Volume 112, Issue 11, 15 March 2000
 THEORETICAL METHODS AND ALGORITHMS


Convergent summation of Møller–Plesset perturbation theory
View Description Hide DescriptionRational and algebraic Padé approximants are applied to Møller–Plesset (MP) perturbation expansions of energies for a representative sample of atoms and small molecules. These approximants can converge to the full configuration–interaction result even when partial summation diverges. At order MP2 (the first order beyond the Hartree–Fock approximation), the best results are obtained from the rational [0/1] Padé approximant of the total energy. At MP3 rational and quadratic approximants are about equally good, and better than partial summation. At MP4, MP5, and MP6, quadratic approximants appear to be the most dependable method. The success of the quadratic approximants is attributed to their ability to model the singularity structure in the complex plane of the perturbation parameter. Two classes of systems are distinguished according to whether the dominant singularity is in the positive half plane (class A) or the negative half plane (class B). A new kind of quadratic approximant, with a constraint on one of its constituent polynomials, gives better results than conventional approximants for class B systems at MP4, MP5, and MP6. For with the C–H distance at twice the equilibrium value the quadratic approximants yield a complex value for the groundstate electronic energy. This is interpreted as a resonance eigenvalue embedded in the ionization continuum.

Approximate calculation of femtosecond pump–probe spectra monitoring nonadiabatic excitedstate dynamics
View Description Hide DescriptionAn approximate theory of femtosecondspectroscopy of nonadiabatically coupled electronic states is developed. Neglecting the commutators of vibrational Hamiltonians pertaining to different diabatic electronic states, the formulation represents a generalization of the semiclassical Franck–Condon approximation to the case of nonadiabaticdynamics. Explicit expressions for various time and frequencyresolved spectra are derived which allow for a simple interpretation of femtosecondspectroscopy of vibronically coupled molecular systems. Employing multidimensional model problems describing (i) the nonadiabaticcis–transisomerization of an electronic twostate system, and (ii) the internal conversion of pyrazine, exact reference data are compared to approximate calculations of transient absorbance and emission as well as timeresolved photoelectron spectra. In all cases considered, the approximation is shown to be appropriate for probe–pulse durations that are shorter than the period of the fastest relevant vibrational mode of the molecular system. Reducing the numerical costs of pump–probe simulations to the costs of a standard timedependent wavepacket propagation, the approximate theory leads to substantial computational savings.

Critical points and reaction paths characterization on a potential energy hypersurface
View Description Hide DescriptionMost of the time, the definitions of minima, saddle points or more generally order p critical points, do not mention the possibility of having zero Hessian eigenvalues. This feature reflects some flatness of the potential energy hypersurface in a special eigendirection which is not often taken into account. Thus, the definitions of critical points are revisited in a more general framework within this context. The concepts of bifurcation points, branching points, and valley ridge inflection points are investigated. New definitions based on the mathematical formulation of the reaction path are given and some of their properties are outlined.

Are properties derived from varianceoptimized wave functions generally more accurate? Monte Carlo study of nonenergyrelated properties of He, and LiH
View Description Hide DescriptionIt is commonly believed that varianceoptimized wave functions yield “satisfactory” if not, in principle, better estimates of nonenergyrelated physical properties than their energyoptimized counterparts. We test this notion by calculating a number of groundstate physical properties using a variety of variance and energyoptimized wave functions for He, and LiH. We gauge the quality of the properties using as a “metric” the sum of absolute relative errors. Our results suggest that the energyoptimized wave functions consistently provide better estimates of nonenergyrelated properties than varianceoptimized ones. We present qualitative arguments supporting these findings.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Infrared spectroscopy of ArOH: A direct probe of the potential energy surface
View Description Hide DescriptionAn infraredultraviolet (IRUV) doubleresonance technique has been implemented to obtain the infrared spectrum of ArOH in the vicinity of the fundamental OH stretch at 2.8 μm. A rotationally resolved spectrum of the fundamental OH stretching band of ArOH is observed at 3567.85(1) cm^{−1} (origin). A combination band, involving both OH stretch and intermolecular bending excitation, is identified at 3577.00(1) cm^{−1} (origin). The intermolecular energy of the excited bending state provides a direct measure of the anisotropy of the interaction potential. The rotational structure of the combination band reveals a large splitting between parity components with the same total angular momentum in the excited bending state [0.69(1) cm^{−1} for The experimentally derived parity splitting is compared with previous experimental and theoretical determinations of this parameter. The parity splitting associated with the excited bending state reflects the change in the intermolecular potential when the orbital containing the unpaired electron of OH lies in or out of the ArOH plane.

Ab initio potential energy surface for the interaction and bound rovibrational states
View Description Hide DescriptionAdiabatic potential energy surfaces for the and states of the complex were calculated using supermolecular unrestricted fourthorder Møller–Plesset perturbation theory and a large correlation consistent basis set supplemented with bond functions. The potential energy surface (PES) of the state has two minima. The global minimum from the unrestricted coupledcluster calculations with single, double, and noniterative triple excitations occurs for the collinear geometry Ar–H–O at with a well depth of There is also a local minimum for the skewed Tshaped form, whereas the Ar–O–H arrangement corresponds to a saddle point. The PES of the state also has two minima, which occur for the two collinear isomers. A variational calculation of the bound rovibrational states was performed. The calculated binding energy, and the energies of the bound vibrational states are in good agreement with experiment [see Berry et al., Chem. Phys. Lett. 178, 301 (1991) and Bonn et al., J. Chem. Phys. 112, 4942 (2000), preceding paper].

A selected ion flow tube study of the reactions of small ions with O atoms
View Description Hide DescriptionThe reactions of thirteen ions with atomic and molecular oxygen and nitric oxide have been measured using a selected ion flow tube operating at room temperature. Rate coefficients and product distributions are reported for each reaction. Most of the hydrocarbon ions studied exhibit relatively rapid reactions with O atoms and proceed at substantial fractions of the collision rate. All O atom reactions showed multiple product channels and the formation of a –C–O bond, either in the ion product or the neutral product of reaction.

Negative ion photoelectron spectroscopy of
View Description Hide DescriptionThe 351 nm photoelectron spectra of and the deuterated analogs exhibit two broad peaks. Ab initio calculations of the anion and neutral potentialenergysurfaces have been carried out using an MP2 (secondorder Mo/ller–Plesset)/ basis set. The geometries, frequencies, and energetics from these calculations aid in the interpretation of the experimental results. An estimate of the electron affinity is based on experimental and theoretical results. Calculations of the anion vibrational wave functions indicate that following electron photodetachment, the neutral potentialenergysurface is accessed from the reactant entrance channel through the transition state region.

Photodissociation spectroscopy of the complex
View Description Hide DescriptionThe weakly bound complex is produced by laser ablation in a pulsed nozzle cluster source and lowlying electronic states are studied with resonance enhanced photodissociationspectroscopy (REPD). The lowest band system correlates to the forbidden atomic transition. Sharp structure to the blue of this transition is assigned to the system. A vibrational progression and its convergence limit determine the excitedstatedissociation energy of Two electronic systems in the complex are derived from the atomic transition. A doublet progression to the red of the atomic transition is assigned to the system. Extrapolation of the vibrational progression determines an excitedstatedissociation energy of A broad continuum to the blue of the atomic transition is assigned to the transition. Using the excitedstate convergence limit, the groundstatedissociation energy is determined to be Rotational analyses from bands in both systems produce a groundstatebond length of

An energyresolved study of the partial fragmentation dynamics of Ar–HCl into H+Ar–Cl after ultraviolet photodissociation
View Description Hide DescriptionThe UVphotolysis of Ar–HCl is simulated by an exact wave packet calculation. Partial fragmentation of the cluster into H and Ar–Cl fragments is studied by projecting out the asymptotic wave packet onto the product states, at several excitation energies in the range of the Ar–HCl absorptionspectrum. The partial fragmentation pathway is found to dominate the photolysis process at very low excitation energies, and to be intense also at high energies. At medium excitation energies the other competing fragmentation pathway, namely total fragmentation into H, Ar, and Cl, dominates almost completely the photodissociationdynamics. The relative intensity of the two fragmentation pathways depends on the extent to which the hydrogen is initially blocked by Ar and Cl. The Ar–Cl radicals are produced with high rotational and low vibrational excitation at most of the Ar–HCl energies studied. The internal energy distributions of Ar–Cl show remarkable differences in shape depending on the regions of the absorptionspectrum which are excited. This effect can be exploited to control both the efficiency of Ar–Cl generation and the internal excitation of the radical prepared, by changing the excitation energy of the parent cluster.

Crossed beam reaction of phenyl radicals with unsaturated hydrocarbon molecules. I. Chemical dynamics of phenylmethylacetylene formation from reaction of with methylacetylene,
View Description Hide DescriptionThe chemical reactiondynamics to form phenylmethylacetylene, via reactive collisions of the phenyl radical with methylacetylene, are unraveled under single collision conditions in a crossed molecular beam experiment at a collision energy of 140 kJ mol^{−1}. The laboratory angular distribution and timeofflight spectra of at indicate the existence of a phenyl radical versus hydrogen replacement pathway. Partially deuterated methylacetylene, was used to identify the site of the carbon–hydrogen bond cleavage. Only the loss of the acetylenic hydrogen atom was observed; the methyl group is conserved in the reaction. Electronic structure calculations reveal that the reaction has an entrance barrier of about 17 kJ mol^{−1}. Forwardconvolution fitting of our data shows that the chemical reactiondynamics are on the boundary between an osculating complex and a direct reaction and are governed by an initial attack of the radical to the π electron density of the C1 carbon atom of the methylacetylene molecule to form a short lived, highly rovibrationally excited intermediate. The latter loses a hydrogen atom to form the phenylmethylacetylene molecule on the surface. The phenylallene isomer channel was not observed experimentally. The dynamics of the title reaction and the identification of the phenyl versus hydrogen exchange have a profound impact on combustion chemistry and chemical processes in outflows of carbon stars. For the first time, the reaction of phenyl radicals with acetylene and/or substituted acetylene is inferred experimentally as a feasible, possibly elementary reaction in the stepwise growth of polycyclic aromatic hydrocarbon precursor molecules and alkyl substituted species in high temperature environments such as photospheres of carbon stars and oxygen poor combustion systems.

Coupling between the internal rotation of the methyl group and proton/deuteron transfer in jetcooled 5methyl9hydroxyphenalenone(OH) and 5methyl9hydroxyphenalenone(OD): Tunneling rate dependence of coupling potential
View Description Hide DescriptionThe energy levels and the potentials arising from coupling between the two large amplitude motions, the internal rotation of the methyl group, and the proton/deuteron transfer have been investigated by measuring the fluorescence excitation, dispersed fluorescence, and holeburning spectra in the region of jetcooled 5methyl9hydroxyphenalenone(OH)/5methyl9hydroxyphenalenone(OD) and 5methyl9hydroxyphenalenone(OD)–water 1:1 complex. The symmetry of the potential functions for the internal rotation of the methyl group have been analyzed by a onedimensional periodic potential where is the barrier height for nfold symmetry and φ is the rotational angle. The internal rotation of the methyl group in the and states of the 5methyl9hydroxyphenalenone(OD)–water complex has been described well by threefold potentials. The potential for the state of 5methyl9hydroxyphenalenone(OD) is threefold, whereas that for the state of 5methyl9hydroxyphenalenone(OD) is sixfold. The potentials for the and states of 5methyl9hydroxyphenalenone(OH) are suggested to be sixfold. It has been shown that the coupling of the two motions reduces the symmetry of the tunneling potential when the tunneling rate is slow and decreases the tunneling rate, but the symmetry of the tunneling potential does not change and only provides a small effect on the rate of proton transfer when the tunneling rate is very fast. The tunneling rates for 5methyl9hydroxyphenalenone(OH)/5methyl9hydroxyphenalenone(OD) are much larger than those for 5methyltropolone(OH)/5methyltropolone(OD) reported previously. The difference in the coupling between these molecules has been discussed.

Anisotropic Coulomb explosion of irradiated with a highintensity femtosecond laser pulse
View Description Hide Descriptionvapor was irradiated with an intense femtosecond laser pulse W/cm^{2} in 120 fs at a wavelength of 800 nm). Multiply charged carbon ions, up to were detected in the timeofflight spectra. We have measured both energy and angular distributions with respect to the laser polarization direction for ions with different charge number. The kinetic energy of ions are distributed above 1 keV. The angular distribution measurement shows that the highly charged ions of and are mostly distributed in the directions parallel to the laser polarization, and the ions are slightly distributed in the direction perpendicular to it. These observations clearly indicate that an anisotropic explosion takes place. The average energy of ions with the different charge number is found to be proportional to the square of the charge number, while the maximum energy is proportional to the charge number. Classical molecular dynamics simulations have been successfully carried out reproducing not only the energy spectra but also the angular distributions of ions. The ions are shown to be produced by the cascade hopping of electrons induced by the intense laser light. The simulations suggest that the most crucial process for the anisotropicCoulomb explosion of is not the electron impact ionization, but the cascade hopping of electrons.

Theoretical description of the nonlinear response functions associated with eight distinctive threedimensional vibrational spectroscopies
View Description Hide DescriptionThe threedimensional (3D) vibrational spectroscopies are theoretically considered in terms of the associated nonlinear response functions. Since the 3D vibrational spectroscopy involves three vibrational coherence evolutions in the ground electronic state, it is found that there are eight distinctive possibilities when a vibrational coherence state can be created via an infrared field–matter interaction or two offresonant optical field–matter interactions via Raman. The nonlinear response functions associated with eight distinctive 3D vibrational spectroscopies, where seven of them are novel methods, are presented and expressed in terms of the linear response functions by taking the lowestorder contributions. The analytic expressions of the 3D Fourier spectra are obtained. By using the results, how to utilize the 3D vibrational spectroscopic methods to measure the higherorder vibrational mode coupling arising from the anharmonicity of the multidimensional potential energy surface as well as from the nonlinearity of the dipole moment or polarizability with respect to the vibrational degrees of freedom is discussed. Numerical calculations of the results for a threeoscillator model system are presented, and a few characteristic peaks uniquely appearing in the 3D vibrational spectra are discussed in detail. Finally, the thirdorder nonlinear terms of dipole moment and polarizability are found to be of critical use in the structure determination, assuming that the collective dipole moment and polarizability is mainly determined by the dipoleinduced–dipole interaction effect.

Experimental and theoretical study of the electronic spectrum of the complex: Transition to the excited valence state
View Description Hide DescriptionThe valence transition in the cluster is investigated in a collaborative experimental and theoretical study. Laser fluorescence excitation spectra of a supersonic expansion of B atoms entrained in Ar at high source backing pressures display several features not assignable to the BAr complex. Resonance fluorescence is not observed, but instead emission from the lower state. Sizeselected fluorescence depletion spectra show that these features in the excitation spectrum are primarily due to the complex. This electronic transition within is modeled theoretically, similarly to our earlier study of the transition [M. H. Alexander et al., J. Chem. Phys. 106, 6320 (1997)]. The excited potential energy surfaces of the fivefold degenerate state within the ternary complex are computed in a pairwise–additive model employing diatomic BAr potential energy curves which reproduce our previous experimental observations on the electronic states emanating from the asymptote. The simulated absorptionspectrum reproduces reasonably well the observed fluorescence depletion spectrum. The theoretical model lends insight into the energetics of the approach of B to multiple Ar atoms, and how the orientation of B porbitals governs the stability of the complex.

An accurate semiclassical calculation of collisioninduced dissociation
View Description Hide DescriptionCollisioninduced dissociation, is studied by using a semiclassical method in which one degree of freedom (i.e., intermolecular radial motion) is described by classical mechanics and the others by quantum mechanics. In the present semiclassical treatment, the quantum motions, i.e., vibration, dissociation, molecular rotation, and intermolecular angular motion, are solved accurately without introducing any decoupled approximations. The energy dependence of the dissociation cross section and the translational and angular momentum distributions of dissociative fragments are calculated at the total energies eV. Also carried out is the semiclassical calculation using a centrifugal sudden approximation, and the reliability of this approximation for the dissociation process is examined.

Quantum dynamics of photoexcited cyclohexadiene introducing reactive coordinates
View Description Hide DescriptionThe ultrafast photochemical ring opening reaction of 1,3cyclohexadiene is investigated theoretically. To allow for a quantum mechanical treatment of this highdimensional problem we introduce reactive coordinates which contain the modes active on the femtosecond time scale. A reduced Hamiltonian is derived in the corresponding subspace and twodimensional potential energy surfaces are interpolated using ab initio data points. The quantum dynamics in the state toward two conical intersections with the ground state is monitored. We find a bifurcation of the wave packet already in the excited state so that both conical intersections are reached but by different parts of the wave packet. By manipulating the initial conditions the branching ratio can be influenced.

Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations
View Description Hide DescriptionThe principle of coherence observation by interference noise [COIN, Kinrot et al., Phys. Rev. Lett. 75, 3822 (1995)] has been applied as a new approach to measuring wavepacket motion. In the COIN experiment pairs of phaserandomizedfemtosecond pulses with relative delay time prepare interference fluctuations in the excited state population, so the correlated noise of fluorescence intensity—the variance —directly mimics the dynamics of the propagating wavepacket. The scheme is demonstrated by measuring the vibrational coherence of wavepacket motion in the Bstate of gaseous iodine. The COIN interferograms obtained recover propagation, recurrences and spreading as the typical signature of wavepackets. The COIN measurements were performed with precisely tuned excitation pulses which cover the bound part of the Bstate surface up to the dissociative limit. In combination with preliminary numerical calculations, comparison has been made with results from previous phaselocked wavepacket interferometry and pumpprobe experiments, and conclusions drawn about the limitations of the method and its applicability to quantum dynamical research.

Vibrations of the carbon dioxide dimer
View Description Hide DescriptionFully coupled fourdimensional quantummechanical calculations are presented for intermolecular vibrational states of rigid carbon dioxide dimer for The Hamiltonian operator is given in collision coordinates. The Hamiltonian matrix elements are evaluated using symmetrized products of spherical harmonics for angles and a potential optimized discrete variable representation (PODVR) for the intermolecular distance. The lowest ten or so states of each symmetry are reported for the potential energy surface (PES) given by Bukowski et al. [J. Chem. Phys. 110, 3785 (1999)]. Due to symmetries, there is no interconversion tunneling splitting for the ground state. Our calculations show that there is no tunneling shift of the ground state within our computation precision (0.01 cm^{−1}). Analysis of the wave functions shows that only the ground states of each symmetry are nearly harmonic. The van der Waals frequencies and symmetry adapted force constants are found and compared to available experimental values. Strong coupling between the stretching coordinates and the bending coordinates are found for vibrationally excited states. The interconversion tunneling shifts are discussed for the vibrationally excited states.

Driving wave packet recurrences with optimally modulated laser pulses
View Description Hide DescriptionIn the weakfield limit, laser pulses optimized to induce vibrational wave packet recurrences in excited state potentials were calculated for Morse oscillators and for a real system [the and states of IBr]. The performance of the optimized pulses was studied via simulated wave packet propagation. Such optimal light fields may be computationally generated given only the form of the electronic potential surfaces, knowledge of the particular ground state supplying population, and simple molecular constants. Thus it should be possible to use the modulation of light fields experimentally optimized to achieve recurrences in order to obtain substantial information regarding previously uncharacterized potential surfaces in both diatomic and polyatomic molecules. Moreover, it should be possible to generalize this approach to the strongfield limit.
