Volume 118, Issue 6, 08 February 2003
 COMMUNICATIONS


An advanced Monte Carlo method for the equilibration of model longchain branched polymers with a welldefined molecular architecture: Detailed atomistic simulation of an Hshaped polyethylene melt
View Description Hide DescriptionWith few exceptions, atomistic simulation work on polymers has been limited to linear chain systems. The main reason for this is the inability of existing Monte Carlo(MC) methods to equilibrate the short and longlength scale characteristics of nonlinear polymers without destroying their complex molecular architecture. We report here the first MC simulation of a welldefined model longchain branched polymer, the Hshaped polyethylene melt, in full atomistic detail. The simulation has been executed with an advanced set of chain connectivityaltering moves based on the endbridging [Pant and Theodorou, Macromolecules28, 7224 (1995); Mavrantzas et al., Macromolecules32, 5072 (1999)] and doublebridging [Karayiannis et al., Phys. Rev. Lett. 88, 105503 (2002); Karayiannis et al., J. Chem. Phys. 117, 5465 (2002)] algorithms. The new scheme provides excellent system equilibration at all length scales. The new method opens up the way toward the simulation of other nonlinear polymersystems where chain branching is precisely known (such as stars and combs) and the study of their unique thermodynamic and rheological properties from first principles.

Rovibrational stateselected study of using the pulsed field ionizationphotoelectronsecondary ion coincidence scheme
View Description Hide DescriptionA highresolution pulsed field ionization photoelectronsecondary ion coincidence (PFIPESICO) method has been developed for absolute cross section measurements of stateselected ion–molecule reactions. Employing this new PFIPESICO scheme, we have measured rovibrationalstateselected absolute cross sections for the reaction of at the centerofmass collision energies of 1.1 and 2.4 eV. The state is the second to the last vibrational level of which lies a mere 0.03 eV below the dissociation limit. The absolute cross sections observed for the formation of and from are consistent with previous experiments, exhibiting strong enhancement of the reaction cross section for However, the values for are found to be nearly constant. The drop in observed for is attributed to the further dissociation of product
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 ARTICLES

 Theoretical Methods and Algorithms

Polarization consistent basis sets. IV. The basis set convergence of equilibrium geometries, harmonic vibrational frequencies, and intensities
View Description Hide DescriptionThe basis set convergence of geometries, vibrational frequencies, and associated infrared intensities is investigated for densityfunctional methods. The recently proposed polarization consistent basis sets give an exponential convergence to the basis set limit, with each step up in quality providing an improvement of almost an order of magnitude. It is shown that the polarization consistent basis sets provide results closer to the basis set limit than alternative basis sets of similar quality.

A new correlation functional based on a transcorrelated Hamiltonian
View Description Hide DescriptionWe propose a new correlation functional based on a transcorrelated Hamiltonian that uses an exponential correlation factor. In our approach, electron–electron correlation effects are not calculated directly but are incorporated into an effective kinetic contribution. Our new functional reproduces accurate correlation energies for H–Ar atoms reasonably well. In order to investigate the behavior of this functional, we have also studied the correlation holes of He and Hooke atoms in detail.

An accurate determination of rovibrational spectra using the externally corrected coupledcluster approaches: LiH ground state
View Description Hide DescriptionRecently acquired highly precise spectroscopic data for the ground state of LiH and its various isotopomers are employed to carry out a critical assessment of the performance of the externally corrected coupledcluster (CC) approaches. Both the amplitude and energycorrected approaches are considered, in particular the reduced multireference CC method with singles and doubles (RMR CCSD) and the asymmetric energy formula based CCSD[MR] method, both exploiting the same modestsize multireference configuration interaction (MR CISD) wave function, based on an Mdimensional reference space, as the source of higher than pair clusters. To assess the size of the basis set errors relative to those of the methods employed, the comparison is also made with the full CI (FCI) results at the ccpVTZ level. The rovibrational energy levels and the corresponding transition frequencies are then computed for various isotopomers of LiH using the theoretically determined potentials at the ccpVXZ (X=D, T, Q, and 5) and the extrapolated completebasissetlimit levels and a comparison is made with the experiment as well as with the existing theoretical results, particularly those exploiting the CC approaches. The role of adiabatic corrections is also assessed. It is shown that both the RMR CCSD and CCSD[4R] methods, yielding an almost indistinguishable results, are capable of accounting for the nondynamical correlation effects that are lacking in the standard singlereference CCSD approaches.

Semiclassical dynamics with quantum trajectories: Formulation and comparison with the semiclassical initial value representation propagator
View Description Hide DescriptionWe present a timedependent semiclassical method based on quantum trajectories. Quantummechanical effects are described via the quantum potential computed from the wave function density approximated as a linear combination of Gaussian fitting functions. The number of the fitting functions determines the accuracy of the approximate quantum potential (AQP). One Gaussian fit reproduces timeevolution of a Gaussian wave packet in a parabolic potential. The limit of the large number of fitting Gaussians and trajectories gives the full quantummechanical result. The method is systematically improvable from classical to fully quantum. The fitting procedure is implemented as a gradient minimization. We also compare AQP method to the widely used semiclassical propagator of Herman and Kluk by computing energyresolved transmission probabilities for the Eckart barrier from the wave packet timecorrelation functions. We find the results obtained with the Herman–Kluk propagator to be essentially equivalent to those of AQP method with a oneGaussian density fit for several barrier widths.

The electron cusp condition and the virial ratio as indicators of basis set quality
View Description Hide DescriptionWe consider two measures of the quality of oneelectron basis sets for quantumchemical calculations: The electron–electron coalescence curvature and the correlation energy virial ratio. The former is based on the Kato cusp condition that manyelectron wave functions must exhibit discontinuous first derivatives with respect to as the coordinates of any two electrons coalesce. The latter is based on a simple modification of the quantummechanical virial theorem that makes use of only the correlation contributions to the kinetic and potential energy expectation values. The two measures are tested using coupled clusterwave functions for helium, neon, argon, calcium, and phosphorus atoms and are found to indicate good correlation with the quality of the basis set. These techniques may provide a foundation for the development of reliable basis set diagnostics for a variety of quantumchemical applications.

A direct optimization method for calculating density functionals and exchange–correlation potentials from electron densities
View Description Hide DescriptionA direct optimization method is developed for the computation of the Kohn–Sham kinetic energy density functional from a given electron density and the exchange–correlation potential if this density is from a ground state. The method is based on the construction of a variational functional of the oneelectron potential. This functional is derived from the conventional Levy constrainedsearch formulation and is shown to be closely related to the Lieb functional construction. The oneelectron potential is expanded in terms of some fixed terms plus a linear expansion in a basis set. The determination of the Kohn–Sham kinetic energy for an input density is then turned into the maximization of this functional of potential. The analytic first and second derivatives of the variational functional with respect to the linear basis set expansion coefficients and also the nonlinear parameters in the basis set are derived. This enables very efficient iterative optimization of the potential and hence the calculation of and The efficiency and accuracy of the method is shown in the numerical implementation for atomic and molecular calculations with Gaussian basis set expansions both for molecular orbitals and for oneelectron potentials. Finally, this direct optimization method is extended to general density functionals and the analytic derivatives are also developed for use in optimization methods.

Algorithms and novel applications based on the isokinetic ensemble. I. Biophysical and path integral molecular dynamics
View Description Hide DescriptionIn this paper (Paper I) and a companion paper (Paper II), novel new algorithms and applications of the isokinetic ensemble as generated by Gauss’ principle of least constraint, pioneered for use with molecular dynamics 20 years ago, are presented for biophysical, path integral, and Car–Parrinello based ab initiomolecular dynamics. In Paper I, a new “extended system” version of the isokinetic equations of motion that overcomes the ergodicity problems inherent in the standard approach, is developed using a new theory of nonHamiltonian phase space analysis [M. E. Tuckerman et al., Europhys. Lett. 45, 149 (1999); J. Chem. Phys. 115, 1678 (2001)]. Reversible multiple time step integrations schemes for the isokinetic methods, first presented by Zhang [J. Chem. Phys. 106, 6102 (1997)] are reviewed. Next, holonomic constraints are incorporated into the isokinetic methodology for use in fast efficient biomolecular simulation studies. Model and realistic examples are presented in order to evaluate, critically, the performance of the new isokinetic molecular dynamic schemes. Comparisons are made to the, now standard, canonical dynamics method, Nosé–Hoover chain dynamics [G. J. Martyna et al., J. Chem. Phys. 97, 2635 (1992)]. The new isokinetic techniques are found to yield more efficient sampling than the Nosé–Hoover chain method in both path integral molecular dynamics and biophysical molecular dynamics calculations. In Paper II, the use of isokinetic methods in Car–Parrinello based ab initiomolecular dynamics calculations is presented.

Algorithms and novel applications based on the isokinetic ensemble. II. Ab initio molecular dynamics
View Description Hide DescriptionIn this paper (Paper II), the isokinetic dynamics scheme described in Paper I is combined with the planewave based Car–Parrinello (CP) ab initiomolecular dynamics (MD) method [R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)] to enable the efficient study of chemical reactions and metallic systems. The Car–Parrinello approach employs “on the fly” electronic structure calculations as a means of generating accurate internuclear forces for use in a molecular dynamics simulation. This is accomplished by the introduction of an extended Lagrangian that contains the electronic orbitals as fictitious dynamical variables (often expressed directly in terms of the expansion coefficients of the orbitals in a particular basis set). Thus, rather than quench the expansion coefficients to obtain the ground state energy and nuclear forces at every time step, the orbitals are “propagated” under conditions that allow them to fluctuate rapidly around their global minimum and, hence, generate an accurate approximation to the nuclear forces as the simulation proceeds. Indeed, the CP technique requires the dynamics of the orbitals to be both fast compared to the nuclear degrees of freedom while keeping the fictitious kinetic energy that allows them to be propagated dynamically as small as possible. While these conditions can be easy to achieve in many types of systems, in metals and highly exothermic chemical reactions difficulties arise. (Note, the CP dynamics of metals is incorrect because the nuclear motion does not occur on the ground state electronic surface but it can, nonetheless, provide useful information.) In order to alleviate these difficulties the isokinetic methods of Paper I are applied to derive isokinetic CP equations of motion. The efficacy of the new isokinetic CPMD method is demonstrated on model and realistic systems. The latter include, metallic systems, liquid aluminum, a small silicon sample, the reconstruction of the silicon 100 surface, and the Diels–Alder addition of 1,3butadiene to the reconstructedsilicon 100 surface.

Accuracy of spectroscopic constants of diatomic molecules from ab initio calculations
View Description Hide DescriptionThe basisset convergence of basis sets is investigated for the MP2 and CCSD equilibrium bond distances and harmonic frequencies of BH, HF, CO, and by comparing with explicitly correlated R12 results. The convergence is, in general, smooth but slow—for example, for harmonic frequencies at the quadruplezeta level, the basisset error is typically 7 cm^{−1}; at the sixtuplezeta level, it is about 2 cm^{−1}. For most constants, the convergence can be accelerated by using a twopoint linear extrapolation procedure. Equilibrium bond distances, harmonic frequencies, anharmonic contributions, vibrationrotation interaction constants, and rotational constants for the vibrational ground state have been calculated for the same set of molecules using standard wave function and basisset levels of ab initiotheory. The accuracy of the calculated constants has been established by carrying out a statistical analysis of the deviations with respect to experiment. The largest errors for bond distances and harmonic frequencies calculated at the corecorrected CCSD(T)/ccpV6Z level are 0.4 pm and 13.4 cm^{−1}, respectively. Much smaller errors occur for the anharmonic contributions.

Calculations of nuclear magnetic shielding in paramagnetic molecules
View Description Hide DescriptionWe propose and evaluate first principles methods for calculating the nuclear shielding tensor in openshell, paramagnetic molecules, dealing with the case of small spin–orbit coupling that, in turn, implies the best applicability to light, organic compounds. The formalism is consistent up to second order in the fine structure constant, and includes orbital, fully anisotropic dipolar, and isotropic contact contributions to the tensor. The proposed method is implemented within the ab initio single and multiconfiguration selfconsistent field as well as density functional theory frameworks. The applications include small maingroup radicals and larger nitroxide radicals. The analysis of the results and comparison with the experimental nuclear magnetic resonance data, which are available for the latter compounds, indicate promising accuracy and applicability of the density functional theory method to chemically interesting problems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dissociative electron attachment near threshold, thermal attachment rates, and vertical attachment energies of chloroalkanes
View Description Hide DescriptionThe peaks appearing near zero energy in the dissociative electron attachment cross section of 18 chloroalkanes are studied by electron beam methods. Fits to the experimental data are made using model cross sections having appropriate energy dependences and inclusion of the broadening due to the electron energy distribution. The magnitudes of the zero peaks are found to be well correlated with the vertical attachment energies (VAE) associated with occupation of the lowest empty orbitals of the compounds. The magnitudes rise exponentially by more than five orders of magnitude as VAE decreases from 2 eV to a slightly negative value. This dependence is a consequence not only of the thermal population of vibrational levels, but also of an approximately linear relationship between VAE and the energy of the crossing between the neutral and anion potential curves. Franck–Condon factors for the transition to the anion curve are computed for model potential curves, and the nature of the attachment from vibrational levels with energies near that of the crossing point is explored in a local potential resonance picture. A substantial contribution arises from tunneling to the anion state from vibrational levels below the barrier. Thermal attachment rate constants are also computed from our data. These are also shown to vary exponentially with VAE.

The nuclear shielding tensor surfaces for Xe interacting with rare gas atoms
View Description Hide DescriptionThe shielding tensorsurfaces for the Xe–Xe, Xe–Kr, Xe–Ar, and Xe–Ne dimers are calculated as a function of separation, using gaugeincluding atomic orbitals (GIAO) at the Hartree–Fock level, and also using density functional theory with the B3LYP hybrid functional. Since the highest quality potential energy functions are available for these systems, the available experimental data (temperature dependent second virial coefficients of the nuclear magnetic resonancechemical shifts) are from measurements on welldefined physical systems (Xe at low mole fraction in the gas phase), and the relation between the observed quantity and the shielding function is welldefined, these systems provide a means by which the dispersion component of the isotropic shielding function of Xe–Rg can be determined. The parallel component of the intermolecular shielding tensor is small and nearly independent of the method of calculation. Therefore, the dispersion component of the perpendicular component of the shielding function can be determined.

The partitioning of energy amongst vibration, rotation, and translation during the dissociation of pdifluorobenzene–Ar neutral and cation complexes
View Description Hide DescriptionThe dissociation dynamics of pdifluorobenzene–Ar and pdifluorobenzene have been investigated from the level in and the level in respectively. The technique of velocity map imaging has been used to determine the translational energy release distributions. In the case of pdifluorobenzene–Ar, dispersed fluorescence spectra provide the distribution of vibrational energy in the pdifluorobenzene fragment. A significant fraction of the pdifluorobenzene products are formed in the level. From the translational energy release data the rotational energy distribution within can be inferred. The results show that the average rotational energy is 380 >5 times the average translational energy of 70 This rotational excitation infers that dissociation occurs with the Ar atom significantly displaced from its equilibrium position above the center of the aromatic ring. From the average rotational energy it is determined that the Ar atom is, on average, displaced by 1.8–3.7 Å from the center of the aromatic ring at dissociation, i.e., the Ar atom is beyond the carbon atoms. In the case of dissociation from the level of pdifluorobenzene the vibrational distribution within the product is not known, however it can be inferred from previous studies of dissociation within As for the pdifluorobenzene–Ar case, the evidence suggests that dissociation leads to significant rotational excitation of There are a limited number of destination vibrations within the pdifluorobenzene and fragments for dissociation from and respectively. Hence there are only a few, widely separated, values for the combined translational and rotational energy available. Despite this, the translational energy release distributions in both cases are smooth and structureless. In the limit of no rotational excitation of the polyatomic fragment, the translational energy release distributions would show peaks only at energies corresponding to populated vibrational states of the product. The absence of such peaks indicates that rotational excitation of the product occurs for all vibrational states, reducing the average translational energy released and smearing the distribution.

Photodissociation dynamics of enolicacetylacetone at 266, 248, and 193 nm: Mechanism and nascent state product distribution of OH
View Description Hide DescriptionThe photodissociation dynamics of acetylacetone which exists predominantly as an enolic form in gas phase, is studied using pulsed laserphotolysislaser induced fluorescence(LIF) “pumpandprobe” technique at room temperature. Although two pathways for OH formation have been observed, we have focused on the nascent state of the primary OH radical, formed after photoexcitation of the molecule to its and Rydberg states. The and Rydberg transitions are prepared by excitation with fourth harmonic of Nd:YAG (266 nm)/KrF (248 nm) and ArF (193 nm) lasers, respectively. The rovibrational distribution of the nascent OH photofragment is measured in collisionfree conditions using LIF. The OH fragments are formed in vibrationally cold state at all the above wavelengths of excitation, but differ in rotational state distributions. The rotational distribution is Boltzmannlike, and characterized by rotational temperatures of and at 266, 248, and 193 nm photodissociation, respectively. The spin–orbit and Λdoublets ratios of OH fragments formed in the dissociation process are also measured. The average translational energy partitioned into the photofragment pairs in the centerofmass coordinate is found to be and at 266, 248, and 193 nm excitation, respectively. The energy partitioning into various degrees of freedom of products is interpreted with the help of different models, namely, statistical, impulsive, and hybrid models. To understand the nature of the dissociativepotential energy surface involved in the OH production channel, detailed ab initio calculations are performed using configuration interactionsingles method. Although acetylacetone is initially prepared in the state at 266 and 248 nm excitation, it is concluded that the OH fragment is formed from the lowest state. However, upon excitation at 193 nm, the initially prepared Rydberg state of acetylacetone crosses over fast to the nearby repulsive state along the C–OH bond, and dissociates to give the OH radical.

Proton transfer in gasphase ammonium dinitramide clusters
View Description Hide DescriptionProton transfer in gaseous ammonium dinitramide (ADN) clusters up to is studied by using densityfunctional theory.Proton transfer between the hydrogen dinitramide and ammonia units does not occur in the ADN monomer, rather the ammonia–hydrogen dinitramide complex is stabilized by strong hydrogen bonding. However, proton transfer between hydrogen dinitramide and ammonia is observed in the ADN dimer ADN solvated with a single ammonia molecule and ADN solvated with a hydrogen dinitramide molecule Structural changes in the complexes relative to the free molecules and the binding energies of the clusters are given. Using population analysis, the total electrostatic interaction energy in each cluster is calculated. The electrostaticenergy is a measure that distinguishes between the ionic or hydrogenbonded nature of the clusters. Some implications of proton transfer in ADN clusters on the decomposition mechanism of ADN are discussed.

Dynamical ionization of the trimer: A timedependent modeling of its fragmentation
View Description Hide Descriptiontrimer 3Dphotoionization has been studied using a new quantum timedependent model based on a wavelet expansion of the timedependent vibrational selfconsistentfield equations. Dissociation probabilities and final vibrational populations of the fragment molecules, together with timesnapshots of the angular distributions during fragmentation, are analyzed. Special emphasis is given to the internal vibrational rearrangements occurring during the fragmentation process following the photoionization event. Our calculations found to be preferentially formed in one of its vibrationally excited states and also that the amount of surviving the fragmentation, is mostly left in vibrationally excited states involving its ionic part.

Structural and spectroscopic trends in the ground states of the monohalosilylenes: Emission spectroscopy of jetcooled HSiI and DSiI
View Description Hide DescriptionSingle vibronic level emission spectra of jetcooled HSiI and DSiI have been recorded by laser excitation of selected bands of the electronic transition. The data have been used to derive the ground state harmonic frequencies and anharmonicities for both isotopomers. A normal coordinate analysis of the harmonic frequencies yielded reliable values for five of the six force constants. Using previously determined ground staterotational constants and the force field data, average and approximate equilibrium structures were calculated, with and A comparison of trends in the structural parameters and vibrational frequencies of the monohalosilylenes shows that the bond angle increases significantly and the Si–H bond length decreases slightly with heavier halogen substitution. These trends have been rationalized based on the inductive effect and the electronegativity of the halogen substituent.

Permanent electric dipole moments and hyperfine interaction in ruthenium monocarbide, RuC
View Description Hide DescriptionThe band system of a molecular beam sample of RuC has been recorded field free and in the presence of a static electric field using high resolution laser induced fluorescencespectroscopy. The Stark shifts of the optical features for the isotopomer were analyzed to produce permanent electric dipole moments of 3.31(4) and 4.09(14) D for the and states, respectively. The hyperfine structure associated with spectral features for the and isotopomers was analyzed to produce electric quadrupole and magnetic hyperfine coupling parameters. The hyperfine structure and dipole moments are interpreted using a molecular orbital correlation model and compared with predictions from electronic structure calculations and isovalent iron monocarbide, FeC.