Volume 119, Issue 2, 08 July 2003
 ARTICLES

 Theoretical Methods and Algorithms

Normalmode analysis without the Hessian: A driven moleculardynamics approach
View Description Hide DescriptionWe point out that normal modes and frequencies of molecules and molecular complexes can be obtained directly from a harmonically driven molecular dynamics calculation. We illustrate this approach for HOD and and then discuss its potential advantages over the standard Hessianbased approach for large molecules.

Molecular gradients for the secondorder generalized Van Vleck variant of multireference perturbation theory
View Description Hide DescriptionRecently, a revised secondorder generalized Van Vleck perturbation theory (GVVPT2) for the description of molecular electronic structure has been reported [J. Chem. Phys. 117, 4133 (2002)] that is both state selective and of the “perturbthendiagonalize” type of multireference perturbation theory (MRPT). Herein, formulas for analytic derivatives of the GVVPT2 energy with respect to nuclear perturbations are presented, as are illustrative calculations on model problems. Specifically, it is shown that the modification of the energy denominator, which addresses the socalled intruderstate problem of MRPT, is analytically differentiable with respect to nuclear perturbation and only requires use of matrices available, or directly obtainable, from the underlying multiconfigurational selfconsistent field calculation. The developed formalism takes full advantage of the theoretical and computational characteristics of the GVVPT2 energy. In particular, the calculations are performed directly in a spinadapted basis and utilize the recently introduced concept of macroconfigurations. Moreover, the full flexibility of the energy calculations with respect to arbitrariness of reference—i.e., no restriction to complete active space selfconsistent field—is retained. Test calculations on and comparing the analytic derivatives with the results of finitedifference calculations corroborate the formulas and implementation.

NonMarkovian effects on quantum optimal control of dissipative wave packet dynamics
View Description Hide DescriptionOptimal control within the density matrix formalism is applied to the creation of a specified superposition state in condensed phases. The primary system modeled by a displaced harmonic oscillator is surrounded by a boson heat bath, the dynamics of which is described by a nonMarkovian master equation. A newly developed monotonically convergent algorithm is used to solve the pulse design equations. The control mechanisms are strongly dependent on the bath correlation time that is characterized by the inverse of an exponential decay constant, If the correlation time is shorter than the temporal width of a typical subpulse involved in an optimal pulse, the solution is reduced to that in the Markovian case. If we assume a longer correlation time, by weighing less physical significance on the penalty due to pulse fluence, an optimal pulse with high intensity is obtained, the temporal width of which approaches We also see considerable changes in the shape of the optimal pulse with increasing intensity, suggesting that strong fields open up control mechanisms that are qualitatively different from those in weak fields.

Combined electronic and nuclear dynamics in a simple model system
View Description Hide DescriptionWe investigate the combined electronic and nuclear motion in a simple model system as proposed by Shin and Metiu [J. Chem. Phys. 102, 9285 (1995)]. A variation of the electron–nuclei interaction energy allows us to study the transition from an adiabatically uncoupled situation to the case where the adiabatic approximation breaks down. Wavepacket calculations illustrate the dynamical changes of electronic and nuclear probability densities for the case of an adiabatic motion and during a nonadiabatic transition. The influence of the coupling on the transport of electron density between different nuclei is characterized with the help of timedependent Laplacians.

Quantum phasespace function formulation of reactive flux theory
View Description Hide DescriptionOn the basis of a coherentstate representation of the quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee et al., Phys. Rev. E 65, 021109 (2002); 66, 051105 (2002)]. We extend this approach to formulate reactive flux theory in terms of quantum phase space distribution functions and to derive a timedependent quantum transmission coefficient—a quantum analog of the classical Kramers–Grote–Hynes coefficient in the spirit of Kohen and Tannor’s classical formulation. The theory is valid for arbitrary noise correlation and temperature. The specific forms of this coefficient in the Markovian as well as in the nonMarkovian limits have been worked out in detail for the intermediate to strong damping regimes with an analysis of quantum effects. While the classical transmission coefficient is independent of temperature, its quantum counterpart has significant temperature dependence particularly in the lowtemperature regime.

Accurate adiabatic connection curve beyond the physical interaction strength
View Description Hide DescriptionIn order to better approximate and understand the exchangecorrelation functional in density functional theory, the adiabatic connection curve is accurately calculated beyond the physical interaction strength using a simulated scaling method. This is done for Hooke’s atom, two interacting electrons in a harmonic well potential. Extrapolation of the accurate curve to the infinitecoupling limit agrees well with the strictly correlated electron hypothesis. The interaction strength interpolation is shown to be a good, but not perfect, fit to the adiabatic curve. Arguments about the locality of functionals and convexity of the adiabatic connection curve are examined in this regime.

Relativistically corrected nuclear magnetic resonance chemical shifts calculated with the normalized elimination of the small component using an effective potentialNMR chemical shifts of molybdenum and tungsten
View Description Hide DescriptionA new method for relativistically corrected nuclear magnetic resonance(NMR)chemical shifts is developed by combining the individual gauge for the localized orbital approach for density functional theory with the normalized elimination of a small component using an effective potential. The new method is used for the calculation of the NMRchemical shifts of and in various molybdenum and tungsten compounds. It is shown that quasirelativistic corrections lead to an average improvement of calculated NMRchemical shift values by 300 and 120 ppm in the case of and respectively, which is mainly due to improvements in the paramagnetic contributions. The relationship between electronic structure of a molecule and the relativistic paramagnetic corrections is discussed. Relativistic effects for the diamagnetic part of the magnetic shielding caused by a relativistic contraction of the orbitals in the core region concern only the shielding values, however, have little consequence for the shift values because of the large independence from electronic structure and a cancellation of these effects in the shift values. It is shown that the relativistic corrections can be improved by level shift operators and a B3LYP hybrid functional, for which Hartree–Fock exchange is reduced to 15%.

A new efficient approach to the direct restricted active space selfconsistent field method
View Description Hide DescriptionWe present an implicitly parallel method for integralblock driven restricted active space selfconsistent field (RASSCF) algorithms. Our algorithm entirely avoids testing the index space for nonzero contributions to the CI vector, by finding entire blocks of contributions through use of simple algebraic rules (propagation rules). The blocks themselves are efficiently identified by introducing a RAS model space. Our algorithm is capable of making efficient use of modern supercomputer hardware, supporting both shared and distributed memory architectures and hybrids. Applicability of our method is demonstrated with a RASSCF investigation of the first two excited states of indole.

Computational method for calculating multidimensional Franck–Condon factors: Based on Sharp–Rosenstock’s method
View Description Hide DescriptionNormal mode coordinates of vibrational states associated with one electronic state are generally different from those of vibrational states associated with other electronic states in polyatomic molecules (normal coordinate mixing). This has prevented the multidimensional Franck–Condon integrals from being widely used in spite of their importance. We introduce a simple, noncumbersome numerical computer method for calculating those integrals despite including a mixing of the normal coordinates in the harmonic oscillator approximation on the basis of the expressions by Sharp and Rosenstock. We also introduce more simple expressions of Sharp–Rosenstock’s formulas.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Theoretical study of the lowlying excited singlet states of furan
View Description Hide DescriptionThe lowest two Rydberg and two valence excited singlet states of furan [referred to as and respectively, at the groundstatemolecular configuration] have been studied using the equationofmotion coupledcluster singles and doubles method (EOMCCSD). Full geometry optimizations with subsequent computation of harmonic vibrational frequencies have been performed in order to locate and characterize stationary points on the potential energy surfaces (PES). The latter optimization work was enabled by the availability of analytic energy gradient techniques for the EOMCCSD approach. A major new finding is that both the and valence states are unstable with respect to nontotally symmetric distortions at the configuration. The symmetry breaking in the state involves an inplane coordinate of symmetry. The relaxation process begins on the adiabatic PES and, after passing through a conical intersection of the and PES, continues on the surface, taking the system finally to the adiabatic minimum of state). The valence state is found to be unstable with respect to the outofplane bending coordinates of and symmetry. The resulting relaxed molecular structures have and symmetry, respectively. The present findings are analyzed in terms of a linear vibronic coupling model and spectroscopic implications are discussed.

Cluster dynamics in the range High resolution infrared spectra of
View Description Hide DescriptionInfrared spectra of complexes with N up to about 20 have been observed in the 2145 cm^{−1} region of the C–O stretch vibration using a tunable diode laserspectrometer to probe pulsed supersonic expansions from moderately high pressure (⩽40 atm) cooled (>−150 °C) jet sources. Cooler (⩽0.2 K) or warmer (⩽0.5 K) effective rotational temperatures were obtained using pinhole or slit jet nozzles, respectively. Two series of transitions were observed, each correlating smoothly with the known atype and btype lines of the binary complex, He–CO. Although the btype series starts off about 7 times stronger for it was observed to lose intensity to the a series with increasing Nvalue. The numbering of cluster size was reliably established up to for the atype and for the btype series. Some warmer lines due to higher Jvalue transitions [e.g., were observed and tentatively assigned, but these were not sufficient to enable rotational analysis. Thus it has not yet been possible to separate the effects of vibrational shifts and rotational dynamics on the line positions. Two critical regions were observed in the cluster size evolution around and 15, and these may be related to the theoretically calculated maximum and minimum, respectively, in the incremental binding energy per helium atom.

Molecular simulation study of nanoscale friction between alkyl monolayers on Si(111) immersed in solvents
View Description Hide DescriptionNonequilibrium molecular dynamics simulations were performed to study nanoscale friction between two Si(111) surfaces covered with alkyl monolayers immersed in liquid solvents. Three pairs of interfaces, ranging from hydrophobic to hydrophilic OH/OH, were studied. Three solvents, including water, methanol, and decane were used to represent different solvent polarities. It was showed that friction was dependent not only on surfacehydrophobicity, but also on solvent polarity. In polar solvents (e.g., water), friction is much larger for hydrophilic than hydrophobic interfaces, while in nonpolar solvents, e.g., decane, friction has no significant difference for both hydrophobic and hydrophilicmonolayers. A fundamental understanding of friction at different interfaces in various solvents is very important to micro or nanoelectromechanical systems (MEMS/NEMS), particularly, bioMEMS/NEMS.

Velocitymap imaging study of the product channel following 193 nm photolysis of
View Description Hide DescriptionVelocitymap imaging has been used to characterize the velocity and angular momentum alignment distributions of the products of photolysis at 193 nm. The measuredvelocity and spatial anisotropy distributions indicate that around 60% of the available energy appears in product translation, with the remainder being released into internal excitation of the cofragment. The measured alignment parameters have been interpreted in terms of an instantaneous dissociation model, which suggests preferential population of states and an electron density distribution peaking perpendicular to the direction of the breaking bond. This is consistent with dissociation on a surface of symmetry, the most likely candidate correlating with ground state products being the asymptotic surface. There are several possible routes to this surface, and these are considered in light of the measuredvelocity distributions and velocitydependent spatial anisotropy parameters of the products relative to the dominant dissociation channel.

Theoretical studies of photoelectron spectra of clusters and the extrapolation to bulk solution
View Description Hide DescriptionPhotoelectron spectra of hydrated doubly charged anion clusters, have been studied by performing firstprinciples electronic structure calculations on 12, and 13). The calculated adiabatic electron ionization energies are in good agreement with available experimental data. A detailed analysis of the calculated results suggests that for the observed threshold ionization energy of the low binding energy band in the recently reported photoelectron spectra of is associated with the electron ionization from the solute, whereas the observed threshold ionization energy of the high binding energy band is associated with the electron ionization from the water molecules in the first solvation shell of For both threshold ionization energies of the low and high binding energy bands are all associated with the electron ionizations from the solute. This shows that the bulk solution value extrapolated from those threshold ionization energies of the high binding energy band of the clusters should refer to the first ionization energy of the water molecules in the first solvation shell of in aqueous solution and, therefore, should be significantly smaller than the measured threshold ionization energy of liquid water. This differs from the recent result that the value of 10.05 eV extrapolated from the threshold ionization energies of the high binding energy band based on a simple model was nearly identical to the measured threshold ionization energy (10.06 eV) of liquid water. To address this difference, we have used a new approach for the extrapolation of solvated ion cluster data to bulk solution. We show that the new extrapolation approach consistently produces extrapolated bulk solution results in significantly better agreement with those observed directly in bulk solution for the first ionization energies of the ions in and The same extrapolation approach predicts a bulk solution value of 7.20 eV extrapolated from the threshold ionization energies of the high binding energy band, consistent with our assignment of the high binding energy band.

Accurate dipole polarizabilities of small silicon clusters from ab initio and density functional theory calculations
View Description Hide DescriptionWe report conventional ab initio and density functional theory calculations for the static dipole polarizability for the small silicon clusters to Our effort relies on the design of flexible basis sets of Gaussiantype functions. The dependence of the calculated mean polarizability per atom on basis set type and level of theory is brought forth and discussed. The effect of electron correlation is found to be small for all studied clusters. The density functional theory based methods are seen to predict reliable values for By introducing and analyzing the differential mean polarizability per atom, we show that in fact ab initio and density functional theory calculations yield distinctly different pictures of the polarizability of small silicon clusters. Computational strategies are proposed for the extension of theoretical studies to larger structures.

Relativistic and correlated calculations on the ground and excited states of ThO
View Description Hide DescriptionWe report on the performance of the thirdorder Douglas–Kroll ab initiomodel potential (DK3AIMP) methodbased electroncorrelated spin–orbit calculations. Our treatment assumes that the problem can be separated into a spin–free correlation treatment and a spin–orbit calculation. The correlation effects were calculated using the multistate complete active space secondorder perturbation method, and the spin–orbit effects were treated by means of the restricted active space state interaction spin–orbit method, where the spin–orbit effects were approximated by the Douglas–Kroll type of atomic meanfield spin–orbit method. We used our method for illustrative calculations on the ground and lowlying electronic states of thorium monoxide. For a proper description of the inner core region in the spin–orbit calculations, an auxiliary spin–orbit basis set was introduced. The DK3AIMPbased electroncorrelated spin–orbit calculations on ThO yield good agreement with corresponding allelectron results and with the available experimental data. This confirms that the DK3AIMP method can be easily combined with highly accurate correlation treatments and relativistic effects, both of which are vital for studying the actinides. To our knowledge, the literature contains no references to AIMP calculations on the lowlying states of ThO.

Shape dependent small cluster kinetics in the twodimensional Ising model beyond the classical approximations
View Description Hide DescriptionThe kinetics of small clusters of “up” spins in the twodimensional Ising model on a square lattice is examined without the usual approximations of fixed cluster shape, constant number of “down” spins and nonsplitting–noncoagulating dynamics. New kinetic equations for the number densities of clusters of various sizes and shapes are derived and solved numerically. It is shown that the kinetic behavior of small clusters depends on their shape and that the timedependence of the total number of down spins and the splitting and coagulation of clusters significantly affect various characteristics of the system, e.g., the range of validity of the steadystate approximation, the transient time to that state, the values of mass fluxes, etc. The influence of these factors grows with increasing temperature and supersaturation.

Gas phase electronic spectra of the linear carbon chains
View Description Hide DescriptionThe transitions of and have been measured in the gas phase, exhibiting broad, Lorentzian shaped bands. More extensive spectra have been observed for than before with many new vibronic bands identified. The spectra were obtained by means of a mass selective resonant twocolor twophotonionization technique coupled to a supersonic plasma source. The electronic structures of this series of molecules in both the ground and excited states have been investigated using DFT, MP2, and stateaveraged CASSCF theories. The three lowest dipole allowed electronic transition systems are and located, for the smaller members of the series, in the visible, UV and VUV range, respectively. The system is found to be of medium intensity and the transition is predicted to be very strong. This is a result of configuration mixing in the excited states. The oscillator strength of the lowest energy transition is not strongly dependent on the length of the chain, but that of the system increases monotonically with size. The state is Rydberg in character. The astrophysical implications are considered and an upper limit of the column densities of these carbon chains in diffuse clouds has been estimated as based on calculated oscillator strengths.

Production of electronically excited CH via the vacuum ultraviolet photodissociation of ethylene and the possible role of the ethylidene isomer
View Description Hide DescriptionThe visible fluorescence of CH fragments and transitions) formed in the vacuum ultraviolet photodissociation of ethylene in the 11.7–21.4 eV energy region, was recorded. Two formation thresholds for each excited fragment, (A) or (B), were identified and associated with two dissociation channels namely and Unlike previous studies of the dissociationdynamics on the groundstatepotential energy surface, neither of these channels exhibit an energy barrier within the experimental uncertainty, even in the latter case of molecular elimination. It is proposed that both channels pass via an ethylidene intermediate an isomer never previously experimentally detected and whose existence has been debated in theoretical publications. The observed behavior, at the excitation energies used in the present work, also suggests that fast isomerization and internal conversion to excited states of ethylene precede fragmentation. Above 18.5 eV, that is around the ionization limit dissociativeionization starts to compete with neutral dissociation into excited CH fragments giving rise to a substantial decrease in the neutral fragment signal.

Photodissociation dynamics of propene at 157.6 nm: Kinetic energy distributions and branching ratios
View Description Hide DescriptionPhotodissociationdynamics of propene at 157.6 nm has been investigated in a molecular beam apparatus using the photofragment translational spectroscopic technique combined with the vacuum ultraviolet ionization method. Eleven photofragments have been successfully detected and ascribed to eight (five binary and three triple) dissociation channels: namely, and Their branching ratios have been determined to be 1%, 7%, <0.2%, 17%, 6%, 4%, 5%, and 60%, respectively. The complicated multichannel dissociation process has a propensity towards triple dissociations, notably the channel. In addition, the averaged kinetic energy releases and the fractions in translational energy have also been determined from the measured kinetic energy distributions. For the binary dissociation channels, the fractions in translational energy are less than 18% except the channel, whereas they are more than 42% for the triple dissociation channels. An intriguing finding indicates that the channel has a nearly identical kinetic energy distribution and a similar branching ratio to the channel, although the former undergoes a threecenter elimination process different from the C–C bond rupture occurring in the latter.