Volume 118, Issue 16, 22 April 2003
 COMMUNICATIONS


Nonclassical effects in liquidphase nuclear magnetic resonance spectra of 9methyltriptycene derivatives
View Description Hide DescriptionThe dynamics of strongly hindered methyl groups in 9methyltriptycene derivatives, monitored by liquidphasenuclear magnetic resonance spectra, were investigated using an iterative, leastsquares method of line shapeanalysis. For two of the compounds, apart from nonclassical effects in the stochastic dynamics, anomalously strong dependence on temperature (ca. 0.05 and 0.08 Hz/K) of the J coupling between the methyl protons was observed. The latter effect was attributed to the occurrence of coherent quantum tunneling of the methyl rotor. For methyl group, this would be the first observation of coherent tunneling above cryogenic temperatures.

Determination of the triplet state lifetime of vibrationally excited
View Description Hide DescriptionThe lifetime of the ground triplet state of vibrationally excited has been determined in a twocolor pump–probe experiment. An intense pump pulse (337 nm, 4 ns) was used to excite the neutral molecules. The triplet state was probed via single photonionization with a weak probe pulse (193 nm). The lifetime was found to be on the order of 1 μs. This is rather low to explain recent delayed ionization results but higher than expected from an extrapolation of earlier measurements at lower temperatures.
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 ARTICLES

 Theoretical Methods and Algorithms

Nuclear spinspin coupling density in molecules
View Description Hide DescriptionIt is shown that nuclear spinspin coupling in a molecule can be rationalized in terms of property density functions which depend on the position in threedimensional space. The spinspin coupling density surface, calculated as a table of values for a grid of coordinates on a plane through the molecular domain, yields a direct physical picture and offers a physical interpretation of the phenomenology, by showing the path whereby coupling takes place. The different role and the relative importance of the Fermi contact, spindipolar, and diamagnetic and paramagnetic spinorbit mechanisms is readily assessed. The display of the spinspin density reveals that the major contribution comes from the electrons close to the coupled nuclei. The economy of thinking achieved by the use of functions of three coordinates in real space, instead of nelectron wave functions depending on coordinates in Hilbert space, is evident in the present case. The utility of spinspin coupling densities has been discussed for the molecules of hydrogen fluoride, water, ammonia, and methane.

Time averaging the semiclassical initial value representation for the calculation of vibrational energy levels
View Description Hide DescriptionAn application of the initial value representation (IVR) of semiclassical (SC) theory to approximate the quantum mechanical time evolution operator, requires an integral over the phase space of initial conditions of classical trajectories. The integrand of this integral is complex, i.e., has a phase, from which quantum coherence (in fact, all quantum) effects arise, but which also makes SCIVR calculations more difficult than ordinary classical molecular dynamics simulations (the semiclassical version of the “sign problem”). A number of approaches have been devised to ameliorate the sign problem, and here we show how a time averaging procedure—the integrand of the phase space integral is timeaveraged over the classical trajectory originating from each initial condition—can be profitably used in this regard, particularly so for the calculation of spectral densities (from which vibrational energy levels can be identified). This time averaging procedure is shown to greatly reduce the number of initial conditions (i.e., the number of classical trajectories) that are needed to converge IVR phase space averages. In some cases useful results can be obtained with only one classical trajectory. Calculations are carried out for vibrational energy levels of and to illustrate the overall procedure.

Exchangecorrelation energy and potential as approximate functionals of occupied and virtual Kohn–Sham orbitals: Application to dissociating
View Description Hide DescriptionThe standard local density approximation and generalized gradient approximations fail to properly describe the dissociation of an electron pair bond, yielding large errors (on the order of 50 kcal/mol) at long bond distances. To remedy this failure, a selfconsistent Kohn–Sham (KS) method is proposed with the exchangecorrelation (xc) energy and potential depending on both occupied and virtual KS orbitals. The xc energy functional of Buijse and Baerends [Mol. Phys. 100, 401 (2002); Phys. Rev. Lett. 87, 133004 (2001)] is employed, which, based on an ansatz for the xchole amplitude, is able to reproduce the important dynamical and nondynamical effects of Coulomb correlation through the efficient use of virtual orbitals. Selfconsistent calculations require the corresponding xc potential to be obtained, to which end the optimized effective potential (OEP) method is used within the common energy denominator approximation for the static orbitalGreen’s function. The problem of the asymptotic divergence of the xc potential of the OEP when a finite number of virtual orbitals is used is addressed. The selfconsistent calculations reproduce very well the entire potential curve, describing correctly the gradual buildup of strong left–right correlation in stretched

Computing accurate forces in quantum Monte Carlo using Pulay’s corrections and energy minimization
View Description Hide DescriptionIn order to overcome the difficulty of optimizing molecular geometry using quantum Monte Carlo methods, we introduce various approximations to the exact force expectation value. We follow Pulay’s suggestion [Mol. Phys. 17, 153 (1969)] to correct the Hellmann–Feynman estimator by introducing the contributions due to the changes in the wave function with respect to the nuclear positions. When used in conjunction with energyoptimized explicitly correlated trial wave functions for and LiH, these approximations appear to yield accurate forces using both the variational and diffusionMonte Carlo methods. Also, the accuracy of the secondorder estimate of the Hellmann–Feynman force estimator was investigated employing our energyoptimized trial wave functions, and an erratic behavior was uncovered for some of the studied bond lengths. The additional computational cost required to compute the corrections to the Hellmann–Feynman estimator was found to be only a small fraction of the cost for a simple mean energy calculation. The same approach could be exploited also in computing the derivative of other energydependent quantummechanical observables.

Eckart frames for planar molecules
View Description Hide DescriptionExplicit analytic expressions of Eckart frames for planar molecules in Radau, Jacobi and bond coordinates have been presented. The orientation of the frame axis system with respect to the molecular plane at equilibrium is specified by an angle

An Eckartframe kinetic energy operator for tetraatomic planar molecules
View Description Hide DescriptionA closedform kinetic energy operator (KEO) for tetraatomic planar molecules in Eckart frame has been expressed explicitly in terms of the internal coordinates with a parameter which labels a specific Eckart frame. This KEO has zero Coriolis coupling at equilibrium and an expression for the best has been given that makes zero centrifugal coupling. A method treating the singularities of this KEO has been shown and all matrix elements are finite in the basis presented in this paper.

Fundamental vibrational frequencies of small polyatomic molecules from densityfunctional calculations and vibrational perturbation theory
View Description Hide DescriptionAn extensive study of fundamental frequencies and anharmonic vibrational constants for polyatomic molecules obtained from Becke three parameter Lee–Yang–Parr (B3LYP) and Becke–Perdew (BP86) density functional calculations is presented. These calculations are based on standard perturbation theory, and are compared to correlationcorrected vibrational selfconsistent field (CCVSCF) calculations for the water dimer. The anharmonic corrections obtained from densityfunctional calculations compare well with experimental values and with results from correlated ab initio methods. While fundamental frequencies from B3LYP calculations are reliable, they are considerably too small for BP86 calculations. Consequently, the good agreement of unscaled harmonic frequencies from BP86 calculations with experimental frequencies is due to an error cancellation effect. This is of importance for the prediction of vibrational spectra for large molecules, because the perturbation theory approach naturally becomes unreliable for very large molecules due to the increasing number of anharmonic resonance effects. These resonances seriously limit the applicability of perturbation theoretical approaches to anharmonic vibrational constants, whereas the computational effort for the calculation of cubic and quartic force constants, is feasible because calculations can be performed very efficiently by a parallelized calculation of harmonic force constants for several structures, which are distorted along the normal coordinates, followed by numerical differentiation.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

High level ab initio studies of the excited states of sulfuric acid and sulfur trioxide
View Description Hide DescriptionWe have calculated the vertical excitation energies and oscillator strengths of the lowest energy electronic transitions in sulfuric acid and sulfur trioxide with a range of ab initio methods. We have found that the highest level calculations with the complete active space selfconsistent field and multireference configuration interaction (MRCI) methods predict transition energies much lower than those previously calculated with the simpler configuration interactionsingles method. The MRCI calculated electronic transitions for are in good agreement with the experimental results, whereas electronic transitions in vapor phase have yet to be observed. Our MRCI results suggest that the lowest lying electronic excitation in occurs around 144 nm and that the cross section in the actinic region is very small.

Spectroscopic observation of the preferentially stabilized, linear complex
View Description Hide DescriptionSpectroscopic features attributed to rovibronic transitions from both the Tshaped and linear and groundstate complexes have been recorded in the ICl 2–0 and 3–0 spectral regions using laserinduced fluorescencespectroscopy. Experiments performed using varying expansion conditions indicate that the complex with a linear equilibrium orientation lies lower in energy than the separately localized Tshaped isomer even though the transition energies of the Tshaped and linear complexes are shifted by ∼3.5 and ∼14 cm^{−1} to higher energy than the band origins, respectively. Based on comparison with the excited state theoretical predictions of Waterland et al. [J. Chem. Phys. 92, 4261 (1990)], estimates of the binding energies for the ground state Tshaped and linear complexes are 17 and 21 cm^{−1}, respectively, in qualitative agreement with the recently published predictions of 15.2 and 18.3 cm^{−1} obtained using high level ab initio theory for the ground statepotential energy surface [J. Chem. Phys. 117, 7017 (2002)].

Change of geometry by vibrational excitation: The spectrum and structure of
View Description Hide DescriptionWe have observed the levels of in the region 11 150 to 11 210 cm^{−1} using intracavity Tisapphire laser induced fluorescence. The complex shown to be quasilinear at and 1 becomes a semirigid bent species at with the submolecule oriented at an angle near 40° with respect to the connector of the and HF centers of mass. Transitions to the and 2 levels of the from the (0 000 000) ground state and to of (3 000 000) from the (0 000 001) level are observed, showing a 198.36(5) cm^{−1} HF vibrational redshift. The rotational constants of the (3 000 000) state are 0.0717(10) and 0.0696(10) cm^{−1} for the 1, and 2 levels, respectively, and the centrifugal distortion which is large but in agreement with mechanical expectation. The observed transition intensities are a consequence of an appreciable rotation of the inertial axes in the transition. The spectral lines are Lorentzian with full width at halfmaximum equal 9.0(9), 7.2(6), and 4.5(6) GHz for the 1, and 2 levels of the (3 000 000) state. In addition, the soft mode bending combination transitions to the and 2 level of (3 000 001) are also observed and fit with and 0.0714(10) cm^{−1}, and 6.0(9) GHz, respectively, and The bending frequency, is 24.75(10) cm^{−1}. The HF bending level (3 000 010) has been observed at 11 538.92(10) cm^{−1} by the perpendicular transition from the ground state, indicating a HF bending frequency of 362.47(15) cm^{−1}. The spectroscopic constants of (3 000 010) are and

Theoretical characterization of the disilaethynyl anion
View Description Hide DescriptionThe singletstate potential energy surface of the disilaethynyl anion has been investigated using ab initio selfconsistentfield (SCF), configuration interaction with single and double excitations (CISD), coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triple excitations [CCSD(T)] levels of theory with large basis sets. Four stationary points [cyclic (monobridged) linear bent and quasilinear structures] were located with the correlated wave functions, while only two stationary points [cyclic (monobridged) and linear structures] were found with the SCF method. The cyclic structure is predicted to be the global minimum at all levels of theory. The linear structure is found to be a transition state between the two quasilinear structures at the correlated levels of theory, while the SCF linear structure is predicted to be a transition state between the two cyclic structures. The quasilinear structure possesses a Si–Si–H bond angle similar to that of the monobridged molecule. The bent geometry is assigned to a transition state for the isomerization reaction between the cyclic and quasilinear structures. With the most reliable level of theory, augmented correlationconsistent polarized valence quadrupleζ CCSD(T), the quasilinear structure is predicted to be 8.6 kcal/mol [7.9 kcal/mol with the zeropoint vibrational energy (ZPVE) correction] above the cyclic (monobridged) structure, and the energy barrier for the cyclic→quasilinear isomerization reaction is determined to be 12.1 kcal/mol (11.0 kcal/mol with the ZPVE correction). The inversion reaction between the quasilinear and linear structures is found to have a very small energy barrier. With the estimated augccpCVQZ CCSD(T) method the electron affinity of is predicted to be 2.31 eV, which is in excellent agreement with the experimental value 2.31±0.01 eV.

Infrared spectra and density functional calculations of the copper thiocarbonyls: CuCS, and in solid argon
View Description Hide DescriptionMicrowavedischarge through vapor yielded CS which was cocondensed with laserablated copper atoms at 12 K in an argon matrix. Binary copper thiocarbonyl complexes: CuCS, and were formed via the reactions of ground statecopper atoms or dimers with CS in solid argon. On the basis of isotopic shifts and splittings as well as density functional calculations, absorptions at 1187.2, 1291.3, and 1353.9 cm^{−1} are assigned to the C–S stretching vibrations of the bent CuCS, linear and endon bonded molecules, respectively. The calculation results show that these copper thiocarbonyl complexes are more strongly bonded than the corresponding copper carbonyl complexes.

Probing highly excited vibrational eigenfunctions using a modified single Lanczos propagation method: Application to acetylene (HCCH)
View Description Hide DescriptionA modified version of the single Lanczos propagation method is proposed, which allows both energies and overlaps between multiple target functions and all eigenfunctions to be computed from a single Lanczos recursion with no explicit construction of the eigenfunctions. This method is employed to help assigning some highly excited bending levels of acetylene (HCCH) using a sixdimensional exact quantum Hamiltonian and target functions designed to extract information about the shape of the eigenfunctions. In the special case of the state vibrational eigenfunctions being the target functions, the resonanceemission spectra are obtained. The assignments on the Bramley et al. [J. Mol. Spectrosc. 157, 301 (1993)] potential energy surface show a strong resemblance to the experimentally observed normaltolocal mode transition in the bending overtones, while that of Halonen et al. [Mol. Phys. 47, 1097 (1982)] supports no such transition in the same energy range.

Blueshifting hydrogen bonding in
View Description Hide DescriptionAn ab initio computational study of the properties of the weakly bound linear complex was undertaken at three different levels of theory using a basis set. The dimer was found to have a zeropoint vibrational energy corrected binding energy of −2.8 kJ mol^{−1} with respect to the monomer subunits, at the highest level of theory used in this study. This complex exhibits a large harmonic vibrational frequency blueshift of about 60 cm^{−1} for the H–Kr stretching mode with a decrease in the infrared intensity for this mode on formation of the complex. This unusual result was rationalized mainly by consideration of the effect of the electrostatic interaction and charge transfer between the HKrF and molecules.

A study of electronic and bonding properties of Sn doped clusters and aluminum based binary clusters through electron localization function
View Description Hide DescriptionWe have carried out a thorough investigation of bonding and energetics in two different class of heteroatomic clusters viz. single impurity based clusters and mixed aluminumbased binary clusters (X=Be, Mg, B, Si). We employ first principle Born–Oppenheimer molecular dynamics within the framework of density functional theory using generalized gradient approximation. The bonding characteristics have been analyzed using electron localization function (ELF) along with charge density and valence molecular orbital pictures. The analysis of bonding through ELF reveals that in clusters there is a transition from ionic bond to a metallic bond through an intermediate ionic–metallic bond. On the other hand, it is found that (X=Be, Mg, B, Si) clusters show interesting characteristics of lone pairs on Al, polar covalent bonding, and a multicenter bonding. We demonstrate that ELF can play an important role in analyzing different types of bonding characteristics in heteroatomic clusters.

Shape resonance of anion stabilized in a molecular trap
View Description Hide DescriptionThe possibility of stabilizing an electronically metastable anion in a molecular trap is studied using ab initioelectronic structure methods. The lowenergy wave shape resonance state is used as the metastable anion solute, and a pair of inwardly oriented LiCN molecules is used as a molecular trap. It is found that for the trap at its local minimum geometry, the state (that corresponds to the state for the isolated becomes electronically stable and is the ground state of the system. It is also found that, in this model trap, two other (excited) anionic states are bound and Detailed numerical results are presented for the species (i.e., the trapped whose vertical electron detachment energy is 3.429 eV at the CCSD(T) level with the augccpVDZ basis sets.

Quasiclassical trajectory study of the dynamics of the reaction on a new potential energy surface
View Description Hide DescriptionA new ab initiopotential energy surface (PES) for the reaction has been constructed using the GROW package of Collins and coworkers. The ab initio calculations have been done using the Becke threeparameter nonlocal exchange functional with the nonlocal correlation of Lee, Yang, and Parr density functional theory. A detailed quasiclassical trajectory study of integral and differential cross sections, product rovibrational populations, and internal energy distributions on the new PES is presented. The theoretical integral cross sections as a function of collision energy are in qualitative agreement with the experimental measurements. A good correspondence is found between the calculated rovibrational populations and the recent measurements of Brouard and coworkers at 1.48 eV collision energy. In particular, the calculated kinetic energy release distributions for state resolved products predict a substantial fraction of total energy going into rotational excitation of the coproduct, in good agreement with the experimental findings.

Lowtemperature behavior of capture rate constants for inverse power potentials
View Description Hide DescriptionThe energy dependence of the capture cross section and the temperature dependence of the capture rate constants for inverse power attractive potentials is considered in the regime where the quantum character of the relative motion of colliding partners is important. For practically interesting cases and a simple formula for the cross section is suggested which interpolates between the classical and the quantum Bethe limits. We have shown that the classical approximation for the capture cross section performs well far below the simple estimations of the onset the quantum regime. This seemingly “classical” feature of the cross section and the rate constant is due to the large quantum effects of the waves in transmission through and reflection above the centrifugal potential barriers.