Volume 115, Issue 8, 22 August 2001
 ARTICLES

 Theoretical Methods and Algorithms

The convergence of spin–orbit configuration interaction calculations for TlH and (113)H
View Description Hide DescriptionTo test the convergence of spin–orbit effects for molecules, the ground states of TlH and (113)H are calculated by configuration interaction(CI) calculations using relativistic effective core potentials with oneelectron spin–orbit operators. The employed CI methods are the Kramers’ restricted CI (KRCI) and the spin–orbit CI (SOCI) methods. The KRCI method includes the spin–orbit interactions in the generation of oneelectron basis space through the use of the twocomponent molecular spinors obtained by the Kramers’ restricted Hartree–Fock (KRHF) method, whereas the SOCI adds the spin–orbit term only at the CI level. For systems with heavy atoms, orbital relaxations due to the spin–orbit interaction could become sizable, resulting in slow convergences for the SOCI method. Spin–orbit effects on bond lengths and energies using single and multireference CI calculations at the SOCI level of theory are evaluated and compared with KRCI results for TlH and (113)H. The spin–orbit effects on energies converge easily for TlH but slowly for (113)H. Especially, bond lengths do not converge for the seventhrow (113)H in our calculations. The present results imply that largescale multireference SOCI calculations are necessary for some molecules to recover orbital relaxation effects due to large spin–orbit interactions in the SOCI scheme. In those cases, the KRCI scheme based upon twocomponent spinors will have advantages over SOCI and other onecomponent orbital based methods.

Electronic properties of hard and soft ions in solution: Aqueous and compared
View Description Hide DescriptionThe electronic structure of model aqueous solutions of and is investigated using ab initio moleculardynamics methods. We compute a number of electronic response coefficients in solution, such as global hardness and nuclear Fukui functions. The nuclear Fukui functions are found to be particularly sensitive to the chemical nature of the component species giving for a susceptibility 3.5 times the value for a molecule while the result for is more than a factor of 4 smaller compared to a solvent molecule. The electronic structure of the solution is further characterized by construction of effective molecular orbitals and energies. This analysis reveals that the effective highest occupied molecular orbital (HOMO) of the hard cation, remains buried in the valence bands of the solvent, whereas the HOMO of is found to mix with the lone pair electrons of its four ligand molecules to form the (global) HOMO of the solution. This observation, highlighting the importance of the electronic structure of the solvent, is used to rationalize the results for the electronic response.

The influence of the detachment of electrons on the properties and the nature of interactions in complexes
View Description Hide DescriptionThe theoretical study of anionic and neutral halogen–water complexes is presented. The detachment of an electron from an anion leads to drastic changes in the structure and thermodynamic properties. Two possible neutral isomers separated by transition state were located. It is suggested that different neutral species are observed in photoelectron and mass spectrometry experiments.

On the correlation energy features in planar heteroatomic molecular systems
View Description Hide DescriptionThe correlation energy in planar heteroatomic open chain polyene systems involving N, O, and F atoms is considered by the CASSCF and CASPT2 methods employing a number of the (VDZ, VTZ, etc.) correlation consistent basis sets. A thorough study of the smallest molecules shows that the nondynamical correlation energy is virtually independent of the quality of the basis set. In contrast, the dynamical correlation energy is very sensitive to the basis set and, in estimating reliable dynamical correlation effects for larger systems, one has to rely on adequate extrapolation formulas to obtain the infinite basis set limit. We find that a method recently proposed by Truhlar offers economical yet reasonable estimates of the complete basis set results. Investigation of the sensitivity of the results to the choice of active space and the comparison to single reference MP2 calculations indicate that such extrapolations offer a good general method for saturating the basis set in multireference calculations. Thus a simple refinement of the conventional multireference coupled cluster method is proposed. It is also shown that both nondynamical and dynamical correlation energies follow very simple additivity rules in linear and branched planar chain heteroatomic polyenes, making possible their prediction in very large systems without calculation.

Extended benchmark studies of coupled cluster theory through triple excitations
View Description Hide DescriptionCoupled clustertheory through quasiperturbative triple excitations [CCSD(T)] was used with large correlation consistent basis sets to obtain optimized structures, harmonic vibrational frequencies and atomization energies for 37 molecules from the G2/97 test set. In some cases, it proved possible to include the triple excitations iteratively via CCSDT. Use of various correlation consistent basis set sequences facilitated estimation of frozen core energies in the complete basis set limit. Tight d functions were added for all second row atoms in order to improve the basis set convergence properties. Core/valence correlation corrections were obtained from all electron calculations. Scalar relativistic contributions to the atomization energy were obtained from configuration interaction massvelocity/oneelectron Darwin calculations and CCSD(T) Douglas–Kroll–Hess calculations. By combining results from the present work with previously reported findings, a total of 114 comparisons with reliable experimental data for molecular atomization energies were possible. A statistical analysis of the level of agreement with experiment was performed, leading to a mean absolute deviation of 0.8 kcal/mol and maximum absolute error of −4.4 kcal/mol. This represents the most thorough study to date of the reliability of a composite approach to computational thermochemistry based on coupled clustertheory. The approach avoids the use of additivity approximations to estimate the complete basis set limit and does not include empirical corrections to the electronic energy. Results from three parameterized methods (G2, G3, and CBSQ) for the same set of molecules are compared to the coupled cluster results.

Electronic energy density in chemical reaction systems
View Description Hide DescriptionThe energy of chemical reaction is visualized in real space using the electronic energy density associated with the electron density The electronic energy density is decomposed into the kinetic energy density the external potential energy density and the interelectron potential energy density Using the electronic energy density we can pick up any point in a chemical reaction system and find how the electronic energy E is assigned to the selected point. We can then integrate the electronic energy density in any region R surrounding the point and find out the regional electronic energy to the global E. The kinetic energy density is used to identify the intrinsic shape of the reactants, the electronic transition state, and the reaction products along the course of the chemical reaction coordinate. The intrinsic shape is identified with the electronic interfaceS that discriminates the region of the electronic drop from the region of the electronic atmosphere in the density distribution of the electron gas. If the R spans the whole space, then the integral gives the total E. The regional electronic energy in thermodynamic ensemble is realized in electrochemistry as the intrinsic Volta electric potential and the intrinsic Herring–Nichols work function We have picked up first a hydrogenlike atom for which we have analytical exact expressions of the relativistic kinetic energy density and its nonrelativistic version These expressions are valid for any excited bound states as well as the ground state. Second, we have selected the following five reaction systems and show the figures of the as well as the other energy densities along the intrinsic reaction coordinates: a protonation reaction to He, addition reactions of HF to and hydrogen abstraction reactions of from HF and Valence electrons possess their unique delocalized drop region remote from those heavily localized drop regions adhered to core electrons. The kinetic energy density and the tension density can vividly demonstrate the formation of the chemical bond. Various basic chemical concepts in these chemical reaction systems have been clearly visualized in real threedimensional space.

Exchange energy density of an atom as a functional of the electron density
View Description Hide DescriptionAn electrondensity functional for the conventionally defined exchange energy density of an atom is constructed using Becke’s inhomogeneity parameter based on the density matrix expansion of the exchange hole. The proposed functional (the energy density metageneralized gradient approximation or EDMGGA) has the following properties: (i) The exchange energy density has correct nuclear cusp and densitytail behaviors. (ii) The corresponding exchange potential is finite near the nucleus and decays asymptotically as in the tail. Numerical results show that our functional yields total exchange energies for atoms with about the same accuracy as Becke’s widely used functional B88, but significantly improves the local description of the exchange energy density. In one Appendix, by introducing a general coordinate transformation, we show that the asymptotic behavior of the conventionally defined exchange energy density depends upon the choice of the coordinate transformation and the established tail behavior, for a finite system is only a special case in the general coordinate transformation. In another Appendix, we discuss alternative definitions of the exchange energy density.

A dual length scale method for planewavebased, simulation studies of chemical systems modeled using mixed ab initio/empirical force field descriptions
View Description Hide DescriptionMixed ab initio/empirical forcefield simulation studies, calculations in which one part of the system is treated using a fully ab initio description and another part is treated using an empirical description, are becoming increasingly popular. Here, the ability of the commonly used, plane wavebased generalized gradient approximation to density functional theory is extended to model systems in which the electrons are assumed to be localized in a single small region of space, that is, itself, embedded within a large chemically inert bath. This is accomplished by introducing two length scales, so that the rapidly varying, short range, electron–electron and electron–atom interactions, arising from the region where the electrons are localized, can be treated using an appropriately large plane wave basis, while the corresponding, slowly varying, long range interactions of the electrons with the full system or bath, can be treated using a small basis. Briefly, a novel Cardinal Bspline based formalism is employed to derive a smooth, differentiable, and rapidly convergent (with respect to the small basis) expression for the total electronic energy, which explicitly contains the two length scales. The method allows reciprocal space based techniques designed to treat clusters, wires, surfaces and solids/liquids (open, and 1D and 2D periodic boundary conditions, respectively) to be utilized. Other plane wavebased “mixed” methods are restricted to clusters. The new methodology, which scales as at fixed size of the chemically active region, has been implemented for parallel computing platforms and tested through applications to both model and realistic problems including an enzyme, human carbonic anhydrase II solvated in an explicit bath of water molecules.

A longrange correction scheme for generalizedgradientapproximation exchange functionals
View Description Hide DescriptionWe propose a new longrange correction scheme that combines generalizedgradientapproximation (GGA) exchange functionals in densityfunctional theory(DFT) with the ab initio Hartree–Fock exchange integral by using the standard error function. To develop this scheme, we suggest a new technique that constructs an approximate firstorder density matrix that corresponds to a GGA exchange functional. The calculated results of the longrange correction scheme are found to support a previous argument that the lack of the longrange interactions in conventional exchange functionals may be responsible for the underestimation of interconfigurational energies of the firstrow transition metals and for the overestimation of the longitudinal polarizabilities of πconjugated polyenes in DFT calculations.

CC3 triplet excitation energies using an explicit spin coupled excitation space
View Description Hide DescriptionTriplet excitation energies are derived in the approximate triples model CC3 using an explicit spin coupled triplet excitation space. The explicit spin coupled excitation space gives considerable computational savings compared to the spin–orbital approach. Sample calculations are performed on the and systems and the performance of the CC3 results are evaluated from a comparison with full configuration interaction (FCI) results.

Basis set superposition error free selfconsistent field method for molecular interaction in multicomponent systems: Projection operator formalism
View Description Hide DescriptionThe selfconsistent field method for molecular interaction (SCF MI) by Gianinetti, Raimondi, and Tornaghi is extended to multicomponent systems. A set of equations are written with projection operators, and the accurate approximate equations are derived. The method is applied to water clusters and to a fluoride anion complex with a water dimer. The calculated interactionenergies are compared with those estimated with the counterpoise method, and they converge to smaller values for extensive basis sets. The underestimation of the binding energy results from the omission of the most part of charge transfer contribution in the wave function.

Relativistic Gaussian basis sets for molecular calculations: H–Xe
View Description Hide DescriptionRelativistic Gaussian basis sets suitable for molecular calculations are presented for the 54 atoms H through Xe. The basis sizes are rather compact and the same as the corresponding nonrelativistic basis sets reported by Koga et al. The exponent parameters of the Gaussian basis functions have been fully optimized separately for the and symmetry species. The maximum truncation error in the total energies is 2.9 mhartree, and the virial deviation from −1 is less than Test calculations are carried out on the molecule.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Resonant and nonresonant electron impact detachment of and
View Description Hide DescriptionAbsolute cross sections for electronimpact detachment and electronimpact dissociation of and were measured for electron energies from threshold to 40 eV. With both ions we see only little dissociation when electron detachment occurs. In the case of a resonance in the detachment cross section is discovered at an energy of ∼10 eV. No resonances were seen in the case of We argue that the resonance observed for is due to an excited state of the dianion. The nonresonant part of the detachment cross section is found to follow the classical prediction given by Andersen et al. [Phys. Rev. Lett. 74, 892 (1995)].

Isotopic probing of weak intermolecular forces: Infrared spectrum and energy levels of the dimer
View Description Hide DescriptionThe infrared spectrum of the fully substituted 13C carbon monoxide dimer, has been studied in the region of the C–O stretching vibration, around 2096 cm^{−1}. Over 120 transitions have been assigned to transitions involving 49 rotational levels in the excited state and 23 levels in the ground state. Relative energies for all these levels have been accurately (≈0.0003 cm^{−1}) determined without model dependence, except for the interval between the lowest levels of A and B symmetry. The observed stacks of levels were similar to those determined previously for the normal isotope, and could therefore be identified with the same labeling scheme, but the differences between them constitute a subtle probe of the intermolecular forces in this system. In both isotopes, the stacks fall into two groups, characterized by larger (4.4 Å) or smaller (4.0 Å) intermolecular separations. The energy splitting between the ground states of these two isomers is 0.877 cm^{−1} in and 1.285 cm^{−1} in The observed isotope shifts may be explained in terms of a simple anharmonic interaction model.

Characterization of clusters using zero electron kinetic energy and partially discriminated threshold photodetachment spectroscopy
View Description Hide Descriptionclusters have been investigated by anion zero electron kinetic energy (ZEKE) and partially discriminated threshold photodetachmentspectroscopy. The experiments yield sizedependent electron affinities (EAs) and electronic state splittings for the X, I, and II states accessed by photodetachment. Cluster minimum energy structures have been determined from calculations based on a “simulated annealing” approach employing our recently presented pair potentials from anion ZEKE spectroscopy [T. Lenzer, I. Yourshaw, M. R. Furlanetto, G. Reiser, and D. M. Neumark, J. Chem. Phys. 110, 9578 (1999)] and various nonadditive terms. The EAs calculated without manybody effects overestimate the experimental EAs by up to 1500 cm^{−1}. Repulsive manybody induction in the anion clusters is found to be the dominant nonadditive effect. In addition, the attractive interaction between the chloride charge and the exchange quadrupole is important. These findings are consistent with our earlier results for and clusters and highlight again the necessity of an adequate implementation of manybody effects to describe the energetics of such systems. For clusters with we find some deviations between experimental and calculated (0 K) EA which can be explained by the population of less stable anion structures due to the finite temperatures of the clusters in our experiments. This results in lower EAs than predicted for the corresponding global minimum energy structures.

Coherent control of quantum chaotic diffusion: Diatomic molecules in a pulsed microwave field
View Description Hide DescriptionExtensive phase control of quantum chaotic diffusion is demonstrated for diatomic molecules periodically kicked with microwave pulses. In particular, both complete suppression of chaotic diffusion as well as its enhancement can be achieved by varying the phase of the initial superposition state. The origin of this control in deviations from random matrix theory is also discussed. The results should motivate experiments that are relevant to both coherent control and to quantum chaos.

Concentration measurements in molecular gas mixtures with a twopump pulse femtosecond polarization spectroscopy technique
View Description Hide DescriptionRecently, we have demonstrated the ability of the Ramaninduced polarizationspectroscopy (RIPS) technique to accurately determine concentration or polarizabilityanisotropy ratio in lowpressure binary molecular mixtures [E. Hertz, B. Lavorel, O. Faucher, and R. Chaux, J. Chem. Phys. 113, 6629 (2000)]. It has been also pointed out that macroscopic interference, occurring when two revivals associated to different molecules time overlap, can be used to achieve measurements with picosecond time resolution. The applicability of the technique is intrinsically limited to a concentration range where the signals of both molecules are of the same magnitude. In this paper, a twopump pulse sequence with different intensities is used to overcome this limitation. The relative molecular responses are weighted by the relative laser pump intensities to give comparable signals. Furthermore, by tuning the time delay between the twopump pulses, macroscopic interference can be produced regardless of the accidental coincidences between the two molecular temporal responses. The study is performed in a gas mixture and the concentration is measured with and without macroscopic interference. Applications of the method in the field of noninvasive diagnostics of combustion media are envisaged.

Ab initio prediction of the vibrationrotationtunneling spectrum of
View Description Hide DescriptionQuantum calculations of the vibrationrotationtunneling (VRT) levels of the trimer are presented. Two internal degrees of freedom are considered—the rotation angles of the two nonhydrogenbonded (flipping) hydrogens in the complex—together with the overall rotation of the trimer in space. The kinetic energy expression of van der Avoird et al. [J. Chem. Phys. 105, 8034 (1996)] is used in a slightly modified form. The experimental microwave geometry of Kisiel et al. [J. Chem. Phys. 112, 5767 (2000)] served as input in the generation of a planar reference structure. The twodimensional potential energy surface is generated ab initio by the iterative coupledcluster method based on singly and doubly excited states with triply excited states included noniteratively [CCSD(T)]. Frequencies of vibrations and tunnel splittings are predicted for two isotopomers. The effect of the nonadditive threebody forces is considered and found to be important.

Femtosecond dissociation of ozone studied by the Auger Doppler effect
View Description Hide DescriptionA Dopplertype shift in the kinetic energy of atomic Auger electrons emitted after fast dissociation of molecules is observed. The resonant Auger spectrum from the decay of repulsive coreexcited states reflects both the early molecular ozone decay and that from excited dissociation fragments. The kinetic energy of the fragment is manifested as an energy shift of the atomic Auger lines when the measurement is made under certain conditions. We report measurements of the energysplit atomic fragment emission lines arising from dissociation on a time scale comparable to the corehole lifetime. For the O states the kinetic energy release amounts to several electron volts. We report measurements for excitation of both the terminal and central oxygen electrons. A simple kinematic model for extracting a lower limit for the kineticenergy release is presented and is compared with the result of a Born–Haber cycle, which may be seen as an estimate of the maximum energy release.

Theoretical studies of the reaction. II. Classical trajectory calculations on an ab initio potential for temperatures between 300 and 5000 K
View Description Hide DescriptionA comparably simple new analytical expression of the potential energy surface for the reaction system is designed on the basis of previous high precision ab initio calculations along the minimum energy path of the and dissociations. Thermal rate constants for the reaction are determined by extensive classical trajectory calculations. The results depend on the policy to solve the zeropoint energy problem. We show that, with the chosen policy, there are nearly equal amounts of statistical and nonstatistical backdissociations following however, backdissociations become important only at temperatures above about 500 K. Below 500 K, the reaction is completely capturecontrolled. Below 300 K, classical trajectory treatments become inadequate, because quantum effects then are so important that only the quantum statistical adiabatic channel model gives reliable results. For the reaction and the range 300–5000 K, a rate constant of is obtained from the trajectory calculations. Converting experimental results for the reaction to the reverse reaction on the basis of the revised enthalpy of formation of OH, agreement between experiment and theory within better than 20% is obtained between 300 and 5000 K.