Volume 113, Issue 21, 01 December 2000
 COMMUNICATIONS


Mixing quantum and classical dynamics using Bohmian trajectories
View Description Hide DescriptionA novel timedependent hybrid quantum/classical propagation scheme based on Bohmian quantum trajectories is presented. The quantum subsystem is described by a wave packet depending on the quantum variables and, via the total potential energy of the system, parametrically on the classical trajectories The wave packet is used to calculate de Broglie–Bohm quantum trajectories which are used to calculate the force acting on the classical variables. Quantum corrections of the classical equation of motion are also included. The method is applied to a simple case of two coupled oscillators. Comparison between exact quantum and approximate results demonstrates that these MQCB (Mixed Quantum/Classical Bohmian) trajectories provide a good description of the energy exchange between the two oscillators.

Ionic dissociation of NaCl on frozen water
View Description Hide DescriptionLowenergy reactive ion scattering (RIS) experiments show that NaCl dissociates almost completely on condensed icesurfaces prepared on Ru(001) even at 100 K forming solvated ions. NaCl by itself does not dissociate on a Ru(001) substrate; however, submonolayer coverages of water setsin dissociation. ions thus created are immobile such that they do not migrate across one water bilayer (BL) over several minutes. Accumulation of positive charge at the icesurface makes diffuse into the sublayers.
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 ARTICLES

 Theoretical Methods and Algorithms

A set of standard enthalpies of formation for benchmarking, calibration, and parametrization of electronic structure methods
View Description Hide DescriptionA comprehensive set of 600 experimental standard enthalpies of formation is presented. With its diverse species, many possessing less usual geometries and bonding situations, this compilation is capable of uncovering deficiencies in approaches of quantum chemistry that are not detectable with smaller sets of values. Its usefulness in benchmarking, calibration, and parametrization of new electronic structure methods is illustrated with the development of the bond density functional scheme. This scheme, which is sufficiently inexpensive in terms of computer time and memory to allow predictions even for molecules as large as the fullerene, requires only single point calculations at optimized geometries. It yields values of with the average absolute error of 3.3 kcal/mol, rivaling more expensive methods in accuracy (especially for larger systems). A list of species that are poorly handled by a typical hybrid density functional used in conjunction with a moderatesize basis set is given. This list is intended for rigorous testing of new density functionals.

Simplified calculation of the stability matrix for semiclassical propagation
View Description Hide DescriptionWe present a simple method of calculation of the stability (monodromy) matrix that enters the widely used semiclassical propagator of Herman and Kluk and almost all other semiclassical propagators. The method is based on the unitarity of classical propagation and does not involve any approximations. The number of auxiliary differential equations per trajectory scales linearly rather than quadratically with the system size. Just the first derivatives of the potential surface are needed. The method is illustrated on the collinear system.

An assessment of theoretical methods for the study of transition metal carbonyl complexes: and as case studies
View Description Hide DescriptionA comparative theoretical study of the equilibrium geometries, vibrational frequencies, and reaction energetics of Rh–CO bond activation in the and complexes has been performed using the B3LYP density functional method and the traditional correlated secondorder Møller–Plesset (MP2), quadratic configuration interaction with single and double substitutions (QCISD) and coupledcluster single double (triple) [CCSD(T)] methods. CCSD(T) is employed herein as a benchmark method to examine the validity of the B3LYP and MP2 methods in studies of transition metal complexes. The results show that the geometries and energies obtained with the B3LYP method agree quite well with the QCISD and CCSD(T) results. The conventional MP2 method yields poor results for all geometries, vibrational frequencies, and reaction energies. It is noteworthy that the relative reaction energies calculated at the highest correlated CCSD(T) level using the B3LYP and MP2 geometries are comparable even though the B3LYP and MP2 geometries differ significantly from each other. The absolute energies calculated with the QCISD and CCSD(T) methods at the B3LYP geometries are all lower than those obtained with the MP2 geometries, indicating that the B3LYP method could be more reliable for the study of the geometries and energetics of the catalyticreactions. Basis set effects have been examined by B3LYP calculations. The present results provide a comprehensive assessment of the widely used ab initiotheoretical methods for the study of transition metal carbonyl complexes.

Analytical calculation of nuclear magnetic resonance indirect spin–spin coupling constants at the generalized gradient approximation and hybrid levels of densityfunctional theory
View Description Hide DescriptionA fully analytical implementation of the nuclear magnetic resonance(NMR) indirect nuclear spin–spin coupling constants at the densityfunctional theory(DFT) level is presented. The implementation involves all four contributions of the nonrelativistic Ramsey theory: The dia and paramagnetic spin–orbit contributions as well as the paramagnetic Fermicontact and spin–dipole contributions. Three different exchangecorrelation functionals—LDA (local density approximation), BLYP (Becke–Lee–Yang–Parr), and B3LYP (hybrid BLYP)—are tested by comparison with experiment and highlevel ab initio calculations for a series of molecules containing firstrow elements. All three levels of theory represent a significant improvement on restrictred Hartree–Fock (RHF) theory in the sense that the RHF instability problems are absent in DFT. Also, there is a steady improvement in the quality of the calculated spin–spin couplings in the sequence LDA, BLYP, and B3LYP. For the firstrow molecules investigated by us, the hybrid B3LYP functional performs particularly well, with errors similar to those observed at the best ab initio levels of theory.

Nuclear spin–spin coupling constants from regular approximate relativistic density functional calculations. II. Spin–orbit coupling effects and anisotropies
View Description Hide DescriptionBased on our recently published twocomponent relativistic formulation of the nuclear spin–spin coupling hyperfine terms, we present a full implementation into the Amsterdam Density Functional program. The scalar relativistic code has been extended to include the relativistic analogue of the spin–dipole operator in the coupling calculations, which can now in addition be based on twocomponent spin–orbit coupled Kohn–Sham orbitals. Onebond coupling constants for some plumbanes are in good agreement with experiment, slightly improving the scalar relativistic values. Coupling constants and anisotropies for the and series are compared to experimental data and for ClF additionally to recently published ab initio calculations. The spin–dipole term contributes largely to the coupling constants in XF. Spin–orbit effects are essential for the TlX couplings, where they can yield the most important contributions. In addition, data is reported for the benchmark systems ethane, ethene, and ethyne.

Twocenter nonexchange integrals over Slater orbitals
View Description Hide DescriptionWe have used computer algebra (CA) to construct general formulas for the twocenter overlap, resonance, Coulomb and hybrid integrals over Slater orbitals (STOs). Individual formulas then were produced for the Coulomb integrals containing all combinations of and shell orbitals. The numerical evaluation of these formulas is very rapid and allows unrestricted accuracy. Tests give complete agreement with the output of numerical programs written by other workers. Computer algebra eliminates terms of equal magnitude and opposite sign that can cause catastrophic loss of accuracy in a purely numerical computation. Strong parallelization is possible in the construction and evaluation of the formulas. Their availability opens up the prospect of carrying symbolic computation into the eigenvalue finding stage of quantum chemistry. The present calculations also highlight several needs and opportunities in the field of computer algebra.

Theory for determining alignment parameters of symmetric top molecule using LIF
View Description Hide DescriptionExpressions used for extracting the population and alignment parameters of a symmetric top molecule from laserinduced fluorescence(LIF) are derived by employing the tensor density matrix method. The molecular population and alignment are described by molecular state multipoles. The LIF intensity is a complex function of the initial molecular state multipoles, the dynamic factors, and the excitationdetection geometrical factors. The problem of how to extract the initial molecular state multipoles from as an example, is discussed in detail.

Loworder scaling local correlation methods II: Splitting the Coulomb operator in linear scaling local secondorder Møller–Plesset perturbation theory
View Description Hide DescriptionA novel multipole approximation for the linear scaling local secondorder Møller–Plesset perturbation theory (MP2) method is presented, which is based on a splitting of the Coulomb operator into two terms. The first one contains the singularity and is rapidly decaying with increasing distance. It is treated by a conventional twoelectron transformation, where the rapid decay leads to significant savings. The second term is long range, but nonsingular and can therefore be approximated by a multipole expansion. Reliability, accuracy, and efficiency of this method are demonstrated by an extensive benchmark study. It is shown that the goal to further improve the efficiency of the existing linear scaling local MP2 algorithm has been achieved. Moreover, the new method is a promising starting point for future developments, such as coupling of MP2 with density functional theory.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Theoretical studies of intersystem crossing effects in the reaction
View Description Hide DescriptionWe present a general procedure for studying intersystem crossing effects in bimolecular chemical reactions, along with an application of this to the reaction. In this procedure, we use previously derived singlet and triplet potential energy surfaces that were based on high quality multireference configuration interaction (MRCI) nonrelativistic electronic structure calculations, and the coupling surface is obtained from lower level complete active space selfconsistent field (CASSCF) calculations using the effective nuclear charge oneelectron Breit–Pauli expression for the spinorbit interaction. We find that the resulting spinorbit splittings match the known values for and sufficiently accurately to be useful for dynamics calculations. Also, the electronic basis can be truncated to seven states and without seriously distorting these asymptotic splittings. We show that the seven states may be exactly decoupled into a set of four, which contains the singlet, and a set of three states from the triplets. We find that the spinorbit matrix elements vary smoothly with geometry, so that a relatively simple function can be used to interpolate matrix elements for all geometries. The cross sections for reaction are calculated using a trajectory surfacehopping (TSH) approach in conjunction with a “diabatic” representation based on the nonrelativistic potentials and the CASSCF spinorbit coupling matrix. An application of this approach is presented to the reaction, using the state of Dobbyn and Knowles, and and states of Walch and Kuppermann [slightly modified so that they are asymptotically degenerate in the product region]. The states show a singlet–triplet crossing that is generally on the product side of the barrier on the triplet surfaces. The TSH results indicate that only a few percent of the trajectories undergo intersystem crossing (either from singlet to triplet, or vise versa) at the crossing, so the effect of these transitions on measurable properties of the reaction dynamics is small. However, those trajectories that undergo triplet to singlet transition have much higher product rotational excitation than those that react on the triplet alone. We find that a much larger fraction of trajectories (20%–40%) undergo hopping between the two triplet states, and this leads to an averaging of the dynamical results for the two states.

Metastable vibrationally excited HF in helium nanodroplets
View Description Hide DescriptionHighresolution infrared laserspectroscopy is used to study hydrogen fluoride solvated in helium nanodroplets. The results clearly show that the vibrationally excited HF does not relax on the time scale of the experiments (0.5 ms) and that the large linewidth of the transition results from rotational relaxation. A large dcelectric field is applied to induce a transition, providing an accurate value for the rotational constant of HF in solution only 2% smaller than in the gas phase.

Microsolvation of similarsized aromatic molecules: Photoelectron spectroscopy of bithiophene–, azulene–, and naphthalene–water anion clusters
View Description Hide DescriptionWe perform a comparison of electron affinities (EA) of the conjugated molecules bithiophene, azulene, naphthalene, and their water clusters. Bithiophene and azulene monomers have positive EAs of and but naphthalene has a negative EA. Despite their different EAs and their different molecular orbital energies the three molecules show very similar microsolvation shifts per water unit. This is explained by similar sizes of the π orbitals in which the surplus electron is delocalized leading to a similar electrostatic water to chargeinteraction. This qualitative dependence of solvation energy on anion size agrees well with classical solvation concepts. A comparison of our binding energies with previous calculations for other systems shows that formation of a water subcluster can be assumed. For all three molecules the cluster EAs increase nearly linearly with the number of waters. Using a linear approach and a calibration for the error in the first solvation step we extrapolated the naphthalene cluster series to a monomer in good agreement to previous measurements. To become new insights structures and energies have been calculated for azulene, naphthalene, and their clusters with one water and compared with experimental EAs.

Theoretical study of the photodetachment spectroscopy of the IHBr and IDBr anions
View Description Hide DescriptionThe coupledcluster method with a large basis set with quasirelativistic effective core potentials on the halogens was utilized to investigate the ground electronic state of the IHBr anion. A semiglobal, threedimensional potential energy surface was obtained via spline interpolation of ab initio data. Variational rovibrational calculations were carried out with this potential energy surface, and assignment of fundamentals and lowlying overtones, as well as combination bands, is presented for IH(D)Br anions. Photodetachment spectra for were computed using threedimensional timeindependent real and complex methods and a recently developed real wave packet propagation technique; all methods employed a previous London–Eyring–Polanyi–Sato empirical potential for the neutral system. Well resolved fine structure is found in photodetachment spectra of This structure is assigned to bending excitation based on analysis of the wave functions and the neutral potential energy surface near the Franck–Condon region. This fine structure is largely eliminated in the spectrum. The photodetachment spectrum for the first excited asymmetric stretch of shows a new feature that is associated with sampling of the transition state region of the neutral surface. Spinorbit corrected multireference configuration interaction calculations indicate that the first excited electronic state is only about 0.06 eV above the ground electronic state of the neutral IHBr system in the Franck–Condon region. The model empirical potential used in the calculations of photodetachment spectra is shown to have roughly the average behavior of these two ab initio potentials.

Nonlinear wavepacket interferometry for polyatomic molecules
View Description Hide DescriptionWe investigate the application of a previously considered nonlinear wavepacket interferometry scheme to molecules with a single stable conformation in the electronic ground state. It is shown that interference experiments with pairs of phaselocked ultrashort pulsepairs can be used to determine the complex overlaps of a nonstationary nuclear wavefunction evolving in an excited electronic state with a collection of compact displaced wavepackets moving in specified ways in the groundstate potential.

An intramolecular theory of the massindependent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state
View Description Hide DescriptionA theory is described for the variation in the rate constants for formation of different ozone isotopomers from oxygen atoms and molecules at low pressures. The theory is implemented using a simplified description which treats the transition state as loose. The two principal features of the theory are a phase space partitioning of the transition states of the two exit channels after formation of the energetic molecule and a small (ca. 15%) decrease in the effective density of states, ρ [a “nonRice–Ramsperger–Kassel–Marcus (RRKM) effect”], for the symmetric ozone isotopomers [B. C. Hathorn and R. A. Marcus, J. Chem. Phys. 111, 4087 (1999)]. This decrease is in addition to the usual statistical factor of 2 for symmetric molecules. Experimentally, the scrambled systems show a “massindependent” effect for the enrichments δ (for trace) and E (for heavily) enriched systems, but the ratios of the individual isotopomeric rate constants for unscrambled systems show a strongly massdependent behavior. The contrasting behavior of scrambled and unscrambled systems is described theoretically using a “phase space” partitioning factor. In scrambled systems an energetic asymmetric ozone isotopomer is accessed from both entrance channels and, as shown in paper I, the partitioning factor becomes unity throughout. In unscrambled systems, access to an asymmetric ozone is only from one entrance channel, and differences in zeropoint energies and other properties, such as the centrifugal potential, determine the relative contributions (the partitioning factors) of the two exit channels to the lifetime of the resulting energetic ozone molecule. They are responsible for the large differences in individual recombination rate constants at low pressures. While the decrease in ρ for symmetric systems is attributed to a small nonRRKM effect η, these calculated results are independent of the exact origin of the decrease. The calculated “massindependent” enrichments, δ and E, in scrambled systems are relatively insensitive to the transition state (TS), because of the absence of the partitioning factor in their case (for a fixed nonRRKM η). They are compared with the data at room temperature. Calculated results for the ratios of individual isotopomeric rate constants for the strongly massindependent behavior for unscrambled systems are quite sensitive to the nature of the TS because of the partitioning effect. The current data are available only at room temperature but the loose TS is valid only at low temperatures. Accordingly, the results calculated for the latter at 140 K represent a prediction, for any given η. At present, a comparison of the 140 K results can be made only with room temperature data. They show the same trends as, and are in fortuitous agreement, with the data. Work is in progress on a description appropriate for room temperature.

Semiclassical molecular dynamics simulations of intramolecular proton transfer in photoexcited
View Description Hide DescriptionA fulldimensional excited statepotential energy surface is constructed, and the proton transferdynamics associated with the ketoenolic tautomerization reaction in photoexcited is simulated according to an approximate version of the semiclassical initial value representation method introduced by Miller and coworkers [V. Guallar, V. S. Batista, and W. H. Miller, J. Chem. Phys. 110, 9922 (1999)]. The fulldimensional potential energy surface is developed according to an ab initioreactionsurface model obtained at the CIS level of quantum chemistry. Proton transfer is found to be substantially affected by isotopic substitution, and significantly coupled to the internal oxazole–hydroxyphenyl intheplane bending mode. The nascent tautomer is found to be stabilized primarily through vibrational energy redistribution into all of the remaining intheplane vibrational modes. The accuracy of the methodology is verified by reducing the dimensionality of the system and comparing our semiclassical results with full quantum mechanical calculations.

An ab initio study of the interaction in dimethylamine dimer and trimer
View Description Hide DescriptionClusters consisting of two and three dimethylamine molecules were studied by using the HF, DFT/B3LYP, and MP2 ab initio methods in conjunction with the and augccpvdz/ccpvdz basis sets. Three different minima were located for the dimer, two of which form a hydrogen bond and present similar interaction energies. The most stable structure of the dimer possesses symmetry and an interaction energy of −15.6 kJ/mol. The least stable minimum has an interaction energy of −7.9 kJ/mol and exhibits no hydrogen bonds (the interaction is established via the methyl hydrogen atoms). In all the structures, electron correlation exhibits a significant contribution (more than 40% of the overall energy). Only cyclic structures were considered for the trimer, the most stable of which possesses an interaction energy of −43.9 kJ/mol. The dipole moments for the dimer differ by up to 30% from the vector addition of the molecular dipoles (in the trimer minima, this difference amounts to 40%); also, N–H distances are lengthened by effect of the interaction (by up to 0.004 Å in the dimer and 0.009 Å in the trimer), which suggests the presence of cooperative phenomena. Nonadditive terms contribute about 12% of the overall interaction energy, the contribution being primarily of the inductive type. Calculations predict significant red shifts in the vibrational frequency of the N–H group when it takes part in the formation of a hydrogen bond. Similarly, the N–H wagging frequency undergoes a blue shift with hydrogen bonding.

Discovery of benzene cation in a very longlived excited electronic state
View Description Hide DescriptionPresence of benzene cation in a longlived excited electronic state at ∼2.3 eV above the ground state was found through photodissociation kinetics and charge exchangeionizationmass spectrometry. The lifetime of this state seems to be longer than 10 μs, maybe much longer. The experimental energy level of this state suggests that is the best candidate. The radiative transition from the latter state to the ground state, is electric dipole forbidden. Then, a very long lifetime requires an inefficient radiationless decay of the state. This is in contrast with the very fast decay proposed previously to account for the lack of fluorescence from the state. The present finding opens the possibility of studying a new excited state chemistry.

Theoretical study of
View Description Hide DescriptionIn connection with the recent photoelectron spectroscopy of negatively chargedNa atom in ammonia clusters, the geometries, electronic state, vertical detachment energies, and harmonic frequencies of have been studied by the ab initio MO method. Structures having as many Na–N bonds as possible becomes more stable than other isomers as n grows. The electrons are widely spread and delocalized in space outside the core for The dramatic redshifts of the photoelectron band for the type transition with increasing n reflect the electronic change from an atomic state to onecenter Rydbergtype states in the neutrals. The frequencies of the combined vibrations of the mode are nearly degenerate and are expected to coalesce into only one strong IR band in the NH stretch region irrespective of n.