Volume 109, Issue 16, 22 October 1998
 COMMUNICATIONS


Configurational temperature: Verification of Monte Carlo simulations
View Description Hide DescriptionA new diagnostic that is useful for checking the algorithmic correctness of Monte Carlocomputer programs is presented. The check is made by comparing the Boltzmann temperature, which is input to the program and used to accept or reject moves, with a configurational temperature Here, Φ is the potential energy of the system and represents the dimensionless gradient operator with respect to the particle positions q. We show, using a simulation of LennardJones particles, that the configurational temperature rapidly and accurately tracks changes made to the input temperature even when the system is not in global thermodynamic equilibrium. Coding and/or algorithm errors can be detected by checking that the input temperature and agree. The effects of system size and continuity of Φ and its first derivative on are also discussed.

Molecular simulation of the intercrystalline phase of chain molecules
View Description Hide DescriptionOfflattice Monte Carlo simulations of the interphase between crystals for freely rotating chains are reported. Both conformational and topological spaces are sampled during a single simulation. The transition region between the crystal and the amorphous phase is characterized in terms of density, bond orientation order, and interfacial energy. The topology of the interphase is quantified in terms of loop and bridge chain populations, and the position of loop reentry sites.
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 THEORETICAL METHODS AND ALGORITHMS


Equivalentcore calculation of corelevel relaxation energies in photoelectron spectroscopy: A molecularorbital approach
View Description Hide DescriptionThe equivalentcore approximation is implemented in a novel way so as to calculate corelevel relaxation energies in photoelectron spectroscopy. The method is based on selfconsistent field (SCF) Hartree–Fock molecularorbital calculations via linear combinations of atomic orbitals, and involves evaluating the difference of sums of twoelectron Coulomb and exchange integrals, for all electrons in an atom and in its equivalentcore ion. By thus avoiding SCF calculations with a core hole present (the true final state of photoemission), this procedure is shown to significantly save computing time in comparison with an exact SCF directhole calculation. Application of the method in single atoms and selected molecules shows about a 10% difference with respect to directhole calculation results. The approximation introduces about 1–6 eV errors compared to the experimental results of gas phase molecules. This method thus should be a generally useful procedure for estimating relaxation energies in core spectra.

Exact distribution function for discrete time correlated random walks in one dimension
View Description Hide DescriptionA discrete time correlated random walk in one dimension is investigated. Combinatorial arguments are used to calculate the exact probability distribution the probability that the correlated random walker arrives at a distance L steps to the right of its starting point after exactly N steps. is calculated using arbitrary initial conditions which permit the influence of end effects and boundary conditions to be calculated and several special cases are considered in detail. with arbitrary initial conditions is calculated both with and without a bias for motion in one direction yielding a useful model for the combined diffusion and drift of charged particles undergoing a correlated random walk in an applied field. The relation of the correlated random walk to the Ising model is also discussed.

Converging toward a practical solution of the Holstein molecular crystal model
View Description Hide DescriptionWe present selected results for the Holstein molecular crystal model in one space dimension as determined by the Global–Local variational method, including complete polaron energy bands, ground state energies, and effective masses. We juxtapose our results with specific comparable results of numerous other methodologies of current interest, including quantum Monte Carlo, cluster diagonalization, dynamical mean field theory, density matrix renormalization group, semiclassical analysis, weakcoupling perturbation theory, and strongcoupling perturbation theory. Taken as a whole, these methodologies are mutually confirming and provide a comprehensive and quantitatively accurate description of polaron properties in essentially any regime. In particular, this comparison confirms the Global–Local variational method as being highly accurate over a wide range of the polaron parameter space, from the nonadiabatic limit to the extremes of high adiabaticity, from weak coupling through intermediate coupling to strong coupling.

Timedependent and timeindependent approaches to study effects of degenerate electronic states
View Description Hide DescriptionTwo types of phases are discussed in this article: (1) The topological phase as introduced by Berry [Proc. R. Soc. London, Ser. A 392, 45(1984)] and Aharonov and Anandan [Phys. Rev. Lett. 58, 1593 (1987)] and (2) the Longuet–Higgins phase [Proc. R. Soc. London, Ser. A 344, 147 (1975)]. The two types of phases have a common origin, namely the multivaluedness of the electronic adiabatic basis, a phenomenon associated with the existence of a degeneracy in configuration space. It will be shown, by studying an electronic model Hamiltonian that arises from a twostate approximation to the Mathieu equation, that the two phases differ from each other substantially, coinciding only in the adiabatic limit upon completion of a cycle.

Time correlation functions in lowdimensional conservative chaotic systems: A memory function approach
View Description Hide DescriptionTime correlation functions are studied for some conservative chaotic systems with both discrete and continuous time dynamics. For lowdimensional systems a memory function formalism on a microcanonical ensemble turns out to be able to yield useful information on the time correlation function and its energy dependence.

Productoperator formalism in and Jcoupled nuclear spins: Application to J assessment via SEDOR experiment
View Description Hide DescriptionProductoperator formalism has been extended to weakly coupled and nuclear spins to describe the result of nuclear SEDOR (spin echo double resonance) experiments for such spin numbers. By SEDOR modulation, the indirect nuclear spin–spin coupling constant can be measured also when the quadrupolar broadening hides the high resolution evaluation of and the method based on scalar relaxation of the second kind cannot be utilized because of the low quadrupolar relaxation efficiency. Furthermore, the nuclear SEDOR modulation can be performed in low intensity and homogeneity magnetic field. The theory has been applied to estimate of the coupled nuclear spins and in (octahedral symmetry) and of and in (icosahedral symmetry).

An efficient direct method for geometry optimization of large molecules in internal coordinates
View Description Hide DescriptionA new efficient procedure has been developed for geometry optimization of large molecules using internal coordinates. The method stores only the nonzero elements of the large transformation matrices, in the spirit of direct methods in electronic structuretheory.Matrix inversion has been replaced by iterative solution of linear systems of equations by the preconditioned conjugate gradient method. A new incomplete Cholesky preconditioner proved essential to accelerate the conjugate gradient procedure. The geometries of several alpha helical alanine polypeptides, up to 50 alanine units, have been optimized by the new method, using the SYBYL force field. For larger systems, the number of energy/gradient evaluations is reduced by a factor of 6–10, compared to Cartesian optimization, and the cost of the optimization is small compared to the energy calculation. We expect this method to be useful in molecular mechanics and in mixed quantum mechanics/molecular mechanics calculations.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Theory of vibrational relaxation processes in resonant collisions of lowenergy electrons with large molecules
View Description Hide DescriptionThe effect of intramolecular vibrational relaxation in resonant collisions of lowenergy electrons with large molecules is investigated. The vibrational relaxation results from the coupling of a few active modes, which are strongly coupled to the electronic degrees of freedom and therefore coherently excited during the formation of the collision complex, to a large number of inactive bath modes. The theory is formulated within the framework of the projectionoperator formalism. Starting from a model Hamiltonian which includes all vibrational modes, the bath degrees of freedom are eliminated, using perturbation theory in the systembath coupling and projection techniques within the bath Hilbert space. The result is an effectiveHamiltonian description of inelastic electron scattering and electron attachment which incorporates vibrational dissipation. In addition, the timedependent description of resonantelectronmolecule scattering is extended to include the possibility of vibrational relaxation in the resonance state. This timedependent formulation, which is based on the Markovian master equation for the reduced density operator, provides more direct insight into the dynamics of the collision complex. Calculations for simple model systems are performed which yield insight into the characteristic effects of vibrational relaxation on electron scattering and attachment cross sections, as well as on the timedependent dynamics of shape resonances. In particular, the competition between autodetachment and vibrational relaxation in shape resonances close to threshold is studied in some detail. The inclusion of vibrational relaxation allows us to develop a microscopic dynamical description of the nondissociative capture of lowenergy electrons by large molecules.

Electron impact ionization of the and free radicals
View Description Hide DescriptionWe measured absolute cross sections for the electronimpact ionization and dissociativeionization of the and free radicals from threshold to 200 eV using the fastneutralbeam technique. The total single ionization cross sections at 70 eV were found to be and The cross sections reach their maximum at about 100 eV for both radicals, with values of and Dissociativeionization is important only for where the parent ionization cross section and the fragment ionization cross sections have roughly the same value. By contrast, the ionization of is dominated by the formation of parent ions. A comparison of the measured total single ionization cross sections with calculated cross sections, using a modified additivity rule, shows excellent agreement for both radicals in terms of the absolute cross section values and the cross section shapes. Total single ionization cross sections were also calculated for and SF.

Resonant iondip infrared spectroscopy of the and water octamers in and
View Description Hide DescriptionThe techniques of resonant twophotonionization (R2PI), UV–UV (ultraviolet) holeburning, and resonant iondip infrared (RIDIR) spectroscopies have been employed along with density functional theory(DFT) calculations to assign and characterize the hydrogenbonding topologies of two isomers each of the and gasphase clusters. The isomers (B=benzene, W=water) have R2PI spectra which are nearly identical to one another, but shifted by about 5 cm^{−1} from one another. This difference is sufficient to enable interferencefree RIDIR spectra to be recorded. As with smaller clusters, the clusters fragment following photoionization by loss of either one or two water molecules. The OH stretch IR spectra of the two isomers bear a close resemblance to one another, but differ most noticeably in the doubledonor OH stretch transitions near 3550 cm^{−1}. Comparison to DFT calculated minimum energy structures, vibrational frequencies, and infrared intensities leads to an assignment of the Hbondingtopology of the isomers as nominally cubic water octamers of and symmetry surface attached to benzene through a π Hbond. A series of arguments based on the R2PI and holeburning spectra leads to an assignment of additional features in the R2PI spectra to two isomers of The OH stretch RIDIR spectra of these isomers show them to be the corresponding and analogs of in which the benzene molecules each form a π Hbond with a different dangling OH group on the subcluster.

Theoretical study of ion–molecule potentials for and with
View Description Hide DescriptionHighlevel ab initio calculations have been carried out on the lowest chargetransferexcited state of and the ground state, over a range of intermolecular distances R of at a fixed bond length for three orientation angles 45°, and 90°. The calculations employed extended atomic basis sets, chosen to represent accurately the electrical properties of the interacting partners; for the key properties and Θ are within 1.7%, 2.7%, and 2.1% of the best experimental values. All interaction energies were corrected for basisset superposition error by the counterpoise method, and fitted by analytic forms incorporating the proper longrange expansion through Our value for the tetrahexacontapole pole) moment of is −15.95 a.u. The most stable geometries for both systems occur for linear complexes, with minima of −7.00 (−12.65) kcal/mol located at (2.610) Å for the values are in good agreement with previous theoretical results. At small R the splitting between the and surfaces is found to have a radial dependence close to the prediction of the hydrogenic chargetransfer coupling model, while its anisotropy is similar to that of the surfaces themselves.

Structural and electronic properties of small clusters using generalizedgradient approximations within density functional theory
View Description Hide DescriptionNeutral and anionic clusters ( and are studied within density functional theory via the local density approximation(LDA) and the generalizedgradient approximation (GGA) of Perdew and Wang for exchange and correlation. Three different levels of improvement upon the LDA are considered. In the first level, the GGA correction to the exchangecorrelation energy is evaluated using the electronic density and the atomic coordinates obtained in the LDA calculation. In the second level, the electronic density is obtained selfconsistently within the GGA while keeping the LDA structural configurations. In the third level, both electronic density and ionic positions are obtained fully selfconsistently within the GGA. We found that the first level of approximation is already sufficient to correct the overbinding found in the LDA. With respect to the LDA, the selfconsistent GGA enhances the electron charge accumulation around the nuclei by depleting the interatomic bonding regions.

Bondselective photofragmentation of jetcooled HOD at 193 nm: Vibrationally mediated photochemistry with zeropoint excitation
View Description Hide DescriptionPhotofragment yields are reported for supersonically cooled and HOD via one photon, 193 nm photolysis in a slit jet expansion, with OH and OD fragments monitored by laser induced fluorescence methods. Detailed analysis of the dependence of OH vs OD photofragment signals on isotopic composition is used to extract relative photolysis cross sections and branching ratios for bondselective cleavage in HOD, and samples. Specified relative to the 193 nm cross sections for the ratios are 0.392(20), 0.032(20), and 0.0157(19) for (i) HOD→H+OD, (ii) HOD→D+OH and channels, respectively. Specifically, these results indicate a propensity for H–OD vs D–OH bond cleavage in HOD of 12(8):1. This strong H/D isotopic selectivity reflects extreme nonFranck–Condon photolysis out of classically of forbidden regions of the groundstatewave function, i.e., bondselective photochemistry mediated solely by zeropoint vibrational excitation. However, when compared with theoretical predictions from full threedimensional quantum scattering calculations on the ground and excited potentialenergy surfaces (PES) of water, the observed HOD branching ratio is found to be too low by an order of magnitude. These results provide additional evidence that photodissociation of water in the extreme nonFranck–Condon region is not adequately explained by current theoretical models and suggest that contributions from other electronic surfaces may be important.

New aspects of the photodissociation of water in the first absorption band: How strong is excitation of the first triplet state?
View Description Hide DescriptionWe consider the possibility of the excitation of water at wavelengths near 193 nm, i.e., in the red tail of the first absorption band. The corresponding excitedstatepotentialenergysurface is calculated by quantum mechanical methods and the dynamics calculations are performed in the timedependent representation. It is shown that an absorption cross section for exciting the triplet state that at its maximum is about five hundred times (or more) smaller than the corresponding cross section for excitation of the state, might explain the surprisingly small H+OD/D+OH branching ratio in the photodissociation of HOD at 193 nm measured by Plusquellic et al. (the foregoing paper). The singlet–triplet transition dipole moment estimated in this way also explains the unexpectedly small cross section ratio for and measured at 193 nm.

Helicity of orientation parameters of photofragments in fluorescenceimaging experiments
View Description Hide DescriptionA detection scheme in fluorescenceimaging experiments is presented for determining helicity of orientation parameters of photofragments prepared by circularly polarized photolysis lasers. In a framework of density matrix theory, explicit fluorescence intensity formulas are derived for detection of right and leftcircularly polarized fluorescencephotons in various transition sequences. A pattern recognition from fluorescenceimages of photofragments in a state of definite helicity with respect to their recoil directions has been established, where differences between left and rightcircularly polarized fluorescenceimage patterns should be taken. Information on the coherence among various magnetic sublevels of an angular momentum state can be obtained by monitoring fluorescenceimages in a transition (P branch in absorption).

Twophoton ionization spectroscopy and allelectron ab initio study of LiCa
View Description Hide DescriptionResonant twophoton ionization spectra of LiCa have been obtained from a laser vaporization, supersonic expansion source. The ground state of the molecule is confirmed to be Three band systems have been observed near 15 282, 19 310, and and the upper states have been assigned as and, tentatively, Bond lengths and vibrational frequencies are reported for for the various states as and The ionization energy was also measured to be 4.471(1) eV by observing the onset of onephoton ionization. Results of ab initio allelectron calculations on twelve lowlying states [ and ] are also reported, along with results on the ground electronic state of The dissociation energies of into and of into are calculated to be 0.24 and 1.20 eV respectively, and the vertical and adiabatic ionization energies of LiCa have been determined to be almost the same, 4.43 eV, at the quadratic configuration interaction, including singles and doubles with approximate triples and all correlated electrons [QCISD(T,FULL)] level of theory.

Highresolution absorption spectrum of jetcooled between 70 500 and 81 550 cm^{−1}: np and nf Rydberg series converging to the first ionization potential
View Description Hide DescriptionThe absorptionspectrum of jetcooled was photographed between 70 500 and 81 550 cm^{−1} at a resolution limit of 0.0008 nm, i.e., 0.4 to 0.5 cm^{−1}. Wave numbers of over 200 features are reported and assigned in terms of and nf allowed transitions—electronic origin bands and vibronic bands corresponding to excitation of the totally symmetric stretching vibrational mode in the excited electronic states—as well as forbidden and 5), and transitions— and bands involving excitation of the bending vibrational mode in the corresponding excited states—, and the allowed transition, first term of a series converging to the second ionization limit. Ab initio calculations of the electronic energies and transition moments for effective principal quantum numbers about 4 and 5 are carried out for all the observed series. Rotational band contours are calculated using Hund’s case (e) representation for one and threephoton excitation of the and nfRydberg complexes for every observed n value. An approximate Rydberg formula is obtained which allows the calculation of the principal peak wave numbers for to within 1 cm^{−1}. This work completes the study of Rydberg series converging to the first ionization limit initiated previously with the and complexes [C. CossartMagos et al., J. Chem. Phys. 104, 7412 (1996)] and the supercomplex [C. CossartMagos et al., J. Chem. Phys. 107, 1308 (1997)]. Systematic comparison with the resonance enhanced multiphoton ionization (REMPI) spectra recorded by Morgan et al. [J. Chem. Phys. 104, 6117 (1996)] and by Berger et al. [J. Chem. Phys. 107, 8866 (1997)] reveals that only exceptionally the same transition is observed both in the absorption and the REMPI experiments: the two techniques give complementary information, with the absorption providing a much greater volume of data. Previous tentative assignments of the REMPI spectra by Morgan et al. and by Berger et al. are completed, with a few reassignments being necessary. Detailed comparison of the present absorptionspectrum with the vacuumultraviolet laser and synchrotron radiationphotoionization recorded by Huang et al. [J. Chem. Phys. 106, 864 (1996)], shows that, in the common part the same transitions are observed, and that, for the electric field intensities used (up to 1070 V/cm), the Stark shifts are less than 1 cm^{−1}.

Linemixing effects in He and broadened infrared branches of
View Description Hide DescriptionTwo branches of near 579.3 and belonging to the and bands, respectively, of and symmetry, have been studied for He and perturbers at pressures ranging from 0.1 to 2 atm, using a tunable diode laser and a differencefrequency laser spectrometer. To interpret the linemixing effects in these spectra, we have applied a model based on the energy corrected sudden approximation whose parameters have been only derived from linebroadening data for and also from the measured absorption by the branches for This model provides a satisfactory agreement with experimental band shapes, whatever the band, the perturber and the pressure considered. Significantly larger linemixing effects are shown for with respect to Finally, the assumption made in the calculations to treat separately the couplings in the even and odd levels appears to have a negligible influence on the resulting band shapes.
