Volume 123, Issue 19, 15 November 2005
 ARTICLES

 Theoretical Methods and Algorithms

Fundamental limits of the dispersion of the twophoton absorption cross section
View Description Hide DescriptionWe rigorously apply the sum rules to the sumoverstates expression to calculate the fundamental limits of the dispersion of the twophoton absorption cross section. A comparison of the theory with the data suggests that the truncated sum rules in the threelevel model give a reasonable fundamental limit. Furthermore, we posit that the twophoton absorption cross section near the limit must have only three dominant states, so by default, the threelevel model is appropriate. This ansatz is supported by a rigorous analytical calculation that the resonant term gets smaller as more states are added. We also find that the contributions of the nonexplicitly resonant terms cannot be neglected when analyzing real molecules with many excited states, even near resonance. However, puzzling as it may be, extrapolating an offresonant result to resonance using only the resonant term of the threelevel model is shown to be consistent with the exact result. In addition, the offresonant approximation is shown to scale logarithmically when compared with the full threelevel model. This scaling can be used to simplify the analysis of measurements. We find that existing molecules are still far from the fundamental limit; so, there is room for improvement. But, reaching the fundamental limit would require precise control of the energylevel spacing, independently of the transition dipole moments—a task that does not appear possible using today’s synthetic approaches. So, we present alternative methods that can still lead to substantial improvements which only require the control of the transition moment to the first excited state. While it is best to normalize measured twophoton absorption cross sections to the fundamental limits when comparing molecules, we show that simply dividing by the square of the number of electrons per molecule yields a good metric for comparison.

Theoretical study of the electronic spectra of squareplanar platinum (II) complexes based on the twocomponent relativistic timedependent densityfunctional theory
View Description Hide DescriptionIn the present work the electronic spectra of , , and are studied with a recently proposed relativistic timedependent densityfunctional theory (TDDFT) based on the twocomponent zerothorder regular approximation and a noncollinear exchangecorrelation (XC) functional. The contribution to the double group excited states in terms of singlet and triplet single group excited states is estimated through the inner product of the transition density matrix obtained from twocomponent and scalar relativistic TDDFT calculations to better understand the double group excited states. Spinorbital coupling effects are found to be very important in order to simulate the electronic spectra of these complexes. The results show that the twocomponent TDDFT formalism can afford excitation energies with high accuracy for the transitionmetal systems studied here when use is made of a proper XC potential.

Nonlinear response theory with relaxation: The firstorder hyperpolarizability
View Description Hide DescriptionBased on the Ehrenfest theorem, an equation of motion that takes relaxation into account has been presented in wavefunction theory, and the resulting response functions are nondivergent in the offresonant as well as the resonant regions of optical frequencies. The derivation includes single and multideterminant reference states. When applied to electric dipole properties, the response functions correspond to the phenomenological sumoverstates expressions of Orr and Ward [Mol. Phys.20, 513 (1971)] for polarizabilities and hyperpolarizabilities of an isolated system. A universal dispersion formula is derived for the complex secondorder response function. Response theory calculations are performed on lithium hydride and paranitroaniline for offresonant and resonant frequencies in the electrooptical Kerr effect and secondharmonic generation.

Differential virial theorem in relation to a sum rule for the exchangecorrelation force in densityfunctional theory
View Description Hide DescriptionHolas and March [Phys. Rev. A.51, 2040 (1995)] gave a formally exact theory for the exchangecorrelation (xc) force associated with the xc potential of the densityfunctional theory in terms of loworder density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule relating the xc force with the groundstate density . Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A.32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys.119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.

HartreeFock orbitals for complexscaled configuration interaction calculation of highly excited Feshbach resonances
View Description Hide DescriptionWe examine a complexscaled configuration interaction [(CS)CI] for highly excited Feshbach resonances, where we study the resonance of helium as a test case. Sizable fullCI calculations are reduced by using a correctly defined minimum active space. We compare the convergence of the minimum active space for conventional HartreeFock (HF) orbitals obtained as solutions to Hermitian HF equations, to the convergence of minimum active space for complex orbitals obtained as solutions to complexscaled HF equations. Groundstate optimized orbitals are compared to a simple modification of the HF method using the excitedstatemeanfield potential.

An efficient approach for selfconsistentfield energy and energy second derivatives in the atomicorbital basis
View Description Hide DescriptionBased on selfconsistentfield (SCF) perturbation theory, we recast the SCF and the coupledperturbed SCF (CPSCF) equations for timeindependent molecular properties into the atomicorbital basis. The density matrix and the perturbed density matrix are obtained iteratively by solving linear equations. Only matrix multiplications and additions are required, and this approach can exploit sparse matrix multiplications and thereby offer the possibility of evaluating secondorder properties in computational effort that scales linearly with system size. Convergence properties are similar to conventional molecularorbitalbased CPSCF procedures, in terms of the number of derivative Fock matrices that must be constructed. We also carefully address the issue of the numerical accuracy of the calculated second derivatives of the energy, in order to specify the minimum precision necessary in the CPSCF procedure. It is found that much looser tolerances for the perturbed density matrices are adequate when using an expression for the second derivatives that is correct through second order in the CPSCF error.

Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates
View Description Hide DescriptionAn efficient simulation algorithm for chemical kineticsystems with disparate rates is proposed. This new algorithm is quite general, and it amounts to a simple and seamless modification of the classical stochastic simulation algorithm (SSA), also known as the Gillespie [J. Comput. Phys.22, 403 (1976); J. Phys. Chem.81, 2340 (1977)] algorithm. The basic idea is to use an outer SSA to simulate the slow processes with rates computed from an inner SSA which simulates the fast reactions. Averaging theorems for Markov processes can be used to identify the fast and slow variables in the system as well as the effective dynamics over the slow time scale, even though the algorithm itself does not rely on such information. This nested SSA can be easily generalized to systems with more than two separated time scales. Convergence and efficiency of the algorithm are discussed using the established error estimates and illustrated through examples.

Nonadiabatic quantumclassical reaction rates with quantum equilibrium structure
View Description Hide DescriptionTime correlation function expressions for quantum reactionrate coefficients are computed in a quantumclassical limit. This form for the correlation function retains the full quantum equilibrium structure of the system in the spectral density function but approximates the time evolution of the operator by quantumclassical Liouville dynamics. Approximate analytical expressions for the spectral density function, which incorporate quantum effects in the manybody environment and reaction coordinate, are derived. The results of numerical simulations of the reaction rate are presented for a reaction model in which a twolevel system is coupled to a bistable oscillator which is, in turn, coupled to a bath of harmonic oscillators. The nonadiabatic quantumclassical dynamics is simulated in terms of an ensemble of surfacehopping trajectories and the effects of the quantum equilibrium structure on the reaction rate are discussed.

Behavior of polarizable models in presence of strong electric fields. I. Origin of nonlinear effects in water pointcharge systems
View Description Hide DescriptionIn the current opinion, the inclusion of polarization response in classical computer simulations is considered as one of the most important and urgent improvements to be implemented in modern empirical potential models. In this work we focus on the capability of polarizable models, based on the pairwise Coulomb interactions, to model systems where strong electric fields enter into play. As shown by Masia, Probst, and Rey (MPR) [in J. Chem. Phys.121, 7362 (2004)], when a molecule interacts with point charges, polarizable models show underpolarization with respect to ab initio methods. We prove that this underpolarization, clearly related to nonlinear polarization effects, cannot be simply ascribed to the lack of hyperpolarization in the polarizable models, as suggested by MPR. Analysis of the electrondensity rearrangement induced on a water molecule by a point charge reveals a twofold level of polarization response. One level involves intramolecular charge transfer on the whole molecular volume, with the related polarization exhibiting a seemingly linear behavior with the external electric field. The other nonlinear polarization level occurs only at strong electric fields and is found to be strictly correlated to the quantummechanical nature of the water molecule. The latter type of polarization has a local character, being limited to the space region of the water lone pairs.

Multireference calculations of the electronic structure of and
View Description Hide DescriptionWe investigated the electronic structure of two members of the transitionmetal dihalide family, and . Using the configurationinteraction method in large basis sets we calculated the lowest 17 states of these molecules in the vicinity of their groundstate geometry. We compute the groundstatebond lengths, vibrational frequencies, and dissociation energies. In contrast to predictions of ligandfield theory, we find ground states for both molecules.

The directional contact distance of two ellipsoids: Coarsegrained potentials for anisotropic interactions
View Description Hide DescriptionWe obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation measured along their intercenter vector. This directional distance is derived from the elliptic contact function. The geometric meaning behind this approach is clarified. An elliptic pair potential for modeling arbitrary mixtures of elliptic particles, whether hard or soft, is proposed based on this distance. Comparisons with GayBerne potentials are discussed. Analytic expressions for the forces and torques acting on the elliptic particles are given.

Geometry optimization of crystals by the quasiindependent curvilinear coordinate approximation
View Description Hide DescriptionThe quasiindependent curvilinear coordinate approximation (QUICCA) method [K. Németh and M. Challacombe, J. Chem. Phys.121, 2877 (2004)] is extended to the optimization of crystal structures. We demonstrate that QUICCA is valid under periodic boundary conditions, enabling simultaneous relaxation of the lattice and atomic coordinates, as illustrated by tight optimization of polyethylene, hexagonal boron nitride, a (10,0) carbon nanotube, hexagonal ice,quartz, and sulfur at the point RPBE/STO3G level of theory.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photon energy dependence of fragmentation of small argon clusters
View Description Hide DescriptionPhotofragmentation of small argon clusters with size below ten atoms is reported. In this size range significant modifications from the electronic properties and geometry take place. When tuning the photon energy through the argon edge, the fragmentation pattern is changed. Specifically, cation dimer production is enhanced at the resonance, while above the edge almost complete atomization is observed. In both cases, the widths of the peaks in the mass spectra indicate that a large amount of kinetic energy is imparted to the fragment due to the formation of multiply charged clusters. A model based on “Coulomb explosion”—charge separation, simply resulting in a complete atomization of the cluster with no dependence on the photon energy—is insufficient to explain the observed photofragmentation of small clusters.

An eightdegreeoffreedom quantum dynamics study for the system
View Description Hide DescriptionAn eightdegreeoffreedom (8DOF) timedependent wavepacket approach has been developed to study the reaction system. The 8DOF model is obtained by fixing one of the Jacobi torsion angle in the ninedegreeoffreedom reaction system. This study is an extension of the previous sevendegreeoffreedom (7DOF) computation [J. Chem. Phys.119, 12057 (2003)] of this reaction system. This study shows that vibrational excitations of enhance the reaction probability, whereas the stretching vibrational excitations of have only a small effect on the reactivity. Furthermore, the bending excitation of , compared to the groundstatereaction probability, hinders the reactivity. A comparison of the rate constant between the 7DOF calculation and the present 8DOF results has been made. The theoretical and experimental results agree with each other very well when the present 8DOF results are adjusted to account for the lower transition state barrier heights found in recent ab initio calculations.

Measurement of the rate coefficient for collisional removal of by
View Description Hide DescriptionWe report a laboratory measurement of the rate coefficient for the collisional removal of by atoms. In the experiments, 266nm laser light photodissociates ozone in a mixture of molecular oxygen and ozone. The photolysis step produces vibrationally excited that is rapidly converted to in a nearresonant electronic energytransfer process with groundstate. In parallel, a large amount of atoms is generated that promptly relaxes to . Under the conditions of the experiments, only collisions with the photolytically produced atoms control the lifetime of , because its removal by molecular oxygen at room temperature is extremely slow. Tunable 193nm laser light monitors the temporal evolution of the population by detection of laserinduced fluorescence near 360 nm. The removal rate coefficient for by atoms is at a temperature of . This result is essential for the analysis and correct interpretation of the band emission in the Earth’s mesosphere and indicates that the deactivation of by atoms is significantly faster than the nominal values recently used in atmospheric models.

Quantum statetostate rate constants for the rotationally inelastic collision of , , with
View Description Hide DescriptionWe have calculated the statetostate integral cross sections and rate constants for the rotationally inelastic collision of , , with using the quantum coupledstate and closecoupling methods on an ab initiopotentialenergysurface constructed by Alexander et al. [J. Chem. Phys.101, 4547 (1994)]. Overall the calculated rate constants are in good agreements with the three available experimental results. The rate constants are comparable to the usual gas kinetic and decrease with increasing and . For the multiquantum transition cases, the theory underestimates the experiment. We discuss some possible causes to the discrepancies among the theory and the experiments.

Stark slowing asymmetric rotors: Weakfieldseeking states and nonadiabatic transitions
View Description Hide DescriptionStark deceleration is one of the few methods that can be used to slow polyatomic molecules. We present calculations of Stark shift energies, a quantitative analysis of nonadiabatic transition probabilities, and orientational distribution functions applicable to typical Stark slowing conditions for the two small asymmetric rotors nitromethane and acetaldehyde. We show that asymmetric polyatomic molecules are good candidates for Stark slowing.

Dissociative recombination of the weakly bound NOdimer cation: Cross sections and threebody dynamics
View Description Hide DescriptionDissociative recombination (DR) of the dimer ion has been studied at the heavyion storage ring CRYRING at the Manne Siegbahn Laboratory, Stockholm. The experiments were aimed at determining details on the strongly enhanced thermal rate coefficient for the dimer, interpreting the dissociation dynamics of the dimer ion, and studying the degree of similarity to the behavior in the monomer. The DR rate reveals that the very large efficiency of the dimer rate with respect to the monomer is limited to electron energies below . The fragmentation products reveal that the breakup into the threebody channel dominates with a probability of . The second most important channel yields fragments with a probability of . Furthermore, the dominant threebody breakup yields electronic and vibrational groundstate products, , in about 45% of the cases. The internal productstate distribution of the NO fragment shows a similarity with the productstate distribution as predicted by the FranckCondon overlap between a NO moiety of the dimer ion and a free NO. The dissociation dynamics seem to be independent of the NO internal energy. Finally, the dissociation dynamics reveal a correlation between the kinetic energy of the NO fragment and the degree of conservation of linear momentum between the O and N product atoms. The observations support a mechanism in which the recoil takes place along one of the NO bonds in the dimer.

Evanescent high pressure during hypersonic clustersurface impact characterized by the virial theorem
View Description Hide DescriptionMatter under extreme conditions can be generated by a collision of a hypersonic cluster with a surface. The ultrahighpressure interlude lasts only briefly from the impact until the cluster shatters. We discuss the theoretical characterization of the pressure using the virial theorem and develop a constrained moleculardynamics procedure to compute it. The simulations show that for raregas clusters the pressures reach the megabar range. The contribution to the pressure from momentum transfer is comparable in magnitude and is of the same sign as that (“the internal pressure”) due to repulsive interatomic forces. The scaling of the pressure with the reduced mechanical variables is derived and validated with reference to the simulations.

Development of a cooled beam source for measurements of stateresolved collision energy dependence of Penning ionization cross sections: Evidence for a stereospecific attractive well around methyl group in
View Description Hide DescriptionA lowtemperature discharge nozzle source with a liquid circulator for metastable atoms has been developed in order to obtain the stateresolved collision energy dependence of Penning ionization cross sections in a low collision energy range from 20 to 80 meV. By controlling the discharge condition, we have made it possible to measure the collision energy dependence of partialionization cross sections (CEDPICS) for a wellstudied system of in a wide energy range from 20 to 350 meV. The anisotropic interaction potential energy surface for the present system was obtained starting from an ab initiomodel potential via an optimization procedure based on classical trajectory calculations for the observed CEDPICS. A dominant attractive well depth was found to be 423 meV (ca. ) at a distance of 3.20 Å from the center of mass of in the Natom side along the CCN axis. In addition, a weak attractive well (ca. ) surrounding the methyl group has been found and ascribed to the interaction between an unoccupied molecular orbital of and atomic orbital of .