Volume 120, Issue 5, 01 February 2004
 ARTICLES

 Theoretical Methods and Algorithms

A doubly nudged elastic band method for finding transition states
View Description Hide DescriptionA modification of the nudged elastic band (NEB) method is presented that enables stable optimizations to be run using both the limitedmemory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) quasiNewton and slowresponse quenched velocity Verlet minimizers. The performance of this new “doubly nudged” DNEB method is analyzed in conjunction with both minimizers and compared with previous NEB formulations. We find that the fastest DNEB approach (DNEB/LBFGS) can be quicker by up to 2 orders of magnitude. Applications to permutational rearrangements of the sevenatom LennardJones cluster and highly cooperative rearrangements of and are presented. We also outline an updated algorithm for constructing complicated multistep pathways using successive DNEB runs.

The reduced density matrix method for electronic structure calculations and the role of threeindex representability conditions
View Description Hide DescriptionThe variational approach for electronic structure based on the twobody reduced density matrix is studied, incorporating two representability conditions beyond the previously used and conditions. The additional conditions (called and here) are implicit in the work of Erdahl [Int. J. Quantum Chem. 13, 697 (1978)] and extend the wellknown threeindex diagonal conditions also known as the Weinhold–Wilson inequalities. The resulting optimization problem is a semidefinite program, a convex optimization problem for which computational methods have greatly advanced during the past decade. Formulating the reduced density matrix computation using the standard dual formulation of semidefinite programming, as opposed to the primal one, results in substantial computational savings and makes it possible to study larger systems than was done previously. Calculations of the ground state energy and the dipole moment are reported for 47 different systems, in each case using an STO6G basis set and comparing with Hartree–Fock, singly and doubly substituted configuration interaction, Brueckner doubles (with triples), coupled cluster singles and doubles with perturbational treatment of triples, and full configuration interaction calculations. It is found that the use of the and conditions gives a significant improvement over just the and conditions, and provides in all cases that we have studied more accurate results than the other mentioned approximations.

Currentdependent extension of the Perdew–Burke–Ernzerhof exchangecorrelation functional
View Description Hide DescriptionThe probability current density is used in addition to the electron density and its gradient as a variable in the construction of an exchangecorrelation functional. Starting from the Perdew–Burke–Ernzerhof generalized gradient approximation, we employ exact conditions to build a nonempirical exchange functional. Matching the correlation functional to that for exchange yields a currentdependent approximation for correlation. The resulting functional is given in a simple closed form. Application of this approximation to open shell atoms eliminates the artificial level splitting of formally degenerate states observed with generalized gradient approximations.

Stereographic projections path integral for inertia ellipsoids: Applications to clusters
View Description Hide DescriptionThe DeWitt formula for inertia ellipsoids mapped by stereographic projection coordinates is developed. We discover that by remapping the quaternion parameter space with stereographic projections, considerable simplification of the differential geometry for the inertia ellipsoid with spherical symmetry takes place. The metric tensor is diagonal and contains only one independent element in that case. We find no difficulties testing and implementing the DeWitt formula for the inertia ellipsoids of asymmetric tops mapped by stereographic projections. The path integral algorithm for the treatment of manifolds based on a mixture of Cartesian and stereographic projection coordinates is tested for small clusters in the to range. In particular, we determine the quantum effects of the red shift and the isomerization patterns at finite temperatures. Our findings are consistent with previously reported computations and experimental data for small clusters.

Constrained fluid λintegration: Constructing a reversible thermodynamic path between the solid and liquid state
View Description Hide DescriptionA novel λintegration path is proposed for calculating the Gibbs free energy difference between any arbitrary solid and liquid state needed for the location of melting lines. This technique involves reversibly forcing a liquid state to a solid state across the phase transition along a nonphysical path, thermodynamically coupling the two states directly. The process eliminates the need for coupling to idealized reference states as is presently performed and hence simplifies the location of phase transitions for computer simulation systems. More specifically the path involves a three stage process, whereby, initially a liquid state is transformed to a weakly attractive fluid using linear λintegration scaling of the intermolecular potential. In the second stage, the resulting fluid is then constrained to the required solid configurational phase space via the insertion of a periodic lattice of 3D Gaussian wells. The final stage involves reversing to full strength the main intermolecular potential while gradually turning off the constraining 3D Gaussian lattice finally resulting in a stable (or metastable) solid state. Each stage was found to be completely reversible and the resulting change in free energy was thermodynamically integrable. The methodology is demonstrated and validated by calculating solid–liquid coexistence points using the new technique and comparing to those in present literature for the truncated and shifted LennardJones system. The results are found to be in good agreement. The new method is not limited to meltingphase transitions and is readily applicable to any simulation methodology, simulation cell size and/or intermolecular potential including ab initio methods.

Relativistic spinorbit effects on hyperfine coupling tensors by densityfunctional theory
View Description Hide DescriptionA secondorder perturbation theory treatment of spinorbit corrections to hyperfine coupling tensors has been implemented within a densityfunctional framework. The method uses the allelectron atomic meanfield approximation and/or spinorbit pseudopotentials in incorporating one and twoelectron spinorbit interaction within a firstprinciples framework. Validation of the approach on a set of maingroup radicals and transition metal complexes indicates good agreement between allelectron and pseudopotential results for hyperfine coupling constants of the lighter nuclei in the system, except for cases in which scalar relativistic effects become important. The nonrelativistic Fermi contact part of the isotropic hyperfine coupling constants is not always accurately reproduced by the exchangecorrelation functionals employed, particularly for the triplet and πtype doublet radicals in the present work. For this reason, ab initiocoupledcluster singles and doubles with perturbative triples results for the firstorder contributions have been combined in the validation calculations with the densityfunctional results for the secondorder spinorbit contributions. In the cases where spinorbit corrections are of significant magnitude relative to the nonrelativistic firstorder terms, they improve the agreement with experiment. Antisymmetric contributions to the hyperfine tensor arise from the spinorbit contributions and are discussed for the radical, whereas rovibrational effects have been evaluated for RhC, NBr, and NI.

A second quantization formulation of multimode dynamics
View Description Hide DescriptionA new formalism for calculating and analyzing manymode quantum dynamics is presented. The formalism is similar in spirit to the second quantization formulation of electronic structure theory. The similarity means that similar techniques can be employed for calculating the manymode nuclear wave function. As a consequence a new formulation of the vibrational selfconsistentfield (VSCF) method can be developed. Another result is that the formalism opens up for the construction of new methods that go beyond the VSCF level. A vibrational coupled cluster (VCC) theory is constructed using the new formalism. The sizeextensivity concept is introduced in the context of multimode wave functions and the size extensivity of approximate VCC methods is illustrated in comparison with the nonsizeextensive vibrational configuration interaction method.

Vibrational coupled cluster theory
View Description Hide DescriptionThe theory and first implementation of a vibrational coupled cluster (VCC) method for calculations of the vibrational structure of molecules is presented. Different methods for introducing approximate VCC methods are discussed including truncation according to a maximum number of simultaneous mode excitations as well as an interaction space order concept is introduced. The theory is tested on calculation of anharmonic frequencies for a threemode model system and a formaldehyde quartic force field. The VCC method is compared to vibrational selfconsistentfield, vibrational Møller–Plesset perturbation theory, and vibrational configuration interaction (VCI). A VCC calculation typically gives higher accuracy than a corresponding VCI calculation with the same number of parameters and the same formal operation count.

Path integral hybrid Monte Carlo algorithm for correlated Bose fluids
View Description Hide DescriptionPath integral hybrid Monte Carlo (PIHMC) algorithm for strongly correlated Bose fluids has been developed. This is an extended version of our previous method [S. Miura and S. Okazaki, Chem. Phys. Lett. 308, 115 (1999)] applied to a model system consisting of noninteracting bosons. Our PIHMC method for the correlated Bose fluids is constituted of two trial moves to sample pathvariables describing system coordinates along imaginary time and a permutation of particle labels giving a boundary condition with respect to imaginary time. The pathvariables for a given permutation are generated by a hybrid Monte Carlo method based on path integral molecular dynamics techniques. Equations of motion for the pathvariables are formulated on the basis of a collective coordinate representation of the path, staging variables, to enhance the sampling efficiency. The permutation sampling to satisfy Bose–Einstein statistics is performed using the multilevel Metropolis method developed by Ceperley and Pollock [Phys. Rev. Lett. 56, 351 (1986)]. Our PIHMC method has successfully been applied to liquid helium4 at a state point where the system is in a superfluid phase. Parameters determining the sampling efficiency are optimized in such a way that correlation among successive PIHMC steps is minimized.

Onthefly localization of electronic orbitals in Car–Parrinello molecular dynamics
View Description Hide DescriptionThe ab initio moleculardynamics formalism of Car and Parrinello is extended to preserve the locality of the orbitals. The supplementary term in the Lagrangian does not affect the nuclear dynamics, but ensures “on the fly” localization of the electronic orbitals within a periodic supercell in the Γpoint approximation. The relationship between the resulting equations of motion and the formation of a gaugeinvariant Lagrangian combined with a gaugefixing procedure is briefly discussed. The equations of motion can be used to generate a very stable and easy to implement numerical integration algorithm. It is demonstrated that this algorithm can be used to compute the trajectory of the maximally localized orbitals, known as Wannier orbitals, in ab initiomolecular dynamics with only a modest increase in the overall computer time. In the present paper, the new method is implemented within the generalized gradient approximation to Kohn–Sham densityfunctional theory employing plane wave basis sets and atomic pseudopotentials. In the course of the presentation, we briefly discuss how the present approach can be combined with localized basis sets to design fast linear scaling ab initio moleculardynamics methods.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

The openshell interaction of He with the state of An ab initio study and its comparison with a diatomicsinmolecule perturbation model
View Description Hide DescriptionThe interaction of He with in electronically excited state is investigated using spinunrestricted single and double coupledcluster approach with noniterative perturbative treatment of triple excitations. Internal electrons of the Br atom are described by effective core pseudopotentials. The validity of this approach is analyzed by comparing the lowest and electronic states of the HeBr molecule with those obtained in all electron calculations [J. Chem. Phys. 115, 10438 (2001)]. In this context, we examine the performance of different basis sets and saturation with bond functions. The comparison of theoretical blueshifts with the experiment provides confidence about the present ab initio calculations. In addition, He–Br results of ab initio calculations at the same level are used to obtain approximate interactions in the framework of the diatomicsinmolecule first order perturbation theory (IDIMPT1) [J. Chem. Phys. 104, 9913 (1996)]. Overall, the IDIMPT1 model results show a good agreement with the ab initio ones, being the main difference the sensitivity to the elongation of the Br–Br bond.

Photodissociation dynamics of the methyl radical at 212.5 nm: Effect of parent internal excitation
View Description Hide DescriptionPhotodissociation dynamics of the radical at 212.5 nm has been investigated using the H atom Rydberg tagging timeofflight method with a pure radical source generated by the photolysis of at 266 nm. Timeofflightspectra of the H atom products from the photolysis of both cold and hot methyl radicals have been measured at different photolysispolarizations. Experimental results indicate that the photodissociation of the methyl radical in its ground vibrational state at 212.5 nm excitation occurs on a very fast time scale in comparison with its rotational period, indicating the dissociation at 212.5 nm occurs on the excited Rydberg statesurface. Experimental evidence also shows that the photodissociation of the methyl radical in the state of the umbrella mode at 212.5 nm excitation is characteristically different from that in the ground vibrational state.

Electron localization–delocalization transitions in dissociation of the anion: A largeD analysis
View Description Hide DescriptionWe present a study, employing high level ab initio methods, of electron localization–delocalization transitions along the dissociation path of the anion to and We find that at the equilibrium geometry, the symmetrical and nonsymmetrical configurations of the linear anion are almost isoenergetic. However, along a collinear dissociation path, the dipole moment drops abruptly to zero when the separation between the two middle carbon nuclei reaches about The dipole moment remains zero until about and then continuously increases as dissociation proceeds. This behavior is analogous to critical phenomena: The abrupt drop to zero of the dipole moment resembles a firstorder phase transition, the later steady rise resembles a continuous phase transition. We show that a simple subHamiltonian model, corresponding to the largedimension limit for an electron in the field of four collinear carbon atoms, exhibits both kinds of phase transitions along the dissociation path.

Hydrates of the most stable gasphase mono and diprotonated glycine derivatives: Origin of no reservation energy bond in
View Description Hide DescriptionSeries of hydrates of the most stable in the gas phase are presented at the B3LYP level. The results show that only the amino hydrogens and hydroxyl hydrogens can be monohydrated for the and the amino hydrogens are preferred. The H6(O4) of is the best site for a water molecule to attach, i.e., the corresponding hydrate is the most stable one among its isomers. Calculations reveal that the binding energies of hydrated hydrogens decrease relative to their counterparts in the isolated complexes and they are positive values and without proton transfer except those of monohydrated complexes with the combination modes of The complex is formed by the combination of a molecule and one hydroxylsite proton of and with the proton transfer to Here the interaction between the proton of and the mainly depends on an electronic one instead of an initial covalent one of the isolated The generation of the bond between the and the makes the energy of the complex higher than the energy sum of its two separated species (or two reactants of the complex), just like the case of bond The observation can explain satisfactorily why the combinations of both a proton and an alkali ion or two alkali ions to a glycine molecule can make the corresponding complex hold reservation energy bond(s), while the combination of two protons and a glycine in our previous work cannot [H. Ai et al., J. Chem. Phys. 117, 7593 (2002)]. For the monohydration at the any site of its amino hydrogens can make the binding strength of any other neighboring proton (hydrogens) stronger relative to its counterpart in the isolated Further hydration, especially at the site of either of hydroxyl hydrogens, would disfavor the reservation energy of the system.

A combined crossed beam and theoretical investigation of
View Description Hide DescriptionThe radical–radical reaction dynamics of groundstate atomic oxygen with propargyl radicals has first been investigated in a crossed beam configuration. The radical reactants and were produced by the photodissociation of and the supersonic flash pyrolysis of precursor propargyl bromide, respectively. A new exothermic channel of was identified and the nascent distributions of the product OH in the ground vibrational state showed bimodal rotational excitations composed of the low and high components without spin–orbit propensities. The averaged ratios of were determined to be 0.60±0.28. With the aid of ab initio theory it is predicted that on the lowest doublet potential energy surface, the reaction proceeds via the addition complexes formed through the barrierless addition of to The common direct abstraction pathway through a collinear geometry does not occur due to the high entrance barrier in our low collision energy regime. In addition, the major reaction channel is calculated to be the formation of propynal (CHCCHO)+H, and the counterpart of the probed OH product in the title reaction is cyclopropenylidene after considering the factors of barrier height, reactionenthalpy and structural features of the intermediates formed along the reaction coordinate. On the basis of the statistical prior and rotational surprisal analyses, the ratio of population partitioning for the low and high is found to be about 1:2, and the reaction is described in terms of two competing additioncomplex mechanisms: a major shortlived dynamic complex and a minor longlived statistical complex. The observed unusual reaction mechanism stands in sharp contrast with the reaction of with allyl radical a second significant conjugated hydrocarbon radical, which shows totally dynamic processes [J. Chem. Phys. 117, 2017 (2002)], and should be understood based upon the characteristic electronic structures and reactivity of the intermediates on the potential energy surface.

Kinetics of radical reactions with alkanes by LIF
View Description Hide DescriptionThe reactions of radicals with a series of alkanes have been studied at room temperature and 6.5 torr total pressure using the pulsed laser photolysis/laserinduced fluorescence technique. radicals were generated by photolysis of with the focused output from the fourth harmonic of a Nd:YAG laser at 266 nm. The relative concentration of radicals was monitored on the (0,0) band of the transition at 516.5 nm by laserinduced fluorescence. From the analysis of the relative concentrationtime behavior of under pseudofirstorder conditions, the rate constants for the reactions of with alkanes were determined. The rate constant increases linearly with the increasing of the number of groups in the alkanes. The experimental results indicate that the reaction of with small alkanes follows the typical hydrogen abstraction process. Based on the correlation of the experimental results with the bond dissociation energy of the alkanes, the reactions of with small alkanes likely proceed via the mechanism of hydrogen abstraction.

Imaging the quantumstate specific differential cross sections of HCl formed from reactions of chlorine atoms with methanol and dimethyl ether
View Description Hide DescriptionCenterofmass frame scattering angle distributions obtained directly from crossed molecular beam velocity map images are reported for HCl formed in different rotational levels of its vibrational ground state by reaction of Cl atoms with and Products are observed to scatter over all angles, with peaks in the distribution in the forward and backward directions and with respect to the relative velocity vectors of the Cl atoms). Products of both reactions exhibit differential cross sections that vary with the rotational quantum number of the HCl, with a greater propensity for forward scatter for shifting to more pronounced backward scatter for This trend is, however, more evident for reaction of dimethyl ether than for methanol. The mean fractions of the available energy channeled into product kinetic energy vary with scattering angle, but the angleaveraged fractions are, respectively, 0.37 and 0.42 for the methanol and dimethyl ether reactions. On average, 46% or more of the available energy of the reactions becomes internal energy of the radical coproduct. Results are interpreted with the aid of computed energies of transition states and molecular complexes along the reaction pathways, and comparisons are drawn with recent measurements of the scattering distributions and energy release for reactions of Cl atoms with small alkanes.

Measurements and simulations of high energy angular scattering: Single and multicollision regimes
View Description Hide DescriptionWe present differential angular cross sections for scattering at collision energies near 90 kcal mol^{−1} (∼8 km s^{−1} relative velocity) from molecular beammeasurements and highlevel theoretical calculations. Beams of hyperthermal are now being used to investigate novel gasphase and gassurface chemistries, and the comparison of theory and measurements on this simple system will be a stringent test of the experimental methodology. Potential energy curves were generated for using a large ccpVQZ basis within a valence multiconfiguration plus perturbation theory treatment. These curves were then used in quantum scattering calculations to generate differential cross sections. Agreement between experiment and theory is excellent. In addition to these comparisons, the cross sections were used in direct simulation Monte Carlo calculations to investigate effects of increasing the Ar flux above the “singlecollision” regime. As the Ar flux increases, the observed differential angular cross sections change in two ways. In addition to the main “singlescatter” peak along the incident Oatom beam direction, a secondary Oatom peak appears in the direction of the incident Ar beam, and the multiplescattered Oatom translational energy starts to reflect the energy of the relatively slow moving Ar beam.

Quantum reactive scattering with a transmissionfree absorbing potential
View Description Hide DescriptionA recently derived transmissionfree absorbing potential is applied to the study of atom–diatom chemical reactions. This absorbing potential only depends on a single parameter—the width of the absorbing region—and its reflection properties are guaranteed to improve as this parameter is increased. Converged results can therefore be obtained very easily, as we illustrate with timedependent wave packet calculations on the and reactions.

Anomalous splittings of torsional sublevels induced by the aldehyde inversion motion in the state of acetaldehyde
View Description Hide DescriptionThe grouptheoretical highbarrier formalism developed previously for internally rotating and inverting is used to interpret the abnormal torsional splittings in the state of acetaldehyde for levels and where denotes the upper inversion tunneling component of the aldehyde hydrogen and 15 denotes the methyl torsional vibration. This formalism, derived using an extended permutation–inversion group treats simultaneously methyl torsional tunneling, aldehyde–hydrogen inversion tunneling and overall rotation. Fits to the rotational states of the four pairs of inversion–torsion vibrational levels and are performed, giving rootmeansquare deviations of 0.003, 0.004, 0.004, and 0.004 cm^{−1}, respectively, which are nearly equal to the experimental uncertainty of 0.003 cm^{−1}. For torsional levels lying near the top of the torsional barrier, this theoretical model, after including higherorder terms, provides satisfactory fits to the experimental data. The partially anomalous Kdoublet structure of the state, which deviates from that in a simple torsion–rotation molecule, is fitted using this formalism and is shown to arise from coupling of torsion and rotation motion with the aldehyde–hydrogen inversion.