Volume 114, Issue 12, 22 March 2001
 COMMUNICATIONS


Degenerate conical intersections: The interaction between the and electronic states of as a case study
View Description Hide DescriptionIn this Letter are presented and analyzed conical intersections which appear on the two symmetric sides of the line of the molecule. Two conical intersections (CI) of this kind, between the and electronic states, were found to be only a short distance apart, e.g., ∼0.3 Å for the CC distance of 1.25 Å. It is shown that these two CIs—to be termed CI twins—have opposite “charges” thus forming altogether a weak interaction. By increasing the CC distance, to 1.35 Å, the two twins coalesce to form a single CI. The interaction of this merged pair varies with the distance as (as is the case for conical intersections) but, in contrast to ordinary CIs, does not exhibit any topological effects and its intensity is shown to be zero. These features led us to term it as a degenerate CI or concisely DCI.

Electronic transitions with quantum trajectories
View Description Hide DescriptionThe quantum trajectory method (QTM) is extended to the dynamics of electronic nonadiabiatic collisions. Equations of motion are first derived for the probability density, velocity, and action function for wave packets moving on each of the coupled electronic potential surfaces. These discretized equations are solved in the Lagrangian (moving with the fluid) picture to give the trajectory dynamics of fluid elements evolving on each potential surface. This trajectory method is fully quantum mechanical and does not involve “trajectory surface hopping.” The method is applied to nonadiabiatic collision models involving two coupled electronic states. The quantum trajectory results are in excellent agreement with solutions computed (using spacefixed grid methods) directly from the timedependent Schrödinger equation.
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 ARTICLES

 Theoretical Methods and Algorithms

Electronic excitation and ionization spectra of azabenzenes: Pyridine revisited by the symmetryadapted cluster configuration interaction method
View Description Hide DescriptionElectronic excited and ionized states of pyridine were reinvestigated by the symmetryadapted cluster configuration interaction (SACCI) method using an extended basis set and a wide active space. The present SACCI results for the singlet and triplet excited states are greatly improved and agree well with the experimental observations, providing a firm assignment of all lowlying and valence excited states observed in the vacuum ultraviolet spectrum and electron energylossspectrum. The ionization potentials were reexamined by the SACCI generalR (R represents excitation operator) method. The first four ionization potentials are greatly improved compared with our previous results obtained by the SACCI single and doubleR (SDR) method. The present theoreticalionization potentials are in good agreement with the experimental values in highresolution synchrotron photoelectron spectrum for energy regions up to 25 eV (which contain outer and innervalence regions), and give a detailed theoretical assignment for the photoelectron spectra.

Electron propagator method with a multiconfigurational secondorder perturbation theory wave function as the initial state in the fermion operator block
View Description Hide DescriptionWe have developed an electron propagator method using a multiconfigurational secondorder perturbation theory (CASPT2) wave function as the initial state [electron propagator CASPT2 (EPCASPT2)] in the fermion operator block (block 1). In the other blocks a multiconfigurational selfconsistent field wave function is the initial state. We apply our new method to directly determine the lowlying vertical ionization potentials of Be, and We compare our results with the results of the calculations using multiconfigurational spin tensor electron propagator (MCSTEP), full configuration interaction (FCI), and multireference configuration interaction (MRCI) methods with the same geometries and basis sets. The calculations are performed using complete active space (CAS) choices that are usually excellent for MCSTEP ionization potential (IP) calculations and also for CAS choices that are inadequate for MCSTEP IP calculations. We show that EPCASPT2 generally improves MCSTEP IPs compared to ΔFCI when the MCSTEP IPs are in very good to excellent agreement with ΔFCI IPs and that EPCASPT2 can effectively mimic ΔFCI even when the CAS choice for the initial state is inadequate for MCSTEP.

Single molecule waiting time distribution functions in quantum processes
View Description Hide DescriptionThe statistics of single molecule blinking events often reveal underlying quantum mechanisms. The golden rule rate expression for quantum transitions is shown to be the inverse of the mean waiting time. The distribution function for the waiting time is related to the density of states such that simple powerlaw distribution functions can be predicted based on the functional form for the density of states. Explicit formulas are derived for waiting time distribution functions in three kinetic processes: Quantum tunneling, intersystem conversion, and nonstationary electron transfer.

The calculation of thermal rate constants for gas phase reactions: A semiclassical flux–flux autocorrelation function (SCFFAF) approach
View Description Hide DescriptionA semiclassical approach to the calculation of thermal rate constants, based on the flux–flux autocorrelation function method, is presented with its applications. The autocorrelation function is generated along classical trajectories using a classical interpretation of the Boltzmannized flux operator. The activation energies for considered reactions are calculated using the G2/MP2 procedure. The forces are generated using a new parametrization of the PM3 NDDO Hamiltonian optimized for accurate gradients. Thermal rate constants for hydrogen abstraction from ethane and haloethanes by hydroxyl radical serve as a first test of this approach. Calculated results are in good agreement with cumulative rate constants for all systems considered over a range of temperature including room temperature. The approach is able to distinguish between α and β abstraction with a result for fluoroethane at room temperature that is consistent with the available experiment and trends that are in line with those expected.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Hydrogen bonding and stacking interactions of nucleic acid base pairs: A densityfunctionaltheory based treatment
View Description Hide DescriptionWe extend an approximate density functional theory(DFT) method for the description of longrange dispersive interactions which are normally neglected by construction, irrespective of the correlation function applied. An empirical formula, consisting of an term is introduced, which is appropriately damped for short distances; the corresponding coefficient, which is calculated from experimental atomic polarizabilities, can be consistently added to the total energy expression of the method. We apply this approximate DFT plus dispersion energy method to describe the hydrogen bonding and stacking interactions of nucleic acid base pairs. Comparison to MP2/631G^{*}(0.25) results shows that the method is capable of reproducing hydrogen bonding as well as the vertical and twist dependence of the interaction energy very accurately.

Lowtemperature dynamics and spectroscopy in exohedral raregas fullerene complexes
View Description Hide DescriptionThe adatom dynamics in exohedral fullerene complexes of raregas atoms are studied with a three degrees of freedom model. The eigenvalue problem of the corresponding quantum Hamiltonian is solved and the electricdipole spectra for and in the lowtemperature range from 5 to 40 K are simulated. The most important spectral features are related to the degree of angular anisotropy in the adatom– interaction. The and complexes present very simple spectra which can be assigned in terms of threemode oscillators; the corresponding motion takes place in the deep hexagon wells (also in the pentagon wells for of the interaction potential. On the contrary, the complex shows more complicated spectra with important tunneling effects due to the smaller angular anisotropy of the interaction. The onset of almost free internal rotation takes place in this complex at rather low energies, and this gives rise to a lowfrequency rotational band in the spectra at temperatures above

UV photodissociation dynamics of ethyl radical via the state
View Description Hide DescriptionHatom channels in the photodissociation of jetcooled ethyl radical via the state are studied near 245 nm by using the highn Rydbergatom timeofflight technique. Bimodal product translational energy release and energydependent angular distribution suggest two dissociation pathways. A slow and isotropic channel corresponds to unimolecular dissociation of the radical, presumably after internal conversion. A previously unobserved fast and anisotropic channel is consistent with direct Hatom scission via a nonclassical Hbridged transition state from the state to yield The fast/slow branching ratio is ∼0.2. Siteselective loss of the β hydrogen atom is confirmed by using the partiallydeuterated radical.

The first radical with stable cyclic isomers
View Description Hide DescriptionThe potentialenergysurface of the interstellar molecule is explored at the B3LYP/6311G(d) level of theory. Thirteen isomers including the linear, threemembered ring, fourmembered ring, Alike, Ylike, and cagelike structures are located as minima connected by 23 interconversion transition states. The structures of the most relevant isomers and transition states are further optimized at the QCISD/6311G(d) level followed by singlepoint energy calculations at the MP4SDTQ, CCSD(T), and QCISD(T) levels with the 6311G(2df) basis set. At the CCSD(T)/6311G(2df)//QCISD/6311G(d) level, the lowestlying isomer is a linear structure CCCCN 1 followed by a CCC threemembered ring structure 4 with exocyclic CCN bonding that lies only 2.8 kcal/mol higher. The third and fourth lowlying isomers possess a CCC threemembered ring structure 5 with exocyclic CNC bonding at 21.4 kcal/mol and a linear structure CCCNC 2 at 23.4 kcal/mol, respectively. All the four isomers 1, 2, 4, and 5 and another highlying isomer 3 with a linear CCNCC structure at 62.5 kcal/mol are shown to have considerable kinetic stability towards isomerization and dissociation. Thus, all the five isomers may be experimentally observable. Possible formation of these five stable isomers in interstellar space is discussed. Finally, our calculations show that the Møller–Plesset methods fail to predict even qualitatively the energetic properties between the four lowlying isomers 1, 2, 4, and 5, in comparison with the QCISD and CCSD results. This paper indicates that may be the first interstellar molecule with stable lowlying cyclic isomers among the radical series to be detectable in near future. The results presented in this paper may provide useful information for future laboratory and interstellar identification of various isomers.

Kinetics of condensation of gases: A new approach
View Description Hide DescriptionA recently developed new approach for the determination of the work of critical cluster formation in nucleation is applied here to the description of the kinetics of condensation of gases. This method is a generalization of the classical Gibbs’ approach retaining its advantages and avoiding its shortcomings. For an illustration, the method is developed here for the case of condensation in a onecomponent van der Waals gas. The surface tension between liquid and gas is described by a modification of Macleods equation. However, any other relationships specifying the state of the system under consideration, which may be considered eventually as more appropriate, can be employed as well. For relatively small supersaturations, the classical Gibbs’ results (employing the capillarity approximation) are retained as a special case. However, similarly to the van der Waals–Cahn and Hilliard and more recent methods of density functional calculations in the determination of the work of critical cluster formation, for initial states, approaching the spinodal curve, the work of critical cluster formation is shown to tend to zero. In the intermediate range of supersaturations, it leads to smaller values of the work of critical cluster formation as predicted by the classical theory. The method can be extended also straightforwardly to the description of condensation in multicomponent gases as well as to bubble formation in liquids.

Nearside–farside analysis of differential cross sections using Jacobi functions of the first and second kinds: Application to rotationally inelastic scattering
View Description Hide DescriptionWe report the first nearside–farside (NF) analysis of angular scattering for an inelastic molecular collision in which the partial wave series for the scattering amplitude is expanded in a basis set of reduced rotation matrix elements where θ is the scattering angle, J is the total angular momentum quantum number, and are initial and final helicity quantum numbers, respectively. The practical implementation of the NF theory is described in detail; it exploits in an essential way the properties of a function that we denote and call a reduced rotation matrix element of the second kind. The caustic structure of and is taken into account via a restricted nearside–farside decomposition of the scattering amplitude. The theory is used to analyze polarization and degeneracy averaged differential cross sections for the collision system, treated as an The analysis always provides a clear physical interpretation of the scattering (except sometimes for for phenomena such as diffraction oscillations and potential rainbows, as well as for more complicated (unnamed) interference effects. We also report results for some approximations to the theory. Mathematical properties of the required for the analysis are derived.

Relativistic density functional study of gold coated magnetic nickel clusters
View Description Hide DescriptionCoating of magnetic clusters by gold atoms is becoming an experimental technique of increasing interest for passivation and stabilization of these small metal particles. To computationally investigate the effect of goldcoating, we have studied the magnetic clusters and employing an allelectron scalarrelativistic density functional method. We examine two series of octahedral clusters with increasing gold coverage of up to a monolayer: and Structural features, binding energies, and goldadsorption energies are determined and discussed. The different atomic radii of Au and Ni lead to rather short Au–Au and relatively long Ni–Ni distances in these clusters. The Au–Ni contacts are found to be the longest nearestneighbor distances; a detailed analysis indicates these bonds to be the strongest in these Aucovered Niclusters. The atomization energies change only slightly with increasing Au coverage. Also, the effect of goldadsorption on the magnetic properties of the Ni cores is analyzed. For the series the magnetism decreases with n, while for a maximum cluster magnetization is calculated for incomplete gold coverage. This different behavior of the two cluster series can be traced to differing numbers of unpaired electrons per atom in the pure Niclusters and to an increased magnetic moment due to the adsorption of isolated Au atoms. Both series exhibit a residual magnetism at full monolayer coverage of the Ni cores.

Theoretical study of the water activation by a cobalt cation: Ab initio multireference theory versus density functional theory
View Description Hide DescriptionThe reaction mechanism of with has been studied by the ab initio multireferencebased theory (MR–SDCI and MC–QDPT) and the density functional theory (B3LYP and BLYP). In the energetics derived by the MR–SDCI(+Q) plus the B3LYP zeropoint vibrational energy, the ion–dipole complex, is initially formed with the binding energy of 38.2 (triplet) and 34.1 (quintet) kcal/mol, which is the most stable complex in the respective potential energy surfaces. Then, activates one O–H bond of leading to the insertion complex, There are three possible dissociation channels from i.e., and The third dissociation is expected to occur through the transition state of a fourcentered structure, with the activation barrier of 61.6 (triplet) and 49.2 (quintet) kcal/mol, although this dissociation has not been detected in the experiment. The ground state of is predicted to be and the lowest triplet state is with the energy level of 20.8 kcal/mol above. The B3LYP provides the energetics qualitatively similar to the MR–SDCI(+Q) ones through the reactions, with the maximum deviation of 13 kcal/mol. The calculated results are consistent with experimental observations.

Doubleresonant photoionization efficiency spectroscopy: A precise determination of the adiabatic ionization potential of DCO
View Description Hide DescriptionWe report the first highresolution measurement of the adiabatic ionization potential of DCO and the fundamental bending frequency of Fixing a firstlaser frequency on selected ultraviolet transitions to individual rotational levels in the (000) band of the intermediate Rydberg state of DCO, we scan a second visible laser over the range from 20 000 to to record double resonance photoionization efficiency (DR/PIE) spectra. Intermediate resonance with this Rydberg state facilitates transitions to the threshold for producing groundstate cations by bridging the Franck–Condon gap between the bent neutral radical and linear cation. By selecting a single rotational state for ionization, doubleresonant excitation eliminates thermal congestion. Spectroscopic features for firstphoton resonance are identified by reference to a complete assignment of the band system of DCO. Calibration with HCO, for which the adiabatic ionization threshold is accurately known, establishes an experimental instrument function that accounts for collisional effects on the shape of the photoionization efficiency spectrum near threshold. Analysis of the DR/PIE threshold for DCO yields an adiabatic ionization threshold of By extrapolation of vibrationally autoionizing Rydberg series accessed from the component of the intermediate state, we determine an accurate rotationally stateresolved threshold for producing This energy, together with the threshold determined for the vibrational ground state of the cation provides a first estimate of the bending frequency for as Assignment of the (010) autoionization spectrum further yields a measurement of an energy of for the (21) rotational transition in the state of

Symmetry specificity in the unimolecular decay of the complex: Twomode quantum calculations on a coupledcluster [CCSD(T)] potential energy surface
View Description Hide DescriptionThe decay of resonance states in the complexforming nucleophilic substitution reaction is investigated by means of twodimensional quantum mechanical calculations on a coupledcluster [CCSD(T)] potential energy surface. The dynamics calculations employ Radau coordinates to describe the two C–Cl stretching degrees of freedom, filter diagonalization, and an absorbing (optical) potential. The resonance widths and the corresponding decay rates vary by several ordersofmagnitude, reflecting the large degree of separability of the intramolecular and the intermolecular mode. The decay is found to be strongly symmetry specific: For energies above the reaction barrier, the smallest rates of the ungerade states are about two ordersofmagnitude smaller than the smallest rates of the gerade states. An explanation is given in terms of an adiabatic model formulated in hyperspherical coordinates. The nonadiabatic coupling elements, which control the energy transfer between the two modes and therefore determine the decay rate, are substantially larger for the gerade states. Ultimately, the differences are caused by the different structures of the gerade and the ungerade wave functions at the barrier.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

The temperature dependent dielectric function of liquid benzene: Interpretation of THz spectroscopy data by molecular dynamics simulation
View Description Hide DescriptionThe dielectric function of liquid benzene at −4 °C, 21 °C, and 65 °C has been calculated from molecular dynamics simulations. The simulated dielectric loss curves reproduce the experimental temperature and density trends. In order to investigate the detailed influence of temperature and density changes as well as the underlying molecular mechanism we have taken advantage of different partitioning and projection schemes for the total dipole moment time correlation function (TCF). The study of the nbody partitioning showed that the temperature dependence of the two and threebody contributions at can be explained solely by density change arguments. The molecular projection scheme showed that the dielectric loss is governed by outofplane libration at all temperatures. Inplane libration was found to contribute significantly only below 2 THz. Below 1 THz, diffusion, manifested as the negative cross correlation between the outofplane and the inplane TCF’s, plays a role very different from that of the directly observed diffusion in dipolar liquids. It has further been established that it is highly problematic to carry out an analysis of the dielectric loss function in terms of the molecular axis rotational TCF’s which is a common procedure for the absorptionspectrum. This problem was, however, solved by employing a molecular projection scheme.

An ab initio study of the lattice distortions induced by nonisovalent and substitutional impurities in crystalline NaCl
View Description Hide DescriptionA theoretical analysis of the lattice distortions induced by nonisovalent and substitutional impurities in crystalline NaCl, and of the offcenter equilibrium position adopted by those impurities in their ground electronic configuration is presented. The calculations are based in the cluster approach, and involve large active clusters embedded in an accurate quantal representation of the crystalline environment. The charge compensation problem is dealt with by considering several allocations of a cationic vacancy in the host lattice. The obtained distortions involve in all cases the concerted movement of a large number of host crystal ions. Those distortions are presented and discussed in terms of simple packing and Madelung considerations.

The medium response to an impulsive redistribution of charge in solid argon: Molecular dynamics simulations and normal mode analysis
View Description Hide DescriptionExcitation of the Rydberg state of NO leads to an extensive rearrangement of the environment, which we have investigated by classical molecular dynamics simulations and normal modeanalysis, using pair potentials from the literature. We find that the medium response is independent of the details at long range of the excited state NO potential, stressing the fact that it is mainly driven by the short range repulsive forces between the Rydberg electron and the matrix atoms. We establish the inertial character of the first shell response in the initial 100–150 fs after excitation, as the next shells are silent over this time scale. The expansion of the first shell at early times, induces the propagation of a supersonic wave along the (011) axis of the crystal, which define 12 linear chains of atoms with the impurity. The early time response is followed by vibrational coherences with a complex behavior. The normal modesanalysis of the crystal shell by shell shows good agreement with the power spectra of the MD trajectories. It allows us to identify the most significant modes in the medium response. Overall, the dynamics of the system may be regarded as that of a supermolecule, embedded in an Ar lattice and undergoing vibrational energy redistribution.

Ion pair correlations near critical points of ionic fluids: Experimental investigation of the static permittivity
View Description Hide DescriptionWe report on data for the concentration dependence of the static dielectric constant of solutions of tetranbutylammonium naphtylsulfonate (TBNAS) in toluene derived from measurements of the frequencydependent complex permittivity. The system shows an upper consolute point at and a mole fraction of the salt. The measurements were performed along a slightly supercritical isotherm at 338.15 K at mole fractions increases with increasing salt concentration. At the critical point compared with for pure toluene. In the concentration range covered by the experiments, the effective dipole moments calculated from these data are of the order of which is distinctly lower than an estimate for the isolated molecule, The difference is attributed to compensation effects due to preferred antiparallel ion pair orientations, as described by a Kirkwood–Fröhlichtype theory with correlation factors of At the critical point we find Due to these orientational correlations, dipole–dipole interactions between ion pairs may provide a significantly smaller contribution to the free energy than predicted by theory. This may explain the good performance of theories that ignore dipole–dipole interactions between pairs.