Volume 118, Issue 23, 15 June 2003
 ARTICLES

 Theoretical Methods and Algorithms

Nuclear magnetic resonance implementation of the Deutsch–Jozsa algorithm using different initial states
View Description Hide DescriptionThe Deutsch–Jozsa algorithm distinguishes constant functions from balanced functions with a single evaluation. In the first part of the work, we present simulations of the nuclear magnetic resonance application of the Deutsch–Jozsa algorithm to a 3spin system for all possible balanced functions. Three different kinds of initial states are considered: a thermal state, a pseudopure state, and a pair (difference) of pseudopure states. Then, simulations of several balanced functions and the two constant functions of a 5spin system are described. Finally, corresponding experimental spectra obtained by using a 16frequency pulse to create an input equivalent to either a constant function or a balanced function are presented, and the results are compared with those obtained from computer simulations.

Peculiarities of time dependence of the current–current correlation function
View Description Hide DescriptionThe similarity and difference in the behavior of the current–current correlation function (CCCF) and the velocity correlation function of a molecule are discussed in detail. It is shown that the oscillations and longtime decay of the transversal and longitudinal components of CCCF are explained naturally within the Lagrange theory of thermal hydrodynamic fluctuations.

Accurate quantum calculations on threebody collisions in recombination and collisioninduced dissociation. II. The smooth variable discretization enhanced renormalized Numerov propagator
View Description Hide DescriptionWe introduce a novel solution of the coupledchannel Schrödinger equation. This new procedure dramatically improves on our previous paper on this subject. The method uses a truly adiabatic internal basis and combines a smooth variable discretization (SVD) with an enhanced renormalized Numerov (ERN) propagator. Although the basis is truly adiabatic, this method does not require derivative coupling terms, and it involves less numerical work than previous SVD approaches. Boundary conditions are applied using Jacobi coordinates for bound states and using hyperspherical coordinates for continuum states; that allows application of the boundary conditions at smaller distances. We apply this new algorithm to the model collisioninduced dissociation process for zero total angular momentum. We study the convergence of the probabilities as a function of the number of channels, distance propagated, and step size in the propagation. The method is fast, reliable, and provides considerable savings over previous propagators.

Mixed quantumclassical Liouville molecular dynamics without momentum jump
View Description Hide DescriptionAn alternative Liouville formulation of mixed quantumclassical dynamics outlined recently [K. Ando, Chem. Phys. Lett. 360, 240 (2002)] is expanded in detail by taking an explicit account of the parametric dependence of the electronic (adiabatic) basis on the nuclear coordinates. As a consequence of the different operational order of the partial Wigner transformation for the nuclear coordinates and the calculation of the matrix elements in the adiabatic electronic basis, the present formula differs from the previously proposed one, slightly in the appearance but significantly in the treatment of nonadiabatic transitions in the trajectory implementation in that the former does not contain the “offdiagonal Hellmann–Feynman forces” representing the socalled “momentumjump” associated with the nonadiabatic transitions. Because of this, the present formula is free from the numerical instability intrinsically coming from the momentumjump operation at around the classical turning points of the nuclear motion. It is also shown that the density matrices from the two approaches coincide when the electronic basis is independent of the nuclear coordinates and hence the momentumjump approximation stems from the dependence of the adiabatic electronic basis. Improved stability and comparable to better reproduction of the quantum reference calculations are demonstrated by applications to one and three dimensional spinboson models and a twostate threemode model of the internal conversion of pyrazine. Also discussed is the importance of electronic coherence for the proper treatment of nonadiabatic transition rates which is naturally described by the Liouville methods compared to the conventional independent trajectory approaches.

Quantitative prediction of gasphase nuclear magnetic shielding constants
View Description Hide DescriptionBenchmark calculations of nuclear magnetic shielding constants are performed for a set of 16 molecules. It is demonstrated that nearquantitative accuracy deviation from experiment) can be achieved if (1) electron correlation is adequately treated by employing the coupledcluster singles and doubles (CCSD) model augmented by perturbative corrections for triple excitations [CCSD(T)], (2) large (uncontracted) basis sets are used, (3) calculations are performed at accurate equilibrium geometries (obtained from CCSD(T)/ccpVTZ or CCSD(T)/ccpVQZ calculations), and (4) vibrational averaging is included. In this way calculations corrected for vibrational effects], the mean deviation and standard deviation from experiment are 1.6 and 0.8 ppm, respectively. Less complete theoretical treatments result in larger errors. Consideration of relative shifts might reduce the mean deviation (through an appropriately chosen reference compound), but cannot change the standard deviation. Densityfunctional theory calculations of nuclear magnetic shielding constants are found to be less accurate, intermediate between Hartree–Fock selfconsistentfield and secondorder Møller–Plesset perturbation theory.

On the performance of fourcomponent relativistic density functional theory: Spectroscopic constants and dipole moments of the diatomics HX and XY (X,Y=F, Cl, Br, and I)
View Description Hide DescriptionWe have tested the performance of fourcomponent relativistic density functional theory(DFT) by calculating spectroscopic constants and and dipole moments in the vibrational ground state for a selected set of 14 molecules: the hydrogen halides HX, the dihalogens as well as the interhalogens XY (X,Y=F, Cl, Br, and I). These molecules have previously been studied by fourcomponent relativistic wave function based methods by Visscher and coworkers [J. Chem. Phys. 108, 5177 (1998); 104, 9040 (1996); 105, 1987 (1996)]. We have used four different nonrelativistic functionals at the DZ and TZ basis set level. What is perhaps the most striking result of our study is the overall good performance of the local density approximation functional SVWN5; at the triple zeta basis set level it predicts bond lengths harmonic frequencies anharmonicities and dipole moments with relative errors of 0.46%, 0.39%, −16.3%, and −0.74%, respectively. The corresponding values for the B3LYP hybrid functional are 1.27%, −2.10%, −20.4%, and 4.71%. The two generalized gradient approximation functionals PW86 and BLYP show a less convincing performance, characterized by a systematic overestimation of bond lengths and underestimation of harmonic frequencies. We show that only the constant term is modified in secondorder vibrational perturbation theory upon the inclusion of a linear term, corresponding to the choice of a nonstationary reference geometry. Upon shifting the reference geometry from the optimized to the experimental geometry the calculated harmonic frequencies are significantly improved, whereas the anharmonicities are basically unchanged. Dipole moments calculated at the experimental geometry at the B3LYP/TZ level appear to be remarkably accurate with a mean relative error of −1.1% and a standard deviation of less than 4%. Our study reveals that anharmonicities are quite sensitive to the numerical integration scheme employed in the DFT calculations, and for the interhalogens we had to modify the Becke partitioning scheme by using atomic adjustments along the lines of the atom in molecules approach of Bader.

New rovibrational kinetic energy operators using polyspherical coordinates for polyatomic molecules
View Description Hide DescriptionWe illustrate how one can easily derive kinetic energy operators for polyatomic molecules using polyspherical coordinates with very general choices for axis embeddings and angles used to specify relative orientations of internal vectors. Computer algebra is not required.

Openshell localized Hartree–Fock approach for an efficient effective exactexchange Kohn–Sham treatment of openshell atoms and molecules
View Description Hide DescriptionWithin the framework of the symmetrized Kohn–Sham (KS) formalism an effective exactexchange approach, the openshell localized Hartree–Fock (OSLHF) method, is derived. The derivation relies on an approximation of energy denominators in KS oneparticle Greens functions, the approximation of average magnitudes of eigenvalue differences, which is introduced. With the OSLHF method openshell molecules can be treated efficiently and numerically stable without running into the symmetry problem encountered in conventional KS methods. The selfinteraction free Hamiltonian operator of the OSLHF approach is in all cases nonspinpolarized and exhibits the full molecular point group symmetry in real space. Results for atoms as well as small and medium size molecules are presented. A procedure is introduced which yields special basis sets required for an efficient construction of the Slater potential which enters the effective KS potential of localized Hartree–Fock methods.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photoinduced reactions in the ion–molecule complex
View Description Hide DescriptionIon–molecule complexes of magnesium cation with ethyl isocyanate were produced in a laserablation supersonic expansion nozzle source. Photoinduced reactions in the 1:1 complexes have been studied in the spectral range of 230–410 nm. Photodissociationmass spectrometry revealed the persistent product from nonreactive quenching throughout the entire wavelength range. As for the reactive channels, the photoproducts, and were produced only in the blue absorption band of the complex with low yields. The action spectrum of consists of two pronounced peaks on the red and blue sides of the atomic transition. The ground state geometry of was fully optimized at B3LYP/631+G** level by using GAUSSIAN 98 package. The calculated absorptionspectrum of the complex using the optimized structure of its ground state agrees well with the observed action spectrum. Photofragment branching fractions of the products are almost independent of the photolysisphotonenergy for the excitations. The very low branching ratio of reactive products to nonreactive fragment suggests that evaporation is the main relaxation pathway in the photoinduced reactions of

Sodium hydroxide formation in water clusters: The role of hydrated electrons and the influence of electric field
View Description Hide DescriptionThe stability, structure and reactivity of and clusters have been investigated by means of the density functional theory(DFT) method. In all cases, the Na electrons are located far from their nuclei and hydrated. Particular emphasis has been placed on the influence of the watergenerated electric field on sodium dimer polarization. The metal atoms hydrolysis reaction has been studied for the lone sodium atom as well as for the sodium pair; the calculated activation energies are found to be very similar in terms of magnitude. Reaction mechanisms are proposed that exhibit the role of the hydrogen bond cooperative effects in combination with proton tunneling.

Highresolution jetcooled and room temperature infrared spectra of the stretch of vinoxy radical
View Description Hide DescriptionRotationally resolved jetcooled and room temperature spectra of the stretch of vinoxy radical have been obtained near 2800 cm^{−1} by means of tunable infrared laserspectroscopy. About 500 transitions corresponding to btype selection rules have been assigned in the jetcooled spectrum recorded in the region 2809–2860 cm^{−1}. The band origin has been determined to be 2827.913 cm^{−1}. A number of lines are split into doublets by the electron spin–rotation interaction. The jetcooled spectrum has been supplemented by transitions with high N or K values observed in the room temperature spectrum, which was recorded over the spectral region 2754–2894 cm^{−1}. Both local and global perturbations have been found in the upper state energy levels. Leastsquares fitting of the apparently unperturbed levels yielded molecular constants as well as centrifugal distortion and spinrotational constants for the upper state.

Experimental and theoretical investigation of the AlH electronic transition
View Description Hide DescriptionThe laser fluorescence excitation spectrum of the (0,0) band of AlH and AlD is reported. The state was prepared in a freejet supersonic expansion by the reaction of photolyzed trimethylaluminum with hydrogen or deuterium. Spectroscopic constants for the upper and lower vibronic levels were derived from fits to the measured transition wave numbers of the rotational lines. Lifetimes of rotational/finestructure levels of electronically excited were determined from fluorescence decay waveforms with laser excitation on isolated rotational lines. The measured lifetimes were compared with values obtained in a theoreticaltreatment of the excitedstate decay dynamics, wherein both radiative decay to the state and nonradiative decay through the repulsive state were considered. The experimental and theoretical lifetimes are in good agreement. The theoreticaltreatment shows that the nonradiative excitedstate decay dominates over radiative decay. The observed finestructure dependence of the lifetimes results is due to the nature of the spin–orbit coupling of the state with the continuum.

Ion dissociation dynamics of the chlorine azide cation investigated by velocity map imaging
View Description Hide DescriptionThe velocity map imaging technique was applied to study the unimolecular dissociationdynamics of the chlorine azide cation fragmenting into and and the results have been compared to quantum chemical calculations. The ion was produced in a molecular beam by twophotonionization of chlorine azide with laser light at Rotationally resolved REMPI spectra and velocity map images of state selected quantify the energy deposition into and products. Photoelectron velocity map images show near zeroenergy electron production. Angular distributions of the photofragments suggest we are witnessing the influence of the ions first excited electronic state on its decomposition. The dissociation products are mainly in the vibrational ground state, but rotationally excited with J up to ∼60. An unusual vibrational distribution in the product was observed, which is evidence of nonstatistical ion decomposition. This work also provides an accurate determination of the energetics for the reaction, from which one may use prior photoionization threshold data to derive the energetics of the dissociation.

Photodissociation of 1,1 and at 248 nm: A simple C–Br bond fission versus a concerted threebody formation
View Description Hide DescriptionThe photodissociation of (DBM), 1,1 and (DBE) at 248 nm was investigated using product translational spectroscopy. The results show that DBM and 1,1DBE undergo a simple C–Br bond fission with fragments recoiling anisotropically. When the laser energy increased from 10 to 40 mJ/pulse, the nascent products, and absorbed an additional photon to produce the secondary Br atom. In contrast, 1,2DBE dissociates into the triple products Br (fast) + Br (slow) + in a concerted reaction. This is confirmed from the measuredanisotropy of the products, which indicates that the reaction is completed in a fraction of rotational period. Following an asynchronous concerted reaction, the simulation for the triple products was derived with the distributions coupled by asymmetric angular distributions. The results are discussed in terms of the weakness of the C–Br bond strength in the βbromoethyl radical that a rapid scission of the second C–Br bond occurred asynchronously with the cleavage of the first C–Br bond along the potential energy surface.

Quantum reactive scattering calculations for the reaction
View Description Hide DescriptionThe results of accurate quantum scattering calculations in symmetrized hyperspherical coordinates are reported for the reaction at 48 values of total energy in the range 0.4–2.32 eV. Integral and differential cross sections are computed using the Boothroyd–Keogh–Martin–Peterson (BKMP2) potential energy surface for all values of total angular momentum Two sets of calculations are reported: one set includes the effects of the geometric phase and the other does not. By comparing these two sets of calculations, the effects of the geometric phase on the scattering results are investigated both as a function of total energy and total angular momentum. Several transition state resonances survive the sum over J and are observed in many of the fully converged statetostate integral and differential cross sections. In some cases a series of resonances is observed. The energy spacings between many of the resonances are consistent with the energy spacings between the even or odd bending modes of the quantized transition states of

Monodromy in the spectrum of a rigid symmetric top molecule in an electric field
View Description Hide DescriptionWe show that for rigid symmetric top molecules in electric fields the phenomenon of monodromy arises naturally as a “defect” in the lattice of quantum states in the energymomentum diagram. This makes it impossible to use either the total angular momentum or a pendular quantum number to label the states globally. The monodromy is created or destroyed by classical Hamiltonian Hopf bifurcations from relative equilibria. These phenomena are robust and should be observable in quasisymmetric top molecules with field strengths E satisfying where μ is the dipole moment and the rotational constant perpendicular to the symmetry axis of the molecule.

Theoretical investigations on relative stabilities of fullerene
View Description Hide DescriptionThe complete set of 134 isolatedpentagonrule isomers of has been first investigated by various quantumchemical approaches. Twenty lowenergy cage structures are computed by the ab initio Hartree–Fock selfconsistent field method and hybrid density functional theory treatment. All the methods point out a species as the system ground state. The computed temperaturedependent relative concentrations under the interisomeric thermodynamic equilibrium evaluated by a combined quantumchemical and statisticalmechanical treatment, predict two distinct structures as the most thermodynamically populated isomers in the system. This finding agrees quite well with the recently reported experimental observations.

Isomerism of the anion of the indole–water dimer. Ab initio study
View Description Hide DescriptionIn our previous paper [J. Chem. Phys. 112, 3726 (2000)], the experimental group of Schermann, who participated in the study, reported a Rydbergelectron transferspectroscopy (RET) experiments concerning anions of the indole–water clusters. For the RET spectrum showed two peaks. Based on the ab initio calculations one of the peaks was assigned to a dipole–bound (DB) anion with a diffuse excess electron and it was speculated that the second peak could correspond either to an excited electronic state or an excited vibrational state of the DB anion. In this paper we present calculations that describe a second anion of the indole–water dimer where the excess electron is suspended between the indole and water molecules and also occupies a diffuse orbital. The relation of this finding to the RET spectrum is discussed and we propose assigning the two RET peaks to the two anions described in the calculations.

Radiative association of
View Description Hide DescriptionRigorous statetostate quantum calculations of the dynamics of the radiative association reaction are performed. For this purpose the appropriate methodology is described in detail and computational aspects facilitating the actual calculations of the resonances and the freebound phototransition amplitudes are discussed. Under the assumptions that the reaction is a singlestate process proceeding entirely on the ground electronic statepotential energy surface of and that higher dissociation channels of the ion complex can be neglected, all resonances contributing to the association are determined and the rate constant as a function of temperature is calculated for the lowtemperature interval Its maximum value is predicted to be small, at a temperature of about 20 K.

Highresolution electronic spectroscopy of a nonlinear carbon chain radical
View Description Hide DescriptionA highresolution gasphase spectrum of a molecular absorption band around 604 nm is assigned as due to an electronic transition of a nonlinear planar species starting from its electronic ground state. The spectrum is observed in direct absorption by cavity ringdown spectroscopy through a supersonic planar discharge through a mixture of acetylene in helium. The spectrum has a clear rotational and Ktype structure. This allows an accurate determination of the B and Crotational constants and an estimate for the Arotational constant in ground and electronically excited states. The resolved spectrum of the fully deuterated species has been obtained as well. The results are compared both to the outcome of ab initio geometry optimizations and lowresolution absorption spectra in 6 K neon matrices obtained after massselective deposition.