Volume 125, Issue 3, 21 July 2006
 COMMUNICATIONS


Resolving the emission times of solute and solvent fourwave mixing signals by spectral interferometry
View Description Hide DescriptionElectric fieldresolved transient grating measurements are used to distinguish the fourwave mixing signal emission from a resonant solute and a nonresonant solvent. The two components of the solution (i.e., solute and solvent) emit signal fields at different times with respect to the arrival of the probe pulse to the sample. This gives rise to a recurrence in the temporal profile of the total signal field. We show that the origin of this interference is the difference in relaxation time scales of the holographic gratings associated with the solute and solvent. The grating of the resonant solute relaxes on the time scale of a few picoseconds due to depopulation of its excited electronic state, whereas the electronic polarizability response of the solvent relaxes on the femtosecond time scale. This separability of responses is a general phenomenon that is particularly useful for studying weakly absorbing solute dynamics in polarizable solvents.
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 ARTICLES

 Theoretical Methods and Algorithms

The stress tensor of a molecular system: An exercise in statistical mechanics
View Description Hide DescriptionWe prove that conservation of the stress tensor is a consequence of the invariance of the partition function under canonical diffeomorphisms. From this observation a simple and general derivation of the formula which gives the local expression of the stress tensor of a molecular system in terms of its microscopic degrees of freedom readily follows. The derivation is valid in the canonical as well as the microcanonical ensemble. It works both in the classical and in the quantum mechanical settings and for arbitrary boundary conditions. In particular, if periodic boundary conditions are assigned to the system, the usual minimalimage prescription is naturally born out for mathematical consistency. An interesting outcome of our general analysis is that only in the case of a shortrange interaction potential a truly local formula for the stress tensor can exist.

Calculation of originindependent optical rotation tensor components in approximate timedependent density functional theory
View Description Hide DescriptionWe outline an implementation of the originindependent optical rotationtensor, which includes electric dipolemagnetic dipole and electric dipoleelectric quadrupolepolarizability. The method is based on approximate timedependent density functional theory. We utilize timeperiodic magneticfielddependent basis functions as well as a modified velocitygauge formulation of dynamic polarizabilitytensors in order to obtain a gaugeorigin independence. To ensure gaugeorigin independence of the results within a given numerical accuracy, density fit coefficient derivatives are employed. A damping constant has been introduced into the linear response equations to treat both resonance and nonresonance regions of optical activity. We present calculations for trans2,3dimethyloxirane and derivatives thereof as well as calculations for androst4,17dien3one. In the Appendix, we derive the equivalence between the commongauge origin and gaugeincluding atomic orbitals formulations for the optical rotationtensor in timedependent DFT.

Fundamental importance of the Coulomb hole sum rule to the understanding of the ColleSalvetti wave function functional
View Description Hide DescriptionIn this paper we consider the general form of the correlateddeterminantal wave function functional of Colle and Salvetti (CS) for the He atom. The specific form employed by CS is the basis for the widely used CS correlation energy formula and the LeeYangParr correlation energy density functional of KohnSham density functional theory. We show the following: (i) The key assumption of CS for the determination of this wave function functional, viz., that the resulting singleparticle density matrix and the HartreeFock theoryDirac density matrix are the same, is equivalent to the satisfaction of the Coulomb hole sum rule for each electron position. The specific wave function functional derived by CS does not satisfy this sum rule for any electron position. (ii) Application of the theorem on the onetoone correspondence between the Coulomb hole sum rule for each electron position and the constraint of normalization for approximate wave functions then proves that the wave function derived by CS violates charge conservation. (iii) Finally, employing the general form of the CS wave function functional, the exact satisfaction of the Coulomb hole sum rule at each electron position then leads to a wave function that is normalized. The structure of the resulting approximate Coulomb holes is reasonably accurate, reproducing both the short and the longrange behavior of the hole for this atom. Thus, the satisfaction of the Coulomb hole sum rule by an approximate wave function is a necessary condition for constructing wave functions in which electronelectron repulsion is represented reasonably accurately.

Reversible measurepreserving integrators for nonHamiltonian systems
View Description Hide DescriptionWe present a systematic method for deriving reversible measurepreserving integrators for nonHamiltonian systems such as the NoséHoover thermostat and generalized Gaussian moment thermostat (GGMT). Our approach exploits the (nonPoisson) bracket structure underlying the thermostat equations of motion. Numerical implementation for the GGMT system shows that our algorithm accurately conserves the thermostat energy function. We also study position and momentum distribution functions obtained using our integrator.

Including quantum subsystem character within classical equilibrium simulations
View Description Hide DescriptionA mixed quantum/classical density matrix approximation is derived. The density matrix makes use of quantum subsystem vibrational wave functions. The diagonal of the density matrix can be used as an equilibrium distribution in Monte Carlo simulations. The approximate distribution compares well with the path integral distribution for a model system. Since it includes quantum subsystem information, it performs much better than the quadratic FeynmanHibbs distribution. These types of distributions can aid in including quantum vibrational information in otherwise classical simulations.

A new ligand field approach to linear transition metal dihalides
View Description Hide DescriptionWe have performed theoretical multiconfigurational calculations of the molecular energy levels based on two axial ligand fieldmodels and determined the model parameters to reproduce ab initio energies of , , , and . We develop two extensions to ligand fieldtheory (LFT) for linear transition metal dihalides, which are incorrectly described by standard LFT. The standard LFT is augmented (1) by including the ligand induced hybridization of the orbital with the orbital or (2) by using a different radial part for the orbital. Both models reproduce the energies of the first electronic states in very good agreement with numerical multireference configuration interaction results. Furthermore the model parameters are very close to experimental known Racah parameters describing the term energies of and .
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dynamics of radiation induced isomerization for HCN–CNH
View Description Hide DescriptionWe have analyzed the dynamics underlying the use of sequential radiation pulses to control the isomerization between the HCN and the CNH molecules. The appearance of avoided crossings among Floquet eigenphases as the molecule interacts with the radiation pulses is the key to understanding the isomerizationdynamics, both in the adiabatic and nonadiabatic regimes. We find that small detunings of the incident pulses can have a significant effect on the outcome of the isomerization process for the model we consider.

Infrared spectroscopy of clusters for
View Description Hide DescriptionInfrared spectra of clusters as a function of size are reported for the first time. Spectra have been recorded in the N–H stretching region for using a massselective photodissociation technique. For the cluster, three distinct IR absorption bands are seen over a relatively narrow region, whereas the larger clusters yield additional features at higher frequencies. Ab initio calculations have been carried out in support of these experiments for the specific cases of and 5 for various isomers of these clusters. The bands observed in the spectrum for can all be attributed to N–H stretching vibrations from solvent molecules in the first solvation shell. The appearance of higher frequency N–H stretching bands for is assigned to the presence of ammonia molecules located in a second solvent shell. These data provide strong support for previous suggestions, based on gas phase photoionization measurements, that the first solvation shell for is complete at . They are also consistent with neutron diffraction studies of concentrated lithium/liquid ammonia solutions, where is found to be the basic structural motif.

Unimolecular processes in below the dissociation barrier: O–H stretch overtone excitation and dissociation
View Description Hide DescriptionThe OHstretch overtone spectroscopy and dynamics of the hydroxymethyl radical, , are reported in the region of the second and third overtones, which is above the thermochemical threshold to dissociation to . The second overtone spectrum at is obtained by double resonance IRUV resonance enhanced multiphoton ionization (REMPI) spectroscopy via the electronic state. It is rotationally resolved with a linewidth of and displays properties of localmode vibration. No dissociation products are observed. The third overtone spectra of and are observed at by monitoring Hatom photofragments while scanning the excitation laser frequency. No double resonance REMPI spectrum is detected, and no D fragments are produced. The spectra of both isotope analogs can be simulated with a linewidth of , indicating dissociation via tunneling. By treating the tunneling as one dimensional and using the calculated imaginary frequency, the barrier to dissociation is estimated at about , in good agreement with theoretical estimations. The BirgeSponer plot is linear for OHstretch vibrations , demonstrating behavior of a onedimensional Morse oscillator. The anharmonicity parameter derived from the plot is similar to the values obtained for other small OH containing molecules. Isomerization to methoxy does not contribute to the predissociation signal and the mechanism appears to be direct O–H fission via tunneling. presents a unique example in which the reaction coordinate is excited directly and leads to predissociation via tunneling while preserving the localmode character of the stretch vibration.

Energy pooling in multiple ionization and Coulomb explosion of clusters by nanosecondlong, megawatt laser pulses
View Description Hide DescriptionWe report the results of experiments that establish the possibility of bringing about multiple ionization and Coulomb explosion of molecular clusters with nanosecond laser pulses at intensities as small as . We demonstrate several new facets of the lasercluster interaction in the lowintensity, longpulse domain: (i) The choice of laser wavelength for a given cluster species is very crucial. (ii) Excited electronic states play a very important role in the ionization dynamics. (iii) When field ionization is insignificant and ponderomotive energies are very small, it is energy pooling rather than inverse bremsstrahlung that determines how clusters absorb energy from the optical field.

Anharmonic vibrational levels of the two cyclic isomers of
View Description Hide DescriptionUsing coupledcluster approach full sixdimensional analytic potential energy surfaces for two cyclic isomers [C–C transannular bond (I) and Si–C transannular bond (II)] have been generated and used to calculate anharmonic vibrational wave functions. Several strong lowlying anharmonic resonances have been found. In both isomers already some of the fundamental transitions cannot be described within the harmonic approximation. Adiabatic electron affinities and ionization energies have been calculated as well. The FranckCondon factors for the photodetachment processes and are reported.

H(D)atom yields in the quenching of by methane, ethane, ethene, ethyne, and their deuterated isotopologues
View Description Hide DescriptionThe yields for the production of H(D) atoms in the reactions of with simple hydrocarbons and their deuterated variants were determined. was produced by twophoton laser excitation of followed by concomitant amplified spontaneous emission. H(D) atoms are detected using a vacuumultraviolet laserinduced fluorescence(LIF) technique. The H(D)atom yields were evaluated from the LIF intensities and the overall rate constants for the quenching, which were determined from the temporal profile measurements of the resonance fluorescence from . isotope effects were observed not only in the overall rate constants but also in the H(D)atom yields. The yields for , , and were determined to be 0.89, 1.43, 1.03, respectively, while those for , , and were found to be smaller; 0.63, 0.86, and 0.79, respectively. The yield ratio for was 1.76. The presence of the isotope effects both in the rate constants and the yields suggests that electronictoelectronic energy transfer processes and abstractive processes are competing.

Laser control of reactions of photoswitching functional molecules
View Description Hide DescriptionLaser control schemes of reactions of photoswitching functional molecules are proposed based on the quantum mechanical wavepacket dynamics and the design of laser parameters. The appropriately designed quadratically chirped laser pulses can achieve nearly complete transitions of wave packet among electronic states. The laser parameters can be optimized by using the ZhuNakamura theory of nonadiabatictransition. This method is effective not only for the initial photoexcitation process but also for the pump and dump scheme in the middle of the overall photoswitching process. The effects of momentum of the wave packet crossing a conical intersection on the branching ratio of products have also been clarified. These control schemes mentioned above are successfully applied to the cyclohexadiene/hexatriene photoisomerization (ringopening) process which is the reaction center of practical photoswitching molecules such as diarylethenes. The overall efficiency of the ring opening can be appreciably increased by using the appropriately designed laser pulses compared to that of the natural photoisomerization without any control schemes.

Fluorescence and ultraviolet absorption spectra and structure of coumaran and its ringpuckering potential energy function in the excited state
View Description Hide DescriptionThe fluorescence excitation (jet cooled), single vibrational level fluorescence, and the ultraviolet absorption spectra of coumaran associated with its electronic excited state have been recorded and analyzed. The assignment of more than 70 transitions has allowed a detailed energy map of both the and states of the ringpuckering vibration to be determined in the excited states of nine other vibrations, including the ringflapping and ringtwisting vibrations. Despite some interaction with and , a onedimensional potential energy function for the ring puckering very nicely predicts the experimentally determined energy level spacings. In the state coumaran is quasiplanar with a barrier to planarity of and with energy minima at puckering angles of . The corresponding ground state values are and . As is the case with the related molecules indan, phthalan, and 1,3benzodioxole, the angle strain in the fivemembered ring increases upon the transition within the benzene ring and this increases the rigidity of the attached ring. Theoretical calculations predict the expected increases of the carboncarbon bond lengths of the benzene ring in , and they predict a barrier of for this state. The bond length increases at the bridgehead carboncarbon bond upon electron excitation to the state give rise to angle changes which result in greater angle strain and a nearly planar molecule.

Ionization spectra and electronic decay in small iodide clusters: Fully relativistic results
View Description Hide DescriptionSingly ionized systems in highlying energetic final states can stabilize themselves via various electronic decay mechanisms. With increasing system size interatomic and intermolecular processes dominate over intraatomic (Auger) decay channels. For the small and clusters fully relativistic ionizationspectra are calculated and the subsequent electronic decay of the cations is investigated. Due to the presence of the iodine atom a fully relativistic description is mandatory and was performed by the algebraic diagrammatic construction technique in its fourcomponent form. The lifetimes of the singly ionized final states are estimated by the application of WeisskopfWigner [Z. Phys.63, 54 (1930)] theory.

Intermediate state polarization in multiphoton ionization of HCl
View Description Hide DescriptionThe paper presents the detailed theoretical description of the intermediate state polarization and photofragment angular distribution in resonance enhanced multiphoton ionization (REMPI) of molecules and the experimental investigation of these effects in the and states of HCl populated by twophoton transitions. It is shown that the intermediate state polarization can be characterized by the universal parameter which is in general a complex number containing information about the symmetry of the twophoton excitation and possible phase shifts. The photofragment angular distribution produced by one or multiphoton excitation of the polarized intermediate state is presented as a product of the intermediate state axis spatial distribution and the angular distribution of the photofragments from an unpolarized intermediate state. Experiments have been carried out by two complementary methods: REMPI absorption spectroscopy of rotationally resolved and transitions and REMPI via the and rotational transitions followed by threedimensional ion imaging detection. The values of the parameter determined from experiment manifest the mostly perpendicular nature of the initial twophoton transition. The experimentally obtained ion fragment angular distributions produced via the rotational transition show good agreement with theoretical prediction.

Real space pseudopotential calculations for copper clusters
View Description Hide DescriptionNeutral and anion clusters of copper, , are examined using real space pseudopotentials constructed within the local spin density approximation. We predict the ground state structure for each cluster, the binding energy, and the corresponding photoelectron spectra, which we compare to experiment. We find strong final state effects in the photoelectron spectra, especially for the smaller clusters. The binding energy as a function of cluster size tracks well with the measured values, although the magnitude of the binding energy exceeds the experimental values by , as expected for the local spin density approximation.

A Hirshfeld partitioning of polarizabilities of water clusters
View Description Hide DescriptionA new Hirshfeld partitioning of cluster polarizability into intrinsic polarizabilities and charge delocalization contributions is presented. For water clusters, densityfunctional theory calculations demonstrate that the total polarizability of a water molecule in a cluster depends upon the number and type of hydrogen bonds the molecule makes with its neighbors. The intrinsic contribution to the molecular polarizability is transferable between water molecules displaying the same Hbond scheme in clusters of different sizes, and geometries, while the charge delocalization contribution also depends on the cluster size. These results could be used to improve the existing force fields.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Phase coexistence in polydisperse multiYukawa hardsphere fluid: High temperature approximation
View Description Hide DescriptionHigh temperature approximation (HTA) is used to describe the phase behavior of polydisperse multiYukawa hardsphere fluid mixtures. It is demonstrated that in the frames of the HTA the model belongs to the class of “truncatable free energy models,” i.e., the models with thermodynamicalproperties(Helmholtz free energy,chemical potential, and pressure) defined by the finite number of generalized moments. Using this property we were able to calculate the complete phase diagram (i.e., cloud and shadow curves as well as binodals) and size distribution functions of the coexisting phases of several different models of polydisperse fluids. In particular, we consider polydisperse oneYukawa hardsphere mixture with factorizable Yukawa coefficients and polydisperse LennardJones (LJ) mixture with interaction energy parameter and/or size polydispersity. To validate the accuracy of the HTA we compare theoretical results with previously published results of more advanced mean spherical approximation (MSA) for the oneYukawa model and with the Monte Carlo(MC)computer simulation results of [Wilding et al.J. Chem. Phys.121, 6887 (2004); Phys. Rev. Lett.95, 155701 (2005)] for the LJ model. We find that overall predictions of the HTA are in reasonable agreement with predictions of the MSA and MC, with the accuracy range from semiquantitative (for the phase diagram) to quantitative (for the size distribution functions).