Volume 119, Issue 18, 08 November 2003
 ARTICLES

 Theoretical Methods and Algorithms

Simulation algorithms for multidimensional nonlinear response of classical manybody systems
View Description Hide DescriptionThe numerical effort and convergence of equilibrium and nonequilibrium (finite field) techniques for simulating the response of classical systems to a sequence of n short pulses are examined. The former is recast in terms of n point correlation functions and order stability matrices which contain higher order generalized Lyapunov exponents, whereas the latter involves sums over perturbed trajectories. The two methods are tested for a highly chaotic system: The Lorentz gas, and for the less chaotic quartic oscillator.

Bonding in the homologous series CsAu, CsAg, and CsCu studied at the 4component density functional theory and coupled cluster levels
View Description Hide DescriptionWe have studied the effect of relativity, electron correlation and the lanthanide contraction on the spectroscopic constants, dissociation energies and dipole moments of the homologous series CsAu, CsAg, and CsCu. We observe a relativistic strengthening of the bond in all cases, particularly for CsAu, but all three compounds are predicted to exist on both the relativistic and nonrelativistic levels of theory with bond strengths more than 1 eV. The effect of the lanthanide contraction on the bonding in CsAu has been studied using a pseudoatom model of the Au atom and is shown to contribute to the strength and polarity of the bond, albeit to a lesser degree than relativity. We present a new estimate of the experimentally derived value of the CsAu dissociation energy using spectroscopic constants calculated at the coupled cluster CCSD(T) level. The new value (2.53 eV) is slightly lower than the previous estimate by Busse and Weil (2.58 eV) and is in excellent agreement with the corresponding CCSD(T) value. We have employed 4component density functional theory at the B3LYP level, and the spectroscopic constants calculated with this method are in good agreement with coupled cluster results. For dipole moments the B3LYP values appear on the other hand to be too low and this requires further investigation.

Direct configuration interaction and multiconfigurational selfconsistentfield method for multiple active spaces with variable occupations. I. Method
View Description Hide DescriptionIn order to reduce the number of ineffective configurations in a priori generated configuration spaces, a direct configuration interaction method has been developed which limits the electron occupations of orbital groups making up a total active space. A wave function is specified by first partitioning an active space into an unrestricted number of orbital groups and second by providing limiting values, in the form of minima and maxima, for the electron occupancies of each group. The configuration interaction problem corresponding to all possible determinants satisfying these conditions is solved in a fully direct manner by the use of Slater–Condon expressions in conjunction with single and double replacements. This configuration interaction approach, termed occupation restricted multiple active spaceconfiguration interaction, has also been linked with orbital optimization programs to produce the occupation restricted multiple active spaceself consistent field method.

Direct configuration interaction and multiconfigurational selfconsistentfield method for multiple active spaces with variable occupations. II. Application to oxoMn(salen) and
View Description Hide DescriptionIn a previous paper, a new direct configuration interaction method for multiple active spaces with variable occupations was described. The present article illustrates how this method may be applied to the oxoMn(salen) complex and the molecule. In the first application it is shown how completeactivespace selfconsistentfield wave functions of the oxoMn(salen) system may be approximated by a drastically reduced number of configurations with negligible loss of accuracy in terms of energetics. In the second application, to it is demonstrated how the fully optimized reaction space wave function may be approximated and also how the recovery of dynamic correlation effects may be achieved. The best predictions of the structure ∠(ONO)=134.4°) and binding energy are both in very good agreement with experiment ∠(ONO)=134.46°, .

Geometry optimization in quantum Monte Carlo with solution mapping: Application to formaldehyde
View Description Hide DescriptionThe solution mapping methodology is presented as a method of geometryoptimization of molecules in the quantum Monte Carlo method. Applied to formaldehyde as a test system, this approach is found to yield optimized bond lengths and bond angle in the diffusionMonte Carlo method that lie within experimental error. The variational Monte Carlo optimized geometry also lies within experimental error, with the exception of the CH bond length, which is slightly underestimated. Additionally, the resulting quadratic representation of the potential energy surface in the region of the minimum is used to calculate three of the force constants and harmonic frequencies.

Relations among several nuclear and electronic density functional reactivity indexes
View Description Hide DescriptionAn expansion of the energy functional in terms of the total number of electrons and the normal coordinates within the canonical ensemble is presented. A comparison of this expansion with the expansion of the energy in terms of the total number of electrons and the external potential leads to new relations among common density functional reactivity descriptors. The formulas obtained provide explicit links between important quantities related to the chemical reactivity of a system. In particular, the relation between the nuclear and the electronic Fukui functions is recovered. The connection between the derivatives of the electronic energy and the nuclear repulsion energy with respect to the external potential offers a proof for the “Quantum Chemical le Chatelier Principle.” Finally, the nuclear linear response function is defined and the relation of this function with the electronic linear response function is given.

Fisher information in density functional theory
View Description Hide DescriptionThe Euler equation of the density functional theory is derived from the principle of minimum Fisher information. Both timeindependent and timedependent cases are analyzed. It is shown that Fisher information is a measure of the quality of the approximate density.

An improved Monte Carlo method for direct calculation of the density of states
View Description Hide DescriptionWe present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities—that is, the probabilities associated with move proposal only—we are able to extract excellent estimates of the density of states. When this estimator is used in conjunction with a Wang–Landau sampling scheme [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)], we quickly achieve uniform sampling of macrostates (e.g., energies) and systematically refine the calculated density of states. This approach requires only potential energy evaluations, continues to improve the statistical quality of its results as the simulation time is extended, and is applicable to both lattice and continuum systems. We test the algorithm on the LennardJones liquid and demonstrate good statistical convergence properties.

Coarsegrained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles
View Description Hide DescriptionWe derive a hierarchy of successively coarsegrained stochastic processes and associated coarsegrained Monte Carlo (CGMC) algorithms directly from the microscopic processes as approximations in larger length scales for the case of diffusion of interacting particles on a lattice. This hierarchy of models spans length scales between microscopic and mesoscopic, satisfies a detailed balance, and gives selfconsistent fluctuation mechanisms whose noise is asymptotically identical to the microscopic MC. Rigorous, detailed asymptotics justify and clarify these connections. Gradient continuous time microscopic MC and CGMC simulations are compared under far from equilibrium conditions to illustrate the validity of our theory and delineate the errors obtained by rigorous asymptotics. Information theory estimates are employed for the first time to provide rigorous error estimates between the solutions of microscopic MC and CGMC, describing the loss of information during the coarsegraining process. Simulations under periodic boundary conditions are used to verify the information theory error estimates. It is shown that coarsegraining in space leads also to coarsegraining in time by where q is the level of coarsegraining, and overcomes in part the hydrodynamic slowdown. Operation counting and CGMC simulations demonstrate significant CPU savings in continuous time MC simulations that vary from for short potentials to for long potentials. Finally, connections of the new coarsegrained stochastic processes to stochastic mesoscopic and Cahn–Hilliard–Cook models are made.

A spectroscopy oriented configuration interaction procedure
View Description Hide DescriptionA multireference configuration interaction (MRCI) based method (Spectroscopy ORiented CI, SORCI) is proposed to calculate energy differences between several electronic states of possibly different multiplicity and which can be extended to fairly large molecules. It combines several wellknown concepts in order to achieve efficiency, balance, generality, stability and accuracy: (a) the use of any kind of (preferably small) reference space and any kind of initial selfconsistent field treatment, (b) the use of average approximate natural orbitals (AANOs) for the states of interest, (c) a variational treatment of the strongly interacting many electron states combined with second order multireference Møller–Plesset perturbation theory for the much larger weakly interacting remainder, (d) the concept of differencededicated CI developed and extensively used by Malrieu and coworkers that avoids contributions which are expected to cancel in energy differences, (e) the use of the resolutionofthe identity approximation to avoid exceedingly large integral files. The method is completely devoid of intruder state problems and makes extensive use of truncation techniques in order to achieve computational efficiency. Currently three cutoffs are introduced that control the size of the reference space, the size of the variational treatment and the size of the AANO basis. Test calculations show that the method is stable against variations of these parameters over a wide range. A study of prototypical molecules ranging in size between diatomics and freebase porphin indicates that the method yields accurate results even with moderate basis sets and CI dimensions that typically do not exceed configuration state functions. Transition energies are typically predicted within 0.1–0.3 eV from the experimental values.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Theoretical study of the structure of lithium clusters
View Description Hide DescriptionLithium clusters to 20) were studied by Kohn–Sham theory with local spin density and gradientcorrected energy functionals. We used a Tabu Search algorithm for structure optimization. The lowest energy isomers that we found fall in two categories: (i) the pentagonal bipyramid, icosahedron, and related structures which are typical of most pair potentials, and (ii) structures containing centered square antiprisms which are reminiscent of the bulk bcc structure and have two characteristic peaks in the pair distribution function, one near 2.60 Å and the other near 3.05 Å. Calculated isomer energies and vibrational frequencies suggest that, at room temperature, many cluster sizes should show liquidlike behavior or coexistence of multiple isomers. The number of unpaired electrons “M” as a function of cluster size “n” generally alternates between 0 (singlet) and 1 (doublet), but some cluster sizes display anomalous spin magnetic moments they are and The and clusters are particularly stable: they each have a very compact structure and a shape consistent with the ellipsoidal jellium model.

Comparison of quantum and mixed quantum–classical semirigid vibrating rotor target studies for isotopic reactions
View Description Hide DescriptionWe present mixed quantum–classical (QC) study of reaction with D, and T using the semirigid vibrating rotor target (SVRT) model to investigate the mass effect of isotopereactions by comparing with the results from quantum SVRT calculations. In this mixed quantum–classical (QCSVRT) approach, the relative translational motion between the atom and the molecule is treated by classical mechanics while the rest of the coordinates are treated quantum mechanically. The reaction probabilities and rate constants of three isotopic reactions are calculated on the potential energy surface of Jordan and Gilbert. Our study shows that the mixed QCSVRT reaction probabilities and rate constants from the ground vibrational state of the reagent become progressively more accurate as the mass of the projectile is increased. This phenomenon is related to the diminishing role of the zeropoint energy of the projectile as the reduced translational mass is increased. Our study also finds that the QCSVRT results from vibrationally excited reagent are in substantial deviations from the quantum SVRT results which is due to the failure of the single configuration nature of the mixed quantum–classical approach.

Effect of collisions on onecolor polarization spectroscopy of OH
View Description Hide DescriptionThe effect of collisions on the magnitude of polarization spectroscopy (PS) signals from the OH radical on the (0,0) band has been studied. OH was produced by the 266nm photolysis of and detected by onecolor degenerate PS, using ≈5ns pulses from a Nd:YAG pumped dye laser. Spectra with both circular and linear pump polarizations are reported, together with signal dependence on OH number density and pump pulse fluence. The relative line intensities in the spectra and measured square dependence on OH number density are consistent with a description of PS as a variant of fourwave mixing spectroscopy. The pump pulse fluence dependence is fitted well by literature saturation curves. The collisional dependence of the PS signal was investigated by adding increasing pressures of He, Ar, or collider gases for fixed overlapping pump and probe pulses. The principal finding is the very rapid loss of the PS signal with increasing collider pressure. The resulting phenomenological rate constants are in the range We discuss these rate constants with reference to the literature rotational energy transfer and dephasing rate constants. We propose that the very large observed values may be explained by the effect of elastic velocity changing collisions.

Statistical evaporation of rotating clusters. II. Angular momentum distribution
View Description Hide DescriptionThe change in the angular momentum of an atomic cluster following evaporation is investigated using rigorous phase space theory (PST) and molecular dynamics simulations, with an aim at the possible rotational cooling and heating effects. Influences of the shape of the interaction potential, anharmonicity of the vibrational density of states (DOS), and the initial distribution of excitation energies are systematically studied in the example of the LennardJones cluster For this system, the predictions of PST are in quantitative agreement with the results of the simulations, provided the correct forms for the vibrational density of states and the interaction potential are used. The harmonic approximation to the DOS is used to obtain explicit forms for the angular momentum distribution in larger clusters. These are seen to undergo preferential cooling when thermally excited and preferential heating when subject to a strong vibrational excitation.

Velocity map imaging of the photodissociation of in the band
View Description Hide DescriptionThe photodissociation dynamics of has been investigated within the band by means of velocity map ion imaging. The cation is prepared by resonanceenhanced multiphoton ionization of via the band, and the groundstate population in the ion is unambiguously characterized by using photoelectron spectroscopy.Photodissociation of the stateselected ion results in fragmentation to both and The translational energy distribution derived from the twodimensional images of the fragments shows vibrational progressions that provide detailed information on the channeling of the parent internal energy into the dissociation process. The translational energy distribution of the fragment shows a onetoone dependence on the excitation energy, which is typical of a singlephoton dissociation process. The observation of a repeated pattern of rings in the images with an interval of ∼800 cm^{−1} indicates that the umbrella mode of the fragment is excited upon dissociation. The lowkineticenergy release observed in this channel indicates that substantial energy is deposited into the internal degrees of freedom of the fragment and suggests that the dissociation is controlled by the Franck–Condon factors between the parent ion and fragments. The translational energy distribution of the fragment is independent of the excitation wavelength and includes a feature peaking at nearzero kinetic energy. Plausible mechanisms for the and dissociation channels are discussed in terms of the observed kinetic energy and anisotropy distributions derived from the twodimensional ion images.

Conformationally induced vibronic transitions in spectra of npropylbenzene
View Description Hide DescriptionDispersed fluorescence spectra of two conformational isomers of npropylbenzene have been measured in a supersonic free jet expansion. The results show that the vibronic features in emission from the zeropoint levels in two conformers are significantly different, and most notably, the transitions due to ringchain torsional mode are active only in the spectra of the gauche conformer. Relative stability of the conformers in the ground state has been reinvestigated by the ab initio quantum chemistry method at the and MP2/ccpVTZ levels of theory. In contrast to earlier reports, the present theoretical studies predict that the gauche conformer is ∼2.5 kJ/mol more stable than the trans. The effects of propyl substitution on phenyl ring vibrational modes have been analyzed by comparing the calculated (ab initio, DFT/B3LYP/631G^{*} ^{*}) displacements of ring atoms for different normal modes with those of the vibrational modes of unsubstituted benzene. The implications of spectral dissimilarity of the conformers on their excited state lifetimes [Borst et al., J. Chem. Phys. 116, 7057 (2002)] have been discussed.

Infrared laser spectroscopy of CCO radical in the region of the C–C stretching fundamental
View Description Hide DescriptionThe C–C stretching fundamental and the difference band of the CCO radical have been measured in the gas phase using a tunable infrared diode laserspectrometer. The CCO radical was produced using a flowing mixture of carbon suboxide and helium subjected to a hollowcathode discharge. The spectral region between was probed. Fiftyfive and fiftythree rovibrational transitions were measured in the and bands, respectively. The analyses of these bands yielded spectroscopic constants for (001) and (002) vibrational states. The band origins for and were determined to be 1066.82407(54) and respectively. To check the consistency of the data in this work and those in the C–O stretching region, several lines from the band were also recorded. These lines were observed at their predicted frequency.

The pure rotational spectrum of transition metal fluorides revisited
View Description Hide DescriptionThe pure rotational spectrum of TiF in its ground state has been measured using millimeter/submillimeter wave direct absorption techniques in the range 140–530 GHz. In ten out of the twelve rotational transitions recorded, all four spin–orbit components were observed, confirming the ground state assignment. Additional small splittings were resolved in several of the spin components in lower J transitions, which appear to arise from magnetic hyperfine interactions of the nucleus. In contrast, no evidence for Λdoubling was seen in the data. The rotational transitions of TiF were analyzed using a case (a) Hamiltonian, resulting in the determination of rotational and fine structure constants, as well as hyperfine parameters for the fluorine nucleus. The data were readily fit in a case (a) basis, indicating strong first order spin–orbit coupling and minimal secondorder effects, as also evidenced by the small value of λ, the spin–spin parameter. Moreover, only one higher order term, η, the spin–orbit/spin–spin interaction term, was needed in the analysis, again suggesting limited perturbations in the ground state. The relative values of the a, b, and chyperfine constants indicate that the three unpaired electrons in this radical lie in orbitals primarily located on the titanium atom and support the molecular orbital picture of TiF with a single electron configuration. The bond length of TiF (1.8342 Å) is significantly longer than that of TiO, suggesting that there are differences in the bonding between transition metal fluorides and oxides.

Ab initio study of the reaction: Ground and excited potential energy surfaces
View Description Hide DescriptionThe two potential energy surfaces and PESs) adiabatically correlating the reactants and products asymptotes of the title reaction were studied by means of the CASSCF and CASPT2 ab initio methods. The minimum energy path determined for the ground PES evolved through the barrierless insertion of the atom into a C–H bond. The products result from the dissociation of the methanol intermediate formed. Reactivity on the excited PES was found to proceed via an abstraction pathway. The energy barrier involved is low enough to expect the PES to play a nonnegligible role in the title reaction, even at the usual conditions attained in the experiments. The crossing between the and PESs was also investigated, the latter surface correlating with the excited product.

Influence of the aliphatic chain on the (hydrogenbonded) paminobenzonitrile complexes with methanol and ethanol
View Description Hide DescriptionThe 4aminobenzonitrile (ABN) molecule has two active sites amenable to hydrogen bonding to methanol (MeOH) and ethanol (EtOH): the amino, and the cyano, –CN, groups. Twocolor resonance enhanced multiphoton ionization timeofflight mass spectroscopy and hole burning spectroscopy in addition to the ionization energies provides sound evidence of the occurrence of two isomers in the complex and one single isomer for the complex. Combining the outcomes from the ABN/methanol and ABN/ethanol experiments with ab initio computations at reliable theory levels one identifies the preferred solvation sites and the optimized geometries. A discussion of the role of the aliphatic chains on the geometry of the isomers and other properties is presented.