Volume 118, Issue 2, 08 January 2003
 ARTICLES

 Theoretical Methods and Algorithms

Connections between secondorder Görling–Levy and manybody perturbation approaches in density functional theory
View Description Hide DescriptionFormal connections between the highdensity scaling limit of the correlation energy functional in density functional theory and secondorder energy expressions from different perturbation theory formulations are presented. It is demonstrated that the secondorder correlation potential considered by Grabowski et al. [J. Chem. Phys. 116, 4415 (2002)] is equivalent to the highdensity limit of the exact correlation potential, and thus provides the first selfconsistent finitebasisset implementation of a Kohn–Sham (KS) potential correct through secondorder. A different secondorder correlation functional based on the exchangeonly KS approach is introduced. It is shown that this secondorder correlation functional leads to the same selfconsistent KS realization as the one derived from the secondorder component of

Relativistic effects on the nuclear magnetic shielding tensor
View Description Hide DescriptionA new approach for calculating relativistic corrections to the nuclear magnetic shieldings is presented. Starting from a full relativistic second order perturbation theory expression a twocomponent formalism is constructed by transforming matrix elements using the elimination of small component scheme and separating out the contributions from the novirtual pair and the virtual pair part of the second order corrections to the energy. In this way we avoid a strong simplification used previously in the literature. We arrive at final expressions for the relativistic corrections which are equivalent to those of Fukui et al. [J. Chem Phys. 105, 3175 (1996)] and at some other additional terms correcting both the paramagnetic and the diamagnetic part of the nuclear magnetic shielding. Results for some relativistic corrections to the shieldings of the heavy and light nuclei in HX and at both random phase and second order polarization propagator approach levels are given.

Valence basis sets for relativistic energyconsistent smallcore actinide pseudopotentials
View Description Hide DescriptionGaussian atomic natural orbital valence basis sets have been generated for relativistic energyconsistent smallcore actinide pseudopotentials of the Stuttgart–Bonn variety. Effective valence spin–orbit operators supplementing the scalarrelativistic pseudopotentials have been derived from multiconfiguration Dirac–Hartree–Fock reference data. Pseudopotentials, basis sets and spin–orbit operators have been used to determine the first and second ionization potentials of all actinide elements at the multiconfiguration selfconsistent field and multireference averaged coupledpair functional level. Comparison is made to results obtained from largescale calculations using uncontracted basis sets up to type functions and extrapolation to the basis set limit as well as to experimental data. Molecular calibration studies using the coupledcluster singles, doubles, and perturbative triples approach are reported for the ground states of AcH, AcO, AcF, and ThO.

Molecular motors driven by laser pulses: Role of molecular chirality and photon helicity
View Description Hide DescriptionThe results of a theoretical study on molecular motors driven by laser pulses are presented. The roles of molecular chirality and photon helicity in determination of their unidirectional rotation are clarified. An expression for an instantaneous angular momentum of motors driven by lasers in the density matrix formalism was derived. Assuming randomly oriented molecular motors, the initial distributionaveraged instantaneous angular momentum in the dipole approximation was obtained. Taking into account parity inversion symmetry of molecular motors in the averaged instantaneous angular momentum, it is shown that the directions of the averaged instantaneous angular momentum of (R) and (S)chiral molecular motors are opposite, but that the magnitudes are the same. This is independent of polarization of laser fields. That is, the chiral motors driven by a linearly polarized optical field creates a unidirectional motion in a molecular fixed frame. On the other hand, the direction of rotation in the laboratory fixed frame is decided by a circularly polarized laser regardless of its molecular chirality. A simple example of real chiral molecular motors is used to demonstrate the interplay of molecular chirality and photon helicity in determination of their unidirectional rotation. The internal rotation of the CHO group plays the role of the engine of the motor. The time evolution of the rotational wave packets of the molecular motors driven by linearly or circularly polarized laser pulses was numerically evaluated and the dynamical behaviors were analyzed. Effects of temperature on the instantaneous angular momentum of the molecular motors are presented as well.

Analytical timedependent HartreeFock evaluation of the dynamic zeropoint vibrationally averaged (ZPVA) first hyperpolarizability
View Description Hide DescriptionA procedure to compute analytical second derivatives of the dynamic first hyperpolarizability with respect to vibrational coordinates has been developed and implemented at the timedependent HartreeFock level. Simplifications are obtained by the same techniques as those employed to derive the rule and the interchange relations. This scheme is used to determine the firstorder ZPVA correction for three small molecules. It is found that the frequency dispersion coefficients are similar to those obtained for the pure electronic contribution in and but not

A discrete solvent reaction field model within density functional theory
View Description Hide DescriptionIn this work we present theory and implementation for a discrete reaction field model within Density Functional Theory(DFT) for studying solvent effects on molecules. The model combines a quantum mechanical (QM) description of the solute and a classical description of the solvent molecules (MM). The solvent molecules are modeled by point charges representing the permanent electronic charge distribution, and distributed polarizabilities for describing the solventpolarization arising from manybody interactions. The QM/MM interactions are introduced into the Kohn–Sham equations, thereby allowing for the solute to be polarized by the solvent and vice versa. Here we present some initial results for water in aqueous solution. It is found that the inclusion of solventpolarization is essential for an accurate description of dipole and quadrupole moments in the liquid phase. We find a very good agreement between the liquid phase dipole and quadrupole moments obtained using the Local Density Approximation and results obtained with a similar model at the Coupled Cluster Singles and Doubles level of theory using the same water cluster structure. The influence of basis set and exchange correlation functional on the liquid phase properties was investigated and indicates that for an accurate description of the liquid phase properties using DFT a good description of the gas phase dipole moment and molecular polarizability are also needed.

Linear response at the 4component relativistic level: Application to the frequencydependent dipole polarizabilities of the coinage metal dimers
View Description Hide DescriptionLinear response theory based on the timeaveraged quasienergy of Floquet states is generalized to the 4component relativistic level for molecular calculations based on an analytical basis set. An efficient implementation of the theory for 4component closedshell Hartree–Fock is described. This level of approximation is also called the 4component relativistic random phase approximation. The structure of the reduced response equations is analyzed in terms of Hermiticity and time reversal symmetry and leads to restrictions on the form chosen for the trial vectors as well as rules indicating when the linear response function is real, imaginary or zero. A key ingredient of the AOdriven algorithm is the formulation of the Hessian times a trial vector as the construction of modified Fock matrices. To reduce computational cost a previously reported quaternion symmetry scheme has been extended to non totally symmetric operators such that possible symmetry reductions are obtained as a reduction of algebra from quaternion to complex or real. We report the calculations of the frequencydependent dipole polarizabilities for and at the 4component Dirac–Coulomb Hartree–Fock level. Comparison of the relativistic and nonrelativistic results show an increasing discrepancy with increasing nuclear charge, leading to qualitatively different results. Analysis of the firstorder wave function shows that in the case of the gold dimer at the relativistic level of theory the generally dominant excitations from the HOMO are supplemented by excitations from the manifold. This may significantly alter the molecular spectra and will be studied in a subsequent paper.

Counterpoisecorrected geometries and harmonic frequencies of Nbody clusters: Application to
View Description Hide DescriptionThe differences between three previously defined counterpoise (CP) schemes for removing the BSSE in molecular complexes formed by more than two subunits have been assessed by CPcorrected geometry optimizations and frequency calculations for the hydrogen fluoride trimer and tetramer. The types of the functional counterpoise (FC) procedures included the site–site (SSFC), pairwise additive, and hierarchical Valiron–Mayer (VMFC) schemes. The latter approach takes into account the basis set extension of the dimers in the trimer, dimers and trimers in the tetramer, etc. The number of different calculations required to apply this counterpoise scheme increases very rapidly with the cluster size. The symmetry of the chosen systems makes the test of this approach computationally feasible. All the optimizations and frequency calculations have been carried out automatically using a new program that generates the necessary input files and repeatedly calls a slightly modified version of a Gaussian link. The results show that geometrical parameters, zeropoint vibrational energies, and redshifts computed on the CPcorrected potential energy surfaces differ considerably from those evaluated on the uncorrected surfaces. The structural and energetic properties obtained with the conventional SSFC procedure are almost identical to those predicted by the more costly and complex VMFC method. Hence, the former seems to be more appropriate in the present case. Furthermore, symmetryadapted perturbation theory calculations show the importance of computing the interaction energies at the CPcorrected geometries.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electronic and photophysical properties of
View Description Hide DescriptionThis work examines, by using quantumchemical calculations, the electronic and optical properties of three highly symmetrical isomers of the halogenofullerene. The ground stateproperties of these derivatives are calculated using the semiempirical Hartree–Fock AM1 approach and discussed in terms of symmetry, charge distribution and electronic conjugation on the fullerene cage. Starting from the optimized geometry, the optical absorptionspectrum of each molecule is calculated at the semiempirical Hartree–Fock INDO/S level, using a large configuration interaction scheme. The results are compared to a visible and nearinfraredabsorptionspectrum of recorded in solid matrices, at low temperature. From the comparison, it is concluded that a isomer is responsible for the spectrum observed. The spectrum is analyzed in terms of electronic singlet transitions.

A computational study of chlorofluoromethyl radicals
View Description Hide DescriptionChorine and fluorinecontaining methyl radicals have been investigated by ab initio methods. Geometries and vibrational frequencies were derived with quadratic configuration methods at the level of theory, and energies via and Gaussian 3 theory. Anharmonicity of the out of plane bending mode was taken into account by numerical integration of the Schrödinger equation with a potential derived from a relaxed scan of this mode. The results are in good accord with experimental data where available. For the radicals and we compute values of −241.2, −465.9, 117.0, 91.1, and 72.2 kJ mol^{−1}, respectively, which agree with wellestablished experimental values to within 2.2 kJ mol^{−1}. For the more poorly characterized molecules CHClF, and we compute values of −29.0, −63.8, −274.7, and −94.3 kJ mol^{−1}, respectively, with recommended confidence limits of ±4.1 kJ mol^{−1}.

Quantum mechanical and quasiclassical trajectory study of the reaction dynamics
View Description Hide DescriptionFirst accurate quantum mechanical (QM) calculations of integral and differential cross sections for the insertion reaction have been performed on a newly developed ab initiopotential energy surface [B. BusseryHonvault et al., J. Chem. Phys. 115, 10701 (2001)]. These results have been compared with those obtained with a quasiclassical trajectory(QCT) method. A Gaussianweighted binning procedure to assign product quantum states in the QCT calculations yields vibrational branching ratios and rotational distributions in better agreement with the QM calculations than those obtained when the usual histogramatic binning method is employed. This is the first time that the Gaussianweighted binning procedure is used for an insertion reaction.

Quantum reactive scattering in three dimensions using adiabatically adjusting principal axis hyperspherical coordinates: Periodic distributed approximating functional method for surface functions
View Description Hide DescriptionPeriodic distributed approximating functionals are proposed and used to obtain a coordinate representation for the adiabatically adjusting principal axis hyperspherical coordinate kinetic energy operator. The approach is tested and accurate results for adiabatic surface functions for the reaction are calculated and compared to those of some existing methods.

Analytical fittings for the global potential energy surface of the ground state of methylene
View Description Hide DescriptionThe global potential energy surface (PES) corresponding to the dissociationreaction of the ground state of methylene is studied with the coupledcluster method with single, double and perturbative triplet excitations, CCSD(T), in conjunction with the correlationconsistent ccpVTZ basis set, and fitted by three analytical potential functions in terms of the Simons–Parr–Finlan (SPF) polynomial, Jensen function and the Sorbie–Murrell (SM) function. Ab initio singlepoint calculations over a distributed range of grids are performed first, and totally 12 085 converged points are fed into these functions. The fitting of each analytical PES function is done with an unconstrained minimization of the difference between the evaluations of the analytical function and the ab initio results, solved by a modified Levenberg–Marquardt algorithm with a finitedifference Jacobian in the IMSL package. The SPF polynomial is found to have the best global description, while the SM function behaves superior in the dissociation region forming three atoms. The spline function is potentially feasible to interpolate the computationally divergent points in the ab initio calculations.

Control of vibrational ionization branching through feedbackoptimized tailored femtosecond laser pulses
View Description Hide DescriptionWe report the control of the ionization yield ratio to different vibrational levels of the electronic ground state of by feedback optimization of shaped ultrashort laser pulses. The nitric oxide NO molecule is excited by the second harmonic of a phaseshaped Ti:sapphire femtosecond laser. The optimization of pulse tailoring by a learning evolutionary algorithm leads to significant modifications of the vibrational ionic distribution observed by photoelectron spectroscopy. The control exerted over two groups of photoelectrons is robust and reveals some selectivity.

Photodissociation of the ArHBr complex investigated with the multiconfiguration timedependent Hartree approach
View Description Hide DescriptionWe apply the multiconfiguration timedependent Hartree method to the study of the photodissociation of the Ar–HBr van der Waals complex. The dynamics is studied in both Jacobi and valence coordinates. The evolution of the probability density in the different modes shows that the direct or nearly direct mechanism, where the hydrogen atom interacts only very weakly with the Ar and Br atoms, dominates the dissociation process. By projecting the quantum flux onto the vibrational levels of ArBr, we find at the maximum of the absorption profile, i.e., around that 65% of the dissociation gives rise to partial fragmentation into hot H fragments and bound ArBr molecules.

Theoretical investigation of the temperature dependence of the exchange reaction
View Description Hide DescriptionThe exchange reaction and, in particular, its dependence on the transition state region is investigated by classical trajectories on three potential energy surfaces, all based on highlevel electronic structure calculations. The first one is the original potential recently constructed by Siebert, Schinke, and Bittererová [Phys. Chem. Chem. Phys. 3, 1795 (2001)]; it has a very small barrier above the asymptote. The second potential is a modification of the first one in that the transition state region is adjusted according to new electronic structure calculations on higher levels of theory; it has a small barrier below the asymptote. The third potential is obtained by artificially removing this barrier. The variation of the exchange reaction cross section with collision energy and the magnitude of the thermal rate constant at and below room temperature depend drastically on the shape of the potential at intermediate distances. The second potential, which is believed to represent the transition state structure of the true groundstate potential of ozone best, yields a reaction rate for room temperature that is about a factor of three smaller than the experimental rate. The neglect of nonadiabatic transitions between the several electronic states in the entrance channel may explain this discrepancy. The very slight negative temperature dependence found in the calculations is caused by the strong decrease of the reaction cross section with the initial rotational excitation of the oxygen molecule. Statistical calculations give poor agreement with the classical energy and initialstate dependent cross sections. Nevertheless, the statistical thermal rates are in fair agreement with the classical ones, because the overestimation of the cross sections for low ’s and the underestimation for high ’s partly compensate.

CF and study by broadband absorption spectroscopy in a plasma etch reactor: Determination of transition probabilities, CF concentrations, and gas temperatures
View Description Hide DescriptionBroadband absorption spectroscopy was applied to study the CF and transitions in a plasmaetch reactor. We report a previously unobserved band, which is assigned as CF (3,0). This band is significantly broadened by predissociation, and we estimate the average collisionfree lifetime of the CF level to be 0.30±0.08 ps. Experimental relative oscillator strength measurements, together with ab initio calculations, Rydberg–Klein–Reesbased wave functions and experimental lifetimes were used to calculate a full set of transition probabilities for the CF and bands. The maximum observed number densities of CF were with sensitivity to measure to The excited state and ground statetemperatures were determined by comparing the spectra to simulations. The ground state rotational temperature was and the vibrational temperature was near the substrate surface. The CF excited state rotational temperatures are higher than those of the ground state. We show that this absorption technique is practical for determining gas temperatures and absolute concentrations in plasmaetch reactors.

Kinetic and mechanistic studies on the abstraction reactions of atomic with and
View Description Hide DescriptionThe reactions of atomic with and have been studied theoretically using ab initio molecular orbital theory for the first time. Geometries have been optimized at the MP2 level with the and basis sets. The singlepoint energy calculations have been carried at the level. Theoretical analysis provides conclusive evidence that the main process occurring in each reaction is the hydrogen abstraction from the Si–H bonds leading to the formation of the and silyl radical; the hydrogen abstraction from the C–H bonds has higher barrier and is difficult to react. Two nearly degenerate transition states of and symmetries have been located for each hydrogen abstraction reaction from the Si–H bonds. Changes of geometries, generalized normalmode vibrational frequencies, and potential energies along the reaction paths are discussed and compared. The rate constants have been deduced over a wide temperature range of 200–3000 K using canonical variational transitionstate theory (CVT) with small curvature tunneling effect (SCT). The calculated CVT/SCT rate constants exhibit typical nonArrhenius behavior, threeparameter ratetemperature formulas are fitted as follows (in units of and for the reactions of with and respectively. The calculated rate constants are compared with the available experimental values.

Tunneling dynamics of the NH chromophore in during and after coherent infrared excitation
View Description Hide DescriptionThe time dependent quantum dynamics of the large amplitude motion of the NH stretching chromophore in is investigated during and after coherent multiphoton excitation by calculation of the wave packet evolution using global analytical potential energy and electric dipole hypersurfaces of ammonia derived from ab initio calculations. Intramolecular vibrational redistribution between the NH stretching and bending motion and coupling to the radiation field induces a diffusion of probability density into the NH chromophore space, which includes the inversion coordinate. However, inversion remains essentially dominated by a tunneling process, even at average energies well above the inversion barrier.

Intramolecular vibrational energy redistribution, mode specificity, and nonexponential unimolecular decay dynamics of vibrationally highly excited states of DCO
View Description Hide DescriptionThe unimolecular dynamics of vibrationally highly excited states of DCO in the energy region up to beyond the D–CO dissociation threshold, has been investigated using an effective polyad Hamiltonian obtained by fitting to the term energies from the measuredstimulated emission pumping (SEP) spectra of the molecule [Stöck et al., J. Chem. Phys. 106, 5333 (1997); Temps and Tröllsch, Z. Phys. Chem. 215, 207 (2001)]. An added absorbing negative imaginary potential allowed for the unimolecular dissociation of the highly excited DCO via distinctive open reaction channels of the DC stretching vibration. The ensuing dynamics was explored using a wave packet propagation approach. Time profiles describing the intramolecular vibrational energy redistribution (IVR) and unimolecular decay kinetics were computed for the CO stretching zeroorder basis states up to 6 quanta of excitation and the DCO bending zeroorder basis states up to 12 quanta of excitation. The computed decay curves for the CO stretching zeroorder basis states compare nicely with those of the respective coherent superposition states constructed directly from the measured SEP spectra (assuming the CO stretching mode as the Franck–Condon active bright zeroorder mode that determines the observed transitions). A comparison of the decay curves with those of the almost isoenergetic DCO bending zeroorder basis states in the respective polyads reveals large differences in the couplings of the two vibrational modes among each other and with the open dissociation channels. The obtained unimolecular decay profiles exhibit pronounced nonexponential kinetics. Comparison with statistically calculated decay rates shows a substantial degree of mode specificity of the dynamics, which can be attributed to a bottleneck in the IVR from the CO stretching vibration to the reaction coordinate. The model calculations explain the twotothree orders of magnitude large difference between the measured eigenstate specific DCO decay constants [Stöck et al.] and predictions by microcanonical statistical rate theories.