Volume 113, Issue 23, 15 December 2000
 ARTICLES

 Theoretical Methods and Algorithms

High order finite difference algorithms for solving the Schrödinger equation in molecular dynamics. II. Periodic variables
View Description Hide DescriptionVariable high order finite difference methods are applied to calculate the action of molecular Hamiltonians on the wave function using centered equispaced stencils, mixed centered and onesided stencils, and periodic Chebyshev and Legendre grids for the angular variables. Results from onedimensional model Hamiltonians and the threedimensional spectroscopic potential of demonstrate that as the order of finite difference approximations of the derivatives increases the accuracy of pseudospectral methods is approached in a regular manner. The high order limit of finite differences to Fourier and general orthogonal polynomial discrete variable representation methods is analytically and numerically investigated.

Concerted electron and proton transfer: Transition from nonadiabatic to adiabatic proton tunneling
View Description Hide DescriptionA concerted electron–proton transfer reaction is discussed, in which protontunneling occurs simultaneously with electronic transition. It is assumed that the potential in which the proton moves is formed by two electronic states, which in the absence of their interaction would cross in the region between the two minima of the proton adiabatic potential. The protontunneling between the two wells is, therefore, coupled to a switch between the two electronic states. The later occurs only when the proton is in the tunneling region under the barrier. A simple analytical expression for the tunneling matrix element is derived, which is uniformly correct for small and large values of the electronic coupling. For small electronic coupling our expression coincides with that obtained in the nonadiabatictheory of protoncoupled electron transferreactions. For large electronic coupling the expression is reduced to that obtained in the Born–Oppenheimer approximation. The transition from nonadiabatic to adiabatic tunneling is governed by the magnitude of the Landau–Zener parameter defined for the tunneling process. The obtained result is discussed in the context of the protontunneling time.

Scaling reduction of the perturbative triples correction (T) to coupled cluster theory via Laplace transform formalism
View Description Hide DescriptionA reformulation of the perturbative triples correction to coupled cluster singles and doubles (CCSD) based on the numerical Laplace transform of the energy denominator is presented. Rearranged equations reduce the canonical scaling to where N is a size measure of the electronic system. Two to three quadrature points is adequate for chemical predictions. The Laplace ansatz permits simple, noniterative expressions in noncanonical orbital representations. Furthermore, substituting canonical by generalized CCSD natural orbitals, the Laplace ansatz exhibits scaling close to while retaining accuracy and providing crossover with respect to canonical triples for small size systems. A developing atomic orbital formulation is also introduced.

Ewald sums for Yukawa potentials
View Description Hide DescriptionThe numerical simulation of systems involving Yukawa interaction (e.g., colloids, dusty plasmas,…) needs some caution in the case where the potential cannot be neglected on the boundaries of the cubic simulation cell [i.e., when side of the cube — is larger than the absolute uncertainties wanted for the thermal average of the energy]. In that case the usual minimum image convention fails and it is necessary to introduce Ewald sums similar to those used for Coulomb systems. In this study we derive the expression of the Ewald sums associated to Yukawa interactions and discuss the numerical errors induced by their truncation.

Optimal chargeshaping functions for the particle–particle—particle–mesh (P^{3}M) method for computing electrostatic interactions in molecular simulations
View Description Hide DescriptionThe application of the particle–particle—particle–mesh method for computing electrostatic interactions in molecular simulations relies on the use of a chargeshaping function to split the potential into two contributions, evaluated in real and reciprocal space, respectively. Although the chargeshaping function is traditionally taken to be a Gaussian, many other choices are possible. In the present study, we investigate the accuracy of the method employing, as chargeshaping functions,polynomials truncated to a finite spacial range (TP functions). We first discuss and test analytical estimates of the rootmeansquare force error for both types of shaping functions. These estimates are then used to find the optimal values of the free parameters defining the two types of chargeshaping function (width of the Gaussian or coefficients of the TP function). Finally, we compare the accuracy properties of these optimized functions, using both analytical estimates and numerical results for a model ionic system. It is concluded that the use of specific TP functions instead of the traditional Gaussian function leads to improvements in terms of computational speed, simplicity of use, and accuracy of results.

On the role of coherence in the transition from kinetics to dynamics: Theory and application to femtosecond unimolecular reactions
View Description Hide DescriptionWe consider the relation between observed pump–probe signals in the femtosecond regime and the kinetics of unimolecular reactions, that is, the exponential decay of reactants and the exponential rise of the product population, respectively. It is shown that the signals cannot be fully accounted for within standard approaches of unimolecular decay, conventionally used in the past, since interference effects between the quasibound vibrational states within the bandwidth of the pump laser cannot be neglected. When these effects are included, all features of the signals can be accounted for. We apply this theoretical treatment of coherent interference to examine the dynamics and kinetics of the quasibound transition configurations, and relate them to the decay rates of individual quasibound resonance states. The signals show multiexponential behavior, reflecting the different decay rates of the resonance states, with an average rate constant (within the bandwidth of the pump laser) which can be extracted directly from the signals. The persistence of coherence is evident in the observed signals. The predissociation of NaI is used as a prototype for numerical illustration. © 2000 American Institute of Physics.

Densityfunctional study of intramolecular ferromagnetic interaction through mphenylene coupling unit (II): Examination of functional dependence
View Description Hide DescriptionAs a first step toward examination of ferromagneticpolymers and dendrimers by ab initio crystal orbital methods, we elucidated candidates for monomer units with the highspin ground states in the previous study of Part I [J. Chem. Phys. 113, 4035 (2000)] by employing densityfunctional (DFT) methods using Becke’s and Becke’s three parameter exchanges with Lee–Yang–Parr correlation or Hartree–Fock (HF) molecular orbital and post HF approximations. However, it was found that further computations applying other DFT functionals should be carried out to clarify the level of approximations which appropriately describe the electronic structures of magnetic molecules. In this part II, we present details of numerical results concerning magnetic properties and electronic structures for mphenylene molecules with three neutral and one cation radicals by spinpolarized density functional methods using variety of local and nonlocal functionals and unrestricted molecular orbital methods including Mo/ller–Plesset and coupledcluster (CC) correlation corrections. The dependence of total, exchange and correlation energies, and spin densities on various approximated functionals is investigated thoroughly. The effective exchange integrals in the Heisenberg model are calculated by local and nonlocal DFT methods, and they are compared with those of complete active space (CAS) CI, CASSCF, and CASPT2. It is concluded that nonlocal DFT with densitygradient corrections can be used as a practical alternative to UCCSD(T) and CASPT2. The brokensymmetry Unrestricted Hartree–Fock (UHF) and DFT calculations of mphenylene polyradicals with polar substituents are carried out to elucidate roles of superexchange interactions arising from the significant mixing of chargetransfer (CT) configurations. The resonance of covalent structures with CT or zwitterionic structures entails antiferromagnetic exchange interactions even in polyradicals with mphenylene bridges; for example, substituted nitroxide polyradicals. Stable ferromagneticpolymers and dendrimers are designed on the basis of the theoretical grounds.

Quantitative harmonization of the three molecular orbital, valence bond, and broken symmetry approaches to the exchange coupling constant: Corrections and discussion
View Description Hide DescriptionThree current methods, used to evaluate exchange coupling constants in molecular magnetism, i.e., the molecular orbital (MO) model [Hay et al., J. Am. Chem. Soc. 94, 4884 (1975)], the valence bond (VB) model [Kahn and Briat, J. Chem. Soc. Trans. II 72, 268 (1976)], and the broken symmetry (BS) model [Noodleman, J. Chem. Phys. 74, 5737 (1981)], have been revisited. In effect, the three published antiferromagnetic contributions seem mutually inconsistent, as far as their magnitudes are concerned. As it turns out, the VB term where Δ is the singly occupied MO gap in the triplet state and S the (natural) magnetic orbital overlap, is shown to be overestimated by a factor of 2 (the VB ferromagnetic term, supposedly small, is actually of the order of Moreover, Noodleman’s explicit condition derived from the variational optimization of the BS state energy results in fact from the implicit neglect of the VB ionic contribution right from the start of his methodology. Alternative (both rigorous and approximate) expressions are proposed in both VB and BS cases. The MO approach, although not being the best physically appropriate for the study of weakly interactingmonomers (i.e., defined by is left untouched at this level of the theory.

Critical assessment of the performance of the semiempirical divide and conquer method for single point calculations and geometry optimizations of large chemical systems
View Description Hide DescriptionWe present a detailed analysis of the performance of the semiempirical divide and conquer method as compared with standard semiempirical MO calculations. The influence of different subsetting schemes involving dual buffer regions on the magnitude of the errors in energies and computational cost of the calculations are discussed. In addition, the results of geometry optimizations on several protein systems (453 to 4088 atoms) driven by a quasiNewton algorithm are also presented. These results indicate that the divide and conquer approach gives reliable energies and gradients and suggest that protein geometry optimization using semiempirical methods can be routinely feasible using current computational resources.

Rovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. III. Global vs local axis system and angular coordinates
View Description Hide DescriptionWe study different parametrizations of the angular space of polyatomic molecules for an orthogonal description of the molecular geometry. Kinetic energy operators for pentatomic molecules, given by compact and computationally useful forms in a global and a local formulation of the axis system, are compared and discussed. A new decomposition of for sequentially bonded pentatomic molecules in conjunction with a basis of Wigner and associated Legendre functions provides kinetic energy matrix elements which are free of singularities. Practical problems caused by an unusual volume element for a description involving only intervector (bending) angles are addressed. The corresponding rovibrational kinetic energy operators are derived for the twovector bodyfixed formulation.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

First overtone helium nanodroplet isolation spectroscopy of molecules bearing the acetylenic CH chromophore
View Description Hide DescriptionHighresolution heliumnanodroplet isolation spectra of the first overtone of the acetylenic stretch of several substituted acetylenes at K, have been observed for the first time. A tunable 1.5 laser is coupled, using a power buildup cavity, to a beam of He droplets seeded with the molecule to be studied. Absorption spectra are recorded by monitoring the beam depletion as a function of laser frequency with a thermal detector. The spectra of hydrogen cyanide (HCN), monodeuteroacetylene (DCCH), cyanoacetylene (NCCCH), propyne trifluoropropyne 3,3dimethylbutyne and trimethylsilylacetylene have been recorded. Due to the superfluid nature of the droplet, rotational resolution is achieved despite the presence of some solventinduced broadening. The spectroscopic constants have been extracted by means of spectral simulations. The resulting rotational constants are smaller than for the bare molecule by a factor which depends on the molecule nonsphericity and its gasphase moment of inertia. The linewidths are found to be at least twice as large as those of the corresponding fundamental transitions observed in a heliumdroplet by Nauta et al. [Faraday Discuss. Chem. Soc. 113, 261 (1999) and references therein]. The heliuminduced spectral shifts are found to be very small, but cannot be easily rationalized.

Energy disposal in the twophoton laserassisted reaction in xenon and chlorine gas mixtures
View Description Hide DescriptionThe twophoton laser assisted reaction (LAR) in low pressure xenon and chlorine gas mixtures has been studied over a broad range of excitation wavelengths in order to characterize the role of the entrance channel in determining the vibrational state distribution of the reaction products. We measure a high degree of vibrational excitation in the product, confirming observations from previous studies of the LAR of collision pairs [Ku et al., J. Phys. Chem. 87, 2989 (1983)], and in distinct contrast with the vibrationally cold excimer observed following laser excitation in molecular beam experiments [Boivineau et al., Chem. Phys. Lett. 128, 528 (1986)]. The mean vibrational energy in the XeCl excimer depends strongly on laser wavelength, increasing with decreasing wavelength. Moreover, an increasing fraction of the available energy from the reaction is observed as vibration in the product as the laser is tuned toward shorter wavelengths. The reaction outcomes are interpreted in terms of a selectivity of initial conditions on the ionic potential surface that mediates the reactive collision.

Adiabatic and vertical ionization energies of 1,4diazabicyclo[2,2,2]octane measured by zero electron kinetic energy spectroscopy and Rydberg extrapolation
View Description Hide DescriptionWe have used a combination of highnRydbergspectroscopy and zero electron kinetic energy (ZEKE) spectroscopy to measure the adiabatic and vertical ionization energies of 1,4diazabicyclo[2,2,2]octane to high precision. A comparison of the two methods revealed that where extended and unperturbed Rydberg series can be observed, the precision with which the ionization energy of a molecule can be measured is up to six times better via Rydberg extrapolation than with high resolution ZEKE spectroscopy. The difference in precision derives, not from any inherent shortcoming in the resolution achievable with ZEKE spectroscopy, but from errors that arise in evaluating the field ionizationredshift. Accurate vertical ionization energies of and were obtained for ionization to the and vibrational levels in the ion. A value for the adiabatic ionization energy of has been measured by ZEKE spectroscopy for the first time. The precision with which we have been able to account for the field ionizationredshift has been improved by calibrating the ZEKE spectrum against the Rydberg spectrum. The ZEKE spectra presented here were recorded using a double inverted pulse sequence with field strengths as low as 140 mV cm^{−1}. The result was exceptionally wellresolved spectra revealing the rotational contour of each ZEKE band. For the and bands the spectra revealed a strong central Q branch, with weaker P and R branches, consistent with a propensity for angular momentum transfer to the Rydberg electron rather than within the core. In contrast to what is commonly observed in ZEKE spectroscopy, where rotational autoionization often results in branches associated with negative appearing with enhanced intensity, the R branch appears with significantly enhanced intensity compared to the very weak P branch.

Thirdorder derivatives of the dipole moment function for the ozone molecule
View Description Hide DescriptionThe thirdorder contributions to the dipole moment function of ozone has been evaluated from available experimental values of the transition moment parameters for the second overtone and ternary combination vibration–rotation bands. The calculations are based on the formalism of effective dipole moment operators. The purely vibrational part of the transformed transition moment operators for threequanta bands is presented in the form suitable for an iterative programming. It allows one to determine the values and to make the optimal choice of signs of the third derivatives of the dipole moment function using the transition moment parameters deduced from experimental spectra. The estimation of the errors have been done by an error propagation of uncertainties in anharmonicity parameters of the potential function and previously determined first and secondorder dipole moment derivatives.

Intramolecular vibrational redistribution in aromatic molecules. I. Eigenstate resolved CH stretch first overtone spectra of benzene
View Description Hide DescriptionWe have used infrared–infrared double resonance spectroscopy to record a rovibrational eigenstate resolved spectrum of benzene in the region of the CH stretch first overtone. This experiment is the first of a series aimed at investigating intramolecular vibrational energy redistribution (IVR) in aromatic molecules. The experiment has been carried out in a supersonic molecular beam apparatus using bolometric detection. A tunable resonant cavity was used to enhance the onbeam intensity of the 1.5 μm color center laser used to pump the overtone, and a fixed frequency laser was used to saturate the coinciding transition of benzene. After assigning the measured lines of the highly IVR fractionated spectrum to their respective rotational quantum number J, analysis of the data reveals that the dynamics occurs on several distinct time scales and is dominated by anharmonic coupling with little contribution from Coriolis coupling. After the fast (∼100 fs) redistribution of the energy among the previously observed “early time resonances” [R. H. Page, Y. R. Shen, and Y. T. Lee, J. Chem. Phys. 88, 4621 (1988) and 88, 5362 (1988)], a slower redistribution (10–20 ps) takes place, which ultimately involves most of the symmetry allowed vibrational states in the energy shell. Level spacing statistics reveal that IVR produces a highly mixed, but nonstatistical, distribution of vibrational excitation, even at infinite time. We propose that this nonintuitive phenomenon may commonly occur in large molecules when the bright state energy is localized in a highfrequency mode.

Dissociation dynamics of the water molecule on the electronic surface
View Description Hide DescriptionPhotodissociation of and HOD on the surface through 157.6 nm excitation has been studied using the H(D) atom Rydberg tagging timeofflight technique. Vibrational state distribution has been measured for the OH/OD product from the photodissociation of the and HOD molecules. Comparisons of our results with previous theoretical calculations and experimental results obtained using the laser induced fluorescence(LIF) technique have been made. Experimental results in this work indicate that the relative populations for vibrationally excited products measured using LIF are significantly underestimated, suggesting that LIF as a technique to quantitatively measure vibrational distributions of reaction product OH is seriously flawed. The experimental results presented here are in rather good agreement with previous theoretical calculations. However, our results indicate that the calculated vibrational populations for the higher vibrational states of OH are still somewhat overestimated. Relative branching ratio of H and D productions from HOD has also been estimated. This complete set of data for the photodissociation of should provide an excellent testing ground for improving the theoretical potential energy surface of the first electronically excited state of the water molecule.

Multiple configuration quantum/classical treatments of reaction dynamics
View Description Hide DescriptionThe accuracy of quantum/classical approaches for studies of reactiondynamics is investigated through simulations of the collinear and dynamics of the reaction on two potential surfaces. The results of classical and two types of quantum/classical treatments of this reaction are compared to the results of quantum wave packet simulations. It is found that the accuracy of the single configuration quantum/classical treatment is sensitive to features of the potential surface. Most of this sensitivity is removed when a second configuration is introduced. For collision energies below 0.8 eV, the multiple configuration quantum/classical treatment provides reaction probabilities and product state distributions that are in good agreement with the results of the corresponding quantum simulation. The agreement deteriorates at higher collision energies, but here the agreement between the quantum and classical results is quite good.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Inherent structures and nonequilibrium dynamics of onedimensional constrained kinetic models: A comparison study
View Description Hide DescriptionWe discuss the relevance of the Stillinger and Weber approach to the glass transition investigating the nonequilibrium behavior of models with nontrivial dynamics, but with simple equilibrium properties. We consider a family of 1D constrained kinetic models, which interpolates between the asymmetric chain introduced by Jäckle and Eisinger [Z. Phys. B 84, 115 (1991)] and the symmetric chain introduced by Fredrickson and Andersen [Phys. Rev. Lett 53, 1244 (1984)], and the 1D version of the Backgammon model [Phys. Rev. Lett. 75, 1190 (1995)]. We show that the configurational entropy obtained from the inherent structures is the same for all models irrespective of their different microscopic dynamics. We present a detailed study of the coarsening behavior of these models, including the relation between fluctuations and response. Our results suggest that any approach to the glass transition inspired by meanfield ideas and resting on the definition of a configurational entropy must rely on the absence of any growing characteristic coarsening pattern.

Mass and size dependence of single ion dynamics in molten monohalides
View Description Hide DescriptionThis work is concerned with four molten monohalides with different ionic radii ratios (RbCl, NaI, AgCl, and CuCl) and ideal isotopic systems of these salts with different ionic mass ratios. The velocity autocorrelation functions of the two ionic species in each melt have been studied by both a theoretical approximation and molecular dynamics simulations. It is found that their main features may be qualitatively predicted by considering suitable combinations of the second and fourth frequency moments of their spectra. The analysis of these two parameters allows us to determine how the structure (strongly dependent on the ionic size difference) and the ionic masses contribute to the shape of the velocity autocorrelation functions. The results show that the averaged microscopic motion of the small ions is mainly determined by the first neighboring shell of unlike ions, whereas the nearest shell of like ions also affects the dynamics of the large ions. This effect is more pronounced as the size difference is greater. Furthermore, it is concluded that the size differences encourage the rattling motion of the large ions, whereas the mass difference encourages the backscattering and oscillations of the velocity autocorrelation function of the light ions. A simple rule is derived to determine the interplay between these two effects. Comparison between the mass and nearest distance ratios enables the prediction as to which species will experience a more pronounced backscatteringmotion. The size difference effects prevail in the hydrodynamics regime and the selfdiffusion coefficient of the small ions is higher than that of the large ones. The difference between the selfdiffusion coefficient increases as the size differences increases.

A twochain path integral model of positronium
View Description Hide DescriptionWe have used a path integral Monte Carlo technique to simulate positronium (Ps) in a cavity. The primitive propagator is used, with a pair of interacting chains representing the positron and electron. We calculate the energy and radial distribution function for Ps enclosed in a hard, spherical cavity, and the polarizability of the model Ps in the presence of an electrostatic field. We find that the positron distribution near the hard wall differs significantly from that for a single particle in a hard cavity. This leads to systematic deviations from predictions of freevolume models which treat Ps as an effective, single particle. A virialtype estimator is used to calculate the kinetic energy of the particle in the presence of hard walls. This estimator is found to be superior to a kinetictype estimator given the interaction potentials, cavity sizes, and chain lengths considered in the current study.