Volume 117, Issue 4, 22 July 2002
 ARTICLES

 Theoretical Methods and Algorithms

Gradient symplectic algorithms for solving the Schrödinger equation with timedependent potentials
View Description Hide DescriptionWe show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki’s method of implementing timeordering of operators, produces a new class of powerful algorithms for solving the Schrödinger equation with timedependent potentials. When applied to the Walker–Preston model of a diatomic molecule in a strong laser field, these algorithms can have fourth order error coefficients that are three orders of magnitude smaller than the Forest–Ruth algorithm using the same number of fast Fourier transforms. Compared to the second order splitoperator method, some of these algorithms can achieve comparable convergent accuracy at step sizes 50 times as large. Morever, we show that these algorithms belong to a oneparameter family of algorithms, and that the parameter can be further optimized for specific applications.

Classical polarizable force fields parametrized from ab initio calculations
View Description Hide DescriptionA computationally efficient molecular dynamics implementation of a polarizable force field parametrized from ab initio data is presented. Our formulation, based on a secondorder expansion of the energy density, models the density response using Gaussian basis functions derived from density functional linear response theory.Polarization effects are described by the time evolution of the basis function coefficients propagated via an extended Lagrangian formalism. We have devised a general protocol for the parametrization of the force field. We will show that a single parametrization of the model can describe the polarization effects of LiI in the condensed phase.

Benchmark quantum Monte Carlo calculations
View Description Hide DescriptionFixed nodediffusionMonte Carlo (FNDMC) atomization energies are calculated for a benchmark set of 55 molecules. Using single determinant trial wave functions, comparison with experiment yields an average absolute deviation of 2.9 kcal/mol, placing this simplest form of FNDMC roughly at the same level of accuracy as the CCSD(T)/augccpVQZ method. However, unlike perturbative wave function expansion approaches, FNDMC is applicable to systems containing thousands of valence electrons. For the molecule, a number of possible sources of error are explored in detail. Results show that the main error is due to the fixednode approximation and that this can be improved significantly with multireference trial wave functions.

Assessment of the Handy–Cohen optimized exchange density functional for organic reactions
View Description Hide DescriptionWe have investigated the performance of the new optimized exchange functional (OPTX) developed by Handy and Cohen [Mol. Phys. 99, 403 (2001)] for predicting geometries, heats of reaction, and barrier heights for twelve organic reactions (six closedshell and six radical). OPTX has been used in conjunction with, among others, the wellknown Lee–Yang–Parr (LYP) correlational functional to form two new functionals, OLYP and O3LYP. These are similar to the wellestablished BLYP and B3LYP functionals, respectively, with OPTX replacing the standard Becke exchange functional, B88. Our results strongly support claims made by their developers that OLYP is superior to BLYP, and essentially renders it obsolete. The computed OLYP heats of reaction, barrier heights, and even molecular geometries (with larger basis sets), are comparable with, if not better than, the corresponding B3LYP values. The O3LYP functional is overall better than B3LYP, albeit not by much. Both OLYP and O3LYP are among the best functionals currently available; the performance of OLYP in particular is noteworthy given that this functional includes no exact exchange.

Positron and positronium chemistry by quantum Monte Carlo. VI. The ground state of LiPs, NaPs, and
View Description Hide DescriptionThe ground states of the positronic complexes LiPs, NaPs, and of the parent ordinarymatter systems have been simulated by means of the allelectron fixednode diffusionMonte Carlo (DMC) method. Positron affinities and positronium binding energies are computed by direct difference between the DMC energy results. LiPs was recomputed in order to test the possibility of approximating the electron–positron Coulomb potential with a model one that does not diverge for finding accurate agreement with previous DMC results. As to the effect due to the near degeneracy of the and configurations in Be is found to be relevant also for the positron affinity, and is discussed on the basis of the change in the ionization potential and the dipole polarizability. The DMC estimate of the positron affinity of Mg, a quantity still under debate, is 0.0168(14) hartree, in close agreement with the value 0.015 612 hartree computed by Mitroy and Ryzhihk [J. Phys. B. 34, 2001 (2001)] using explicitly correlated Gaussians.

Molecular integrals evaluated over contracted Gaussian functions by using auxiliary contracted hyperGaussian functions
View Description Hide DescriptionGeneral recurrence formulas for evaluating molecular integrals over contracted Cartesian Gaussian functions are derived by introducing auxiliary contracted hyperGaussian (ACH) functions. By using a contracted Gaussian function, this ACH represents an extension of the Gaussian function named derivative of Fourierkernel multiplied Gaussian [J. Chem. Phys. 94, 3790 (1991)]. The ACH is reducible to contracted Cartesian Gaussian functions, contracted modified Hermite Gaussian functions, and to contracted Gaussian functions multiplied by phase factors, or the socalled GIAO, and is also reducible to various spatial operators necessary for ab initio molecular orbital calculations. In our formulation, all molecular integrals are expressed in terms of ACH. Therefore, the formulations have wide applicability for calculating various kinds of molecular integrals in ab initio calculations. Recursive calculations based on our formulation do not depend on the number of contraction terms, because the contraction step is completed at the evaluation of the initial integrals. Therefore, we expect that more efficient recursive calculations will be accomplished by using our formulas for evaluating molecular integrals over contracted Gaussian functions.

Density functional generalized gradient calculations using Slater basis sets
View Description Hide DescriptionThe most common form of density functional calculations on molecular systems used generalized gradient approximationexchangecorrelation functionals (such calculations can be applied to larger systems because no exact exchange is included). The most efficient and fastest such codes use an auxiliary basis set to fit the density so that only threecenter integrals need to be evaluated. The codes DGAUSS and TURBOMOL use Gaussian basis sets, whereas the longestablished ADF code uses Slater basis sets. We here examine the use of Slater basis sets. Our new code evaluates all required integrals numerically by quadrature. We report calculations on the G2 molecular set, contrasting them with similar calculations using Gaussian basis sets. Our conclusion, as far as energetics and structure are concerned, is that very similar predictions may be obtained from basis sets of the same size, and at approximately the same cost.

Validation of variational transition state theory with multidimensional tunneling contributions against accurate quantum mechanical dynamics for in an extended temperature interval
View Description Hide DescriptionVariational transition state theory with multidimensional tunneling contributions (VTST/MT) is tested against quantum mechanical rate constants for the reaction at temperatures up to 1000 K. The VTST/MT method can be and has been applied to many reactions that cannot be treated by rigorous quantum dynamics methods. Studying the accuracy of VTST/MT by comparison with accurate quantal results that are becoming available for systems of increasing size is important for validating the theory. In the present study, covering a factor of five in temperature, the VTST/MT method is found to have a mean deviation from accurate quantal rate constants for a sixbody reaction of only 13% and maximum deviation of only 23%.

On slow manifolds of chemically reactive systems
View Description Hide DescriptionThis work addresses the construction of slow manifolds for chemically reactive flows. This construction relies on the same decomposition of a local eigensystem that is used in formation of what are known as Intrinsic Low Dimensional Manifolds (ILDMs). We first clarify the accuracy of the standard ILDM approximation to the set of ordinary differential equations which model spatially homogeneous reactive systems. It is shown that the ILDM is actually only an approximation of the more fundamental Slow Invariant Manifold (SIM) for the same system. Subsequently, we give an improved extension of the standard ILDM method to systems where reaction couples with convection and diffusion. Reduced model equations are obtained by equilibrating the fast dynamics of a closely coupled reaction/convection/diffusion system and resolving only the slow dynamics of the same system in order to reduce computational costs, while maintaining a desired level of accuracy. The improvement is realized through formulation of an elliptic system of partial differential equations which describe the infinitedimensional Approximate Slow Invariant Manifold (ASIM) for the reactive flow system. This is demonstrated on a simple reactiondiffusion system, where we show that the error incurred when using the ASIM is less than that incurred by use of the MaasPope Projection (MPP) of the diffusion effects onto the ILDM. This comparison is further done for ozone decomposition in a premixed laminar flame where an error analysis shows a similar trend.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Collision induced fragmentation of small ionic argon clusters
View Description Hide DescriptionThe mechanisms of collision induced fragmentation of small clusters are investigated in the 100 eV centerofmass energy range. The velocity vectors of the fragments are measured in a multicoincidence experiment for two and threebody fragmentation. The relative role of the two basic dynamics, electronic transitions, and momentum transfer in binary collisions is evaluated. The structure of the clusters deeply influences the type of mechanism. This is clearly the case of for which a specific impulsive process called “diatom” mechanism plays an important part in the fragmentation of one isomer.

Using Λdoublet ratios to understand collision geometry in direct bimolecular reactions
View Description Hide DescriptionA model is developed which can be used to understand how collision geometry can dictate product state lambda doublet ratios in direct bimolecular reactions that produce diatomic products in a Π molecular energy state. The predicted lambda doublet ratio is for unconstrained collision geometry, while the two limiting case geometries of exclusive endon collisions and exclusive sideon collisions yield lambda doublet ratios of and respectively. The theory is derived and used to interpret the experimental lambda doublet ratio of OH from the reaction.

The permanent electric dipole moments of iron monocarbide, FeC
View Description Hide DescriptionNumerous branch features in the (0,0) [12.0] and (0,0) [13.1] band systems of the iron monocarbide, FeC, have been studied using optical Stark spectroscopy. The electric field induced splittings in the high resolution laser induced fluorescencespectra were analyzed to produce values for the permanent electric dipole moments, μ, of 4.02(6) D, 4.44(6) D, and 2.36(3) D for the [12.0] Ω=2, [13.1] and states, respectively. A comparison with other iron containing molecules and theoretical predictions is made.

Decay processes of the states of and
View Description Hide DescriptionThe threshold photoelectron photoion coincidence spectra of the rare gas dimers and have been measured in the photon energy region between the first and second dissociation limits of the dimer ions. It has been found that the states of and completely dissociate via an optical transition to the repulsive state, while that of does not dissociate.

Infrared spectra of complex
View Description Hide DescriptionWe report the first rotationally resolved observation of the infrared spectrum of the molecular complex The complex was produced by a supersonic expansion through a pulsed slit jet. By means of a highresolution tunable diode laserspectrometer, we have recorded the spectrum of the HCl stretching vibration for the isotopes and From the analysis of the spectra, we determined the rotational constants and vibrational frequencies of both isotopes. These experimental results have been interpreted in view of obtaining information on the intermolecular interaction. The experimental data have been complemented by standard coupled cluster singles and doubles model including connected triple excitations with a correlation consistent polarized valence triple zeta basis set ab initio followed by grid calculations, in order to study the anharmonicity, the coupling between intramolecular and intermolecular motions, and the basis set superposition error effects. The results obtained in this study are compared to those of our previous work on the [J. Chem. Phys. 113, 4876 (2000)].

The ab initio potential energy surface and vibrationalrotational energy levels of MgOH
View Description Hide DescriptionThe equilibrium structure and potential energy surface of magnesium monohydroxide in its ground doublet state, MgOH, have been determined from largescale ab initio calculations using the spinrestricted coupledcluster method, RCCSD(T), with basis sets of doublethrough quintuplezeta quality. The effects of coreelectron correlation on the calculated molecular parameters were investigated. The vibrationalrotational energy levels of various MgOH isotopomers were calculated using the variational method. The spectroscopic constants determined are found to be in remarkably good agreement with experimental data.

A theoretical study of ozone isotopic effects using a modified ab initio potential energy surface
View Description Hide DescriptionA modified ab initiopotential energy surface (PES) is used for calculations of ozone recombination and isotopic exchange rate constants. The calculated lowpressure isotopic effects on the ozone formation reaction are consistent with the experimental results and with the theoretical results obtained earlier [J. Chem. Phys. 116, 137 (2002)]. They are thereby relatively insensitive to the properties of these PES. The topics discussed include the dependence of the calculated lowpressure recombination rate constant on the hinderedrotor PES, the role of the asymmetry of the potential for a general reaction and the partitioning to form each of the two recombination products: and

The formation of dimers and trimers in free jet cryogenic expansions
View Description Hide DescriptionThe formation of dimers, trimers, and tetramers in a free jet cryogenic expansion of atoms has been studied by diffraction from a nanostructure transmission grating. The final average velocities, speed ratios and ambient temperatures of the expansions for source temperatures of 30, 12, and 6 K and source pressures between 0.1 and 80 bar were determined from timeofflightmeasurements of the He atoms. The final mole fractions of the and clusters in the beam were determined from the intensities of the corresponding firstorder diffraction peaks for the same range of source conditions. For each source temperature, the final mole fractions of these small clusters first rise, pass through a maximum and then decrease with increasing source pressure. The processes leading to the formation of these clusters are simulated with a kinetic model that allows for density and temperature changes in the expanding beam. The bestfit threebody recombination rate constant for dimer formation increases by over three orders of magnitude as the thermal energy decreases from 1 K to 1 mK, in qualitative agreement with recent theories.

Singlet–triplet conversion induced by external magnetic field in gaseous oxalylfluoride excited to different single rotational levels of the state. I. Excitation to the SRLs of the vibronic level
View Description Hide DescriptionFluorescence decay of the rotationally cooled oxalylfluoride excited to the different single rotational levels of the state was measured as a function of an external magnetic field. On excitation to this level, the dynamics in both zero and nonzero fields may be described using the intermediatemolecule limit, with the fluorescence exhibiting biexponential decay. The fast component decay rate constant is the fieldindependent parameter, while that of the slow component depends on the magnetic field strength. The results obtained were explained by the indirect (electronic and nuclearspindecoupling) mechanism, proposed earlier.

Polyatomic molecules in strong laser fields: Nonadiabatic multielectron dynamics
View Description Hide DescriptionWe report the observation and characterization of a new nonresonant strong field ionization mechanism in polyatomic molecules: Nonadiabatic multielectron (NME) dynamics. The strong field response of a given molecule depends on important properties such as molecular geometry and bonding, the path length of delocalized electrons and/or ionization potential as well as on basic laser pulse parameters such as wavelength and intensity. Popular quasistatic tunnelling models of strong field molecular ionization, based upon the adiabatic response of a single active electron, are demonstrated to be inadequate when electron delocalization is important. The NME ionization mechanism greatly affects molecular ionization, its fragmentation and its energetics. In addition, multielectron effects are shown to be present even in the adiabatic long wavelength limit.

Photoelectron spectroscopy of pyrazine anion clusters
View Description Hide DescriptionWe studied the energetics and character of electron binding in the pyrazine anion clusters by mass spectrometry,photoelectron spectroscopy, and theoretical calculations. The mass distribution showed that the minimum number of molecules in a neat cluster of pyrazine to form an anion was two, with a single pyrazine molecule incapable of accommodating an excess electron. On the other hand, even the addition of a very weak solvent such as Ar sufficed to bring the affinity level of pyrazine below the vacuum level. Photoelectron spectra of some pyrazinecontaining anion clusters, and benzene, and water), were obtained. A vibrational progression was observed in the photoelectron spectra of The electron affinity of pyrazine was determined to be from extrapolation. A small drop in incremental electron affinity was observed from to indicating closure of the first solvation shell by four Ar atoms. The pyrazine dimer anion was found to exist in two isomeric forms of comparable energy, one with a symmetric structure and the other with an asymmetric one. The hydrogen bonding with the ring nitrogen strongly affects the binding of the pyrazine dimer anions. The electron affinity of the pyrazine dimer was estimated to be 0.13–0.15 eV.