Volume 119, Issue 9, 01 September 2003
 ARTICLES

 Theoretical Methods and Algorithms

Density fitting in secondorder linear Møller–Plesset perturbation theory
View Description Hide DescriptionDensity fitting is used to approximate all of the 4index 2electron integrals in the explicitly correlated MP2R12 theory of Kutzelnigg and Klopper. The resulting method—DFMP2R12—requires only 2 and 3index integrals over various 2electron operators, and is extremely efficient. The errors arising from the fitting process can be made small by using robust fitting formulas throughout, such that the error in each fitted integral is quadratic in the error of the fitted orbital product densities. Sample calculations on glycine reveal that for large basis sets DFMP2R12 is faster than a standard MP2 calculation and takes only a small fraction of the time for the Hartree–Fock calculation.

Unified analytical treatment of multicenter multielectron integrals of central and noncentral interaction potentials over Slater orbitals using ETOs
View Description Hide DescriptionUsing expansion formulas for the translation of Slatertype orbitals (STOs) obtained with the help of complete orthonormal sets of exponential type orbitals the addition theorems for STOs and interaction potentials are established. These addition theorems enable us to evaluate the multicenter telectron integrals which arise in the solution of Nelectron atomic and molecular problem when a Hylleraas approximation is employed in Hartree–Fock–Roothaan theory. The relationships obtained are valid for the arbitrary location, quantum numbers, and screening constants of STOs.

Distributed dispersion: A new approach
View Description Hide DescriptionDistributed polarizability and dispersion models can be constructed by analyzing the response, at each point in an array surrounding the molecule, to the field due to a point charge at each point of the array in turn, in an extension of the method described by Dehez et al. [Chem. Phys. Lett. 338, 180 (2001)]. Anisotropic distributed polarizabilities and anisotropic distributed dispersion coefficients have been calculated for carbon dioxide, water, benzene and ethane.

Quantum dynamical correlations: Effective potential analytic continuation approach
View Description Hide DescriptionWe propose a new quantum dynamics method called the effective potential analytic continuation (EPAC) to calculate the real time quantum correlation functions at finite temperature. The method is based on the effective action formalism which includes the standard effective potential. The basic notions of the EPAC are presented for a onedimensional double well system in comparison with the centroid molecular dynamics (CMD) and the exact real time quantum correlation function. It is shown that both the EPAC and the CMD well reproduce the exact short time behavior, while at longer time their results deviate from the exact one. The CMD correlation function damps rapidly with time because of ensemble dephasing. The EPAC correlation function, however, can reproduce the long time oscillation inherent in the quantum double well systems. It is also shown that the EPAC correlation function can be improved toward the exact correlation function by means of the higher order derivative expansion of the effective action.

Numerical implementation of some reweighted path integral methods
View Description Hide DescriptionThe reweighted random series techniques provide finitedimensional approximations to the quantum density matrix of a physical system that have fast asymptotic convergence. We study two special reweighted techniques that are based upon the Lévy–Ciesielski and Wiener–Fourier series, respectively. In agreement with the theoretical predictions, we demonstrate by numerical examples that the asymptotic convergence of the two reweighted methods is cubic for smooth enough potentials. For each reweighted technique, we propose some minimalist quadrature techniques for the computation of the path averages. These quadrature techniques are designed to preserve the asymptotic convergence of the original methods.

A new approach to density matrix functional theory
View Description Hide DescriptionStarting from a pairexcitation multiconfiguration selfconsistent field approach considering pairwise excitations of two electrons of opposite spin from a single occupied molecular orbital to a single virtual molecular orbital, we present a natural orbital functional for the electronic energy containing the natural orbitals and the pairexcitation coefficients as variational parameters to be optimized. The occupation numbers of the natural orbitals can be determined from the pairexcitation coefficients in this implicit functional. Test calculations for the water molecule give occupation numbers of the natural orbitals in reasonable agreement with the results of full configuration interaction calculations.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Measurement of the cross section for as a function of angle and energy
View Description Hide DescriptionScattering of the product from the reaction is measured as a function of angle and collision energy from 1.39 to 1.85 eV. The plot of the cross section vs angle and energy is believed to be the first fully experimental plot of its kind reported for this benchmark reaction. Changes in the differential cross section (DCS) are observed in this collision energy range, including a forwardscattering component that peaks at about 1.64 eV and is a strong function of collision energy. This feature has been assigned to result from a barrier resonance, but its full interpretation is presently unsettled. These changes in the DCS do not manifest themselves as variations in the integral cross section (ICS), which varies less than 25% over the energy range measured. Comparisons of the DCSs and the ICS with quantum mechanical calculations show quantitative agreement, although some aspects of the DCS near 1.54 eV are not fully satisfactory.

Observation of a HI leaving group following ultraviolet photolysis of in water and an ab initio investigation of the O–H insertion/HI elimination reactions of the isopolyhalomethane species with and
View Description Hide DescriptionWe report an experimental observation of and being formed following ultraviolet photolysis of in liquid water. The concentration of and are about the same and suggest a reaction that produces a HI leaving group. A preliminary ab initio investigation is reported for the O–H insertion reactions of the isodiiodomethane carbenoid species with and and these are compared to the related reactions for the dichlorocarbene species. The carbenoid reacts with water via an O–H insertion/HI elimination reaction mechanism. These reactions produce a HI leaving group whereas the dichlorocarbene O–H insertion reaction has no need for a leaving group. The differing structures and properties of the and the species can account for the differences in their O–H insertion reactions. The species O–H insertion/HI elimination reactions can be catalyzed by a second water molecule when two water molecules are available and this occurs in a way similar to that previously observed for the reaction of with two water molecules. These results suggest that isopolyhalomethane molecules (like and others) are noticeably reactive towards O–H bonds like those found in water and can likely account for the strong acidformation observed experimentally after ultraviolet photolysis of polyhalomethanes in water. Possible implications for the photochemistry of polyhalomethanes in the atmosphere and oceans are briefly discussed.

Theoretical study of the potential stability of the peroxo nitrate radical
View Description Hide DescriptionThe existence of the peroxo nitrate radical (ONOO) has been discussed for some time and its formation has been used to explain aspects of the scavenging in the Earth’s atmosphere. In this study we report our thorough investigation of the stability of this species by means of highly correlated ab initio calculations. Singlereference coupledcluster singles and doubles (CCSD) as well as multireference configuration interaction (MRCI) calculations were performed to optimize equilibrium structures and obtain harmonic force fields. The force fields were used to calculate the harmonic frequencies as well as isotopic shifts. The CCSD calculations result in shallow minima for both the ground as well as the excited state. However, the calculated isotopic shifts of the ground state show that the experimentally observed shift of 50 cm^{−1} cannot be due to ONOO. In contrast, no minima were found by the MRCI calculations. The analysis of the wave functions indicates that the potential wells obtained by CCSD are artifacts which are due to the singlereference nature of the CCSD method. Our conclusion is that ONOO is not a bound structure and cannot be observed experimentally. Our calculations also show that thermal decomposition of into NO and is not possible under atmospheric conditions and thus this channel cannot be responsible for the unknown scavenging process discussed in the literature.

Dynamics calculations for the reactions using interpolations of accurate ab initio potential energy surfaces
View Description Hide DescriptionComplete active space selfconsistentfield calculations followed by multireference configuration interaction calculations are used to generate potential energy surfaces for the reaction of For interpolation of the potential energy surfaces, a recently proposed interpolant moving least squares(IMLS)/Shepard scheme is used. Trajectory calculations for on the interpolatedpotential energy surface illustrate that the initial vibrational state of LiH plays little role probably due to the absence of the energy barrier for this reaction. The reactive cross section shows a maximum value corresponding to the initial collision energy as low as 0.03 eV. Trajectory calculations for show that high vibrational excitation of molecule is the most efficient way and the collision energy inefficiently induces the reaction.

An ab initio, analytically fitted, global potential energy surface for the ground electronic state of
View Description Hide DescriptionAn analytical, global potential energy surface for the ground electronic potential energy surface (PES) for the ion has been constructed by fitting ab initio energy values calculated at the QCISD(T)/augccpVTZ level of theory for 935 geometric configurations to a many body expansion type functional form appended with ioninduced dipole terms to describe the long range interactions. The PES is adiabatically constrained to the ground electronic state by requiring the two atoms with the shortest separation in any particular geometry to be described by the embedded twobody potential. A transition state for the positional interchange of the middle and end atoms of the linear, centrosymmetric equilibrium geometry is identified and lies about 300 cm^{−1} below the energy of the dissociation products. The nature of the PES near a seam of conical intersections between the ground and first excited electronic states occurring at geometries is discussed.

Isotope dependence of the exchange reaction: Experiment and theory
View Description Hide DescriptionThe isotope dependence of the exchange reaction is investigated by means of kinetic experiments and classical trajectory calculations on an accurate potential energy surface. The measurements confirm the previously reported negative temperature dependence and yield the rate coefficients for both the exothermic and the endothermic reaction between 233 and 353 K: and In addition, the ratio of these two rates, R, has been measured with comparatively higher precision. It is 1.27±0.04 at 300 K and also shows a distinct negative temperature dependence. Four types of classical trajectory calculations are performed in order to interpret the experimental result. They differ by the way in which the quantum mechanical zeropoint energy of the reactants and the differences of zeropoint energies between reactants and products, are phenomenologically incorporated. Only calculations which account for are successful in reproducing the temperature dependence of R. This emphasizes that is an important factor in lowtemperature ozone kinetics. At energies slightly above threshold a dynamical effect is found which additionally favors the exothermic over the endothermic reaction.

Sizedependent dynamics of a quantum solvent: Laser spectroscopy of grown in helium nanodroplets
View Description Hide DescriptionThe progressive solvation of HCN by molecular hydrogen (HD) is studied by highresolution laser spectroscopy. The clusters are grown in helium nanodroplets, an ideal spectroscopic medium which at sufficiently low temperatures permits the study of systems containing HD molecules. A single isomer is observed for each cluster size, independent of the order in which the molecules are added to the helium droplets, indicating that these systems are rather “fluid.” Clusters with an incomplete first solvent shell rotate as a unit, having rotational constants that steadily decrease with increasing size. At the HCN undergoes nearly free internal rotation within the solvent cage of the hydrogens. The fine structure observed in the corresponding transition suggests that the solvent cage is somewhat anisotropic. The further addition of solvent molecules results in a quenching of the HCN internal rotation at suggestive of a significant increase in the anisotropy of the solvent environment.

Charge and bonding redistribution in octatetraene driven by a strong laser field: Timedependent Hartree–Fock simulation
View Description Hide DescriptionThe time evolution of the reduced single electron density matrix for the π electrons in conjugated molecules in an intense laser field is calculated by numerically integrating the timedependent Hartree–Fock equations for the Pariser–Parr–Pople model Hamiltonian. We study the field frequency and intensity dependence of the πelectron response, the chargefluctuations with respect to the ground state, and the molecular polarization in unsubstituted and acceptor–donor substituted octatetraene, where we also examine the interaction between a permanent electric dipole moment and the laser field. Our results demonstrate the origin of large nonperturbative changes in the πelectronic charges and bond orders (diagonal and offdiagonal density matrix elements, respectively) induced by a strong laser field.

Infrared spectra of clusters in solid parahydrogen
View Description Hide DescriptionThe formation of clusters in rapid vapor deposited solid molecular hydrogen containing low concentrations of and has been investigated using highresolution Fourier transform infrared spectroscopy of the C–F stretching mode of the chromophore. Distributions of clusters ranging in size from to are synthesized in crystals by systematically varying the concentration between 100 to 20 000 parts per million. The rotational motion of is quenched in solid this simplifies the spectrum such that a single sharp transition is observed for each cluster. In the fundamental region, the spectrum consists of a series of wellseparated peaks shifted toward lower energy with increasing numbers of nearest neighbor orthohydrogen molecules. The clusters are also investigated in the overtone region and for analogous transitions of the Theoretical calculations based on an electrostatic interaction potential qualitatively reproduce the measured vibrational and isotopomer dependence of the spectra.

The state of NaK: Potential energy curve and hyperfine structure
View Description Hide DescriptionHighresolution spectra, including hyperfine structure, have been observed for numerous vibrationalrotational levels of the Rydberg state of the NaK molecule. The data have been used to construct a Rydberg–Klein–Rees potential curve, and this molecular potential has been further refined using the inverse perturbation approximation method. Boundfree emission from the electronic state to the repulsive state has also been measured and used to determine both the absolute vibrational numbering and the transitiondipole moment function The experimentally derived potential curve and are compared with recent theoretical calculations of Magnier et al.; the agreement is very good. Each of the levels is typically split into three sets of sublevels by the Fermi contact interaction Further splitting (of order has been attributed to the spinrotation interaction γN⋅S. The patterns observed exhibit a clear transition from Hund’s case for small toward Hund’s case for large The data can be fitted very well using a theoretical model based on setting up and diagonalizing a 12×12 Hamiltonian matrix with two adjustable parameters and γ). The values of that fit the data best are with a weak dependence on The best fit values of γ are in the range and depend strongly on The values of γ appear to exhibit anomalous structure for levels perturbed by nearby levels of the state.

Control of bimolecular reactions: Bondselected reaction of vibrationally excited with
View Description Hide DescriptionSelective vibrational excitation permits control of the outcome of a reaction with two competing channels. The thermal reaction of with yields two reaction products: from the Datom abstraction and from the Hatom abstraction. We prepare the first overtone of the C–D stretching vibration at ∼4300 cm^{−1} and react the vibrationally excited molecule with photolytic Cl atoms. The 2+1 resonance enhanced multiphoton ionization spectra for the products show that the vibrational excitation of exclusively increases the probability of breaking the C–D bond, yielding but no By contrast, vibrational excitation of the combination of the antisymmetric C–H stretch and umbrella vibrations, which has total energy similar to that of preferentially promotes the Hatom abstraction reaction to produce over The vibrational action spectra for the two products permit the separation of the two sets of interleaved transitions to give band origins and rotational constants of the state and the state of

Benzene–argon triplet intermolecular potential energy surface
View Description Hide DescriptionThe benzene–Ar lowest energy triplet state intermolecular potential energy surface is evaluated using coupled cluster methods and the augccpVDZ basis set extended with a set of midbond functions. This surface is characterized by an absolute minimum of −392.5 cm^{−1}, where the argon atom is located on the benzene axis at a distance of 3.5153 Å, and has a general shape very close to the ground state and the first singlet excited statesurfaces. Using the potential, the intermolecular vibrational energy levels were evaluated and the results compared to those for the ground and the excited states. The calculated fundamental frequencies for the bending and the stretching modes are lower than those in the state. The calculated data for the state is expected to have the same accuracy as previously calculated data for the state.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Rotational dynamics of nondipolar probes in ethanols: How does the strength of the solute–solvent hydrogen bond impede molecular rotation?
View Description Hide DescriptionRotational dynamics of two structurally similar nondipolar probes; 2,5dimethyl1,4dioxo3,6diphenylpyrrolo[3,4c]pyrrole (DMDPP) and 1,4dioxo3,6diphenylpyrrolo[3,4c]pyrrole (DPP) has been investigated in ethanol (EtOH) and 2,2,2trifluoroethanol (TFE) in the temperature range 243–298 K in an attempt to understand how the strength of the solute–solvent hydrogen bond impedes molecular rotation. It has been observed that the reorientation times of DPP are slower compared to DMDPP by about a factor of 2 in EtOH and this factor is only 1.3–1.4 in TFE. Another interesting observation is that the viscosity normalized reorientation times of DPP at a given temperature are almost identical in EtOH and TFE, whereas those of DMDPP are slower by a factor of 1.5 in TFE compared to EtOH. These observations have been rationalized on the basis of hydrogen bond donating and hydrogen bond accepting abilities of the respective solute and the solvent. Further evidence for such a rationale has been provided with the aid of ab initio molecular orbital methods.

Calorimetric study of plastically crystalline o and mcarboranes
View Description Hide DescriptionThe heat capacities of o and mcarboranes were measured with an adiabatic calorimeter in the temperature range 5–310 K. mcarborane underwent two phase transitions at 170 K and 284 K with transitionentropies of 12.70 and 15.52 J K^{−1} mol^{−1}. The total transitionentropy agreed well with the theoretical value, indicating that mcarborane is ordered at 0 K. ocarborane also exhibited two phase transitions at 160 K and 275 K with transitionentropies of 3.72 and 13.72 J K^{−1} mol^{−1}, and additionally a glass transition at 120 K. This glass transition does occur not in the supercooled intermediatetemperature phase but in the lowtemperature phase of ocarborane. The high and intermediatetemperature phases of ocarborane could not be quenched at the maximum cooling rate (10 K min^{−1}) of this experiment. The total transitionentropy of ocarborane was smaller than that of mcarborane by 10.8 J K^{−1} mol^{−1}, suggesting that ocarborane has residual orientational disorder at 0 K. The enthalpyrelaxation was examined by the temperature jump method around the glass transition of ocarborane. The results were reproduced well by the KWW function. The calorimetric relaxation time and nonexponential parameter agreed with dielectric ones at the glass transition temperature. This indicates that the glass transition of ocarborane is due to the freezing of molecular reorientation.