Volume 118, Issue 7, 15 February 2003
 COMMUNICATIONS


Relativistic, nearly basissetlimit nuclear magnetic shielding constants of the rare gases He–Rn: A way to absolute nuclear magnetic resonance shielding scales
View Description Hide DescriptionRelativistic fourcomponent ab initio calculations using the Dirac–Coulomb Hamiltonian and converged, very large Gaussian oneparticle basis sets are carried out for the nuclear magnetic shielding constants of rare gas atoms He–Rn in their ground state. A discrepancy between two earlier sets of theoretical results for He–Xe is attributed to the basis. Absolute nuclear magnetic resonance shielding scales for the investigated elements are established because electron correlation effects are negligible in this case. Future atomicbeam experiments are discussed.
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 ARTICLES

 Theoretical Methods and Algorithms

Appropriate methods to combine forward and reverse freeenergy perturbation averages
View Description Hide DescriptionWe consider the accuracy of several methods for combining forward and reverse freeenergyperturbation averages for two systems (labeled 0 and 1). The practice of direct averaging of these measurements is argued as not reliable. Instead, methods are considered of the form where A is the free energy, is the reciprocal temperature, is the difference in configurational energy, is a weighting function, and the angle brackets indicate an ensemble average performed on the system indicated by the subscript. Choices are considered in which and the latter being Bennett’s method where C is a parameter that can be selected arbitrarily, and may be used to optimize the precision of the calculation. We examine the methods in several applications: calculation of the pressure of a squarewell fluid by perturbing the volume, the chemical potential of a highdensity LennardJones system, and the chemical potential of a model for water. We find that the approaches based on Bennett’s method weighting are very effective at ensuring an accurate result (one in which the systematic error arising from inadequate sampling is less than the estimated confidence limits), and that even the selection offers marked improvement over comparable methods. We suggest that Bennett’s method is underappreciated, and the benefits it offers for improved precision and (especially) accuracy are substantial, and therefore it should be more widely used.

A Lagrangian, integraldensity direct formulation and implementation of the analytic CCSD and CCSD(T) gradients
View Description Hide DescriptionUsing a Lagrangian formulation an integraldensity direct implementation of the analytic CCSD(T) molecular gradient is presented, which circumvents the bottleneck of storing either twoelectron integrals or density matrix elements on disk. Canonical orbitals are used to simplify the implementation of the frozencore approximation and the CCSD gradient is obtained as a special case. Also a new, simplified approach to (geometrical) derivative integrals is presented. As a first application we report a full geometry optimization for the most stable isomer of using the ccpV5Z basis set with 368 contracted basis functions and the frozencore approximation.

Quantum path minimization: An efficient method for global optimization
View Description Hide DescriptionA new unbiased global optimization approach is proposed, based on quantum staging path integral Monte Carlo sampling and local minimization of individual imaginary time slices. This algorithm uses the quantum tunnelingeffect to speed up the crossing of energy barriers. This method differs in important ways from previous work on quantum annealing and is able to find all the global minima of LennardJones clusters of size up to except for 77, and 98. The comparison between this new algorithm and several other classes of algorithms is presented.

Local treatment of electron excitations in the EOMCCSD method
View Description Hide DescriptionThe EquationofMotion coupled cluster method restricted to single and double excitations (EOMCCSD) and singlet excited states is formulated in a basis of nonorthogonal local orbitals. In the calculation of excited states only electron promotions from localized molecular orbitals into subspaces(excitation domains) of the local basis are allowed, which strongly reduces the number of EOMCCSD amplitudes to be optimized. Furthermore, double excitations are neglected unless the excitation domains of the corresponding localized occupied orbitals are close to each other. Unlike in the local methods for the ground state, the excitation domains cannot be simply restricted to the atomic orbitals that are spatially close to the localized occupied orbitals. In the present paper the choice of the excitation domains is based on the analysis of wave functions computed by more approximate (and cheaper) methods like, e.g., configurationinteraction singles. The effect of various local approximations is investigated in detail, and it is found that a balanced description of the local configuration spaces describing the ground and excited states is essential to obtain accurate results. Using a single set of parameters for a given basis set, test calculations with the local EOMCCSD method were performed for 14 molecules and 49 electronically excited states. The excitation energies computed by the local EOMCCSD method reproduce the conventional EOMCCSD excitation energies with an average error of 0.06 eV.

New optimization method for intermolecular potentials: Optimization of a new anisotropic united atoms potential for olefins: Prediction of equilibrium properties
View Description Hide DescriptionIn this study, we propose a new global procedure to perform optimization of semiempiricalintermolecular potential parameters on the basis of a large reference database. To obtain transferable parameters, we used the original method proposed by Ungerer [Ungerer et al., J. Chem. Phys. 112, 5499 (2000)], based on the minimization of a dimensionless error criterion. This method allows the simultaneous optimization of several parameters from a large set of reference data. However, the computational cost of such a method limits its application, because it implies the calculation of an important number of partial derivatives, calculated by finite differences between the results of several different simulations. In this work, we propose a new method to evaluate partial derivatives, in order to reduce the computing time and to obtain more consistent derivatives. This method is based on the analysis of statistical fluctuations during a single simulation. To predict equilibrium properties of olefins, we optimize the LennardJones potential parameters of the unsaturated hydrocarbon groups using the anisotropic united atoms description. The resulting parameters are consistent with those previously determined for linear and branched alkanes. Test simulations have been performed at temperatures ranging from 150 to 510 K for several αolefins (ethylene, propene, 1butene, 1pentene, 1hexene, 1octene), several βolefins (trans2butene, cis2butene, trans2pentene), isobutene, and butadiene. Equilibrium properties are well predicted, and critical properties can be evaluated with a good accuracy, despite the fact that most of the results constitute pure predictions. It is concluded that the AUA potential, due to a relevant physical meaning, can be transferred to a large range of olefins with good success.

Basis set and correlation dependent extrapolation of correlation energy
View Description Hide DescriptionA simple extrapolation formula of which fits correlation energies with correlation consistent and basis sets to estimate the basis set limit was devised by varying the parameter γ according to basis set quality and correlation level. The explicit extrapolation formulas suitable for calculations at the second order Møller–Plesset perturbation theory and single and double excitation coupled clustertheory with perturbative triples correction level are presented and applications are made to estimate the basis set limit binding energies of various hydrogenbonded and van der Waals clusters. A comparison of the results by this formula with the reference basis set limit results and the results by other extrapolation methods reveals that the extrapolation formulas proposed here can yield the reliable basis set limit estimates even with the small basis sets and could be used effectively for investigating large weakly bound complexes.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Energy relaxation and quenching processes of doped raregas clusters with a shelllike geometric structure
View Description Hide DescriptionEnergy relaxation processes of photoexcited clusters covered with a shell of Ar atoms (up to 40), which are embedded inside large clusters are investigated with energy resolved fluorescence spectroscopy. In the energy range of the characteristic Ne cluster absorption (16.5–18 eV) a strong energy transfer to the embedded Kr cluster is observed, which results in the desorption of electronically excited atoms. atoms move through the Ne cluster,desorb and emit visible and nearinfrared light in the vacuum By coating the Kr clusters with Ar atoms, the Kr lines disappear and transitions of become dominant. Additionally, new emission bands occur, which are assigned to transitions of perturbed atomic Kr states inside Ne clusters. Due to the interaction of electronically excited atoms with neutral Ar atoms in the surrounding shell, several excited Kr states namely and decay nonradiatively. This is in agreement with the wellknown “energygap law.” The results give experimental evidence that clusters with a multishell structure can be prepared by a sequential pickup technique. This allows the preparation of Kr clusters embedded inside Ne clusters and coated with a shell of Ar atoms. Such clusters cannot be prepared with conventional coexpansion techniques.

A survey of ab initio conical intersections for the system
View Description Hide DescriptionIn this article we present a survey of the various conical intersections which govern potential transitions between the three lower electronic states for the title molecular system. It was revealed that these three states, for a given fixed HH distance, usually form four conical intersections: two, between the two lower states and two, between the two upper states. One of the four is the well known equilateral and the others are, essentially, One of them is located on the symmetry line perpendicular to the HH axis (just like the and the other two are located on both sides of this symmetry line and in this way form the twins. The study was carried out for four values, namely, 0.5417, 0.52, and 0.4777 Å. It was also established that there exists one single value designated as located in the interval {0.52, 0.53 Å}, for which all four coalesce to become one kind of “super” which couples the three states. The numerical study was carried out employing the line integral approach for groups of two and three states. As for the twostate calculations we found that all at close proximity, are circular (ordinary) JahnTellertype whereas all at close proximity, are ellipticJahnTeller [Chem. Phys. Lett 354, 243 (2002)]. Particular attention is given to the 3state quantization of the nonadiabatic coupling matrix. The quantization is found to be fulfilled in all situations as long as the regions in configuration space are not too far from the relevant In the Discussion and Conclusion we discuss, among other subjects, the possibility to diabatize the adiabatic potential matrix.

Timeresolved xray Raman spectroscopy of photoexcited polydiacetylene oligomer: A simulation study
View Description Hide DescriptionOffresonant xray diffraction provides a novel realspace and realtime probe of electronic and vibrational dynamics in optically excited molecules. The entire manifold of valence electronic excitations may be monitored through the dependence of the xray Raman peaks on the scattering wave vector and energy The electronic excitation energies and transition density matrices of a polydiacetylene oligomer, computed using the timedependent Hartree–Fock collective electronic oscillator algorithm, are used to simulate the Raman signals and illustrate their information content.

Variational calculations of excited states with zero total angular momentum (vibrational spectrum) of without use of the Born–Oppenheimer approximation
View Description Hide DescriptionVery accurate, rigorous and fully variational, allparticle, nonBorn–Oppenheimer calculations of the vibrational spectrum of the molecule have been performed. Very high accuracy has been achieved by expanding the wave functions in terms of explicitly correlated Gaussian functions with preexponential powers of the internuclear distance. An indicator of the high accuracy of the calculations is the new upper bound for the nonrelativistic nonadiabaticground state energy equal to hartree.

Photodissociation of bromoform cation at 308, 355, and 610 nm by means of timeofflight mass spectroscopy and ion velocity imaging
View Description Hide DescriptionThe photodissociation dynamics of bromoform cation, have been studied at 308, 355, and 610 nm by means of timeofflight mass spectrometry combined with ion velocity imaging. The bromoform cation is produced via vacuum ultraviolet photoionization at 118 nm. The only fragment ions found in the timeofflightspectra at 355 and 610 nm are ions. At 308 nm and ions are also found in the timeofflightspectrum in addition to the ions. These results indicate that there is only one dissociation channel that produces at both 355 and 610 nm, while there are two more channels involved at 308 nm. One is a molecular bromine elimination channel forming and the other is a threebody dissociation channel producing Translational energy and angular distributions for each channel are deduced from the twodimensional images of and A soft fragment impulsive model closely reproduces the fraction of the available energy in translation for the atomic Br channel. The absence of channel at 355 nm may indicate a highly dynamically restricted gateway for the molecular elimination, which requires a specific molecular configuration, i.e., a threecenter transition state, before the molecule falls apart along the much simpler atomic elimination channel.

Kineticenergy release in Coulomb explosion of metastable
View Description Hide Descriptionformed by electron impact ionization of propane, undergoes metastable decay into We have monitored this reaction in a magnetic mass spectrometer of reversed geometry that is equipped with two electric sectors (BEE geometry). Three different techniques were applied to identify the fragment ions and determine the kineticenergy release (KER) of spontaneous Coulomb explosion of in the second and third field free regions of the mass spectrometer. The KER distribution is very narrow, with a width of about 3% [rootmean square standard deviation]. An average KER of is derived from the distribution. High level ab initio quantumchemical calculations of the structure and energetics of are reported. The activation barrier of the reverse reaction, (vinylidene), is computed. The value closely agrees with the experimental average KER, thus indicating that essentially all energy available in the reaction is partitioned into kinetic energy.

A semiclassical study of the effects of rotation on the unimolecular dissociation of and
View Description Hide DescriptionThe influence of rotation on the unimolecular dissociation of and is investigated. The semiclassical method we have been using for treating tunneling within classical trajectory simulations is employed to compute the level widths of selected states in both low and high energy regions. The rotational motion is considered by assigning different rotational energies and orientations of the angular momentum. It is found that the level widths for many of the states studied depend strongly on the magnitude and orientation of the angular momentum, and the variation is more pronounced in the lowenergy tunneling regime.

Direct Monte Carlo simulation of chemical reaction systems: Prediction of ultrafast detonations
View Description Hide DescriptionUltrafast detonations having steadystate velocities greater than predicted by the Chapman–Jouguet (C–J) and the Zeldovich–von Neumann–Döring (ZND) theories are predicted by direct simulations of detonation waves in gaseous reaction systems. The simulations are made using Bird’s direct simulation Monte Carlo method which produces the full details of the coupled gasdynamic and reactioneffects as well as temperature, velocity, density, pressure, and species profiles for the detonation waves. The systems are simplified and clarified by restriction to onedimensional flow with the reaction A+M→B+M having variable energy release and rate characteristics. For a slow reaction the reaction and shock regions are separated and the detonation wave proceeds at the forward speed of sound in the burned gas as predicted by the C–J and ZND theories. For a very fast reaction the reaction and shock waves overlap, the assumptions required for the C–J and ZND theories are no longer valid, the von Neumann spike is reduced, and the detonation velocity exceeds that predicted by the C–J and ZND theories to produce an ultrafast detonation.

Quantum reactive scattering calculations of cross sections and rate constants for the reaction
View Description Hide DescriptionTimedependent quantum wave packet calculations have been performed on the two lowest adiabatic potential energy surfaces and for the reaction. The calculations have been carried out, on these recently published potential energy surfaces, using the real wave packet method together with a new dispersion fitted finite difference technique for evaluating the action of the radial kinetic energy operator. Reaction probabilities, corresponding to the reactant in its ground vibrationalrotational state, have been calculated for both surfaces and for many different values of the total angular momentum quantum number (J), within the helicity decoupling approximation. The reaction probabilities associated with all other relevant J values have been interpolated, and to a smaller extent extrapolated, using a capture model, to yield probabilities as a function of energy. The probabilities have in turn been summed to yield energy dependent cross sections and then used to compute rate constants. These rate constants are compared with ones obtained from quasiclassical trajectory(QCT) and variational transition state theory (VTST) calculations performed on the same surfaces. There is a good agreement between the wave packet and QCT cross sections for reaction on both potential energy surfaces considered, with the exception of the near threshold region, where the reaction probability is dominated by tunnelling. Comparison of the predicted rate constants shows that for the surface, above 300 K, the wave packet, QCT and VTST results are quite similar. For the surface, however, significant differences occur between the wave packet and the other methods. These differences become smaller with increasing temperature. It is likely that these differences arise, at least in part, from the fact that, when calculating the rate constants, the reactants are restricted to be in their lowest vibrationalrotational state in the wave packet calculations but are selected from a thermally equilibrated population in the other methods.

Energy dependence of the Penning ionization electron spectrum of
View Description Hide DescriptionCrossed supersonic beam measurements of the Penning ionization electron spectrum for the title system are reported for a collision energy range to 7.4 kcal/mol. The spectra are deconvoluted to obtain separate line shapes for the four possible combinations of J(Ne) and The reagent fine structure ionization crosssection ratio is found to increase from 1.1 to 1.5 over this energy range, in good agreement with other studies. The anomalous product branching ratios found by Hotop et al. [J. Electron Spectrosc. Relat. Phenom. 23, 347 (1981)] are reproduced; these also depend weakly on E. The width and blueshift of all lines increase with E, while line shape asymmetry increases rapidly at low E and levels off at high. Comparison is made with quantummechanical calculations based on previously proposed potentials; the calculations predict oscillatory E dependence of the linewidth and asymmetry.

Secondorder quadrupoleshielding effects in magicangle spinning solidstate nuclear magnetic resonance
View Description Hide DescriptionWe investigate the nature of higherorder effects arising in solidstate nuclear magnetic resonance(NMR) when quadrupolar nuclei are subject to significant chemical shiftanisotropies. It is shown that the quadrupole interaction can give rise to shieldingderived terms that are not entirely averaged away by conventional magicangle spinning (MAS). These terms are proportional to the square of the component of the spin angular momentum and therefore leave unaffected both the central and other symmetric multiplequantum transitions, yet lead to noticeable effects when monitoring other nonsymmetric transitions within the spin manifold. The recentlydeveloped satellitetransition (ST) MAS NMR method for the simultaneous averaging of the first and secondorder quadrupole effects makes such quadrupoleshielding cross terms observable. Although this may present a resolution limitation to this averaging scheme, it opens up new possibilities for determining the coupling parameters of the quadrupolar nucleus—particularly the relative orientation between its quadrupole and shielding tensors. Average Hamiltonian derivations of these effects are explored, and employed to derive analytical expressions for their resulting splittings. These predictions are then successfully compared with variablefield STMAS NMR spectra of a containing sample. A brief discussion of potential complications arising from thirdorder quadrupole effects when trying to analyze such line shapes is also presented.

Twochannel vibrational relaxation of by He: A bridge between the Landau–Teller and Bethe–Wigner limits
View Description Hide DescriptionWe present a twochannel model of the vibrational relaxation (VR) of molecule, in collisions with a He atom over a broad energy range, bridging the gap between the Landau–Teller and Bethe–Wigner limits. The model is based on the generalized Landau approach for calculating the VR transition matrix element. The analytical expression for the VR cross section qualitatively reproduces the energy dependence of the numerically calculated cross section and identify the key parameters that determine this energy dependence: the steepness of the repulsive part of the potential, the depth of the potential well, and the swave elastic scattering length. On the basis of our findings and available data from the literature, we discuss the manifestation of the attractive interaction on the qualitative features of the VR cross sections and rate constants over a wide range of energies and temperatures.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Superhyperfine interactions in inhomogeneously broadened paramagnetic centers observed via a holeburned free induction decay
View Description Hide DescriptionSuperhyperfine interactions in inhomogeneously broadened paramagnetic centers are observed using a single highturnangle microwave pulse. The free induction signal that follows the holeburning pulse exhibits oscillations that are distinct from the oscillatoryfree induction decay observable in some inhomogeneously broadened systems. It contains frequencies characteristic of the superhyperfine splittings, together with a zero frequency component. Experimental examples of the effect in both orientationally disordered (powdered) and structurally disordered (glassy) systems are presented and compared with the conceptually similar Fourier transformelectron paramagnetic resonance detected nuclear magnetic resonance experiment, together with numerical simulations.