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Volume 124, Issue 1, 07 January 2006
 COMMUNICATIONS


A full dimensional timedependent wave packet study for the fourcenter, collision induced dissociation, and single exchange reactions: Reaction probabilities for
View Description Hide DescriptionA timedependent initial state selected wave packet method has been developed to study the fourcenter (4C) reaction, and two other competing reactions: the collision induced dissociation (CID) and the single exchange (SE) reaction, in full six dimensions. Initial statespecific total reaction probabilities for these three competing reactions are presented for total angular momentum and the effects of reagent vibration on reactions are examined. It is found that (a) the CID process is the dominant process over the whole energy range considered in this study, but the 4C and SE processes also have nonnegligible probabilities; (b) the SE process has a lower threshold energy than the 4C process, but the SE probability increases slower than the 4C probability as collision energy increases; (c) the vibrational excitation of is much more efficient than translational motion for promoting these processes, in particular to the CID process.

Stateresolved reactive scattering by slice imaging: A new view of the reaction
View Description Hide DescriptionWe present stateresolved crossed beam scattering results for the reaction, obtained using direct current slice imaging. The HCl image, recorded at a collision energy of , shows strongly coupled angular and translational energy distributions revealing features of the reaction not seen in previous studies. The overall distribution is mainly forward scattered with respect to the Cl beam, with a translational energy distribution peaking near the collision energy. However, there is a substantial backscattered contribution that is very different. It shows a sharp peak at , but extends to much lower energy, implying substantial internal excitation in the ethyl radical coproduct. These results provide new insight into the reaction, and they are considered in terms of alternative models of the dynamics. This work represents the first genuine crossedbeam study in which a product other than the methyl radical was detected with quantum state specificity, showing the promise of the approach generally for high resolution stateresolved reactive scattering.

 ARTICLES

 Theoretical Methods and Algorithms

Additions to the class of symmetricantisymmetric multiwavelets: Derivation and use as quantum basis functions
View Description Hide DescriptionMultiwavelet bases have been shown recently to apply to a variety of quantum problems. There are, however, only a few multiwavelet families that have been defined to date. ChuiLiantype symmetric and antisymmetric multiwavelets are derived here that equal and exceed the polynomial interpolating power of previously available examples. Adaptations to domain edges are made with a view to use in curvilinear coordinate molecular calculations. The new highestorder multiwavelet family is shown to provide uniformly better performance for (i) basis representation of terms such as in near approach to the singularity at and (ii) eigenvalue calculation of a bending Hamiltonian taken from a curvilinear model of the groundstate vibrations of nitrosyl chloride.

Coupledperturbed densitymatrix functional theory equations. Application to static polarizabilities
View Description Hide DescriptionStarting from the variational equations for the natural occupation numbers and the recently proposed eigenequations for the natural spinorbitals, we derive coupledperturbed densitymatrix equations that furnish a linear response of the oneelectron reduced density matrix to a static perturbation when the total energy is a functional of the oneelectron reduced density matrix. Cases when some occupation numbers achieve exactly 0 or 1 or when the total number of the particles in a system is not preserved are taken into consideration. The scheme is applied to computing static polarizabilities from two simple densitymatrix functionals. The behavior of the functionals is erratic and they provide only little or no improvement over the coupledperturbed HartreeFock results.

The boundary fluctuation theory of transport coefficients in the linearresponse limit
View Description Hide DescriptionIn this paper we present, for the first time, a linearresponse theory of transport coefficients—shear viscosity and thermal conductivity—involving thermal, as opposed to mechanical, fields. The theory involves the explicit treatment of the boundaries and the constraints that are applied to them. Expressions for the shear viscosity and thermal conductivity are obtained in terms of the fluctuations at the boundaries of the variable conjugate to that which is constrained. We explain how the choice of ensemble, as defined by the boundary constraints, determines the form in which the transport coefficients are evaluated.

Exchangehole dipole moment and the dispersion interaction: Highorder dispersion coefficients
View Description Hide DescriptionIn recent publications [A. D. Becke and E. R. Johnson, J. Chem. Phys.122, 154104 (2005); E. R. Johnson and A. D. Becke 123, 024101 (2005)] we have demonstrated that the positiondependent dipole moment of the exchange hole can be used to generate dispersion interactions between closedshell systems. Remarkably accurate coefficients and intermolecular potentialenergy surfaces can be obtained from HartreeFock occupied orbitals and polarizability data alone. In the present work, our model is extended to predict and coefficients as well. These higherorder coefficients are obtained as easily as and with comparable accuracy.

On the emergence of molecular structure from atomic shape in the harmonium model
View Description Hide DescriptionThe formal similarity of the threebody Hamiltonians for helium and the hydrogen molecule ion is used to demonstrate the unfolding of a rotating dumbbelllike proton distribution from a type electron distribution by smooth variation of the particles’ masses in the harmonium model. The harmonium is an exactly solvable modification of the harmonium model (also known as Hooke’s law atom) where the attraction between different particles is harmonic and the repulsion between the two equal particles is given by a potential. The dumbbelllike molecular structure appears as an expression of increasing spatial correlation due to increasing mass. It gradually appears in the onedensity distribution of the two equal particles if their mass exceeds a critical value depending on the mass of the third particle. For large mass of the equal particles, their onedensity distribution approaches an asymptotic form derived from the BornOppenheimer treatment of in the harmonium model. Below the critical value, the one density is a spherical, Gaussiantype atomic density distribution with a maximum at the center of mass. The topological transition at the critical value separates molecular structure and atomic shape as two qualitatively different manifestations of spatialstructure.

Analytical calculations of molecular integrals for multielectron Rmatrix methods
View Description Hide DescriptionClosedform analytical expressions for one and twoelectron integrals between Cartesian Gaussians over a finite spherical region of space are developed for use in ab initiomolecular scattering calculations. In contrast with some previous approaches, the necessary integrals are formulated solely in terms of finite summations involving standard functions. The molecular integrals evaluated over the finite region of space are computed by subtracting the contributions outside the region from the integrals over all space. The latter integrals can be efficiently and accurately obtained from existing boundstate algorithms. Our approach incorporates molecular scattering calculations into current quantum chemistry programs and facilitates the unification of bound and continuumstate calculations for both diatomic and polyatomic molecules. Multidimensional Monte Carlo numerical integrations validate the high accuracy of our closed form results for the twoelectron integrals.

Scalable implementation of analytic gradients for secondorder averaged perturbation theory using the distributed data interface
View Description Hide DescriptionThe analytic gradient expression for secondorder averaged perturbation theory is revised and its parallel implementation is described in detail. The distributed data interface is used to access molecularorbital integral arrays stored in distributed memory. The algorithm is designed to maximize the use of local data and reduce communication costs. The iterative solution and the preconditioner used to induce the convergence of the coupledperturbed HartreeFock equations are presented. Several illustrative timing examples are discussed.

On the relation between quantum lifetimes and classical stability for the systems with a saddletype potential
View Description Hide DescriptionRelations between quantummechanical and classical properties of open systems with a saddletype potential, for which at a given energy only one unstable periodic orbit exists, are studied. By considering the convergence of the Gutzwiller trace formula [J. Math. Phys.12, 343 (1971)] it is confirmed that both for homogeneous and inhomogeneous potentials the poles of the formula are located below the real energy axis, i.e., these kind of potentials do not support bound states, in general. Within the harmonic approximation the widths of resonant (transition) states are proportional to the values of Lyapunov exponent of the single periodic orbit calculated at the energies which are equal to the resonance positions. The accuracy of the semiclassical relation is discussed and demonstrated for several examples.

Irreducible correlation functions of the matrix in the coordinate representation: Application in calculating Lorentzian halfwidths and shifts
View Description Hide DescriptionBy introducing the coordinate representation, the derivation of the perturbation expansion of the Liouville matrix is formulated in terms of classically behaved autocorrelation functions. Because these functions are characterized by a pair of irreducible tensors, their number is limited to a few. They represent how the overlaps of the potential components change with a time displacement, and under normal conditions, their magnitudes decrease by several orders of magnitude when the displacement reaches several picoseconds. The correlation functions contain all dynamical information of the collision processes necessary in calculating halfwidths and shifts and can be easily derived with high accuracy. Their wellbehaved profiles, especially the rapid decrease of the magnitude, enables one to transform easily the dynamical information contained in them from the time domain to the frequency domain. More specifically, because these correlation functions are well time limited, their continuous Fourier transforms should be band limited. Then, the latter can be accurately replaced by discrete Fourier transforms and calculated with a standard fast Fourier transform method. Besides, one can easily calculate their Cauchy principal integrations and derive all functions necessary in calculating halfwidths and shifts. A great advantage resulting from introducing the coordinate representation and choosing the correlation functions as the starting point is that one is able to calculate the halfwidths and shifts with high accuracy, no matter how complicated the potential models are and no matter what kind of trajectories are chosen. In any case, the convergence of the calculated results is always guaranteed. As a result, with this new method, one can remove some uncertainties incorporated in the current width and shift studies. As a test, we present calculated Raman linewidths for the pair based on several trajectories, including the more accurate “exact” ones. Finally, by using this new method as a benchmark, we have carried out convergence checks for calculated values based on usual methods and have found that some results in the literature are not converged.

Finite basis representations with nondirect product basis functions having structure similar to that of spherical harmonics
View Description Hide DescriptionThe currently most efficient finite basis representation (FBR) method [Corey et al., in Numerical Grid Methods and Their Applications to Schrödinger Equation, NATO ASI Series C, edited by C. Cerjan (Kluwer Academic, New York, 1993), Vol. 412, p. 1; Bramley et al., J. Chem. Phys.100, 6175 (1994)] designed specifically to deal with nondirect product bases of structures , , etc., employs very special independent grids and results in a symmetric FBR. While highly efficient, this method is not general enough. For instance, it cannot deal with nondirect product bases of the above structure efficiently if the functions [and/or ] are discrete variable representation (DVR) functions of the infinite type. The optimalgeneralized FBR(DVR) method [V. Szalay, J. Chem. Phys.105, 6940 (1996)] is designed to deal with general, i.e., direct and/or nondirect product, bases and grids. This robust method, however, is too general, and its direct application can result in inefficient computer codes [Czakó et al., J. Chem. Phys.122, 024101 (2005)]. It is shown here how the optimalgeneralized FBR method can be simplified in the case of nondirect product bases of structures , , etc. As a result the commonly used symmetric FBR is recovered and simplified nonsymmetric FBRs utilizing very special dependent grids are obtained. The nonsymmetric FBRs are more general than the symmetric FBR in that they can be employed efficiently even when the functions [and/or ] are DVR functions of the infinite type. Arithmetic operation counts and a simple numerical example presented show unambiguously that setting up the Hamiltonian matrix requires significantly less computer time when using one of the proposed nonsymmetric FBRs than that in the symmetric FBR. Therefore, application of this nonsymmetric FBR is more efficient than that of the symmetric FBR when one wants to diagonalize the Hamiltonian matrix either by a direct or via a basisset contraction method. Enormous decrease of computer time can be achieved, with respect to a direct application of the optimalgeneralized FBR, by employing one of the simplified nonsymmetric FBRs as is demonstrated in noniterative calculations of the lowlying vibrational energy levels of the molecular ion. The arithmetic operation counts of the Hamiltonian matrix vector products and the properties of a recently developed diagonalization method [Andreozzi et al., J. Phys. A Math. Gen.35, L61 (2002)] suggest that the nonsymmetric FBR applied along with this particular diagonalization method is suitable to large scale iterative calculations. Whether or not the nonsymmetric FBR is competitive with the symmetric FBR in largescale iterative calculations still has to be investigated numerically.

Quantum control of molecular vibrational and rotational excitations in a homonuclear diatomic molecule: A full threedimensional treatment with polarization forces
View Description Hide DescriptionThe optimal control of the vibrational excitation of the hydrogen molecule [BalintKurti et al., J. Chem. Phys.122, 084110 (2005)] utilizing polarization forces is extended to three dimensions. The polarizability of the molecule, to first and higher orders, is accounted for using explicit ab initio calculations of the molecular electronic energy in the presence of an electric field. Optimal control theory is then used to design infrared laser pulses that selectively excite the molecule to preselected vibrationalrotational states. The amplitude of the electric field of the optimized pulses is restricted so that there is no significant ionization during the process, and a new frequency sifting method is used to simplify the frequency spectrum of the pulse. The frequency spectra of the optimized laser pulses for processes involving rotational excitation are more complex than those relating to processes involving only vibrational excitation.

A fragment molecularorbital–multicomponent molecularorbital method for analyzing isotope effects in large molecules
View Description Hide DescriptionWe have developed a fragment molecular orbital (FMO)–multicomponent MO (MC_MO) method to analyzeisotope effect due to differences between the quantum effects of protons and deuterons for large molecules such as proteins and DNA. The FMOMC_MO method enables the determination of both the electronic and the protonic (deuteronic) wave functions simultaneously, and can directly express isotope effects, including coupling effects between nuclei and electrons. In our calculations of two polyglycines, which serve as prototypes for biological molecules, by this method, we clearly observed the geometrical relaxation induced by the isotope effect in the intramolecular hydrogen bonding portions of the molecules. The isotope effect on the interfragment interaction energy, including that of the hydrogen bonding parts, was also demonstrated: the hydrogen bond was weakened by replacement of hydrogen with deuterium. We also developed electrostatic potential approximations for use in the FMOMC_MO calculations, and the accuracy of the energy differences induced by the isotope effect was independent of the approximation level of the FMOMC_MO. Our results confirmed that the FMOMC_MO method is a powerful tool for the detailed analysis of changes in hydrogen bonding and interaction energies induced by the isotope effect for large biological molecules.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Microwave and ab initio studies of the van der Waals complex
View Description Hide DescriptionAn ab initiopotentialenergysurface of the van der Waals complex was constructed at the coupled cluster level of theory with single, double, and perturbatively included triple excitations. The recently developed smallcore pseudopotential and augmented correlationconsistent polarized valence quadruplezeta basis set was used for the xenon atom and Dunning’s augmented correlationconsistent polarized valence triplezeta basis set for the other atoms. The basis sets were supplemented with bond functions. Dipole moments were also calculated at various configurations. Rotational spectra of the van der Waals complex were recorded using a pulsednozzle Fourier transform microwave spectrometer. The isotopomers studied include those of , and with the five most abundant Xe isotopes. Transitions within three internal rotor states, namely, the ; and states, were observed and assigned. Nuclear quadrupolehyperfine structures due to the presence of were detected and analyzed. It was found that the state is perturbed by a Coriolis interaction with a nearby state. For isotopomers containing and , the states are no longer metastable and could not be observed. The spectroscopic results were used to derive structural and dynamical information of the complex.

On the effect of a radiation field in modifying the intermolecular interaction between two chiral molecules
View Description Hide DescriptionThe change in the mutual energy of interaction between a pair of chiral molecules coupled via the exchange of a single virtual photon and in the presence of an electromagnetic field is calculated using nonrelativistic quantum electrodynamics. The particular viewpoint adopted is one that has an intuitive physical appeal and resembles a classical treatment. It involves the coupling of electric and magnetic dipole moments induced at each center by the incident radiation field to the resonant dipoledipole interactiontensor. The energy shift is evaluated for fixed as well as random orientations of the molecular pair with respect to the direction of propagation of the field. A complete polarization analysis is carried out for the former situation by examining the effect of incident radiation that is linearly or circularly polarized and traveling in a direction that is parallel or perpendicular to the intermolecular distance vector. After tumble averaging, all polarization dependence of the energy shift vanishes. In both cases the interaction energy is directly proportional to the irradiance of the applied field, and is discriminatory, changing sign when one optically active species is replaced by its enantiomer. The asymptotic behavior of the energy shift at the limits of large and small separations is also studied.

Correlated product distributions from ketene dissociation measured by dc sliced ion imaging
View Description Hide DescriptionSpeed distributions of spectroscopically selected CO photoproducts of ketene photodissociation have been measured by dc sliced ion imaging. Structured speed distributions are observed that match the clumps and gaps in the singlet rotational density of states. The effects of finite time gates in sliced ion imaging are important for the accurate treatment of quasicontinuous velocity distributions extending into the thickly sliced and fully projected regime, and an inversion algorithm has been implemented for the special case of isotropic fragmentation. With accurate velocity calibration and careful treatment of the velocity resolution, the new method allows us to characterize the coincident rotational state distribution of states as a smoothly varying deviation from an unbiased phase space theory (PST) limit, similar to a linearsurprisal analysis. Highenergy rotational states of are underrepresented compared to PST in coincidence with all detected CO rotational states. There is no evidence for suppression of the fastest channels, as had been reported in two previous studies of this system by other techniques. The relative contributions of ground and first vibrationally excited singlet states in coincidence with selected rotational states of CO are well resolved and in remarkably good agreement with PST, despite large deviations from the PST rotational distributions in the fragments. At , the singlet and channels are 2350 and above their respective thresholds. The observed vibrational branching is consistent with saturation at increasing energies of the energydependent suppression of rates with respect to the PST limit, attributed to a tightening variational transition state.

Firstprinciples calculation of geometry and anharmonic vibrational spectra of thioformamide and thioformamide
View Description Hide DescriptionThe equilibrium geometry of thioformamide has been determined at the MP2 and electron correlation levels under symmetry constraints using triplezeta basis sets up to ccpVTZ. All optimized planar structures are true minima on the potentialenergysurface and are characterized by the – bond length within 1.353–, – distances of 1.656–, and NCS angle between and . The wave number of the outofplane wagging mode computed in the harmonic approximation shows stronger dependence on the basis set rather than the electron correlation level and varies from at level to at MP2/augccpVTZ level. Anharmonic vibrational spectra of and have been determined directly from the potentialenergysurfaces computed at MP2 level in triplezeta valence and basis sets using vibrational selfconsistentfield (VSCF) and correlationcorrected VSCF (CCVSCF) methods. CCVSCF wave numbers of fundamental, first overtone, and most intense combination transitions are reported for thioformamide and those of fundamentals for thioformamide. The wagging mode is strongly anharmonic and its fundamentals have been computed at and , which is remarkably close to the experimental energy of . Anharmonically computed fundamentals of this mode in thioformamide, and , are only higher than the transition energy observed in the gas phase spectrum of . The first overtone of the wagging mode of thioformamide has been calculated by CCVSCF procedure at and , which implies “negative” anharmonicity of this mode.

Beyond the resonant dipole interaction model: Resolution of a discrepancy between experimental and calculated structures of the carbon dioxide cyclic planar trimer
View Description Hide DescriptionA dimer and two trimers of carbon dioxide are known experimentally and have also been studied computationally. Whereas the calculated and experimental structures are in excellent agreement for the dimer and in fair agreement for the nonplanar trimer of symmetry, the cyclic planar trimer shows a significant discrepancy in the angle which measures the deviation from symmetry. All calculations yield for this angle values around 40° in contrast to the experimental angle of . The latter was obtained from the experimental shift of the asymmetric vibrational stretch line of the trimer relative to the monomer using the resonant dipoledipole interaction model. This model corresponds to the leading term in the molecular transition multipole expansion (TMPE) of the electrostatic coupling contribution to vibrational shifts. In this paper we go beyond the resonant dipoledipole interaction model and include higherorder moments. To this end we use the firstorder perturbation approach in combination with the ab initio symmetryadapted perturbation theory (SAPT)s potential to calculate the vibrational shifts and scale the SAPTs point charges to reproduce the experimental transitiondipole moment of the gasphase asymmetric stretch. The transition dipoledipole term in the TMPE of the electrostatic coupling plays a predominant role in the vibrational shifts of the dimer and nonplanar trimer, however, to explain the vibrational shifts of the cyclic planar trimer the inclusion of the higherorder vibrationally induced moments is needed. As the angle in this trimer approaches the value of 40° the dipoledipole term in the electrostatic coupling disappears and the sum of the higherorder terms becomes important for the correct description of the vibrational shifts. Hence applying the resonant dipoledipole interaction model to the experimentally observed vibrational shift for the cyclic planar trimer gives the wrong angle for this trimer. The higherorder terms in the TMPE of the electrostatic coupling which are not negligible for the vibrational shifts of the cyclic planar trimer include vibrationally induced dipoleoctupole and quadrupolequadrupole interactions.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Pulse shaping effect on twophoton excitation efficiency of perylene crystals and perylene in chloroform solution
View Description Hide DescriptionWe demonstrated that the twophoton excitation efficiency of perylene in chloroform solution as well as that of crystalline perylene was dramatically increased by optimizing the shape of intense femtosecond laser pulses of a regenerative amplifier output. The efficiency was three times higher than for an unshaped single femtosecond pulse with the pulse width of shorter than . The pulse shape optimized for the solution sample was a pulse train with a repetition frequency of about , and the pulse shape optimized for crystalline perylene was very similar. These results supported our previous findings on perylene crystals using weak femtosecond pulses from a modelocked laser oscillator [T. Okada et al.J. Chem. Phys.121, 6385 (2004)]. Furthermore, it was confirmed that the shaped pulse optimized for the liquid sample could also increase the twophoton excitation efficiency of perylene crystals and vice versa. We concluded that the mechanism for the increase in excitation efficiency of perylene in chloroform was almost the same as that for perylene crystal, and that the efficiency increased mainly through intramolecular dynamical processes. Processes involving intermolecular interactions and/or energy states delocalized over the crystal cannot play the major role.