Volume 114, Issue 1, 01 January 2001
 ARTICLES

 Theoretical Methods and Algorithms

A basis set study for the calculation of electronic excitations using Monte Carlo configuration interaction
View Description Hide DescriptionA systematic study of basis sets and manybody correlations for the treatment of electronic excitations is presented. Particular emphasis is placed on the highly accurate treatment of transition energies within a computationally tractable scheme. All calculations have been performed using the Monte Carloconfiguration interaction method and correlationconsistentbasis sets augmented by diffuse functions constructed for the description of anions, and with the inclusion of additional Rydberg functions. The importance of a balanced description of the excited states and the ground state has been emphasized and the resulting electronic transitions have been compared with experimental values. We have found that the augccpVTZ basis set further augmented with Rydberg functions constitutes a good choice of basis set for which we report electronic excitations in excellent agreement with experiment.

Topological analysis of the electron localization function applied to the study of the [1,3] sigmatropic shift of fluorine in 3fluorpropene
View Description Hide DescriptionThe [1,3] sigmatropic shift of the fluorine atom in the 3fluorpropene system has been studied from the topological analysis of the electron localization function (ELF). All calculations have been carried out at the level of theory. The allowed suprafacial pathway through a concerted fourmembered transition state (TS) has been characterized in terms of an ion pair structure which shows the halogen atom bearing The ionic nature of the TS is supported by the absence of any polisynaptic basin connecting the fluorine and the allyl fragments in this stationary point. Finally, the evolution of the bonding characteristics along the intrinsic reaction coordinate reaction path has been analyzed in detail in terms of the basin properties of the ELF function.

Higher order decouplings of the dilated electron propagator with applications to shape and Auger resonances
View Description Hide DescriptionThe full third order quasiparticle third order and Outer Valence Green’s Function decouplings of the biorthogonal dilated electron propagator have been implemented for the first time and results from their application to shape and Auger resonances are presented and compared with energies and widths obtained using the zeroth order quasiparticle second order and second order decouplings. The energies and widths from third order decoupling for shape resonances are close to those obtained using second order selfenergy approximants. The energy and width calculated using the third order decoupling for Auger resonances provide better agreement with experimental results, with the much more economic quasiparticle third order decoupling being just as effective. The differences between FDAs from different decouplings are analyzed to elicit the role of correlation and relaxation in the formation and decay of shape and Auger resonances.

Parallel Douglas–Kroll energy and gradients in NWChem: Estimating scalar relativistic effects using Douglas–Kroll contracted basis sets
View Description Hide DescriptionA parallel implementation of the spinfree oneelectron Douglas–Kroll–Hess (DKH) Hamiltonian in NWChem is discussed. An efficient and accurate method to calculate DKH gradients is introduced. It is shown that the use of a standard (nonrelativistic) contracted basis set can produce erroneous results for elements beyond the first row elements. The generation of DKH contracted basis sets for H, He, B–Ne, Al–Ar, and Ga–Br is discussed. The effect of DKH at the Hartree–Fock level on the bond distances, vibrational frequencies, and total dissociation energies for and is discussed. It is suggested that the predominant effect of the scalar relativistic correction on the total dissociation energy can be calculated at the Hartree–Fock level if an adequate basis set is used.

Multiarrangement photodissociation calculations utilizing negative imaginary potentials
View Description Hide DescriptionA new method for calculating total and partial cross sections for photodissociation processes which produce more than one chemical product is presented. By using negative imaginary absorbing potentials, the method reduces the multiarrangement problem to a set of singlearrangement problems. In this way, the statetostate photodissociation transition amplitudes are calculated directly using the artificial channel method coupled to an efficient log–derivative propagator. In addition, the discrete position operator representation is used to significantly simplify the calculations of the potential matrix elements. The method is shown to provide accurate cross sections for the resonant photodissociation of a model system.

Study of relativistic effects on nuclear shieldings using densityfunctional theory and spin–orbit pseudopotentials
View Description Hide DescriptionWe combine a perturbational calculation, using spin–orbit pseudopotentials, of the spin–orbit effect on nuclear shieldings with scalar relativistic effects taken into account selfconsistently using quasirelativistic pseudopotentials. The shieldings are calculated for light nuclei in systems containing heavy atoms, for which matching spin–orbit and quasirelativistic pseudopotentials are used. The secondorder spin–orbit contribution arising from the magnetic field dependence of the oneelectron spin–orbit Hamiltonian is also included. The method is implemented within the framework of densityfunctional theory and is capable of treating large molecular systems economically. Calculations are presented for the HX and molecules, thirdrow transition metal carbonyls, and a series of methyl mercurycompounds.

A generalized electronpair density function for atoms
View Description Hide DescriptionFor manyelectron atoms, we discuss a generalized electronpair density function that represents the probability density function for the magnitude of the twoelectron vector to be q, where a and b are realvalued parameters. It is pointed out that the function connects smoothly the singleelectron density the electronpair intracule (relative motion) density and the electronpair extracule (centerofmass motion) density Moreover, is found to be a local extremum function of with respect to the parameter b. Analogously, the singleelectron moments are local extrema of the moments associated with An illustrative example is given for the helium atom within the Kellner approximation.

Mean first passage times across a potential barrier in the lumped state approximation
View Description Hide DescriptionThe lumped state approximation (LSA) is a method for handling boundary conditions for diffusion on an interval which simplifies the description of transitions into and out of the interval. It was originally motivated by the problem of protonconduction through the ion channel gramicidin. This paper discusses the mean first passage time of a diffuser crossing a potential barrier in the lumped state approximation. The LSA mean first passage time is shown to be identical to a different quantity, the interior mean first passage time, clarifying the nature of the approximation. We also discuss a variant of the LSA in which dependence on an applied electrical potential is made explicit; an optimal value for an effective electrical distance is found. A detailed comparison is made of the LSA mean first passage time with several other formulations of the mean time to cross a barrier.

Relativistic calculations of the rotational g factor of the hydrogen halides and noble gas hydride cations
View Description Hide DescriptionThe rotational g factors of the hydrogen halides, HX (X=F,Cl,Br,I), and noble gas hydride cations, (X=Ne,Ar,Kr,Xe), have been calculated at the level of the random phase approximation (RPA) as relativistic fourcomponent linear response functions as well as nonrelativistic linear response functions. In addition, using perturbation theory with the massvelocity and Darwin operators as perturbations, the relativistic corrections have been estimated as quadratic response functions. It was found that the fourcomponent relativistic calculations give in general a more negative electronic contribution to the rotational g factor than the nonrelativistic calculations with relativistic corrections ranging from 0.2% for HF and to 2.9% for and 3.5% for HI. The estimates of the relativistic corrections obtained by perturbation theory with the massvelocity and Darwin operators are in good agreement with the fourcomponent results for HF, HCl, and whereas for HI, and they have the wrong sign.

Reduced dynamics with initial correlations: Multiconfigurational approach
View Description Hide DescriptionDynamical equations for a subsystem interacting with an environment are proposed which are adapted to a multiconfigurational form of the density operator. Initial correlations are accounted for in a nonMarkovian master equation. Two variants of the latter are derived by projection operator techniques and cumulant expansion techniques, respectively. The present scheme is developed in view of describing the ultrafast dynamics in solute–solvent complexes where the details of system–environment correlations are of importance. The master equation is readily integrated into the equations of motion derived by the multiconfiguration timedependent Hartree method, which provides an efficient scheme for the numerical propagation of the density operator.

Electron–electron coalescence and counterbalance functions for atoms
View Description Hide DescriptionFor manyelectron atoms, spherically averaged electron–electron coalescence and counterbalance functions are studied which, respectively, represent the probability densities that any electron pairs with zero interelectronic distance are located at a radius R from the nucleus and that any electron pairs with zero centerofmass radius have a relative distance u. For the exact and Hartree–Fock (HF) wave functions, cusp relations and are derived theoretically, where the prime denotes the first derivative and Z is nuclear charge. At the Hartree–Fock limit level, both functions and are found to be monotonically decreasing with a single maximum at or for all the 102 atoms He through Lr. The longrange asymptotic behavior of the coalescence and counterbalance functions is governed in general by the orbital energy of the highest occupied atomic orbital.

Gaussian3X (G3X) theory: Use of improved geometries, zeropoint energies, and Hartree–Fock basis sets
View Description Hide DescriptionA modification of G3 theory incorporating three changes is presented. The three new features include: (1) geometry; (2) zeropoint energy; and (3) addition of a gpolarization function to the G3Large basis set for secondrow atoms at the Hartree–Fock level. Extension of G3 theory in this manner, referred to as G3X, is found to give significantly better agreement with experiment for the G3/99 test set of 376 reaction energies. Overall the mean absolute deviation from experiment decreases from 1.07 kcal/mol (G3) to 0.95 kcal/mol (G3X). The largest improvement occurs for nonhydrogens. In this subset of energies the mean absolute deviation from experiment decreases from 2.11 to 1.49 kcal/mol. The increased accuracy is due to both the use of new geometries and the larger Hartree–Fock basis set. In addition, five other G3 methods are modified to incorporate these new features. Two of these are based on reduced orders of perturbation theory, G3X(MP3) and G3X(MP2), and have mean absolute deviations for the G3/99 test set of 1.13 and 1.19 kcal/mol, respectively. The other three methods are based on scaling the energy terms, G3SX, G3SX(MP3), and G3SX(MP2). They have mean absolute deviations of 0.95, 1.04, and 1.34 kcal/mol, respectively.

The ab initio model potential method: Lanthanide and actinide elements
View Description Hide DescriptionIn this paper we present relativistic core ab initiomodel potentials based on atomic Cowan–Griffin calculations, together with Wood–Boring spinorbit operators and optimized Gaussian valence basis sets, for the lanthanide elements Ce to Lu and for the actinide elements Th to Lr. This completes the chemically relevant part of the Periodic Table. A core was chosen for Ce–Lu and a core was chosen for Th–Lr. Minimal and valence basis sets were, respectively, optimized for Ce–Lu and Th–Lr, and a contraction is recommended for all these 28 elements in molecular calculations. The atomic and molecular results show the same good quality already observed for the maingroup elements and the transition metal elements.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electronpropagator calculations on the photoelectron spectrum of ethylene
View Description Hide DescriptionElectronpropagator calculations are performed on the vertical ionization energies of ethylene with a sequence of correlationconsistentbasis sets. Two methods are employed: the nondiagonal, renormalized, secondorder (NR2) approximation and the thirdorder, algebraic, diagrammatic construction. The computational efficiency of the NR2 method permits the use of the correlationconsistent, pentuple ζ basis, which contains 402 contracted Gaussian functions. As the size of the basis set grows, NR2 results for outervalence ionization energies steadily increase; NR2 errors with the largest basis set are less than ∼0.15 eV. Agreement with prominent, innervalence peaks is also satisfactory and the ratio of two pole strengths corresponding to innervalence, states is in close agreement with observed intensity ratios.

Electric properties of urea and thiourea
View Description Hide DescriptionThe major linear and nonlinear electric properties of urea and thiourea have been calculated at different levels of approximation with respect to the treatment of the electron correlation contribution. The basis set saturation effects were studied by comparing the results computed in three different basis sets of increasing flexibility. The socalled (firstorder) polarized (Pol) basis have been found to give excellent results for dipole moments and dipole polarizabilities. Their performance in calculations of the first hyperpolarizability is also quite good. However, calculations of the second hyperpolarizability require the use of recently developed secondorder polarized (HyPol) basis sets. The frequencydependent dynamic polarizabilities and first and second hyperpolarizabilities of urea and thiourea have been calculated in the timedependent Hartree–Fock approximation and then scaled to account for the electron correlation contribution and the basis set extension effect. This method gives useful estimates of the magnitude of different nonlinear optical processes. In particular thiourea was found to have attractively high value of the thirdorder optical susceptibility. The replacement of the C=O group of urea by its sulfur counterpart brings in general quite a large increase of the efficiency of the thirdorder optical processes.

Coulomb and centrifugal barrier bound dianion resonances of
View Description Hide DescriptionNew shortlived resonance states of have been studied by bombarding anions by lowenergy, monoenergetic electrons at the ASTRID heavyion storage ring. Storage for several seconds before the measurement ensures full vibrational relaxation of target anions. The dianion resonances were identified by the detection of resonances in the cross section for formation of neutral Two resonances were observed: The one of lowest energy is assigned to be the ground state of based on an ab initio calculation. This state may be held by a Coulomb barrier alone. A second state of significantly higher energy is argued to be held by a combined Coulomb and centrifugal barrier. Finally, a new scheme in which electron recombination may create stable dianions is proposed.

Structure and energetics of clusters deduced from photoionization efficiency curves
View Description Hide DescriptionIonization efficiency curves (IECs) were measured for clusters generated by reactions of laserablated lithiummetal with water vapor, using photoionizationtimeofflight mass spectrometry. The measured IECs are wellreproduced with a simulation involving Franck–Condon factors, enabling to identify the globalminimum structure of the clusters predicted in our theoretical study [Tanaka et al., J. Chem. Phys. 113, 1821 (2000)]. Hyperlithiated structures (HLS), in which an excess electron is delocalized, are identified for the cluster with and 3, while electronlocalized or segregated structure (ELS) are for those with Adiabatic ionization energies were determined as for HLS of for HLS of for ELS of and for ELS of The ionization energy of was determined as by a linear extrapolation of IEC. For the energetics of two lowestenergy isomers is discussed based on the observed abundance ratio.

I. Threecenter versus fourcenter HClelimination in photolysis of vinyl chloride at 193 nm: Bimodal rotational distribution of HCl detected with timeresolved Fouriertransform spectroscopy
View Description Hide DescriptionFollowing photodissociation of vinyl chloride at 193 nm, fully resolved vibrationrotational emission spectra of HCl in the spectral region are temporally resolved with a stepscan Fouriertransform spectrometer. Under improved resolution and sensitivity, emission from HCl up to is observed, with (limited by overlap at the band head) for All vibrational levels show bimodal rotational distribution with one component corresponding to and another corresponding to for Vibrational distributions of HCl for both components are determined; the lowJ component exhibits inverted vibrational population of HCl. Statistical models are suitable for threecenter (α, α) elimination of HCl because of the loose transition state and a small exit barrier for this channel; predicted internal energy distributions of HCl are consistent but slightly less than those observed for the highJ component. Impulse models considering geometries and displacement vectors of transition states during bond breaking predict substantial rotational excitation for threecenter elimination of HCl but little rotational excitation for fourcenter (α, β) elimination; observed internal energy of the lowJ component is consistent with that predicted for the fourcenter elimination channel. Rate coefficients 33.8 and for unimolecular decomposition predicted for threecenter and fourcenter elimination channels, respectively, based on RiceRamsbergerKasselMarcus theory are consistent with the branching ratio of 0.81:0.19 determined by counting vibrational distribution of HCl to for highJ and lowJ components. Hence we conclude that observed highJ and lowJ components correspond to HCl produced from threecenter and fourcenter elimination channels, respectively.

Ultraviolet photochemistry of hydrogenbonded complexes in argon matrices
View Description Hide DescriptionWe have studied the ultraviolet photoreaction of complexes isolated in argon matrices using Fouriertransform infrared spectroscopy.Photoexcitation of the acetone transition, using either 266 or 309 nm, results in the reaction of hydrogenbonded complexes to produce complexes through a novel photoenolization mechanism. Only the hydrogenbonded complexes undergo reaction following midUV irradiation. No significant loss of isolated reactant molecules occurs using either 266 or 309 nm excitation. Detailed ab initio calculations of complex are presented to support these findings. Photoexcitation of similar matrices at 193 nm, which excites the acetone transition and HBr directly, shows extensive reaction of HBr, acetone, and their complexes by a photofragmentation mechanism. We discuss the mechanism of HBr assisted acetone photoenolization in detail and report experimental and calculated band frequencies and structures of complexes.

Collision induced fragmentation of small ionic alkali clusters. III. Heteronuclear clusters
View Description Hide DescriptionFragmentation of small heteronuclear clusters induced by collision with helium atoms is investigated at a laboratory energy of 4800 eV. Populations of the various fragmentation pathways are measured. Detailed analysis of the collision is performed with a multicoincidence technique allowing the determination of the velocity vectors of the fragments. Fragmentation is predominantly induced by momentum transferred in binary collisions between He and alkali cores, electronic excitation accounting only for about 10% of the process. Experiments with heteronuclear clusters allow the study of the various fragmentation mechanisms following the initial momentum transfer. Twostep fragmentation processes are governed by the endothermicity of the pathway while direct ejection of an alkali atom in binary collisions is directly dependent on the relative number of Na and K cores.