Volume 112, Issue 6, 08 February 2000
 COMMUNICATIONS


The zero kinetic energy photoelectron spectrum of the propargyl radical,
View Description Hide DescriptionWe report the zero kinetic energy photoelectron spectrum of the propargyl radical, From the spectrum an ionization energy of (8.673 eV) is deduced. Vibrational frequencies are obtained for the totally symmetric normal modes of the propargyl cation, as well as some combination and overtone bands. Both the frequencies and the relative intensities agree well with the predictions from recent ab initio calculations.
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 THEORETICAL METHODS AND ALGORITHMS


Electrostatically driven electronic molecular bistability: Ab initio calculation for a model system
View Description Hide DescriptionSemiempiricaltheories predict that some donor–acceptor molecules may exhibit longlived electronic metastable states. The states result from a cooperative effect of successive electron transfers from several donor to acceptor moieties of the molecule. Calculations within the Mo/ller–Plesset secondorder perturbation theory following the unrestricted Hartree–Fock, projected unrestricted Hartree–Fock, and complete active space selfconsistent field procedures confirm the effect for the first time at the ab initio level. An equidistant linear chain where the donor (D) and acceptor (A) subunits are the lithium and fluorine atoms, respectively, has been chosen as a model for a molecule with fixed in space D and A substituents. The nearestneighbor LiF distance is set to be sufficiently large to assure the isolated DA pair has lower energy in the neutral DA state than in the ionic one, i.e., a single electron transfer to occur requires energy. In the system, a single electron transfer from D to the nearest A requires a comparable amount of energy It is shown, however, that, due to the cooperative nature of the excitations, the excited state corresponding to m such electron transfers may have an excitation energy lower than Due to this a multiply excited state may be close in energy scale to the nonexcited one, both states separated by energy barrier related to The effect has been checked against perturbations that mimic dimerization of the chain and a lateral extension of the and charge distribution. It turned out that the cooperative effect is likely to survive these perturbations.

Digitally filtered molecular dynamics: The frequency specific control of molecular dynamics simulations
View Description Hide DescriptionA new method for modifying the course of a molecular dynamicscomputer simulation is presented. Digitally filtered molecular dynamics (DFMD) applies the wellestablished theory of digital filters to molecular dynamics simulations, enabling atomic motion to be enhanced or suppressed in a selective manner solely on the basis of frequency. The basic theory of digital filters and its application to molecular dynamics simulations is presented, together with the application of DFMD to the simple systems of single molecules of water and butane. The extension of the basic theory to the condensed phase is then described followed by its application to liquid phase butane and the Syrian hamster prion protein. The high degree of selectivity and control offered by DFMD, and its ability to enhance the rate of conformational change in butane and in the prion protein, is demonstrated.

Direct calculation of anharmonic vibrational states of polyatomic molecules using potential energy surfaces calculated from density functional theory
View Description Hide DescriptionPotential energy surface points computed from variants of density functional theory(DFT) are used to calculate directly the anharmonic vibrational frequencies of and The method is an adaptation to DFT of a recent algorithm for direct calculations of anharmonic vibrational frequencies using ab initioelectronic structure codes. The DFT calculations are performed using the BLYP and the B3LYP functionals and the results are compared with experiment, and also with those calculated directly from a potential energy surface obtained using ab initio MöllerPlesset second–order perturbation theory (MP2). The direct calculation of the vibrational states from the potential energy points is performed using the correlationcorrected vibrational selfconsistent field (CCVSCF) method. This method includes anharmonicity and correlations between different vibrational modes. The accuracy of this method is examined and it is shown that for the experimentally measured transitions the errors in the CCVSCF calculations are much less than the errors due to the potential energy surface. By comparison with the experimentally measured frequencies the CCVSCF method thus provides a test for the quality of the potential energy surfaces. The results obtained with the B3LYP functional, in contrast to those of the BLYP functional, are of comparable quality to those obtained with MP2. The B3LYP anharmonic frequencies are in good agreement with experiment, showing this DFT method describes well the anharmonic part of the potential energy surface. The BLYP results systematically underestimate both the harmonic and anharmonic frequencies and indicate that using this functional for the description of hydrogenbonded systems may cause significant errors.

Quantum mechanical canonical rate theory: A new approach based on the reactive flux and numerical analytic continuation methods
View Description Hide DescriptionWe present the reactive flux analytic continuation (RFAC) method, based on the quantum reactive flux formalism combined with a numerical analytic continuation approach to calculate quantum canonical rates in condensed phase systems. We express the imaginary time reactiveflux correlation function in terms of a frequency dependent rate constant, and use path integral formalism to derive a working expression suitable for Monte Carlo simulation techniques. The imaginary time data obtained by simulation is analytically continued to the real time using the maximum entropy method to obtain the reaction rate. Motivated by the success of the method to predict the rates for a simple one dimensional parabolic barrier model, we assess its accuracy for a condensed phase reaction modeled by a doublewell coupled to a harmonic bath. We note that the method is applicable to a more general Hamiltonian as long as the reaction coordinate can be identified. The reaction rates computed in this fashion are in very good agreement with analytic and numerically exact results. We demonstrate the applicability of the method for a wide range of model parameters and temperatures.

Threedimensional quantum reactive scattering calculations for the nonadiabatic reaction system
View Description Hide DescriptionThreedimensional quantum reactive scattering calculations have been carried out for the nonadiabatic ion–molecule collision. The calculations have been done using the timeindependent closecoupling formalism with hyperspherical coordinates. The diatomicsinmolecule potential energy surfaces have been employed. The result of the accurate quantum scattering calculations have been compared to the results of the quasiclassical trajectorysurface hopping method. Two versions of the method have been used; one uses Tully’s fewest switches algorithm and the other is the trajectory surface hopping method of Tully and Preston, in which electronically nonadiabatic hopping is only allowed at the predefined crossing seams. We have found that the agreement between the quantum result and the result of Tully’s method is generally good, but the Tully and Preston method significantly underestimates the nonadiabatic transition probability.

A transition state real wave packet approach for obtaining the cumulative reaction probability
View Description Hide DescriptionWe show how the transition state wave packet method of Zhang and Light can be applied within a real wave packet formalism. We also implement random superpositions into the approach, as in the recent work of Matzkies and Manthe, which can significantly reduce the number of propagations at higher temperatures. The net result is a very efficient approach for calculating the cumulative reaction probability, and hence the thermal rate constant, for bimolecular chemical reactions. Full dimensional quantum calculations, including all relevant total angular momenta, of the cumulative reaction probability and thermal rate constant for the are used as illustration.

Signatures of nonMarkovian relaxation in twolevel atoms due to environmental perturbations
View Description Hide DescriptionThe effect of environmental perturbations on a system of twolevel atoms is to alter the coupling between the atoms and their surroundings, which manifests itself as a change in the relaxation rates of the atoms. One of the ways in which environmental fluctuations can affect an atom is to modulate its transition frequency in a stochastic manner. We study the response of such twolevel atoms to irradiation by a monochromatic laser, and report the results of numerical experiments on the spectrum of scattered light. It is observed that this spectrum is a sensitive indicator of the parameters that describe the stochastic modulation. In addition, the spectra exhibit substantially different features depending on whether the stochastic process follows a diffusion or a jump mechanism. The numerical results are based on a Monte Carlo procedure, which can be applied to stochastic processes in a wide variety of biological, chemical, and physical processes.

The metaGGA functional: Thermochemistry with a kinetic energy density dependent exchangecorrelation functional
View Description Hide DescriptionThe metaGGA functional recently proposed by Perdew et al. [Phys. Rev. Lett. 82, 2544 (1999)] goes beyond the generalized gradient approximations (GGAs) since it employs the noninteracting kinetic energy density in addition to the local density and the gradient of the local density. In this paper, we focus on thermochemistry and present an extensive assessment of the metaGGA functional. We find that for atomization energies metaGGA is as accurate as the computationally more involved Perdew–Burke–Ernzerhof (PBE) hybrid scheme. However, the geometries and frequencies obtained with metaGGA are worse than those obtained with PBE or PBE hybrid. We give a detailed analysis of our results and propose explanations for the observed differences between PBE, PBE hybrid, and metaGGA. Furthermore, we address the question whether the parameters in the metaGGA functional are optimal for our benchmark set.

Optimization of quantum Monte Carlo wave functions using analytical energy derivatives
View Description Hide DescriptionAn algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on Newton’s method and analytical computation of the first and second derivatives of the variational energy. This direct application of the variational principle yields significantly lower energy than variance minimization methods when applied to the same trial wave function. Quadratic convergence to the local minimum of the variational parameters is achieved. A general theorem is presented, which substantially simplifies the analytic expressions of derivatives in the case of wave functionoptimization. To demonstrate the method, the groundstate energies of the firstrow elements are calculated.

Calculation of the vibrational wave function of polyatomic molecules
View Description Hide DescriptionA modified perturbation approach for the calculation of the vibrational wave function of polyatomic molecules is discussed. It is demonstrated that if the expansion point of the potential is determined variationally, the leading firstorder term in the perturbation expansion of the vibrational wave function vanishes. Furthermore, the new expansion point is a very good approximation to the vibrationally averaged molecular geometry. The required third derivatives of the potential energy with respect to geometrical distortions have been calculated by numerical differentiation. Two approaches are discussed, one based on the differentiation of the molecular Hessian and the other on the molecular gradient. Results are presented for the averaged molecular geometry of a large set of molecules, including studies of electronically excited states and effects of electron correlation. The largest molecule included is butane with a total of 14 atoms.

An efficient approach for calculating vibrational wave functions and zeropoint vibrational corrections to molecular properties of polyatomic molecules
View Description Hide DescriptionWe have recently presented a formalism for calculating zeropoint vibrational corrections to molecular properties of polyatomic molecules in which the contribution to the zeropoint vibrational correction from the anharmonicity of the potential is included in the calculations by performing a perturbation expansion of the vibrational wave function around an effective geometry. In this paper we describe an implementation of this approach, focusing on computational aspects such as the definition of normal coordinates at a nonequilibrium geometry and the use of the Eckart frame in order to obtain accurate nonisotropic molecular properties. The formalism allows for a blackbox evaluation of zeropoint vibrational corrections, completed in two successive steps, requiring a total of two molecular Hessians, molecular gradients, and property evaluations, K being the number of atoms. We apply the approach to the study of a number of electric and magnetic properties—the dipole and quadrupole moments, the static and frequencydependent polarizability, the magnetizability, the rotational gtensor and the nuclear shieldings—of the molecules hydrogen fluoride, water, ammonia, and methane. Particular attention is paid to the importance of electron correlation and of the importance of the zeropoint vibrational corrections for obtaining accurate estimates of molecular properties for a direct comparison with experiment.

Spin–orbit effects on the transactinide pblock element monohydrides MH (M=element 113–118)
View Description Hide DescriptionSpin–orbit effects on the bond lengths and dissociation energies of sixth and seventhrow pblock element monohydrides MH(M=Tl–Rn and element 113–118) are evaluated using relativistic effective core potentials at the coupledcluster level of theory. Spin–orbit effects play a dominant role in the determination of molecular properties for the seventhrow hydrides. Spin–orbit effects on the bond lengths and dissociation energies of seventhrow hydrides are qualitatively similar to, but substantially larger than those of the sixthrow homologs due to the enormous spin–orbit splitting of orbitals. Spin–orbit interactions change the bond lengths of sixth and seventhrow hydrides by Å and Å , respectively. Spin–orbit interactions usually elongate the bond lengths except for the molecules of the valence atoms, i.e., TlH and (113)H. The maximum elongation is predicted for (115)H, where the element 115(ekabismuth) has the configuration outside the inner closedshell. The spin–orbit coupling weakens the bondings between the heavy element and the hydrogen except for BiH and changes the dissociation energies by eV and eV for sixth and seventhrow hydrides, respectively. The dissociation energy of the (114)H molecule is merely 0.39 eV, because the element 114(ekalead) has a closedshell electronic structure in the coupling scheme. The bonding between the element 118(ekaradon), which is another closedshell atom, and hydrogen is very weak and can be regarded as a pure van der Waals bond. But with highly electronegative elements the element 118 seems to form more stable compounds than other closedshell atoms such as the element 112(ekamercury) or the element 114.

A nonequilibrium ensemble formalism: Criterion for truncation of description
View Description Hide DescriptionIn the framework of a nonequilibrium statistical ensemble formalism, consisting of the socalled Nonequilibrium Statistical Operator Method, we discuss the question of the choice of the space of thermohydrodynamic states. We consider in particular the relevant question of the truncation of description (reduction of the dimension of the state space). A criterion for justifying the different levels of truncation is derived. It depends on the range of wavelengths and frequencies which are the relevant ones for the characterization, in terms of normal modes, of the thermohydrodynamic motion in a nonequilibrium open system. Applications to the cases of thermalsensitive resins and of doped polar semiconductors are done, numerical results are presented, and experimental observation is discussed.

Multicanonical jump walk annealing: An efficient method for geometric optimization
View Description Hide DescriptionA new global optimization method, multicanonical jump walk annealing (MJWA), is proposed and applied to the geometric optimization of LennardJones and Morse clusters and the hydrophobic (B), hydrophilic (L), and neutral (N) (BLN) protein model. The method efficiently finds the global minima of these systems. In four comparative studies, MJWA greatly outperforms the conventional simulated annealing in locating the global minima. Theoretical comparison with other global optimization methods is discussed. Through this paper, we demonstrate a criterion for devising stochastic global optimization schemes. Namely, a stochastic global optimization method must favor the global minimum thermodynamically and at the same time be able to cross the high energy barriers.

Distributed polarizabilities derived from induction energies: A finite perturbation approach
View Description Hide DescriptionAn approach based on finite perturbation theory is proposed for deriving models of distributed polarizabilities from quantum mechanically determined induction energies. It relies on the construction of a grid of points, over which the induction energy resulting from the interaction of a charge with the molecule of interest is evaluated at the desired level of approximation. Distributed polarizabilities of any order are then fitted by solving the normal equations of the leastsquares problem, the solution of which provides an optimal description of induction effects. The method is probed by examining several models of distributed polarizabilities of increasing complexity in the case of water, methanol, acetonitrile, and benzene. At a reasonable order of multipole expansion, atomic polarizabilities derived using this approach are found to reproduce the corresponding molecular polarizabilities with an appropriate accuracy. The careful choice of the parameters to be fitted appears to be a key factor for obtaining physically realistic models.

Multiconfiguration molecular mechanics algorithm for potential energy surfaces of chemical reactions
View Description Hide DescriptionWe present an efficient algorithm for generating semiglobal potential energy surfaces of reactive systems. The method takes as input molecular mechanics force fields for reactants and products and a quadratic expansion of the potential energy surface around a small number of geometries whose locations are determined by an iterative process. These Hessian expansions might come, for example, from ab initio electronic structure calculations,density functional theory, or semiempirical molecular orbital theory. A electronic diabatic Hamiltonian matrix is constructed from these data such that, by construction, the lowest eigenvalue of this matrix provides a semiglobal approximation to the lowest electronically adiabatic potential energy surface. The theory is illustrated and tested by applications to rate constant calculations for three gasphase test reactions, namely, the isomerization of 1,3cispentadiene, and
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Electronic structure and dynamics of collisions
View Description Hide DescriptionThe potential energy surfaces of the three lowest electronic triplet states of which lead to and have been computed at the completeactivespaceselfconsistentfield plus secondorder perturbation theory (CASSCFMP2) level with a modest basis. Potential energy surfaces are fit with a global functional form. The state has a well 0.9 eV deep and the state has a 0.2 eV well with respect to the dissociation threshold. The and states are both bent at their minima and have a barrier at 0.2 eV and 0.3 eV above threshold, respectively. The state is mostly repulsive, and has a saddle at geometries. We have run classical trajectory calculations for collisions using these surfaces. Results agree well with available vibrational relaxation and oxygen atom exchange measurements except at low temperature. Comparisons are also made with measured vibrational excitation cross sections and infrared emission spectra of the nascent CO products at 3.4 eV collision energy. These results show a high degree of vibrational and rotational excitation with a nearly statistical population which is evident in a distinct spectral “bandhead” signature. Analysis of the trajectories show that almost all collisions which lead to oxygen atom exchange and/or vibrational energy transfer occur when the approaches the CO at OCO angles between 80° and 140°, passes over the barrier and through the wells of the and states, and interacts with the repulsive wall of the carbon end of the CO nearly perpendicular to the CO bond.

On phase factors and geometric phases in isotopes of A line integral study
View Description Hide DescriptionIn this work we apply the lineintegral technique to study possible geometric phaseeffects in the diabatic double manybody expansion (DMBE) potential energy surface of three hydrogenic systems, namely, and First, we show that the phase obtained by employing the lineintegral method is identical (up to a constant) to the ordinary diabatic angle of the orthogonal transformation that diagonalizes the diabatic potential matrix. Next this angle is studied numerically along the line formed by fixing the two hyperspherical coordinates ρ and θ and letting φ change along the interval [0, 2π]. We find that in the system, where this line always encircles the seam, the corresponding line integral always produces the value π for the geometric (Berry) phase. In the cases of the two isotopic systems we usually find the same results, but we also verify that for substantial regions in configuration space these lines do not encircle the seam and that, therefore, the line integrals produce the value of zero for the geometric phase. Analyzing the results, we establish that the LonguetHiggins phase, which is usually assumed to be equal to is in general significantly different from this value for all studied mass combinations.

Photoinitiated unimolecular decomposition: Accessing products via and pathways
View Description Hide DescriptionThe photoinitiated unimolecular decomposition of formaldehyde via the radical channel has been examined at energies where the and pathways both participate. The barrierless pathway has a loose transition state (which tightens somewhat with increasing energy), while the pathway involves a barrier and therefore a tight transition state. The product state distributions which derive from the and pathways differ qualitatively, thereby providing a means of discerning the respective and contributions. Energies in excess of the threshold have been examined throughout the range by using two complementary experimental techniques; ion imaging and highnRydbergtimeofflight spectroscopy. It was found that dominates at the low end of the energy range. Here, participation is sporadic, presumably due to poor coupling between zerothorder levels and reactive resonances. These resonances have small decay widths because they lie below the barrier. Alternatively, at the high end of the energy range, the pathway dominates, though a modest contribution is always present. The transition from dominance to dominance occurs over a broad energy range. The most reliable value for the barrier is given by the recent ab initio calculations of Yamaguchi et al. It lies near the center of the region where the transition from dominance to dominance takes place. Thus, the present results are consistent with the best theoretical calculations as well as the earlier study of Chuang et al., which bracketed the barrier energy between 1020 and 2100 cm^{−1} above the threshold. The main contribution of the present work is an experimental demonstration of the transition from to dominance, highlighting the sporadic nature of this competition.
