Volume 115, Issue 21, 01 December 2001
 ARTICLES

 Theoretical Methods and Algorithms

Characterization of anharmonicities on complex potential energy surfaces: Perturbation theory and simulation
View Description Hide DescriptionWe have systematically investigated the effect of anharmonicity on the equilibrium properties of systems with a complex potential energy surface. Anharmonicities are modeled by the temperature dependence of the harmonic frequencies near a stationary point of the PES. The lowtemperature behavior is described by a simple thermal expansion where the coefficients are obtained from perturbation theory. Using a simple diagrammatic representation, we give the complete expressions for the first two coefficients and in terms of derivatives of the potential. This approach is illustrated for the example of a bulk LennardJones system of 32 particles, in both the solid and the liquid states. We also determine the anharmonic frequencies from reversiblescaling Monte Carlo simulations, which appear particularly well suited to this problem. As an example, we have studied a model biopolymer that exhibits significant first and second order anharmonicities. To show the importance of treating anharmonicities properly, we have calculated the caloric curve (heat capacity) of the quantum cluster in both the classical and quantum regimes. For this calculation we have used a superposition approximation and exact anharmonic classical corrections to second order in perturbation theory. When every vibrational mode of each inherent structure is treated separately, we find good agreement between our results and previous quantum Monte Carlo calculations.

A single Lanczos propagation method for calculating transition amplitudes. III. Smatrix elements with a complexsymmetric Hamiltonian
View Description Hide DescriptionThe recently proposed single Lanczos propagation method [J. Chem. Phys. 111, 9944 (1999); ibid. 114, 1467 (2001)] is extended to complex–symmetric Hamiltonians. It is shown that the complex–symmetric Lanczos algorithm possesses several useful numerical properties similar to those observed in realsymmetric cases, which enable one to compute multiple transition amplitudes with a single Lanczos propagation. The usefulness of the method is illustrated in calculating the Smatrix elements for the collinear reaction.

Optimization of hyperplanar transition states
View Description Hide DescriptionA method for systematically finding the optimal orientation and location of a hyperplanar dividing surface during a transition state theory calculation of a transition rate is presented. The optimization can be carried out during a reversible work evaluation of the free energy barrier. An application to Al adatom diffusion on an Al(100) surface is described. There, the method can converge to give the free energy barrier for the optimal mechanism, a concerted displacement, even when the calculation is initially set up for the less optimal hop mechanism. This illustrates that the method can reveal the optimal mechanism of a transition even when the calculation is started with an incorrect guess.

Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table
View Description Hide DescriptionWe present a method for carrying out long time scale dynamics simulations within the harmonic transition state theory approximation. For each state of the system, characterized by a local minimum on the potential energy surface, multiple searches for saddle points are carried out using random initial directions. The dimer method is used for the saddle point searches and the rate for each transition mechanism is estimated using harmonic transition state theory.Transitions are selected and the clock advanced according to the kinetic Monte Carlo algorithm. Unlike traditional applications of kinetic Monte Carlo, the atoms are not assumed to sit on lattice sites and a list of all possible transitions need not be specified beforehand. Rather, the relevant transitions are found on the fly during the simulation. A multiple time scale simulation of Al(100) crystal growth is presented where the deposition event, occurring on the time scale of picoseconds, is simulated by ordinary classical dynamics, but the time interval in between deposition events, on the order of milliseconds, is simulated by the long time scale algorithm. The Al(100) surface is found to grow remarkably smooth, even at 30 K because of concerted displacements of multiple atoms with significantly lower activation energy than adatom diffusion on the flat terrace.

Inclusion of meanfield spin–orbit effects based on allelectron twocomponent spinors: Pilot calculations on atomic and molecular properties
View Description Hide DescriptionAn implementation of a twocomponent allelectron treatment of both scalar and spin–orbit relativistic effects in the MOLFDIR program suite is presented. Relativity is accounted for by Douglas–Kroll transformed oneelectron operators: scalar (spinfree) and so called meanfield spin–orbit terms. The interelectronic interaction is represented by the nonrelativistic Coulomb operator. Highlevel correlated calculations of properties of several systems (FO, ClO, Cl, Tl, and TlH) where spin–orbit effects play a dominant role are presented and compared with other data. Agreement with Dirac–Coulomb(–Gaunt) reference values is in general very good.

An improved reactive flux method for evaluation of rate constants in dissipative systems
View Description Hide DescriptionWe present an improved method for numerical evaluation of the least nonvanishing eigenvalue in dissipative systems. It is based on a modified version of the reactive flux formula for the rate which eliminates the principal shortcomings of the original formulation. A new fourthorder algorithm is used to efficiently integrate the underlying generalized Langevin equation. The proposed methodology provides accurate eigenvalues with a small computational effort for systems which could not be accurately treated with the standard techniques. Its efficiency is tested for Brownian motion in a symmetric double well subject to an exponential friction kernel. The presented results demonstrate the applicability of the method in all regimes of interest, reaching from underdamped to overdamped Brownian motion.

Direct optimization of the atomicorbital density matrix using the conjugategradient method with a multilevel preconditioner
View Description Hide DescriptionBased on a recently proposed exponential parametrization of the oneelectron atomicorbital density matrix of a singledeterminant wave function [Chem. Phys. Lett. 327, 397 (2000)], we present an implementation of the direct optimization of the atomicorbital density matrix as an alternative to the diagonalization of the Fock–Kohn–Sham matrix when solving the Roothaan–Hall selfconsistent field equations. The optimization of the density matrix is carried out by the conjugategradient method with a multilevel nondiagonal preconditioner and is well suited to linear scaling. Although a diagonal preconditioner may be sufficient for minimal basis sets and large highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps, a nondiagonal preconditioner is needed in more difficult cases—that is, for basis sets with polarization and diffuse functions and for systems with small HOMO–LUMO gaps. Redundancies of the exponential parametrization of the density matrix are handled by a projection technique, thereby avoiding singular equations in the optimization of the density matrix.

Atomic orbital Laplacetransformed secondorder Møller–Plesset theory for periodic systems
View Description Hide DescriptionWe present an atomicorbital formulation of secondorder Møller–Plesset (MP2) theory for periodic systems. Our formulation is shown to have several advantages over the conventional crystalline orbital formulation. Notably, the inherent spatial decay properties of the density matrix and the atomic orbital basis are exploited to reduce computational cost and scaling. The multidimensional kspace integration is replaced by independent Fourier transforms of weighted density matrices. The computational cost of the correlation correction becomes independent of the number of kpoints used. Focusing on the MP2 quasiparticleenergyband gap, we also show using an isolated fragment model that the long range gap contributions decay rapidly as proof that band gap corrections converge rapidly with respect to lattice summation. The correlated amplitudes in the atomic orbital (AO) basis are obtained in a closedform fashion, compatible with a semidirect algorithm, thanks to the Laplace transform of the energy denominator. Like for its molecular counterpart, the Laplace quadrature can be accurately carried out by using few quadrature points, 3–7 depending on the application. In particular, MP2 quasiparticleenergyband gaps are computed accurately with 3 Laplace quadrature points. All these traits indicate that robust calculations of the correlation correction to the Hartree–Fock (HF) energy and band gap of large systems can be carried out. We present benchmark periodic MP2 calculations on polyacetylene, polyphenylenevinylene, hexagonal boron nitride, and stacked polyacetylene.

A general method to obtain well localized Wannier functions for composite energy bands in linear combination of atomic orbital periodic calculations
View Description Hide DescriptionA method for obtaining spatially localized crystalline orbitals starting from delocalized Bloch functions is proposed. The method, that has been implemented in the LCAO CRYSTAL code, is intrinsic and general for nonconducting systems, and provides a set of well localized Wannier functions that can be used for applications that take advantage of their localized character. Examples are given that illustrate the performances and efficiency of the proposed scheme.

Formulation and implementation of the relativistic Fockspace coupled cluster method for molecules
View Description Hide DescriptionAn implementation of the relativistic multireference Fockspace coupled cluster method is presented which allows simultaneous calculation of potential surfaces for different oxidation states and electronic levels of a molecule, yielding values for spectroscopic constants and transition energies. The method is tested in pilot calculations on the and HgH molecules, and is shown to give a good and balanced description of various electronic states and energies.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photodissociation study of at 193 nm using slice imaging
View Description Hide DescriptionThe photodissociation of at 193 nm (51 700) is studied using the slice imaging technique, and velocity distributions for state selected and photofragments are measured. From the analysis of the speed distributions we determine the branching ratio to be 1.5±0.4. The partially resolved Satom speed distributions peak at intermediate speeds, indicating substantial rovibrational excitation of the CS sibling fragment. By modeling this CS propensity using a Franck–Condon analysis between the and the excited state, we estimate the origin of the excited state to be located at ∼45 600 From the Satom angular distributions, we determine the spatial anisotropy parameter β, and find that the value for is slightly speed dependent with an average value of ∼0.2. The β values for are strongly speed dependent, reaching the value of 0.6 at intermediate speeds and an average value of 0.2 at low and high speeds. From the observed β values we conclude that the molecule is highly bent (∼115°) prior to dissociation, while the dissociation lifetime is on the order of a rotational period.

Electronic states of the phenoxyl radical
View Description Hide DescriptionThe phenoxyl radical and two of its isotopomers were investigated by UVVIS and IR polarizationspectroscopy of molecular samples immobilized in cryogenic argon matrices. Analysis of the combined electronic and infrared linear dichroism data led to determination of absolute transition moment directions and symmetry assignments for four lowlying excited electronic states. The bands observed at 16 000, 25 200, 33 900, and 41 800 cm^{−1} were assigned to and states, respectively. A very weak transition observed in the nearinfrared close to 8900 cm^{−1} was assigned to an optically forbidden state. The electronic transitions predicted by time dependent density functional theory (TDUB3LYP/ccpVTZ) were in good agreement with the observed transitions.

Photodissociation of at 234 and 265 nm: Imaging studies of one and two photon excitation
View Description Hide DescriptionThe photodissociation of at 234 and 265 nm was investigated using a velocity map imaging technique via one and twophoton excitation. The speed and angular distributions of the bromine ions obtained via onephoton excitation following state selective ionization reveal a unique transition to the state. This state dissociates further into at 234 nm, and into and at 265 nm, with relative quantum yields of and The proportionality constant related to the relative [2+1] REMPI strengths of atomic bromine was determined to be 0.42±0.02 for detected at 234.0 nm and for at 233.7 nm, and 0.73±0.02 for at 264.9 nm to detect and 264.8 nm to detect Image analysis of the ions and photoelectrons obtained by twophoton excitation at various wavelengths in the range of 229.4–237.6 nm shows that some fragmented bromine atoms are in highly excited states, and that there exists superexcited Rydberg states converging to the asymptotes, near the ionization threshold.

Activation of methane by sizeselected iron cluster cations, Cluster bond energies and reaction mechanisms
View Description Hide DescriptionThe kinetic energy dependences of the reactions of with are studied in a guided ion beam tandem mass spectrometer over the energy range of 0–10 eV. All reactions exhibit thresholds and two main products, and are formed. These primary products decompose at higher energies to form secondary and higher order products, and The crosssection magnitudes for the dehydrogenation products, are observed to vary considerably as a function of cluster size; subsequent dehydrogenation to form becomes more facile for larger clusters. Thresholds for the various primary and secondary reactions are analyzed and bond energies for iron cluster cation bonds to C, CD, and are determined. As a function of cluster size, these bond energies rapidly reach relatively constant values, which are argued to lie close to bulk phase values. The relative magnitudes in these bond energies are consistent with simple bond order considerations. On the basis of this thermochemistry, we find that there are barriers to the primary dehydrogenation reactions for all the clusters, except and 4. Evidence that this barrier for corresponds to the chemisorption step is discussed.

Rotationally resolved photoionization: Influence of the shape resonance on rotational distributions
View Description Hide DescriptionWe present experimental and theoretical results on rotational distributions of photoions. Rotational distributions were determined for both the and vibrational levels following photoionization of cold neutral CO target molecules. Data were generated using dispersed ionic fluorescence over a wide range of photoelectron kinetic energies, which allows one to interrogate the ionization dynamics. This wide spectral coverage permits illustrative comparisons with theory, and calculated spectra are presented to interpret the data. In particular, the comparison between theory and experiment serves to identify the strong continuum resonant enhancement at in the partial wave of the ionization channel, as this feature has profound effects on the ion rotational distributions over a wide range of energy. Second, there are differences between the rotational substructure for the and vibrational levels. All of the experimentally observed features and trends are reproduced by theory, and the consequences of these comparisons are discussed.

Rotational pathways in electronic energy transfer
View Description Hide DescriptionWe analyze rotational distributions from collisioninduced atom–diatom electronic energy transfer (EET) experiments in terms of the capacity of the diatomic to dispose of the angular momentum (AM) generated in statetostate change. Two pairs of systems are chosen as representative of processes broadly categorized as “efficient” or “inefficient” in this regard, namely, in the former category and CN–Ar in the latter. Note that EET involving electron spin change is not considered here. Using velocityAM diagrams and quantitative calculations we show the factors that govern the probability of statetostate transfer in EET are the same as those controlling the outcome of rotational and rovibrational transfer within an electronic state. This suggests that requirements of orbital and rotational AM are of critical importance in providing pathways that allow EET to proceed.

Sixdimensional variational calculation of the bending energy levels of HF trimer and DF trimer
View Description Hide DescriptionThe bending energy levels of HF and DF trimer were calculated variationally using a sixdimensional kineticenergy operator derived by constraining the stretch degrees of freedom to their equilibrium values. A basis of direct products of spherical harmonics is used to represent the wave function. The symmetry adapted Lanczos method is used to calculate levels of all symmetries from one sequence of matrixvector products. Two efficient ways of implementing the symmetryadapted Lanczos method are presented. To determine the concerted hydrogen bond breaking tunneling splitting in HF and DF trimer one needs to use the point group. By doing calculations, we find that the splitting is negligible for the lowlying levels. If the tunneling is unfeasible, the appropriate group is Our calculation using the most accurate SO3+HF3BG potential developed by Quack, Stohner, and Suhm indicates that two gasphase overtone bending bands of HF trimer should be reassigned, and that the noble gas matrix spectra of the bending fundamental bands are significantly shifted from their gasphase counterparts.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Quantum effect of solvent on molecular vibrational energy relaxation of solute based upon path integral influence functional theory
View Description Hide DescriptionPath integral influence functional theory has been applied to the investigation of the quantum effect of the solvent on vibrational relaxation of the solute. A classical bath approximation was attained by taking the limit with respect to the solvent degrees of freedom. A comparison of the calculated relaxation time for the quantum solvent with that for the classical one showed that the quantum effect is very large and, at the same time, it depends much upon the process, i.e., singlephonon process, twophonon process, or threephonon process. This indicates that the socalled quantum correction does not work since the relaxation is usually a mixture of these multiphonon processes. A numerical example for in water also demonstrates that, although the classical approximation for the solvent significantly overestimates the relaxation time, it presents reliable energy transfer pathways or relaxation mechanism.

Lowenergy excitations of vapordeposited amorphous ice and its annealing and methanoldoping effects studied by inelastic neutron scattering
View Description Hide DescriptionA novel cryostat was developed for in situneutron scattering studies on vapordeposited amorphous samples. By the use of this cryostat, vapordeposited amorphous ice was prepared at ca. 8 K. The neutron scattering spectra of the asdeposited sample and those annealed at ca. 120 K, 160 K, and 250 K were measured at 50 K in energy range below 100 meV. The four samples studied corresponded to vapordeposited amorphous solid water (ASW), hyperquenched glassy water (HGW) (approximately), ice and ice respectively (according to historical nomenclature). The librational frequency of the water molecule is smaller in the order of This indicates that the strength of the intermolecular hydrogen bonds is The absolute value of the vibrational density of states was obtained from the analysis combining the heat capacity and neutron scattering data. of ASW and HGW integrated below 6 meV were larger than that of ice by 0.060 and 0.039 degrees of freedom per water molecule, respectively. Similar experiments were performed on the vapordeposited amorphous ice doped with 5% and 10% of methanol The magnitude of below 6 meV increased with increasing fraction of methanol. All of the results in this study indicate that the low energy excitation [ below 6 meV] of amorphous ice is enhanced by the defects and distortion of the hydrogen bonds.

Ab initio molecular dynamics simulation of liquid water and water–vapor interface
View Description Hide DescriptionThe results of ab initiomolecular dynamics simulations of liquid water and liquid water–vapor interface using the PerdewWang 91 (PW91) exchangecorrelation functional are presented. The structural and transport properties of liquid water are comparable to the previous results using BeckeLeeYangParr (BLYP) functional and experimental data. The shape and the position of the first peak in the oxygen–oxygen radial distribution function is in good agreement with the most recent neutron diffraction data. The ab initiomolecular dynamics simulation of liquid water–vapor interface, which is the first of its kind, suggests a preferred orientation of the surface water dipole towards the bulk region.