Volume 118, Issue 12, 22 March 2003
 ARTICLES

 Theoretical Methods and Algorithms

A simple model for the calculation of nonlinear optical response functions and femtosecond timeresolved spectra
View Description Hide DescriptionA simple model is developed for the calculation of optical response functions for electronically nonadiabatic systems coupled to a heat bath. A phenomenological dissipation ansatz is suggested which describes the major bathinduced relaxation processes, namely excitedstate population decay, optical dephasing, and vibrational relaxation. The model is constructed in such a way that it allows one to express the nonlinear response functions for a dissipative system in terms of those for the corresponding bathfree system. The explicit formulas for the third order response functions are given. Several special cases are considered for which the evaluation of the response functions simplifies considerably. To illustrate the performance and validity of the theory, the response functions have been used for the calculation of time and frequency gated spontaneous emissionspectra. The timedependent spectra derived from the model have been compared with those calculated (i) for the standard damped harmonic oscillator model and (ii) for a model nonadiabaticelectrontransfer system with Redfield theory. It is concluded that the present model provides qualitatively correct response functions and, therefore, may be useful for the interpretation of observed timeresolvedspectra.

Timedependent discrete variable representation method in a tunneling problem
View Description Hide DescriptionWe have investigated the dynamics of a reaction coordinate with or without coupling to a heat bath of harmonic oscillators using a novel timedependent discrete variable representation (TDDVR) method. The proposed method is semiclassical in nature, theoretically rigorous, and rather straightforward to implement. Excellent agreement of the computed tunneling probabilities and timeaveraged tunneling rates with the corresponding exact results demonstrates the efficacy of the proposed approach. Most of the semiclassical calculations reported here have been performed by using classical force, whereas, in a few cases, the quantum force (QF) has been taken into account. It appears that among the TDDVR formulations, it was the first time we have derived a rigorous form of QF from the first principle.

Mixed quantumclassical dynamics response function approach to spectroscopy
View Description Hide DescriptionMixed quantumclassical dynamics formulation of Kapral and coworkers has been successfully employed to systems composed of a quantum subsystem coupled to an environment with classical degrees of freedom to study the dynamics of condensed manybody systems. In this formalism the quantum subsystem and the bath dynamics obey the full quantum mechanics,classical mechanics, respectively, whereas the coupling term dynamics is governed by mixed quantumclassical equations. To this end, the linear response function approach in mixed quantumclassical systems is used to derive the optical linear electronic dipole moment timecorrelation function of a twolevel system coupled to harmonic vibrations in condensed media. The fact that this is an exactly solvable model using full quantum mechanics allows us to test the applicability of the presented approach. An alternative approach to the aforementioned method is also developed as a second method to further test the applicability of the linear response function approach in mixed quantumclassical systems, and to confirm the correctness of the end result when using mixed quantumclassical dynamics formulation of Kapral and coworkers. Both approaches are found to yield identical results. These results are compared to those of the full quantum results in the high temperature limit. Model application of electronic absorption spectra is presented. Optical nonlinear response functions are also obtained in mixed quantumclassical systems with only linear electron–phonon coupling.

Correlation energy estimates in periodic extended systems using the localized natural bond orbital coupled cluster approach
View Description Hide DescriptionA new approach for the determination of correlation energies in periodic extended systems is proposed using the high transferability of amplitudes and integrals from natural bond orbital coupled cluster (NBO CC) calculations performed for small subunits. It is shown that the NBO CC calculations can in fact deliver detailed correlated wave function information for extended periodic systems. As an example we apply the ideas presented in this paper to determine an estimate for the valence correlation energy in diamond at the CCSD level.

Ab initio theoretical studies on and on the structure and spectroscopy of substitutional defects in manifold
View Description Hide DescriptionIn this paper we present the results of spin–orbit relativistic ab initiomodel potential embedded cluster calculations of the excited manifold of embedded in a reliable representation of the elpasolite host. They are aimed at interpreting the absorption bands reported by Karbowiak et al. [J. Chem. Phys. 108, 10181 (1998).] An excellent agreement is found between the calculated energies of the absorption transitions from the ground state and the experimental data, which supports a detailed interpretation of the electronic nature of the absorptionspectrum in the energy region 14 000–23 000 In particular, the three unidentified electronic origins that had been experimentally detected are now assigned, and the observed bands are interpreted as having multiple electronic origins. From the structural point of view, the excited states of the manifold are classified in two sets of main configuration and with bond distances The energies of the manifold of free have also been calculated; experimental data on them are not available in the literature to the best of our knowledge. These results contribute to show that wave function based ab initio methods can provide useful structural and spectroscopic information, complementary to the experimental data, in studies on actinide ion impurities doping ionic hosts, where large manifolds of excited states are involved.

Cell multipole method for molecular simulations in bulk and confined systems
View Description Hide DescriptionOne of the bottlenecks in molecular simulations is to treat large systems involving electrostatic interactions. Computational time in conventional molecular simulation methods scales with where N is the number of atoms. With the emergence of new simulations methodologies, such as the cell multipole method (CMM), and massively parallel supercomputers, simulations of 10million atoms or more have been performed. In this work, the optimal hierarchical cell level and the algorithm for Taylor expansion were recommended for fast and efficient molecular dynamics simulations of threedimensional (3D) systems. CMM was then extended to treat quasitwodimensional (2D) systems, which is very important for condensed matter physics problems. In addition, CMM was applied to grand canonical ensembleMonte Carlo simulations for both 3D and 2D systems. Under the optimal conditions, our results show that computational time is approximately linear with N for large systems, average error in total potential energy is about 0.05% for 3D and 0.32% for 2D systems, and the RMS force error is 0.27% for 3D and 0.43% for 2D systems when compared with the Ewald summation.

Construction of electronic diabatic states within a molecular orbital scheme
View Description Hide DescriptionA new procedure is proposed to construct a diabatic representation that is readily implemented in the molecular orbitalselfconsistent fieldconfiguration interaction scheme. It is based on the calculation of adiabatic wave functions at a reference geometry and of the appropriate modifications to be made to molecular orbitals for in order to force the derivative couplings for all electronic states to be exactly zero in the space around This approach is applied to the construction of the diabatic basis and to the calculation of the associated (adiabatic) vibronic coupling for a number of wellcharacterized systems. The properties and the limitations of this diabatic basis are discussed.

Quadratically convergent algorithm for fractional occupation numbers in density functional theory
View Description Hide DescriptionThe numerical solution of the electronic structure problem in Kohn–Sham density functional theory may in certain cases yield fractional occupancy of the singleparticle orbitals. In this paper, we propose a quadratically convergent approach for simultaneous optimization of orbitals and occupancies in systems with fractional occupation numbers (FONs). The starting guess for orbitals and FONs is obtained via the relaxed constraint algorithm. Numerical results are presented for benchmark cases.

Optimal Hamiltonian identification: The synthesis of quantum optimal control and quantum inversion
View Description Hide DescriptionWe introduce optimal identification (OI), a collaborative laboratory/computational algorithm for extracting quantum Hamiltonians from experimental data specifically sought to minimize the inversion error. OI incorporates the components of quantum control and inversion by combining ultrafast pulse shapingtechnology and high throughput experiments with global inversion techniques to actively identify quantum Hamiltonians from tailored observations. The OI concept rests on the general notion that optimal data can be measured under the influence of suitable controls to minimize uncertainty in the extracted Hamiltonian despite data limitations such as finite resolution and noise. As an illustration of the operating principles of OI, the transition dipole moments of a multilevel quantum Hamiltonian are extracted from simulated population transfer experiments. The OI algorithm revealed a simple optimal experiment that determined the Hamiltonian matrix elements to an accuracy two orders of magnitude better than obtained from inverting 500 random data sets. The optimal and nonlinear nature of the algorithm were shown to be capable of reliably identifying the Hamiltonian even when there were more variables than observations. Furthermore, the optimal experiment acted as a tailored filter to prevent the laboratory noise from significantly propagating into the extracted Hamiltonian.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dissociation of multiply ionized carbonyl sulfide due to electron impact
View Description Hide DescriptionThe dissociation of singly to triply ionized carbonyl sulfide has been studied through electron impact ionization at an electron energy of 200 eV. Two and threedimensional covariance mapping techniques are used, accompanied by a focusing timeofflightmass spectrometer. The absolute cross sections for the various dissociation channels of up to triply ionized carbonyl sulfide (OCS) have been obtained. The unstable OCS dications dissociate mostly into ion pairs, while the OCS trications dissociate into ion triple or ion pair with comparable probabilities. The total single ionization cross section agrees with the result of the binaryencounterBethe method. A metastable decay trace corresponding to is observed on the covariance map.

Preferential formation of neutral upon laser vaporized graphite in He gas as studied by photoionization mass spectroscopy with 10.5 eV photons
View Description Hide DescriptionNeutral carbon clusters produced from laserablated graphite in a supersonic pulsedhelium expansion source were studied by timeofflight (TOF) mass analysis using singlephoton ionization with 10.5 eV photons. Varying the delay time of an ionization laser pulse relative to a vaporization pulse, we found that a signal of along with a weaker signal of was intensified almost exclusively to the other signals with relatively long delay times of 80–250 μs. We observed two distinctly different TOFs for one and the same size, a short TOF at shorter delay times and a long TOF at longer delay times. We attribute the difference in TOF to the difference in initial velocity of the neutral cluster. We also performed the experiment within a high vacuum to find a similar difference in TOF for clusters of the same mass. The bimodal arrivaltime distribution from the source to the ionization region indicates that the bunch of laserablated clusters separates into two bunches with different group velocities. We attribute this separation to the formation of a relatively dense layer of clusters. During collisions behind this layer, the relatively stable neutral probably of a monocyclic structure, is formed preferentially. This must be the origin of the selective detection of at the longer delay times. Using He as a buffer gas, the signal of the was found to be of a magnitude two orders more pronounced than within the high vacuum.

Steric effect in the endothermic Penning ionization reaction of tertbutyl bromide with
View Description Hide DescriptionThe steric opacity function (the dependence of reaction cross section upon mutual molecular orientation) for the endothermic Penning ionization channel of reaction was determined by using an oriented tertbutyl bromide molecular beam at 0.1 eV average collision energy. A remarkably large steric effect was observed in contrast with the reaction. We find that the ionization cross section is maximum at sideways and it becomes “zero” at the tertbutyl end. The Br end is found to be unfavorable as compared with sideways approaches. The stereo selectivity observed in the present work is discussed in terms of the electron exchange mechanism, in which the shielding effect by bulky nonreactive tertbutyl group as well as the smearing effect in impact parameter are taken into account.

Excited state tautomerism of the DNA base guanine: A restricted openshell Kohn–Sham study
View Description Hide DescriptionThe relative stabilities of the six lowest energy tautomers of the DNA base guanine have been investigated in the first excited singlet state, employing the restricted openshell Kohn–Sham (ROKS) method. Comparison of the optimized geometries to the respective groundstate structures reveals large distortions for the keto tautomers, whereas the enol tautomers remain essentially planar. Harmonic vibrational spectra in the state have been calculated using the ROKS potential energy surfaces. Adiabatic excitation energies together with characteristic vibrational features of the individual guanine tautomers enable us to unambiguously assign recent experimental IRUV spectra. Velocity autocorrelation functions obtained from adiabatic excited state Car–Parrinello molecular dynamics simulations demonstrate that anharmonic effects only play a minor role.

Timeresolved kinetic studies on quenching of by alkanes and substituted methane molecules
View Description Hide DescriptionNCO radicals were produced by laser photolysis of at 266 nm followed by the reaction of CH with The radicals were then electronically excited from the ground electronic state to the state with a Nd:YAG laser pumped dye laser at 438.6 nm in the Q subband of The rate constants and thermally averaged cross sections for collision quenching of by and were measured at room temperature (298 K) by observing the timeresolved fluorescence signals of the excited NCO in a cell at total pressure of about 20 Torr. Formation cross sections of complexes of the electronically excited NCO radicals and quenchers were calculated by means of a collision complex model. It was shown that the quenching rates of by alkane molecules increase with the number of C–H bonds of the molecules, and that the attractive forces play a main role in the collisional quenching processes of by the quenchers studied in this work.

The singlet electronic excited states of the molecule
View Description Hide DescriptionBy using multireference single excitation configuration interaction calculations and multireference single and double excitation CI calculations, we consider the and excited states of the molecule which lie between 4.3 and 14.1 eV above the ground state. The basis set is composed of and contracted Gaussiantype functions, and covers molecular orbitals spanned by and Rydberg orbitals. Of the states, is sometimes disregarded, presumably because it is not directly observed by optical measurements, but is inferred from perturbations in the visible and ultraviolet spectra. We find that arises from the shallow local minimum in the lowest potential curve, which also has a stable minimum corresponding to the state designated The experimental excitation energies values) for are 12.81–12.87 eV according to electron energy loss spectroscopy, and our theoretical value is 13.06 eV. Agreement between the experiment and the calculation is quite close. The state has a mixed ionicRydberg character with an interesting Rydberg portion. The experimental and calculated values for are, respectively, 11.57 and 11.59 eV, suggesting that the present calculation for the state is reliable. Ambiguity found in experimental assignments of the vibrational levels for is settled here. The and states are also discussed.

Zeeman spectra of the transition of transglyoxal studied by Dopplerfree twophoton fluorescence excitation spectroscopy
View Description Hide DescriptionDopplerfree twophotonfluorescence excitation spectra of the transition of transglyoxal were measured by propagating a laser beam either polarized parallel (π pump) or perpendicular (σ pump) to the magnetic field of 6 T. π pump and σ pump dependence of the Zeemanspectra of the lines for was measured. Intensities of the Zeeman components of the lines were observed to have the maxima at the high and low wave number ends and the minimum at the middle for π pump, and the minima at the high and low wave number ends and the maximum at the middle for σ pump. By comparing calculated and observed patterns of the Zeemanspectra, it became clear that the transition tensor is dominant and the effective intermediate state is K dependence of the Zeemanspectra of the lines was measured, and the Zeeman splittings were observed to increase proportionally to J dependence of the Zeemanspectra of the lines was measured for and the Zeeman splittings was found to increase proportionally to J. The K and J dependence of the Zeeman splittings were analyzed. It is concluded that the Zeeman splitting of the state is originating from the mixing of the state by spin–orbit interaction, and the magnetic moment is along the molecular top axis.

Ab initio potential energy surface and rovibrational energies of and its isotopomers
View Description Hide DescriptionA new potential energy surface, based on high quality ab initio electronic structure calculations, is presented for the hydronium ion The new potential surface is used in rigorous calculations of vibrational energies of and Comparison with experiment shows significant improvement over our previous calculations using an earlier potential [X. Huang, S. C. Carter, and J. M. Bowman, J. Phys. Chem. B 106, 8182 (2002)]. Vibrational calculations are also presented with a new version of the code MULTIMODE. In this version the maximum number of coupled modes in the potential in any grouping of modes is increased from four (the previous maximum) to five. The importance of fivemode terms in the potential is demonstrated for several vibrational states in and Also, in the new version of MULTIMODE the number of coupled modes in the Coriolis term can be varied independently from the number of coupled modes in the potential. Rovibrational calculations for are also presented for and and compared with experiment for

Variable reaction coordinate transition state theory: Analytic results and application to the reaction
View Description Hide DescriptionA novel derivation is provided for the canonical, microcanonical, and energy and total angular momentum resolved reactive flux within the variable reaction coordinate transition state theory (VRCTST) formalism. The use of an alternative representation for the reaction coordinate velocity yields a new expression for the kinematic factor which better illustrates its dependence on the pivot point location, and which can be straightforwardly evaluated. Also, the use of a geometric approach in place of an earlier algebraic one clarifies the derivation as does the use of Lagrange multiplier methodology for the analytic integration over the total angular momentum. Finally, a quaternion representation for the fragment and lineofcenters orientations is employed in place of the Euler angle or internal/external rotational coordinates used in prior studies. The result is an efficient, and particularly easy to implement, methodology for performing variable reaction coordinate transition state theory calculations. Furthermore, the simplicity of the derivation allows for the straightforward generalization to alternative forms for the dividing surface, as is illustrated by deriving the expressions for the cases of elliptical and planar dividing surfaces. Application to the reaction yields results for the total rate coefficient that are generally only 15% greater than those obtained from related trajectory simulations, thereby demonstrating the accuracy of the VRCTST formalism. Meanwhile, results for the two separate addition channels (frontside and backside) illustrate the difficulty of accurately apportioning the total flux and particularly the inadequacy of canonical predictions for the channel specific optimized dividing surfaces.

Photodissociation of Excited electronic states of and 2 and intracluster electron transfer for and 4
View Description Hide DescriptionPhotodissociationspectra of massselected cluster ions were investigated in the wavelength region from 415 to 225 nm and 495 to 225 nm for and 2, respectively, by monitoring the total yield of fragment ions. The absorption bands exhibit large shifts from the resonance line of In the spectrum of there are two bands at 26 400 and On the other hand, three absorption bands at 22 600, 28 800, and appear in the spectrum of The most stable structures in the ground state for and 2 were obtained by calculations, and transition energies from these structures were obtained by using configuration interaction singles approach with the same basis set. The calculated excitation energies show good agreement with the experimental results. In addition, fragment ions of with and 5 are found to have high intensities from the parent ions of at a dissociation wavelength of 355 nm. From the result of theoretical calculations for and 4, a valence electron of is found to transfer to the solvating acrylonitrile molecules in these sizes, although this process does not cause an anionic polymerization reaction that observed in alkali metal atomacrylonitrile neutral clusters.

Small angle neutron scattering from nanodroplets and binary nucleation rates in a supersonic nozzle
View Description Hide DescriptionSmall angle neutron scattering (SANS) experiments were used to characterize binary nanodroplets composed of and The droplets were formed by expanding dilute mixtures of condensible vapor in a carrier gas through a supersonic nozzle, while maintaining the onset of condensation at a fixed position in the nozzle. It is remarkable, given the small coherent scattering length density of light water, that even the pure aerosol gave a scattering signal above background. The scatteringspectra were analyzed assuming a lognormal distribution of droplets. On average, the geometric radius of the nanodroplets was (±1) nm, the polydispersity was (±0.07), and the number densityN was The aerosol volume fractions derived from the SANS measurements are consistent with those derived from the pressure trace experiments, suggesting that the composition of the droplets was close to that of the initial condensible mixture. A quantitative analysis of the scatteringspectra as a function of the isotopic composition gave further evidence that the binary droplets exhibit ideal mixing behavior. Because both the stagnation temperature and the location of onset were fixed, the temperature corresponding to the maximum nucleation rate was constant at (±1) K. Thus, the experiments let us estimate the isothermal peak nucleation rates as a function of the isotopic composition. The nucleation rates were found to be essentially constant with equal to at a mean supersaturation of 44 (±3).