Volume 115, Issue 15, 15 October 2001
 COMMUNICATIONS


Observation of the cyclic water hexamer in solid parahydrogen
View Description Hide DescriptionWe present infrared (IR) absorption spectra of cryogenic parahydrogen solids doped with small water clusters. We observe a sequence of peaks shifted to the red by ≈15 from the absorptions of cyclic water clusters in liquid heliumdroplets [K. Nauta and R. E. Miller, Science 287, 293 (2000)]; this sequence includes the peak due to the cyclic isomer of the water hexamer: We believe this is only the second spectroscopic observation of isolated and the first report of the IR spectrum of the isolated cluster in the solid phase.

Effects of vibrational excitation of target molecule in charge–transfer reaction of with at thermal energy
View Description Hide DescriptionThe effects of vibrational excitation of target molecule in the chargetransfer (CT) reaction has been studied at thermal energy using a flowing–afterglow method. The vibrational distribution of produced from a microwavedischarge of or mixtures, was determined using emission resulting from the Penning ionization. Although the initial vibrational distribution of produced from the reaction was it was in the reaction. The level, which is the most favorable level in the thermal reaction, is still favored in the reaction. This indicates that the deviation from the energyresonance rule becomes large by the vibrational excitation of The rotational distributions of and 4 were similar between the and reactions, demonstrating that transfer is insignificant for ionization in the reaction.
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 ARTICLES

 Theoretical Methods and Algorithms

Quantum chemistry using the density matrix renormalization group
View Description Hide DescriptionA new implementation of the density matrix renormalization group is presented for ab initio quantum chemistry. Test computations have been performed of the dissociation energies of the diatomics HF. A preliminary calculation on the molecule provides a new variational upper bound to the ground stateenergy.

Higher order derivatives for nuclear indexes in the framework of density functional theory
View Description Hide DescriptionGeneral and exact relationships for higher order derivatives of the nuclear Fukui function with respect to the electron number at constant external potential have been explicitly derived in the framework of the four Legendre transformed ensembles of density functional theory. These relationships complement and extend to nuclear reactivities some developments [F. De Proft, S. Liu, and P. Geerlings, J. Chem. Phys. 108, 7549 (1998)] and recent advances [E. Chamorro, R. Contreras, and P. Fuentealba, J. Chem. Phys. 113, 10861 (2000)] found for the high order electron responses introduced in the framework of a nonlocal (pairsite) reactivity formalism.

Analysis of the linear response function along the adiabatic connection from the Kohn–Sham to the correlated system
View Description Hide DescriptionCareful calculations are performed to obtain the radial density–density response function for the He and the Be series. This is also done along the adiabatic connection of the density functional theory (as the system evolves from the real, physical system to the Kohn–Sham one). In this process the electron density is kept constant, while the strength of the interaction between electrons changes. The response functions are analyzed in terms of their eigenvalues and eigenfunctions. The latter change only little along this process. The absolute value of the eigenvalues is in general reduced by the interaction: A screening effect is present. For the neardegenerate systems, we notice that the opposite effect can appear (antiscreening).

Uncertainty of path integral averages at low temperature
View Description Hide DescriptionBurghardt, Eicke, and Stolze [J. Chem. Phys. 108, 1562 (1998)] have recently presented analytical results for the coherent state path integral (CSPI) approximation to the harmonic oscillator thermal density matrix in a generalized representation. In this work, the variance of the position and momentum operators for the more common Feynman path integral approximation to the density matrix is examined and compared with the results of the generalized CSPI approximation. Both path integral approaches are found to predict minimum uncertainty states at low enough temperatures. Particular attention is given to estimates of internal energy, which can place limits upon the temperature range over which path integral approximations are valid.

A fourthorder realspace algorithm for solving local Schrödinger equations
View Description Hide DescriptionWe describe a rapidly converging algorithm for solving the Schrödinger equation with local potentials in real space. The algorithm is based on solving the Schrödinger equation in imaginary time by factorizing the evolution operator to fourth order with purely positive coefficients. The wave functions and the associated energies extracted from the normalization factor converge as The energies computed directly from the expectation value, converge as When compared to the existing secondorder split operator method, our algorithm is at least a factor of 100 more efficient. We examine and compare four distinct fourthorder factorizations for solving the potential in one dimension and conclude that all four algorithms converge well at large time steps, but one is more efficient. We also solve the Schrödinger equation in three dimensions for the lowest four eigenstates of the spherical analog of the same potential. We conclude that the algorithm is equally efficient in solving for the lowlying boundstate spectrum in three dimensions. In the case of a spherical jellium cluster with 20 electrons, our fourthorder algorithm allows the use of very large time steps, thus greatly speeding up the rate of convergence. This rapid convergence makes our scheme particularly useful for solving the Kohn–Sham equation of densityfunctional theory and the Gross–Pitaevskii equation for dilute Bose–Einstein condensates in arbitrary geometries.

Statistical angular correlation coefficients and second electronpair moments for atoms
View Description Hide DescriptionStatistical correlation coefficients introduced by Kutzelnigg et al. [Phys. Rev. 172, 49 (1968)] provide overall measures of the difference between the electronpair density and the product of singleelectron densities, where is a probe function. It is shown that the angular correlation coefficient a particular case of for is simply expressible in terms of the generalized electronpair moments with two realvalued parameters a and b. Especially, the relation for means that is nothing but the difference between the centerofmass motion and relative motion contributions in the second electronpair moments. Conversely, the electronpair moments are obtained from the singleelectron moment and the correlation coefficient The same is also true in momentum space.

An efficient combination of computational techniques for investigating electronic resonance states in molecules
View Description Hide DescriptionCalculating electronic resonance states in molecules is a serious challenge to theory, because the treatment of both the scatteringand the manyelectron problem is a formidable task. A very promising approach, known as CAP/CI, consists of the combination of a complex absorbing potential with the method of configuration interaction. In this paper we propose the combination of three distinct computational techniques in order to boost the performance of CAP/CI. A complex absorbing potential that can be adjusted flexibly to the geometry of the molecular scattering target is presented and its representation in a Gaussian basis set is discussed. To handle the largescale complex symmetric eigenvalue problem arising in CAP/CI, a subspace projection method is employed and its validity is shown. We advocate the use of parallel filter diagonalization for calculating the eigenvectors required in the projection step. The proposed techniques are applied to determine the lifetime of an autoionizing, innervalence excited state of

Intermediate Hamiltonian Fockspace coupled cluster method in the onehole oneparticle sector: Excitation energies of xenon and radon
View Description Hide DescriptionThe intermediate Hamiltonian Fockspace coupled cluster method developed recently is applied to excitations in the onehole oneparticle sector, taking xenon and radon atoms as test cases. Virtual orbitals are modified to yield better approximations to orbitals occupied in excited states. The usual Fockspace coupled cluster scheme diverges for these systems, but the intermediate Hamiltonian approach converges for large spaces and yields excitation energies in very good agreement with experiment. The average error in the calculated values for the lowest excitation energies (about 20 for each atom) is 0.6%. Predictions are made for the unobserved Rydberg states of Rn.

Accuracy of freeenergy perturbation calculations in molecular simulation. II. Heuristics
View Description Hide DescriptionWe examine issues involved in applying and interpreting freeenergy perturbation (FEP) calculations in molecular simulation, with the aim to develop simple heuristics that can guide their use and warn when a result is likely to be inaccurate. We build on the accuracy model developed in the first paper of this series [N. Lu and D. A. Kofke, J. Chem. Phys. 114, 7303 (2001)], which emphasized the sign of the entropy difference between the target and reference systems as an essential indicator for the correct implementation of FEP calculations: such calculations must be performed in the “insertion” direction, for which or else they are very likely to be systematically incorrect (i.e., inaccurate). We describe here an extended analysis for insertion FEP calculations, and identify the group where M is the number of independent FEP samples taken and k is Boltzmann’s constant, as a relevant quantity for characterizing the accuracy of FEP result. We find that if is of order 100 or larger, then one can expect the FEP calculation to yield a result of minimally acceptable accuracy; for a margin of safety a value of 1000 or greater is preferable for this group. Although the FEPmeasured is required to apply this heuristic, it is “safe” in that any inaccuracy in this will be such that the group is even smaller than it is for the true and will therefore still warn of an inaccurate result. The analysis is demonstrated for a very wide range of values, considering a model FEP calculation, a hardsphere insertion calculation, and a diameterchange FEP in the LennardJones model. We apply the results of this analysis, and earlier work, to consider the question of the optimal number of intermediate stages to use in a staged FEP calculation. The analysis shows that, for optimal accuracy, stages should be selected such that the entropy difference per stage satisfies however, consideration of the precision instead prescribes that Inasmuch as the precision is the larger concern once accuracy reaches an acceptable level, the latter criterion forms our recommendation for selecting the number of intermediate stages.

A note on quantum thermodynamic rate theories
View Description Hide DescriptionThe relationship between quantum transition state theory, the mixed quantum classical rate theory and the Hansen–Andersen analytic continuation methods is analyzed. We prove that the first three time derivatives of a coordinate dependent operator are the same in quantum and classical mechanics. As a result, the mixed quantum classical theory, in which the quantum projection operator is replaced by the classical, may be considered as a specific case of the Hansen–Andersen methodology. The same holds true for quantum transition state theory for one dimensional systems, where the exact quantum propagator is replaced by its parabolic barrier approximation. In the multidimensional case, quantum transition state theory errs somewhat in the second nonzero time derivative, however it may be reformulated to assure that it too remains exact for the first two nonzero initial time derivatives. Further systematic improvement of the mixed quantum classical theory may be obtained by including higher order terms in the expansion of the Wigner–Liouville equation. An iterative solution of the integral form of the Wigner–Liouville equation is suggested, which is based on propagation of classical trajectories only.

Practical implementation of the instanton theory for the groundstate tunneling splitting
View Description Hide DescriptionThe instanton theory is reformulated with use of the path integral approach and the Wentzel–Kramers–Brillouin approximation to the Schrödinger equation. Both approaches are shown to provide the same results. A new practically useful semiclassical formula is derived for the tunneling splitting of the ground state, which can be implemented for highdimensional systems. The theory is applicable to systems of arbitrary Riemannian metric and is also supplemented by a practical numerical recipe to evaluate the instanton trajectory, i.e., periodic orbit, in multidimensional space. Numerical examples are presented for threedimensional (3D) and 21D systems of and malonaldehyde, respectively.

On the direct evaluation of the equilibrium distribution of clusters by simulation. II
View Description Hide DescriptionWe clarify some of the subtle issues surrounding the observational cluster method, a simulation technique for studying nucleation. The validity of the method is reaffirmed here. The condition of the compact cluster limit is quantified and its implications are elucidated in terms of the correct enumeration of configuration space.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Glyoxal photodissociation. II. An ab initio direct classical trajectory study of
View Description Hide DescriptionPhotodissociation of glyoxal via the channel has been investigated by ab initio classical trajectory calculations using Becke’s threeparameter hybrid functional method with split valence and polarized basis set To model the experimental conditions, trajectories were started from a microcanonical ensemble at the transition state with 8.5 kcal/mol excess energy distributed among the vibrational modes and the transition vector. The CO product was produced with a broad rotational distribution but with almost no vibration excitation. When combined with the results from the channel, the calculated vibrational and rotational distributions of CO are in excellent agreement with the experimental observations. The rotational distribution of was very broad ranging up to The product has significant vibrational excitation in the outofplane bending, rocking, scissoring, and CO stretching modes. For both the and the channels, the majority of available energy was partitioned into translations.

Gas phase electronic spectrum of in the visible
View Description Hide DescriptionThe electronic spectrum of has been observed by means of a resonant two color two photonionization technique sampling a supersonic plasma source. On the basis of ab initio calculations, vibrational and rotational analysis, the complex vibronic system observed in the visible and near UV is assigned to three electronic transitions, and of Potential curves along the CCH bending coordinate have been obtained because of its role for the electronic spectrum and dynamics of

An injection seeded narrow bandwidth pulsed optical parametric oscillator and its application to the investigation of hyperfine structure in the PF radical
View Description Hide DescriptionWe describe the construction of an all solidstate, narrow bandwidth, pulsed optical parametric oscillator(OPO) based on βbarium borate nonlinear crystals. The OPO was injection seeded by an external cavitydiode laser in the range 755–855 nm to generate high power narrow bandwidth tunable light in this range and simultaneously at 606–669 nm. The bandwidth of the visible light was ∼130 MHz, and after frequency doubling or sum frequency mixing with the second harmonic of the pump Nd:YAG laser, subDoppler spectra with an overall resolution of 450 MHz were taken in the UV. The system is demonstrated by taking highresolution spectra of the and 5–7 bands of the progression and the band of the transition in PF. These spectra show clear hyperfine structure, and an analysis of this structure is presented and interpreted in terms of the electronic structure of the molecule. As a prelude to this highresolution study, the first ten members of the band system and the first five members of the band system were recorded at the moderate resolution provided by a pulsed dye laser.

Transition state dynamics of the reaction studied by dissociative photodetachment of
View Description Hide DescriptionPhotoelectronphotofragment coincidence (PPC) spectroscopy has been used to study the dissociativephotodetachment of and The observed partitioning of photoelectron and photofragment translational energies provides information on the dynamics in the transition state region of the reaction between two hydroxyl radicals: The data reveal vibrationally resolved product translational energy distributions for both the entrance channel and the exit channel upon photodetachment. The total translational energy distribution shows a convoluted vibrational progression consistent with antisymmetric stretch excitation of in the exit channel and OH stretch in the entrance channel. The photoelectron spectra are compared to twodimensional timedependent wave packet dynamics simulations based on an anharmonic potential in the anion and a model collinear potential energy surface for the neutral complex. The PPC spectra also yield the dissociation energies and

Relative stabilities of H and Dbonded isotopomers of HCN⋯HF and HNC⋯HF
View Description Hide DescriptionAb initio calculations were performed at the SCF, B3LYP, MP2, QCISD, and CCSD(T) levels of theory using the ccpVTZ basis set to obtain optimized geometries, dipole moments, binding energies, and harmonic vibrational frequencies for the linear complexes HCN⋯HF and HNC⋯HF. It was found that HNC⋯HF has a slightly larger binding energy [29 kJ mol^{−1} at CCSD(T)] than HCN⋯HF [27 kJ mol^{−1} at CCSD(T)]. The relative stabilities of the monodeuterated isotopomers DCN⋯HF (DNC⋯HF) and HCN⋯DF (HNC⋯DF) were also determined from their zeropoint energies; vibrational frequency shifts of HF and HCN (HNC) on bonding were also calculated and used to gain insight into these relative stabilities. It was found that the Dbonded isotopomer is more thermodynamically stable than the Hbonded isotopomer. Previous studies on the weakly bound linear complexes CO–acetylene and –acetylene also found that the Dbonded species was more stable than the Hbonded species.

Conditions conducive to the chemiionization reaction
View Description Hide DescriptionWe have determined the favorable geometries and intermediate HCO states that allow the chemiionization reaction to take place in lowenergy collisions, when CH is either in the ground or in the first excited state.