Volume 111, Issue 24, 22 December 1999
 COMMUNICATIONS


Intracluster hydrogen transfer followed by dissociation in the phenol– excited state:
View Description Hide DescriptionThe study of the phenol– cluster with twocolor twophotonionization shows that the main ion observed with delays between the lasers up to a few hundred nanoseconds is the fragment, resulting from direct ionization of the product coming from the reaction:

The infrared spectrum of the benzene–Ar cation
View Description Hide DescriptionThe infrared (IR) absorption spectra of the jetcooled and cations, complexed with Ar, are measured throughout the 450–1500 region via IRlaserinduced vibrational dissociationspectroscopy. The IR spectrum of the cation is dominated by a Fermi resonance between the IR active mode and two components of the combination mode of the lowest frequency modes and A stringent upper limit of 316 is found for the value of the dissociation limit of the neutral complex.

Infrared photodissociation spectra of the C–H stretch vibrations of and
View Description Hide DescriptionVibrational infrared photodissociationspectra of mass selected and ionic complexes are recorded in the spectral range of the C–H stretching vibrations. Transitions at 3095±15 cm^{−1} occur in all spectra and are assigned to C–H stretch fundamentals of the benzene cation in its electronic ground state. In the case of the complexes, additional transitions at 2904±7 and 3010±24 cm^{−1} are observed and attributed to the symmetric and antisymmetric C–H stretch vibrations of the ligands, and The deduced C–H stretching vibrations of in the ground state are roughly 30 cm^{−1} higher than the corresponding frequencies in the electronic ground state of the neutral species, indicating that the C–H bonds become stronger upon removal of an electron from the highest occupied orbital of

Dynamics of reactions
View Description Hide DescriptionThe reactions of ground stateyttrium atoms (Y) with formaldehyde have been studied in crossed molecular beams as a function of collision energy The potential energy barrier for C–H insertion is found to lie below 12 kcal/mol. It is proposed that the reaction is initiated by C–H insertion, producing HYCHO followed by H atom migration forming Although Y–CO bond fission leading to is dominant, a secondary minor channel also leads to the production of Formation of is not observed at 16 kcal/mol, but is clearly seen at 31 kcal/mol, indicating that lies between 58 and 73 kcal/mol.

Ground state and vertical electron detachment energies of icosahedral and
View Description Hide Descriptionclusters are studied with ab initio, manybody methods. Coupledcluster theory places the icosahedral structure 0.54 eV lower than the isomer. Electron propagator predictions on the photoelectron spectrum of are in close agreement with the observed bands and attribute shakeup character to features at higher energy.

A simplified force field for describing vibrational protein dynamics over the whole frequency range
View Description Hide DescriptionThe empirical force fields used for protein simulations contain shortranged terms (chemical bond structure, steric effects, van der Waals interactions) and longranged electrostatic contributions. It is well known that both components are important for determining the structure of a protein. We show that the dynamics around a stable equilibrium state can be described by a much simpler midrange force field made up of the chemical bond structure terms plus unspecific harmonic terms with a distancedependent force constant. A normal mode analysis of such a model can reproduce the experimental density of states as well as a conventional molecular dynamics simulation using a standard force field with longrange electrostatic terms. This finding is consistent with a recent observation that effective Coulomb interactions are short ranged for systems with a sufficiently homogeneous charge distribution.

Grand canonical ensemble Monte Carlo simulation of a lipid bilayer using extension biased rotations
View Description Hide DescriptionThe cavitybiased grandcanonical ensemble method was applied to the simulation of a lipid bilayer using an enhanced Monte Carlo sampling technique. The enhancements include controlling the torsion and molecular rotation step size based on the lipid’s conformation and controlling the order of torsion change attempts. It was found that the proposed sampling technique significantly enhances the rate of sampling of the lipidconformations while the grandcanonical ensemble implementation ensures that the water can both penetrate and escape pockets in the bilayer. The latter will be particularly important for simulating bilayers with embedded molecules.
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 THEORETICAL METHODS AND ALGORITHMS


Configuration interaction singles, timedependent Hartree–Fock, and timedependent density functional theory for the electronic excited states of extended systems
View Description Hide DescriptionA general formalism for timedependent linear response theory is presented within the framework of linearcombinationofatomicorbital crystalline orbital theory for the electronic excited states of infinite onedimensional lattices (polymers). The formalism encompasses those of timedependent Hartree–Fock theory (TDHF), timedependent density functional theory (TDDFT), and configuration interaction singles theory(CIS) (as the Tamm–Dancoff approximation to TDHF) as particular cases. These singleexcitation theories are implemented by using a trialvector algorithm, such that the atomicorbitalbased twoelectron integrals are recomputed as needed and the transformation of these integrals from the atomicorbital basis to the crystallineorbital basis is avoided. Convergence of the calculated excitation energies with respect to the number of unit cells taken into account in the lattice summations and the number of wave vector sampling points is studied taking the lowest singlet and triplet exciton states of alltrans polyethylene as an example. The CIS and TDHF excitation energies of polyethylene show rapid convergence with respect to K and they are substantially smaller than the corresponding Hartree–Fock fundamental band gaps. In contrast, the excitation energies obtained from TDDFT and its modification, the Tamm–Dancoff approximation to TDDFT, show slower convergence with respect to K and the excitation energies to the lowest singlet exciton states tend to collapse to the corresponding Kohn–Sham fundamental band gaps in the limit of We consider this to be a consequence of the incomplete cancellation of the selfinteraction energy in the matrix elements of the TDDFT matrix eigenvalue equation, and to be a problem inherent to the current approximate exchange–correlation potentials that decay too rapidly in the asymptotic region.

Application of the forward–backward initial value representation to molecular energy transfer
View Description Hide DescriptionIt is shown how the forward–backward (FB) approximation to the semiclassical initial value representation (IVR) can be used to calculate the probability (or cross section) for molecular energy transfer. Specifically, the probability for a molecule A to gain (or lose) an amount of internal energy by collision with a bath molecule B is given by the Fourier transform of a time correlation function which is in turn given by a single phase space average over the initial conditions of classical trajectories of the collision system. Application to energy transfer of by collision with He is carried out to demonstrate that the FBIVR provides a good description of quantum effects in

Time propagation and spectral filters in quantum dynamics: A Hermite polynomial perspective
View Description Hide DescriptionWe present an investigation of Hermite polynomials as a basic paradigm for quantum dynamics, and make a thorough comparison with the wellknown Chebyshev method. The motivation of the present study is to develop a compact and numerically efficient formulation of the spectral filter problem. In particular, we expand the time evolution operator in a Hermite series and obtain thereby an exponentially convergent propagation scheme. The basic features of the present formulation vı̀s a vı̀s Chebyshev scheme are as follows: (i) Contrary to the Chebyshev scheme Hamiltonian renormalization is not needed. However, an arbitrary time scaling may be necessary in order to avoid numerical hazards, and this time scaling also provides a leverage to accelerate the convergence of the Hermite series. We emphasize the final result is independent of the arbitrary scaling. (ii) As with the Chebyshev scheme the method is of high accuracy but not unitary by definition, and thus any deviation from unitarity may be used as a guideline for accuracy. The calculation of expansion coefficients in the present scheme is extremely simple. To contrast the convergence property of present method with that of the Chebyshev one for finite time propagation, we have introduced a time–energy scaling concept, and this has given rise to a unified picture of the overall convergence behavior. To test the efficacy of the present method, we have computed the transmission probability for a onedimensional symmetric Eckart barrier, as a function of energy, and shown that the present method, by suitable time–energy scaling, can be very efficient for numerical simulation. Time–energy scaling analysis also suggests that it may be possible to achieve a faster convergence with the Hermite based method for finite time propagation, by a proper choice of scaling parameter. We have further extended the present formulation directed toward the spectral filter problem. In particular, we have utilized the Gaussian damping function for the purpose. The Hermite propagation scheme has allowed all the time integrals to be done fully analytically, a feature not completely shared by the Chebyshev based scheme. As a result, we have obtained a very compact and numerically efficient scheme for the spectral filters to compute the interior eigenspectra of a large rank eigensystem. The present formulation also allows us to obtain a closed form expression to estimate the error of the energies and spectral intensities. As a test, we have utilized the present spectral filter method to compute the highly excited vibrational states for the twodimensional LiCN system and compared with the exact diagonalization result.

Methods for optimizing large molecules. II. Quadratic search
View Description Hide DescriptionGeometry optimization has become an essential part of quantumchemical computations, largely because of the availability of analytic first derivatives. QuasiNewton algorithms use the gradient to update the second derivative matrix (Hessian) and frequently employ corrections to the quadratic approximation such as rational functionoptimization (RFO) or the trust radius model (TRM). These corrections are typically carried out via diagonalization of the Hessian, which requires operations for N variables. Thus, they can be substantial bottlenecks in the optimization of large molecules with semiempirical, mixed quantum mechanical/molecular mechanical (QM/MM) or linearly scaling electronic structure methods. Our approach for solving the equations for coordinate transformations in optimizations has been extended to evaluate the RFO and TRM steps efficiently in redundant internal coordinates. The regular RFO model has also been modified so that it has the correct size dependence as the molecular systems become larger. Finally, an improved Hessian update for minimizations has been constructed by combining the Broyden–Fletcher–Goldfarb–Shanno (BFGS) and (symmetric rank one) SR1 updates. Together these modifications and new methods form an optimization algorithm for large molecules that scales as and performs similar to or better than the traditional optimization strategies used in quantum chemistry.

Combining coupled cluster and perturbation theory
View Description Hide DescriptionSingle reference coupled cluster (CC) singles and doubles theory is combined with loworder perturbation theory (PT) to treat ground state electron correlation. Two variants of the general scheme are discussed that differ in the type of amplitudes that are approximated perturbatively and which are treated to infinite order. The combined CC/PT methods to include ground statecorrelation are merged with equationofmotion (EOM) and similarity transformed EOM methods to describe excitation spectra of the highly correlated stetrazine, and systems. It is shown that the computationally efficient CC/PT schemes can reproduce full CCSD results even if perturbation theory by itself is a very poor approximation, as is the case for many transition metal compounds. In a second test CC/PT is applied to determine ground state equilibrium molecular structures and harmonic vibrational frequencies for a set of small molecules. Using either variant of CC/PT, full CCSD geometries are easily recovered, while vibrational frequencies can be more sensitive to details of the approximation.

High order finite difference algorithms for solving the Schrödinger equation in molecular dynamics
View Description Hide DescriptionThe view of considering global Pseudospectral methods (Sinc and Fourier) as the infinite order limit of local finite difference methods, and vice versa, finite difference as a certain sum acceleration of the pseudospectral methods is exploited to investigate high order finite difference algorithms for solving the Schrödinger equation in molecular dynamics. A Morse type potential for iodine molecule is used to compare the eigenenergies obtained by a Sinc Pseudospectral method and a high order finite difference approximation of the action of the kinetic energy operator on the wave function. Twodimensional and threedimensional model potentials are employed to compare spectra obtained by fast Fourier transform techniques and variable order finite difference. It is shown that it is not needed to employ very high order approximations of finite differences to reach the numerical accuracy of pseudospectral techniques. This, in addition to the fact that for complex configuration geometries and high dimensionality, local methods require less memory and are faster than pseudospectral methods, put finite difference among the effective algorithms for solving the Schrödinger equation in realistic molecular systems.

Periodic orbit–Quantum mechanical investigation of the inversion mechanism of
View Description Hide DescriptionThe inversion mechanism of a Tshaped is studied both classically and quantum mechanically. Regular states, localized in the region of the transition state for the inversion of the axial argon atom are found and are assigned by the symmetric stretch stable periodic orbits which emanate from the saddle point of the potential. These states inhibit the inversion process. States which promote the inversion are mainly irregular, but a few of them are localized and they have their nodes perpendicularly arranged along periodic orbits which originate from saddle nodebifurcations. The two types of periodic orbits, inhibiting and isomerizing, are used to produce distinctly different spectra and to extract the corresponding eigenfunctions by solving the time dependent Schrödinger equation using a variable order finite difference method [J. Chem. Phys. 111, 10827 (1999), preceding paper].

Semiclassical dynamics of nonadiabatic transitions in discretestate systems using spin coherentstate path integrals
View Description Hide DescriptionWe present a semiclassical method for simulating the dynamics of nonadiabatic transitions in a discretestate quantum system coupled to a bath of explicit continuous coordinates. This method employs a coherentstate formulation of the path integrals for the discrete system whose dynamics is described by spin operators. This spin coherentstate formulation allows the discrete system to be mapped onto a continuous coordinate. Stationary approximations of the resulting coherentstate path integrals of the system plus bath lead to quasiclassical equations of motion which can be solved numerically by direct integration. This algorithm reduces the problem to a number of simple classical trajectory calculations and does not require calculating any fluctuation determinants.

A simple semiclassical approach to the Kramers’ problem
View Description Hide DescriptionWe show that the Wigner–Leggett–Caldeira equation for Wigner phase space distribution function which describes the quantum Brownian motion of a particle in a force field in a high temperature, ohmic environment can be identified as a semiclassical version of Kramers’ equation. Based on an expansion in powers of we solve this equation to calculate the semiclassical correction to Kramers’ rate.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


FTICR study on hydrogenation of niobium cluster cations in seeded supersonic jet and multiplecollisioninduced dissociation of hydrides
View Description Hide DescriptionHydrogenation of niobiumcluster cations in a seeded supersonic jet of and multiplecollisioninduced dissociation (MCID) of the resulting hydrides have been studied using a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer. The nascent hydrides trapped in the FTICR cell have broad m distributions with no apparent prevalence of odd or even m. A pulse of argon applied to the trapped clusters causes a dramatic squeezing of the initial m distribution (through the collisioninduced removal of weakly bound molecules), favoring several particular hydrides for each cluster size n, e.g., and for The maximum m values of these stable hydrides are close to the stoichiometric composition of for the clusters with and approach that of NbH at larger n. The hydrides observed in our experiments are different from the products of the reactions performed in the FTICR cell at room temperature, which show only even and strongly ndependent m values. The MCID of the clusters occurs through the sequential desorption of molecules yielding and as final dissociation products for odd and even m, respectively. Based on the experiments on the MCID of an explanation is suggested for different reactivities of the clusters toward in the ICR and fastflowreactor experiments.

Quantum Monte Carlo simulation of intermolecular excited vibrational states in the cage water hexamer
View Description Hide DescriptionRigidbody diffusionMonte Carlo simulations of the ground state and ten lowlying intermolecular excited vibrational states for the cage form of are reported. The excited states are found by a nodal optimization procedure in which the fundamental excitedstatenodes are constructed from the harmonic normal coordinates. The anharmonic effects in the excited states are found to be large. One of the states with relatively large transition intensity involves primarily flipping motions of the free OH bonds on the doubly bound monomers, and is assigned to the vibration–rotation–tunnelling band observed experimentally by Liu et al. [Nature 301, 501–503 (1996)].

Laserinduced fluorescence and Optical/Stark spectroscopy of PtC
View Description Hide DescriptionOptical/Stark measurements have been performed on the (0,0) bands of both the system and the system of platinum monocarbide. The PtC molecules were produced in a pulsed supersonic molecular beamsource following the reaction of laser ablated platinum vapor with a mixture of a few percent of methane in argon. The newly determined permanent electric dipole moments obtained are and These results are discussed in terms of a proposed molecular orbital correlation diagram for platinum containing diatomics. The laserinduced fluorescence spectrum of the transition of PtC has been rerecorded at high resolution (full width of halfmaximum ∼40 MHz) and analyzed to yield rotational constants for the four most abundant isotopomers of PtC, extending the previous analysis [Appelblad, Nilsson, and Scullman, Phys. Scr. 7, 65 (1973)]. The anomalously large value (∼15 MHz) for the newly derived nuclearspin rotation parameter, for the state is discussed.

Spin polarization of zero kinetic energy electrons from HBr
View Description Hide DescriptionThe range of observables in zero kinetic energy (ZEKE) electron spectroscopy of molecules, previously restricted to the total electron intensity, was extended by measuring the integral spin polarization of ZEKE electrons at the thresholds after singlephoton excitation with narrowband circularly polarized light. A comparison with calculated values from multichannel quantum defect theory underlines the importance of autoionization for the decay dynamics.
