Volume 119, Issue 14, 08 October 2003
 ARTICLES

 Theoretical Methods and Algorithms

General Born–Oppenheimer–Huang approach to systems of electrons and nuclei
View Description Hide DescriptionWe reconsider the Born–Oppenheimer–Huang treatment of systems of electrons and nuclei for the case of their interaction with timedependent fields. Initially, we present a framework in which all expressions derived are formally exact since no truncations are introduced. The objective is to explore the general structure of the equations under the most unrestricted conditions, including the possibility that the electronic basis is dependent both on the nuclear coordinates and on time. We then derive an application of the theory applicable to cases of interaction with strong timedependent fields. The method truncates the electronic basis only after the timedependent interaction is taken into account in the electronic wave functions. This leads to theory which is similar to a Born–Oppenheimertype truncation within the interaction picture.

Twodimensional circularly polarized pump–probe spectroscopy
View Description Hide DescriptionA novel twodimensional (2D) circularly polarized (CP) pump–probe (PP) spectroscopy is theoretically studied and proposed. Utilizing circularly polarized pump field, one can measure both the left and rightCP PP spectra in the 2D frequency space spanned by the pump and probe field frequencies. Although the dominant contribution to the measured signal is all electricdipoleallowed fourwavemixing term, it can be removed by taking the difference between the left and rightCP PP signals. Taking the firstorder terms with respect to either magnetic dipole or quadrupolepump field interaction, we find that two distinctively different contributions to the thirdorder CPPP polarization are important. However, by controlling the crossing angle between the pump and probe field propagation directions to be the magic angle, it is shown that the magnetic dipole–field interaction contribution to the thirdorder polarization can be selectively measured. It is observed that the relationship between the linear polarization PP and CPPP is similar to that between the linear absorption and circular dichroism. Numerically calculated 2D CPPP spectra for model systems are presented and compared with the absorption, circular dichroism, and linearly polarized PP spectra.

Evolution of classical and quantum phasespace distributions: A new trajectory approach for phase space hydrodynamics
View Description Hide DescriptionRecently, Donoso and Martens described a method for evolving both classical and quantum phasespace distribution functions, that involves the propagation of an ensemble of correlated trajectories. The trajectories are linked into a unified whole by spatial and momentum derivatives of density dependent terms in the equations of motion. On each time step, these nonlocal terms were evaluated by fitting the density around each trajectory to an assumed functional form. In the present study, we develop a different trajectory method for propagating phasespace distribution functions. A hierarchy of coupled analytic equations of motion are derived for the q and p derivatives of the density and a truncated set of these are integrated along each trajectory concurrently with the equation of motion for the density. The advantage of this approach is that individual trajectories can be propagated, one at a time, and function fitting is not required to evaluate the nonlocal terms. Regional nonlocality can be incorporated at various levels of approximation to “dress” what would otherwise be “thin” locally propagating trajectories. This derivative propagation method is used to obtain trajectory solutions for the Klein–Kramers equation, the Husimi equation, and for a smoothed version of the Caldeira–Leggett equation derived by the Diosi. Trajectory solutions are obtained for the relaxation of an oscillator in contact with a thermal bath and for the decay of a metastable state.

Information uncertaintytype inequalities in atomic systems
View Description Hide DescriptionThe oneelectron Shannon information entropy sum is reformulated in terms of a single entropic quantity dependent on a oneelectron phase space quasiprobability density. This entropy is shown to form an upper bound for the entropy of the oneelectron Wigner distribution. Twoelectron entropies in position and momentum space, and their sum, are introduced, discussed, calculated, and compared to their oneelectron counterparts for neutral atoms. The effect of electron correlation on the twoelectron entropies is examined for the helium isoelectronic series. A lower bound for the twoelectron entropy sum is developed for systems with an even number of electrons. Calculations illustrate that this bound may also be used for systems with an odd number of electrons. This twoelectron entropy sum is then recast in terms of a twoelectron phase space quasiprobability density. We show that the original BialynickiBirula and Mycielski information inequality for the Nelectron wave function may also be formulated in terms of an Nelectron phase space density. Upper bounds for the twoelectron entropies in terms of the oneelectron entropies are reported and verified with numerical calculations.

Compact boundaryconditiondetermined wave function for positronium hydride (PsH)
View Description Hide DescriptionA simple, compact, and accurate wave function for positronium hydride is written as a product of Pade’ approximants for electron–nucleus interactions and of Jastrow functions for electron–electron interactions. Most of the parameters are fixed taking into account both the correct cusp conditions when two particles collide and the correct asymptotic behavior when one or two particles go to infinity. The remaining parameters were optimized by variational Monte Carlo calculations. The energy of this single term wave function is and favorably compares with very long configuration interaction expansions and even with explicitly correlated function expansions. The exam of the wave function and of various twodimensional distribution functions shows that the PsH structure is similar to the hydrogen anion structure, with the positron slightly perturbing it and its motion strongly correlated to the electrons that are squeezed towards each other and towards the nucleus.

A coarse grain model for nalkanes parameterized from surface tension data
View Description Hide DescriptionMolecular dynamics simulations are carried out in a systematic manner to develop a coarse grain model for multipleofthree carbonnalkanes. The procedure involves optimizing harmonic bond and bend parameters, and LennardJones nonbonded parameters, to match observables taken from fully atomistic simulations and from experiment. The experimental values used consist of surface tension and bulk density data. Scaling relations are introduced to allow for the representation of the remaining nalkanes. As n increases these relations converge to the multipleofthree carbon values. The model is assessed by comparing it to both fully atomistic simulation and experimental data which was not used in the fitting procedure.

Selectivity of explicit internal signal stochastic resonance in a chemical model
View Description Hide DescriptionThe explicit internal signal stochastic resonance (EISSR) that happened in the Willamowski–Rössler model was studied. EISSR is a cooperative effect of the intrinsic signal and external noise or internal fluctuation. Our studies have shown that EISSR can exist in the stable periodic2 oscillation state. The output signal to noise ratio (SNR) of the strong signal (SS) versus noise intensity exhibits explicitly nonmonotonic character. The output SNR of the weak signal decreases with the increment of noise intensity. It is clear that EISSR can hold selectivity to the preponderant intrinsic signal when there are two intrinsic signals in the system. At the same time, the fundamental frequency of the SS almost does not alter. These properties imply that the system can resist to the effect of noise and sustain preponderant intrinsic oscillation by itself. Our results will be helpful to better understand circadian rhythm and signal detecting in creatures.

Fokker–Planck–Kramers equation treatment of dynamics of diffusioncontrolled reactions using continuous velocity distribution in three dimensions
View Description Hide DescriptionA theory has been developed for the shorttime dynamics of diffusioncontrolled reactions based on the Fokker–Planck–Kramers equation (FPKE) in three dimensions. A continuous velocity distribution function has been proposed to solve the FPKE approximately. The present theory agrees better with the Langevin dynamics results than the earlier theory using a discontinuous velocity distribution. This indicates the validity of the present theory in three dimensions, because the Langevin dynamics results can be assumed to be the exact solutions to the FPKE. The theory is compared with molecular dynamics (MD) simulations in LennardJones fluids to examine the applicability for realistic systems. The present theory predicts a somewhat smaller rate constant than the MD simulation in the time range of a few picoseconds. The discrepancies can be explained qualitatively in terms of the nonMarkovian effect on the molecular motions.

Aspects of correlation function realizability
View Description Hide DescriptionThe paircorrelation function describes shortrange order in manyparticle systems. It must obey two necessary conditions: (i) nonnegativity for all distances r, and (ii) nonnegativity of its associated structure factor for all k. For the elementary unit stepfunction form, previous work [F. H. Stillinger, S. Torquato, J. M. Eroles, and T. M. Truskett, J. Phys. Chem. B 105, 6592 (2001)] indicates that (i) and (ii) could be formally satisfied, but only up to a terminal density at which the covering fraction of particle exclusion diameters equaled in d dimensions. To test whether the unit step is actually achievable in manyparticle systems up to the apparent terminal density, a stochastic optimization procedure has been used to shift particles in large test systems toward this target Numerical calculations for and 2 confirm that the step function is indeed realizable up to the terminal density, but with substantial deviation from the configurational preferences of equilibrium hardrod and harddisk models. We show that lineal statistical measures are particularly sensitive to this difference. Our results also illustrate the characteristics of “closest approach” to the step function above the terminal density.

Generalized coupling to a heat bath: Extension of the Gaussian isokinetic dynamics and effect of time scaling
View Description Hide DescriptionThe Hamiltonian formulation of the Gaussian isokinetic (GIK) thermostat [C. P. Dettmann and G. P. Morriss, Phys. Rev. E 54, 2495 (1996)] is extended to generalize the coupling of a physical system to a heat bath in molecular dynamics (MD) simulations. This extension gives a theoretical basis for the statistical ensemble recently proposed to understand the characteristics of the weak coupling (wc) thermostat [T. Morishita, J. Chem. Phys. 113, 2976 (2000)]. It is shown that the scaling of the momentum and the time in the Hamiltonian formulation gives a clear picture for understanding the relation between the generalized coupling thermostat and the GIK or wc thermostat. We also discuss time scaling in a Lagrangian formulation and show its effect on equations of motion and statistical ensembles in thermostatted MD simulations.

Integral coalescence conditions in dimension space
View Description Hide DescriptionWe have derived the integral form of the cusp and node coalescence conditions satisfied by the wave function at the coalescence of two charged particles in dimension space. From it we have obtained the differential form of the coalescence conditions. These expressions reduce to the wellknown integral and differential coalescence conditions in space. It follows from the results derived that the approximate Laughlin wave function for the fractional quantum Hall effect satisfies the node coalescence condition. It is further noted that the integral form makes evident that unlike the electron–nucleus coalescence condition, the differential form of the electron–electron coalescence condition cannot be expressed in terms of the electron density at the point of coalescence. From the integral form, the integral and differential coalescence conditions for the paircorrelation function in dimension space are also derived. The known differential form of the pair function cusp condition for the uniform electron gas in dimensions constitutes a special case of the result derived.

Connections between groundstate energies from optimizedeffective potential exchangeonly and Hartree–Fock methods
View Description Hide DescriptionBy using perturbation theory, an expression is derived for the difference between the Hartree–Fock (HF) and optimized effective potential (OEP) exchangeonly groundstate energies. With this expression and a model threeelectron system, we provide the first formal proof of a specific example where the HF and OEP exchangeonly groundstate energies are different. We also give a constrainedsearch variational argument that the two energies are generally, nevertheless, expected to be very close, consistent with known numerical results.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Velocity redistribution of excited atoms by radiative excitation transfer. II. Theory of radiation trapping in collimated beams
View Description Hide DescriptionWe have developed a theory of resonance radiation imprisonment in collimated atomic beams.Treating the integral master equation describing imprisonment as a generalized wave (Schrödinger) equation and using the geometrical quantization technique for its solution, we obtained analytical representations for the effective radiative lifetime, mean scattering number, and trapping factors. We apply this theory to explain the recent observation of a dramatic velocity redistribution of excited atoms by radiative excitation transfer after the photofragmentation of In this process, the fast photofragments transfer their excitation energy efficiently via radiation to the abundant atoms from the primary particle beam. The influence of the hyperfine splitting of the ground state of Na atoms on this process is discussed. The ratio of the number of atoms produced by the radiative excitation transfer to the number of photofragments was found to be 0.13 and 0.19 for photodissociation of molecules in the vibrational levels and respectively. This is in good agreement with the corresponding experimental values of 0.16 and 0.22.

Vacuum synthesis and determination of the ionization energies of different molecular orbitals for BrOBr and HOBr
View Description Hide DescriptionPure BrOBr and HOBr were synthesized in vacuum by heterogeneous reactions of the dried bromine vapor and mixture vapors (5:1) with HgO, respectively, and then characterized by He Iphotoelectron spectroscopy (PES) and augmented by ab initioGAUSSIAN 2 and the outer valence Green’s functional calculations. The first PE band at 10.26 eV with vibrational spacing 550±60 cm^{−1} and the second PE band at 11.23 eV with vibrational spacing 240±60 cm^{−1} are, respectively, assigned as ionizations of the electrons of the highest occupied molecular orbital and the orbitals of BrOBr. The first PE band at 10.73 eV with vibrational spacing 750±60 cm^{−1} and the second PE band at 11.56 eV with vibrational spacing 650±60 cm^{−1} are, respectively, assigned as ionizations of the electrons of the and the orbitals of HOBr. The study does not only provide vacuum synthesis conditions for preparing pure BrOBr and HOBr, but also provide experimental PES results along with theoretical ionization energies of different molecular orbitals for BrOBr and HOBr.

Density functional study on structure and stability of bimetallic clusters and their cations
View Description Hide DescriptionA systematic study on the structure and stability of zincdopedgold clusters has been performed by density functional theory calculations. All the lowestenergy isomers found have a planar structure and resemble pure gold clusters in shape. Stable isomers tend to equally delocalize valence selectrons of the constituent atoms over the entire structure and maximize the number of Au–Zn bonds in the structure. This is because the Au–Zn bond is stronger than the Au–Au bond and gives an extra σbonding interaction by the overlap between vacant and valence orbitals. No threedimensional isomers were found for and clusters containing six delocalized valence electrons. This result reflects that these clusters have a magic number of delocalized electrons for twodimensional systems. Calculated vertical ionization energies and dissociation energies as a function of the cluster size show odd–even behavior, in agreement with recent mass spectrometric observations [Tanaka et al., J. Am. Chem. Soc. 125, 2862 (2003)].

Nitrogeninduced magnetic transition in small chromium clusters
View Description Hide DescriptionUsing density functional theory with generalized gradient approximation for exchange and correlation, we show that otherwise antiferromagnetically coupled chromium atoms in very small chromiumclusters couple ferromagnetically when doped with a nitrogen atom, thus leading to giant magnetic moments. For example, the magnetic moment of is found to be while that of is Strong bonding between Cr and N atoms brings about this magnetic transition. The Cr atoms nearest neighbor to N couple ferromagnetically with each other and antiferromagnetically with nitrogen. The significance of these results in understanding the ferromagnetic order in Crdoped GaN is discussed.

Probing branching mechanism through resonancetype oscillation in the collisionenergy dependence of Penning ionization reaction of with oriented
View Description Hide DescriptionThe collision energy and orientationangleresolved Penning ionization cross sections were determined for the reaction. A remarkable depletion was recognized in the collision energy dependence of the orientationangleresolved Penning ionization cross section. The depletion could be interpreted as the competitive neutral dissociation from the Rydberg states formed by an electron exchange mechanism related to a molecular orbital. The stereo selectivity for the Penning ionization and neutral dissociation were discussed. From the series of our studies on reactions, it was substantiated that the orientation angle and collisionenergyresolved Penning ionization cross section give an important information about the branching mechanism to the Rydberg states that are linked to the neutral dissociation channels.

Electronic structures of azafullerene
View Description Hide DescriptionTwo recently proposed lowenergy azafullerene isomers have been theoretically characterized using xray spectroscopies. The xray photoelectron spectroscopy, the nearedge absorption fine structure, the xrayemission spectroscopy, and the ultraviolet photoelectron spectroscopy for both isomers have been predicted at the gradientcorrected density functional theory level. These spectroscopies together give a comprehensive insight of the electronic structure on the core, valence, and unoccupied orbitals. They have also provided a convincing way for identifying the isomer structures.

Interelectronic angles of group 14, 15, and 16 atoms in their lowlying multiplet states
View Description Hide DescriptionThe average interelectronic angles in position space and in momentum space are examined for the multiplet states arising from the ground electronic configurations of the group 14, 15, and 16 atoms. The angles and are greater than 90 degrees with no exceptions and two electron vectors prefer inverse directions to the same direction on average. Common to all 15 atoms, it is found that in position space, lower multiplets have larger interelectronic angles than higher multiplets. However, the opposite is true in momentum space and the interelectronic angles are smaller in lower multiplets. The differences in the angles and between multiplets have good linear correlations with the relative stability of the multiplets.

Geometry and torsional energies of a C–Cprotonated nalkane
View Description Hide DescriptionThe geometry and relative energies of torsional conformers of centrally protonated were studied with ab initio methods, to (a) obtain the most accurate geometry of the threecenter–twoelectron CHC bond to date, (b) evaluate the performance of lower levels of approximation upon this challenging structure, and (c) gain an understanding of the torsional dynamics of Twentynine combined levels of theory were used to optimize the geometry of the symmetry minimum for trans and the most accurate one [CCSD(T)/ccpVTZ] gave the following CHC bond geometry: Molecularorbitalbased methods generally perform better than density functional methods for describing the threecenter–twoelectron bond. A smaller subset of levels of theory was used to optimize other torsional conformers of centrally protonated varying the CCCC dihedral (trans, gauche, cis) and the dihedral for the bridging proton (various eclipsed and staggered positions). The results show that all conformers lie within a range, with the lowestenergy conformer being either trans or gauche with a staggered dihedral for the bridging proton. The effect of corevalence correlation was also investigated. Finally, the potential energy surface as a function of the CCCC and bridgingproton dihedral angles was qualitatively estimated and drawn, based on our computed data, to aid in understanding the fluxional character of