Volume 130, Issue 2, 14 January 2009
 ARTICLES

 Theoretical Methods and Algorithms

The selfreferential method for linear rigid bodies: Application to hard and LennardJones dumbbells
View Description Hide DescriptionThe selfreferential (SR) method incorporating thermodynamic integration (TI) [Sweatman et al., J. Chem. Phys.128, 064102 (2008)] is extended to treat systems of rigid linear bodies. The method is then applied to obtain the canonical ensembleHelmholtz free energy of the and plastic face centered cubic phases of systems of hard and LennardJones dumbbells using Monte Carlo simulations. Generally good agreement with reference literature data is obtained, which indicates that the SRTI method is potentially very general and robust.

Solving nonBorn–Oppenheimer Schrödinger equation for hydrogen molecular ion and its isotopomers using the free complement method
View Description Hide DescriptionThe Schrödinger equations for the hydrogen molecular ion and its isotopomers (, , , , and ) were solved very accurately using the free iterative complement interaction method, which is referred to in short as the free complement (FC) method, in the nonBorn–Oppenheimer (nonBO) level, i.e., in the nonrelativistic limit. Appropriate complement functions for both electron and nuclei were generated automatically by the FC procedure with the use of the nonBO Hamiltonian, which contains both electron and nuclear operators on an equal footing. Quite accurate results were obtained not only for the ground state but also for the vibronic excited states. For example, we obtained the groundstate energy of as , which is variationally the best in literature. The difference in the nuclear spin states of (para) and (ortho) of and some physical expectation values for several of the isotopomers shown above were also examined. The present study is the first application of the FC method to molecular systems with the nonBO Hamiltonian.

Moving leastsquares enhanced Shepard interpolation for the fast marching and string methods
View Description Hide DescriptionThe number of the potential energy calculations required by the quadratic string method (QSM), and the fast marching method (FMM) is significantly reduced by using Shepard interpolation, with a moving least squares to fit the higherorder derivatives of the potential. The derivatives of the potential are fitted up to fifth order. With an error estimate for the interpolated values, this moving least squares enhanced Shepard interpolation scheme drastically reduces the number of potential energy calculations in FMM, often by up 80%. Fitting up through the highest order tested here (fifth order) gave the best results for all grid spacings. For QSM, using enhanced Shepard interpolation gave slightly better results than using the usual second order approximate, damped BroydenFletcherGoldfarbShanno updated Hessian to approximate the surface. To test these methods we examined two analytic potentials, the rotational dihedral potential of alanine dipeptide and the reaction of methyl chloride with fluoride.

Unrestricted algebraic diagrammatic construction scheme of second order for the calculation of excited states of mediumsized and large molecules
View Description Hide DescriptionAn unrestricted version of the algebraic diagrammatic construction (ADC) scheme of the polarization propagator in second order perturbation theory [UADC(2)] is derived via the intermediate state representation. The accuracy of the extended UADC(2) approach is evaluated by comparison of computed excitation energies of 11 mediumsized radicals with their corresponding experimental literature values and with excitation energies computed at equationofmotionCCSD (coupled clusters singles and doubles) level of theory. Overall, our numerical tests show that UADC(2) exhibits an averaged mean deviation in the excitation energies of only 0.3–0.4 eV compared to experimental gas phase data. It provides thus an alternative to coupledcluster based approaches for the calculation of excited states of mediumsized openshell molecules.

Efficient global representations of potential energy functions: Trajectory calculations of bimolecular gasphase reactions by multiconfiguration molecular mechanics
View Description Hide DescriptionMulticonfiguration molecular mechanics (MCMM) was previously applied to calculate potential energies, gradients, and Hessians along a reaction path and in the largecurvature tunneling swath, and it was shown that one could calculate variational transition state theory rate constants with optimized multidimensional tunneling without requiring more than a few electronic structure Hessians. It was also used for molecular dynamics simulations of liquidphase potentials of mean force as functions of a reaction coordinate. In the present article we present some improvements to the formalism and also show that with these improvements we can use the method for the harder problem of trajectory calculations on gasphase bimolecular reactive collisions. In particular, we apply the MCMM algorithm to the modelreaction, for which we construct the global fulldimensional interpolatedpotential energy surfaces with various numbers of electronic structure Hessians and various molecular mechanics force fields, and we assess the quality of these fits by quasiclassical trajectory calculations. We demonstrate that chemical accuracy (1–2 kcal/mol) can be reached for a MCMM potential in dynamically important regions with a fairly small number of electronic structure Hessians. We also discuss the origins of the errors in the interpolated energies and a possible way to improve the accuracy.

Chemical reaction surface vibrational frequencies evaluated in curvilinear internal coordinates: Application to
View Description Hide DescriptionWe consider the general problem of vibrational analysis at nonglobally optimized points on a reduced dimensional reaction surface. We discuss the importance of the use of curvilinear internal coordinates to describe molecular motion and derive a curvilinear projection operator to remove the contribution of nonzero gradients from the Hessian matrix. Our projection scheme is tested in the context of a twodimensional quantum scattering calculation for the reaction and its reverse . Using zeropoint energies calculated via rectilinear and curvilinear projections we construct two twodimensional, adiabatically corrected, ab initioreaction surfaces for this system. It is shown that the use of curvilinear coordinates removes unphysical imaginary frequencies observed with rectilinear projection and leads to significantly improved thermal rate constants for both the forward and reverse reactions.

Efficient sampling for ab initio Monte Carlo simulation of molecular clusters using an interpolated potential energy surface
View Description Hide DescriptionAn approach is developed to enhance sampling for ab initioMonte Carlo and ab initio path integral Monte Carlo calculations of molecular clusters by utilizing an approximate potential as a guide to move in the configuration space more efficiently. The interpolatedpotential energy obtained by the moving leastsquares method is used as an approximate potential, and this scheme is applied to a water molecule and small protonated water clusters . It is found that the statistical errors are reduced by almost a factor of 3 in most calculations, which translates into a reduction in the computational cost by an order of magnitude. We also provide an automatic scheme where the ab initio data obtained during the simulation is added to the reference data set of interpolation dynamically, which further speeds up the convergence.

Time evolution of dynamic propensity in a model glass former: The interplay between structure and dynamics
View Description Hide DescriptionBy means of the isoconfigurational method, we calculate the change in the propensity for motion that the structure of a glassforming system experiences during its relaxation dynamics. The relaxation of such a system has been demonstrated to evolve by means of rapid crossings between metabasins of its potential energy surface (a metabasin being a group of mutually similar, closely related structures which differ markedly from other metabasins), as collectively relaxing units (clusters) take place. We now show that the spatial distribution of propensity in the system does not change significantly until one of these clusters takes place. However, the occurrence of a cluster clearly decorrelates the propensity of the particles, thus ending up with the dynamical influence of the structural features proper of the local metabasin. We also show an important match between particles that participate in clusters and that which show high changes in their propensity.

Role of noncollinear magnetization for the firstorder electricdipole hyperpolarizability at the fourcomponent Kohn–Sham density functional theory level
View Description Hide DescriptionThe quadratic response function has been derived and implemented at the adiabatic fourcomponent Kohn–Sham density functional theory level with inclusion of noncollinear spin magnetization and gradient corrections in the exchangecorrelation functional—a work that is an extension of our previous report where magnetization dependencies in the exchangecorrelation functional were ignored [J. Henriksson, T. Saue, and P. Norman, J. Chem. Phys.128, 024105 (2008)]. The electricfield induced secondharmonic generation experiments on and are addressed by a determination of for a wavelength of 694.3 nm, and the same property is also determined for . The relativistic effects on the static hyperpolarizability for the series of molecules amount to 1%, 5%, and 9%, respectively. At the experimental wavelength, the contributions to due to the magnetization dependence in the exchangecorrelation functional are negligible for and and small for . The noticeable effect of magnetization in the latter case is attributed to a near twophoton resonance with the excited state (nonrelativistic notation). It is emphasized, however, that the effect of magnetization on for is negligible both in comparison to the total relativistic correction as well as to the effects of electron correlation. It is concluded that, in calculations of hyperpolarizabilities under nonresonant conditions, the magnetization dependence in the exchangecorrelation functional may be ignored.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

A theoretical study of linear beryllium chains: Full configuration interaction
View Description Hide DescriptionWe present a full configuration interaction study of linear chains. A comparative study of the basisset effect on the reproduction of the energy profile has been reported. In particular, the , , , , and bases were selected. For the smallest chains (i.e., and ), smaller basis sets give dissociative energy profiles, so large basis set is demanded for the reproduction of equilibrium minima in the structures. For and linear chains, the energy profiles show a minimum also by using the smallest basis sets, but the largest ones give a much stronger stabilization energy. For all the structures, two spin states have been studied: the singlet and the triplet. It is shown that the energy separation of the two states, in the equilibrium region, is small and decays exponentially with respect to the number of atoms in the chain. Finally an interpolative technique allowing for the estimation of the longchain parameters from shorter ones is presented.

Biradicalic excited states of zwitterionic phenolammonia clusters
View Description Hide DescriptionPhenolammonia clusters with more than five ammonia molecules are proton transferred species in the ground state. In the present work, the excited states of these zwitterionic clusters have been studied experimentally with twocolor pump probe methods on the nanosecond time scale and by ab initio electronicstructure calculations. The experiments reveal the existence of a longlived excited electronic state with a lifetime in the 50–100 ns range, much longer than the excited state lifetime of bare phenol and small clusters of phenol with ammonia. The ab initio calculations indicate that this longlived excited state corresponds to a biradicalic system, consisting of a phenoxy radical that is hydrogen bonded to a hydrogenated ammonia cluster. The biradical is formed from the locally excited state of the phenolate anion via an electron transfer process, which neutralizes the charge separation of the ground state zwitterion.

A study of the ground and excited states of and . I. 488 nm anion photoelectron spectrum
View Description Hide DescriptionThe vibrationally resolved, 488 nm anion photoelectron spectrum of aluminum trimer displays transitions from two electronic states of to four states of . Franck–Condon analyses of the spectra in the independent harmonic oscillator, parallel mode approximation provide information concerning equilibrium bond length and bond angle differences among the observed states. The electron affinity of is measured to be . In the ground state, fundamental symmetric stretching and bending vibrational frequencies are and . In the ground state, these values are and , and the equilibrium bond lengths are the same as those of to within . The transition between the and ground states displays only weak activity in the bending mode, consistent with essentially structures for both states. An excited state at has vibrational frequencies of and . This state has a apex bond angle and its two equal bond lengths are within of the ground state value. Liquid nitrogen cooling of the downstream portion of the long, 0.4–0.7 Torr flow tube anion source increases the observed relative population of this excited triplet state among the sampled anions, evidently slowing its relaxation to the singlet ground state. A excited state of lies above the ground state and has frequencies of and and bonds longer than in the ground state. A excited state at displays and vibrational frequencies. The Franck–Condon analysis of this state, which is accessed only from the anion, indicates a structure with a apex bond angle and bonds longer than in the ground state. A excited state at is also accessed from the anion. The lack of vibrational features observable over overlapping transitions indicates similar structures for the and states. Primary stretching force constants are reported for the and ground states and for three excited states. In the following paper, computational predictions for the ground and excited states of and are reported and compared with these results.

A study of the ground and excited states of and . II. Computational analysis of the anion photoelectron spectrum and a reconsideration of the bond dissociation energy
View Description Hide DescriptionComputational results are reported for the ground and lowlying excited electronic states of and and compared with the available spectroscopic data. In agreement with previous assignments, the six photodetachment transitions observed in the vibrationally resolved photoelectron spectrum of are assigned as arising from the ground and excited states of and accessing the ground and excited , , and states of (with labels for states in parentheses). Geometries and vibrational frequencies obtained by PBE0 hybrid density functional calculations using the basis set and energies calculated using coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations (CCSD(T)) with the augcc {, T, Q} basis sets with exponential extrapolation to the complete basis set limit are in good agreement with experiment. Franck–Condon spectra calculated in the harmonic approximation, using either the Sharp–Rosenstock–Chen method which includes Duschinsky rotation or the parallelmode Hutchisson method, also agree well with the observed spectra. Possible assignments for the higherenergy bands observed in the previously reported UVphotoelectron spectra are suggested. Descriptions of the photodetachment transition between the and ground states in terms of natural bond order (NBO) analyses and total electron density difference distributions are discussed. A reinterpretation of the vibrational structure in the resonant twophoton ionization spectrum of is proposed, which supports its original assignment as arising from the ground state, giving an bond dissociation energy,, of . With this reduction by from the currently recommended value, the present calculated dissociation energies of , , and are consistent with the experimental data.

Regular vibrational state progressions at the dissociation limit of
View Description Hide DescriptionWe observe sharp features in the vibrational spectrum of at and above its two lowestlying dissociation limits. Highly regular vibrational progressions persist at dissociation, as in some smaller molecules studied previously by others. Nearly all of the transitions studied by stimulated emission pumping can be assigned and fitted by a simple effective Hamiltonian without resonance terms, up to a total vibrational excitation of 36 quanta. The character of the highly excited vibrational wave functions is not normal modelike, but it nonetheless arises gradually from the normal modes as the energy increases. The number of sharp vibrational features observed matches a scaling model that predicts localization of nearly all vibrational states near dissociation as the size of a polyatomic molecule increases.

Penning ionization electron spectra of pyrene, chrysene, and coronene in collision with metastable atoms in the gas phase
View Description Hide DescriptionPenning ionization electron spectra (PIES) of pyrene , chrysene , and coronene in the gas phase are recorded using metastable atoms. The assignments of PIES are presented based on the outer valence Green’s function calculations with the correlation consistent polarized valence triplebasis sets and the exterior electron density calculations of contributing molecular orbitals. The definite positions of all of the bands in the PIES are identified making use of the large PIES cross sections. Broad bands are observed in lowelectronenergy regions for chrysene and coronene and are ascribed to ionization processes of nonKoopmans types from orbitals. The anisotropicinteraction potential energy surfaces for the colliding systems are obtained from ab initio model potentials for the related systems with similar outer valences , , and , respectively. The attractive well depths in the outofplane directions are found to be similar between these molecules, and the repulsive walls embrace the inplane perimeters uniformly. Collision energy dependencies for partial Penning ionization cross sections and negative peak shifts in PIES for chrysene support these anisotropicinteractions. Effects from thermal populations in lowfrequency vibrational modes are estimated to be minor in oneelectron ionization processes.

Adiabatic invariance along the reaction coordinate
View Description Hide DescriptionIn a twodimensional space where a point particle interacts with a diatomic fragment, the action integral (where is the angle between the fragment and the line of centers and its conjugate momentum) is an adiabatic invariant. This invariance is thought to be a persistent dynamical constraint. Indeed, its classical Poisson bracket with the Hamiltonian is found to vanish in particular regions of the potential energy surface: asymptotically, at equilibrium geometries, saddle points, and inner turning points, i.e., at remarkable situations where the topography of the potential energy surface is locally simple. Studied in this way, the adiabatic decoupling of the reaction coordinate is limited to disjoint regions. However, an alternative view is possible. The invariance properties of entropy (as defined in information theory) can be invoked to infer that dynamical constraints that are found to operate locally subsist everywhere, throughout the entire reactive process, although with a modified expression.

Ab initio study of stoichiometric gallium phosphide clusters
View Description Hide DescriptionWe have studied the static dipole polarizability of stoichiometric gallium phosphide clusters ( with ) by employing various ab initiowave function based methods as well as density functional theory/time dependent density functional theory (DFT/TDDFT). The calculation of polarizability within DFT/TDDFT has been carried out by employing different exchangecorrelation functionals, ranging from simple local density approximation to an asymptotically correct model potentialstatistical average of orbital potential (SAOP) in order to study their influences. The values obtained by using the model potentialSAOP are lower than those obtained by local density approximation and generalized gradient approximation. A systematic analysis of our results obtained using the DFT/TDDFT with several exchangecorrelation functionals shows that the values of polarizability obtained within generalized gradient approximation by using PerdewBurkeErnzerhof exchange with Lee–Yang–Parr correlation functional and Perdew–Burke–Ernzerhof exchangecorrelation functionals are the closest to the corresponding results from Møller–Plesset perturbation theory. We have found that the value of average static dipole polarizability per atom reaches the bulk limit from the above as the size of the clusters increases.

On the ultraviolet photofragmentation of
View Description Hide DescriptionThe multireference spinorbit configuration interaction method is employed to calculate potential energy surfaces for the ground and lowlying excited states of the cation as functions of the Xe–C bond length and the Xe–C–H angle. It is shown that the ground state of is well bound and dissociates to the limit. In contrast, all lowest excited states of are repulsive in the Franck–Condon region and converge to the strongly spinsplit asymptotes. Transition dipole moments for the lowlying valence states are computed at the equilibrium geometry. It is shown that the first absorption continuum ( band) of is dominated by the parallel transition, which leads to the dissociation products. The perpendicular transitions to the , , and states are found to be significantly weaker. The photodissociation process in its band is analyzed on the basis of the computed data and compared with the photodissociation of the isovalent , HI, and systems.

Fewcycle laser pulses to obtain spatial separation of dissociation products
View Description Hide DescriptionIn a twopart theoretical study, fieldfree orientation of is achieved by means of moderately intense halfcycle, infrared laser pulses. In the first step, a short linearly polarized pulse excites a superposition of rigid rotor rotational eigenstates via interaction with the permanent dipole moment of . After the field has been switched off, pronounced molecular orientation is observed for several picoseconds. In the second step, femtosecond fewcycle laser pulses are applied to the oriented system to steer vibrational dynamics, modeled by anharmonic vibrational wave functions calculated on a potential energy surface obtained with unrestricted fourth order MøllerPlesset ab initio calculations. The result is selective bond breaking of OHF, followed by the spatial separation of dissociation products in the spacefixed frame. Due to revivals in the rotational wavepacket, product yields can be enhanced over long times.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Quasiequilibrium states in thermotropic liquid crystals studied by multiplequantum NMR
View Description Hide DescriptionPrevious work showed that by means of the Jeener–Broekaert (JB) experiment, two quasiequilibrium states can be selectively prepared in the proton spin system of thermotropic nematic liquid crystals (LCs) in a strong magnetic field. The similarity of the experimental results obtained in a variety of LC in a broad Larmor frequency range, with crystal hydrates, supports the assumption that also in LC the two spin reservoirs, into which the Zeeman order is transferred, originate in the dipolar energy and that they are associated with a separation in energy scales: A constant of motion related to the stronger dipolar interactions , and a second one corresponding to the secular part of the weaker dipolar interactions with regard to the Zeeman and the strong dipolar part. We study the nature of these quasiinvariants in nematic 5CB (pentyl4biphenylcarbonitrile) and measure their relaxation times by encoding the multiplequantum coherences of the states following the JB pulse pair on two orthogonal bases, and . The experiments were also performed in powder adamantane at which is used as a reference compound having only one dipolar quasiinvariant. We show that the evolution of the quantum states during the buildup of the quasiequilibrium state in 5CB prepared under the condition is similar to the case of powder adamantane and that their quasiequilibrium density operators have the same tensor structure. In contrast, the second constant of motion, whose explicit operator form is not known, involves a richer composition of multiplequantum coherences of even order on the basis, in consistency with the truncation inherent in its definition. We exploited the exclusive presence of coherences of , besides 0 and under the condition to measure the spinlattice relaxation time accurately, so avoiding experimental difficulties that usually impair dipolar order relaxation measurement such as Zeeman contamination at high fields and also superposition of the different quasiinvariants. This procedure opens the possibility of measuring the spinlattice relaxation of a quasiinvariant independent of the Zeeman and reservoirs, so incorporating a new relaxation parameter useful for studying the complex molecular dynamics in mesophases. In fact, we report the first measurement of in a LC at high magnetic fields. Comparison of the obtained value with the one corresponding to a lower field points out that the relaxation of the order strongly depends on the intensity of the external magnetic field, similarly to the case of the reservoir, indicating that the relaxation of the quasiinvariant is also governed by the cooperative molecular motions.