Padé summation of the energy expansions yields convergent results for the real and the imaginary parts of resonance eigenvalues.

Ab initio calculations of the interaction of He with the state of Cl_{2} as a function of the Cl_{2} internuclear separation
View Description Hide DescriptionAb initio calculations using unrestricted Mo/ller–Plesset perturbation theory to fourth order (UMP4) were carried out for the interaction of He with the state of Cl_{2}. Also, more reliable unrestricted coupled cluster singles, doubles, and noniterative triples (UCCSD(t)) calculations were performed for several points on the B electronic state surface and were used to scale the UMP4 points. Exp6 type two center potential energy functions were fitted to the modified UMP4 points (B state) to construct an analytical threedimensional potential energy surface. An r (Cl–Cl separation) dependence was incorporated in the B state potential energy surface to allow the calculation of HeCl_{2} properties in different vibrational states so that vibrational predissociation rates could be calculated. Excitation spectra, predissociation lifetimes, and rotational product distributions were calculated and compared to the available experimental data. It was found that the calculated B←X, 8←0 spectrum is in good agreement with the experimental one, and the calculated blueshifts for ν=8, 10, 12 show the right trend when compared to the experimental findings, i.e., the blueshifts get larger with increasing ν. The blueshift values are generally too small which suggests that the ab initio calculations underestimate the van der Waals interactions in the B state less than they do in the X state. The calculated vibrational predissociation lifetimes τ are in good agreement with the experiment, as are the rotational product distributions for ν=8, 10, and 12.

Geometries and energy separations of electronic states of and
View Description Hide DescriptionSpectroscopicproperties of the lowlying electronic states of AsCl_{2} and AsBr_{2} have been studied with the complete active space selfconsistent field (CASSCF) followed by multireference singles and doubles configuration interaction (MRSDCI) methods. In addition, the three lowlying electronic states of AsCl_{2} ^{+} and AsBr_{2} ^{+}, (^{1}A_{1},^{3}B_{1},^{1}B_{1}) and the ground states of AsCl and AsBr were investigated. The bond dissociation energies of AsCl_{2}, AsBr_{2}, AsCl, and AsBr have been computed at the CASSCF/MRSDCI and CASSCF/second order configuration interaction (SOCI) levels as D_{e} (ClAs–Cl)=2.56 eV, D_{e} (BrAs–Br)=1.96 eV, D_{e} (As–Cl)=2.68 eV, and D_{e} (As–Br)=2.26 eV. The adiabatic ionization energies obtained in this work are 8.40 eV for AsCl_{2} and 8.33 eV for AsBr_{2}. All these species have been found to possess bent geometries at their ground electronic states.

Cavitation model of electron solvation dynamics: Effect of energy dissipation
View Description Hide DescriptionThe effect of energy dissipation on the electron solvation dynamics is studied within the framework of the cavitation model. Two different energy dissipation mechanisms, associated with the sound emission and viscousfriction, are analysed. The radiational damping of the cavity boundary dynamics is described using the Herring equation. The model is applied to analysis of the electron solvation dynamics in water. Sound emission constitutes the most efficient mechanism of energy dissipation. Energy dissipation does not change the theoretical prediction concerning the small isotope effect on the electron solvation dynamics in water.

Integral equation approaches to mixtures of atomic and molecular fluids
View Description Hide DescriptionA recent extension to mixtures of Verlet’s closure is applied in conjunction with the Ornstein–Zernike relation to solve the structure and thermodynamics of mixtures of hardspheres and homonuclear harddumbbells. This integral equation (IE), which is proven to be very accurate when compared with simulation data, is used to explore the possibility of phase separation in an asymmetric mixture. While our results do not show evidence of such phase separation in the asymmetric binary hardsphere mixture studied by Biben and Hansen [T. Biben and J. P. Hansen, Phys. Rev. Lett. 66, 2215 (1991)], an equivalent mixture of harddumbbells and large hardspheres seems to exhibit a certain tendency to phase separate as far as the integral equation results are concerned. Finally, given the ability of this integral equation to reproduce the hardcore system, we have incorporated these results into a previous Reference Hypernetted Chain scheme to treat a mixture of N and Ar modeled by means of site–site LennardJones potentials. In consonance with the results for pure fluids, the parameterization of a hardcore reference system with the same molecular shape leads to excellent results both for the structure and thermodynamics of real systems.

Thermodynamic properties of aqueous solutions: Nonsymmetric sticky electrolytes with overlap between ions in the meanspherical approximation
View Description Hide DescriptionBased on a stickyelectrolyte model, the Ornstein–Zernike integral equation is solved for nonsymmetric electrolytes with stickiness between ions at various distances equal to or less than the collision diameter. The hypernetted chain or Percus–Yevick approximation is used for the closure inside the hard core, while the meanspherical approximation for electrostatic interactions is used for the closure outside the hard core. Expressions for correlation functions and thermodynamic properties in term of the sticky parameters are derived. Numerical results are presented for various cases.