Volume 117, Issue 13, 01 October 2002
 ARTICLES

 Theoretical Methods and Algorithms

Wavelet formulation of path integral Monte Carlo
View Description Hide DescriptionA wavelet formulation of path integral Monte Carlo (PIMC) is constructed. Comparison with Fourier path integral Monte Carlo is presented using simple onedimensional examples. Wavelet path integral Monte Carlo exhibits a few advantages over previous methods for PIMC. The efficiency of the current method is at least comparable to other techniques.

A geminal model chemistry
View Description Hide DescriptionWe modify the existing model of the antisymmetrized product of strongly orthogonal geminals to define a size consistent variational theory free from any adjustable parameters apart from the usual choice of a basis set. The new theory is only slightly more computationally expensive than Hartree–Fock, gives an exact solution for an ensemble of noninteracting singlet two electron systems, and is applicable to open and closedshell systems. We use it to calculate equilibrium geometries, vibrational frequencies, and dipole moments of diatomic molecules from G2/97 database. We find excellent agreement with experimental values for covalently bound molecules, and overstretched bonds of molecules formed by atoms with extreme electronegativity.

Semiclassical initial value representation propagation of vibrational wave functions
View Description Hide DescriptionTwo new, uniform, semiclassical initial value representation (IVR) expressions are obtained for the timedependent wave function that evolves from the eigenstate of a “zeroorder” Hamiltonian describing an arbitrary, integrable, vibrational system. In contrast to most other IVR approaches, this initial state is, itself, treated semiclassically so that it need not be determined by independent quantum calculations. One of the IVR expressions presented here describes as an integral over only half of the phase space variables of the system, so that it holds the promise of computational advantages over existing treatments that involve integrations over all of phase space. Numerical tests confirm the efficiency and accuracy of the semiclassical approximations.

Spin–spin coupling tensors by densityfunctional linear response theory
View Description Hide DescriptionDensityfunctional theory(DFT) calculations of indirect nuclear magnetic resonance spin–spin coupling tensorsJ, with the anisotropic but symmetric parts being the particular concern, are carried out for a series of molecules with the linear response (LR) method. For the first time, the anisotropic components of J are reported for a hybrid functional. Spin–spin tensors calculated using the local density approximation(LDA), the gradientcorrected Becke–Lee–Yang–Parr (BLYP) functional, and the hybrid threeparameter BLYP (B3LYP) functional are compared with previous ab initio multiconfiguration selfconsistentfield (MCSCF) LR results and experimental data. In general, the B3LYP functional provides reasonable accuracy not only for the isotropic coupling constants but also for the anisotropic components of J, with the results improving in the sequence Error cancellation often improves the total DFT spin–spin coupling when the magnitude of the paramagnetic spin–orbit contribution is overestimated, or when the spin–dipole (SD) and Fermicontact (FC) contributions are far from the MCSCF values. For the nucleus, known to be difficult for DFT, the anisotropic properties of heteronuclear, in particular couplings are often more accurate than the poorly described isotropic coupling constants. This happens since the FC contribution is small at fluorine compared with carbon, leading to a small error in the total SD/FC term. With the recent implementation of the hybrid B3LYP functional, calculations of predictive quality for the Jtensors are no longer restricted to small model molecules, opening up the possibility of studying the anisotropic components of J in large organic and biomolecules of experimental interest.

A density functional study of van der Waals interactions
View Description Hide DescriptionThe applicability of density functional theory(DFT) to van der Waals (vdW) calculations are investigated by using the longrange exchange correction scheme and the Andersson–Langreth–Lundqvist vdW functional. By calculating bond energy potentials of raregas dimers, it was found that the present scheme gives much more accurate potentials for all dimers than conventional sophisticated DFT methods do. We therefore confirmed that vdW bonds are constructed under the balance of longrange exchange and vdW correlation interactions, although neither of these interactions are usually contained in pure exchange–correlation functionals. It was also found that calculated vdW potentials are obviously affected by functional forms for rapidly varying densities. Especially in vdW calculations, we must employ a correlation functional that satisfies the fundamental condition for rapidly varying density.

Correspondence between configurational temperature and molecular kinetic temperature thermostats
View Description Hide DescriptionMolecular fluids undergoing shear flow are often modeled using a homogeneous nonequilibrium molecular dynamics algorithm. To reach a steady state, this method must be used in conjunction with a thermostating mechanism which duplicates the heat dissipation in the experimental setup (e.g., by conduction to the shearing boundaries). The most commonly used type of thermostat involves fixing the center of mass kinetic (c.m.) temperature. Though perfectly valid, this approach does not seem to be the most realistic for a molecular fluid since heat is removed only through the 3 degrees of freedom of the center of mass for each molecule. The second type of thermostat involves fixing the “atomic” kinetic temperature and therefore takes into account all degrees of freedom. However, since the streaming velocity of atoms within their constituent molecules is unknown, the implementation of such a thermostat is problematic and relies on incorrect assumptions on the streaming velocity of atoms. The recently developed configurational temperature thermostat requires no assumption on the streaming velocity of atoms and takes into account all degrees of freedom. Using a configurational temperature thermostat to thermostat homogeneous shear flow thus seems to be a more realistic approach than the c.m. kinetic thermostat. In this work, we apply this configurational temperature thermostat to the study of linear alkanes and undergoing shear flow. The results so obtained are compared with those obtained using a c.m. kinetic thermostat. Our aims are (1) to test the influence of the total number of degrees of freedom of the system, (2) to make a connection between the results obtained with the two types of thermostats. By carefully examining the energies of the internal modes, we have been able to characterize the loss of accuracy of a c.m. kinetic thermostat at high shear rates and for high molecular weight compounds. Finally, we establish a correspondence between the two types of thermostats by showing that, for the internal modes, a simulation at a fixed c.m. kinetic temperature is equivalent to a simulation at a fixed but higher configurational temperature.

Extremal path approach to rate constant calculations by the linearized semiclassical initial value representation
View Description Hide DescriptionTo extend the applicability of the linearized initial value representation (LIVR) method to lower temperatures and realistic potentials, a generalization to barriers other than the inverted parabola is proposed. The LIVR method calculates rate constants of chemical reactions involving quantum effects by weighting classical trajectories by the Wigner distribution function (WDF) of the Boltzmannaveraged flux operator. These calculations can be performed efficiently if the WDF is available in analytical form, which is the case for harmonic barriers only. The proposed generalization to anharmonic barriers is based on the recognition that above a critical temperature where ω is the curvature at the top of the barrier and is the Boltzmann constant, the WDF is dominated by an extremal trajectory. The evaluation of WDFs and thus of thermal rate constants is thereby reduced to the search for the extremal path defined by a steepestdescent condition for the WDF. This extremal trajectory is the hightemperature analogue of the instanton (bounce path), which exists for temperatures lower than Explicit formulas are derived for the generation of realistic WDFs and barrier crossing rate constants for symmetric barriers of arbitrary shape. Approximations are introduced that will reduce the extra computational effort required for these anharmonic barriers. They are based on the fact that above the critical temperature the WDF of any anharmonic potential can be represented with good approximation in an analytical form analogous to that of the parabolic barrier by the introduction of effective parameters. Results obtained for two standard model potentials, the quartic potential and the symmetric Eckart barrier, are compared with the wellknown parabolic barrier results. The formal and actual temperature limits for calculating tunnelingrate constants and the extension of the method to asymmetric barriers are briefly discussed.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Isotope effects in linear dihydrogen bonded complexes containing LiH
View Description Hide DescriptionAn ab initio study of linear dihydrogenbonded complexes containing LiH (acting as a proton acceptor) was undertaken. The complexes studied were LiH⋯HF, LiH⋯HCN, and LiH⋯HCCH. Equilibrium geometries and harmonic vibrational frequencies were computed at various levels of theory using a 631++G(d,p) basis set. It was found that the LiH⋯HF complex was not stable at all levels of theory. The relative stabilities of Hbonded and Dbonded isotopomers of LiH⋯HCN and LiH⋯HCCH were determined by differences in zeropoint vibrational frequencies. For LiH⋯HCN isotopomers, it was found that the LiD⋯HCN was favored over LiH⋯DCN with a relative stability of 54 calculated at the Quadratic Configuration Interaction—Singles and Doubles level. Similarly, LiD⋯HCCH is favored over LiH⋯DCCH, with a lower value for the relative stability. The relative stabilities of the Hbonded and Dbonded species LiH⋯HCCD and LiH⋯DCCH indicated that the Dbonded complex was energetically favored, in accordance with the Buckingham–Liu theory.

Photodissociation of CFX=CHCl (X=H,F) at 193 nm by product translational spectroscopy
View Description Hide DescriptionIn this work, we have studied the photodissociation of CFX=CHCl (X=H,F) at 193 nm using product translational spectroscopy. Results show that while the photoelimination of fast Cl, slow Cl, HCl, and HF occurs for both molecules, the cleavage of the C=C bond is only measurable for Among these, only the fast Cl product was detected with strong angular preference with respect to polarized laser light. Product translational energy distributions were measured for all dissociation channels. The difference in the distributions between threecentered (3C) and fourcentered (4C) molecular elimination reactions was observed. The low recoil energy for 3C HCl elimination from strongly suggests that there is no concerted isomerization from to Although we detected no primary C–F bond fission in the present study, a relatively large yield of the secondary dissociation products was determined for the internally excited fluorovinyl radical CHCHF. The results are discussed in terms of either a direct or an indirect dissociation process arising from excitation to the state, and comparisons between the title molecules are included.

Charge transfer and nonadiabatic dynamics of diatomic anions in clusters
View Description Hide DescriptionWe have studied the photodissociation and recombination dynamics of diatomic anions in sizeselected clusters by using simple model systems. The main purpose of the study is to provide a theoretical background for a better understanding of the salient features of the charge transfer and nonadiabatic transitions involved in the dynamics of solvated molecular ions. Calculations have been performed on the photodissociation and recombination of the model diatomic anion embedded in and clusters. The homonuclear diatomic anion is modeled as oneelectron system consisting of two identical nuclei and an extra electron. The nuclear and electronic dynamics of are treated quantum mechanically, while the motions of the solvent molecules are described by classical dynamics.Nonadiabatic theoretical calculations, in which the electronic and the nuclear dynamics are treated simultaneously, can reveal the importance of nonadiabatic effects by including intrinsically all electronic states. It is found that extensive nonadiabatic transitions between ground and excited electronic states are involved in the dynamics of in molecular clusters. It is suggested that changes in anion electronic structures and corresponding charge switching can lead to a multitude of pathways for dissociationrecombination dynamics. The results of the present study illustrate the microscopic details of the electronically nonadiabatic processes which control the photodissociationdynamics of molecular ions in clusters.

The observation of large changes in the rotational constants of glyoxal in superfluid helium droplets upon electronic excitation
View Description Hide DescriptionThe rotational fine structure of the vibrationless band of the electronic transition of glyoxal in large superfluiddroplets has been interrogated with high resolution laser depletion spectroscopy. In the electronic ground singlet state the rotational constantsA and are less than for the free molecule by a factor of 2.87 and 2.16, respectively. In the electronic excited state the rotational constantA is found to be 17% larger and the average rotational constants to be 25% smaller than in the state. The unexpected large magnitudes and different signs in the observed changes are attributed to modifications in the shape of the outer electron density distribution of the molecule upon excitation. None of the previous models introduced to explain the changes in rotational constants is entirely satisfactory, presumably because of the much weaker interactions with the helium environment.

Photoinduced reactions in the complex ions: Effect of the methyl substitution
View Description Hide DescriptionPhotoinduced reactions in and have been studied in the spectral range of 230–440 nm. Although the N–H bond activation channel was found to be prominent in the photodissociation of [Yoshida, Okai, and Fuke, Chem. Phys. Lett. 347, 93 (2001)], it is very unfavorable as the ammonia is replaced by methylamines in the complex. Instead, C–H bond cleavage products are observed from and exclusively produced from after photoexcitation. For the C–N bond activation product and the charge transfer product are also abundant. The action spectra of the complexes consist of two pronounced peaks on the red and blue side of the atomic transition. The calculated absorption spectra of the two complexes using the optimized structures of their ground states are in good agreement with the observed action spectra. On the basis of the branching fraction data and the calculated complex structures, the C–H bond activation is invoked to account for the MgH loss channel after photoexcitation, followed by a nonadiabatic transition to the ground state by a bondstretch mechanism. However, the formation of from photodissociation of involves the insertion of into the C–N bond. Finally, the photoinduced charge transfer product are also identified from but not from

Excited states of beryllium atom from explicitly correlated wave functions
View Description Hide DescriptionA study of the first excited states of beryllium atom starting from explicitly correlated wave functions is carried out. Several properties are obtained and discussed focusing on the analysis of the Hund’s rules in terms of the singleparticle and electron pair intracule and extracule densities. A systematic study of the differences on the electronic distributions of the singlet and triplet states is carried out. The trial wave function used to describe the different bound states consists of a generalized Jastrowtype correlation factor times a configuration interaction model wave function. This model wave function has been fixed by using a generalization of the optimized effective potential method to deal with multiconfiguration wave functions. The optimization of the wave function and the calculation of the different quantities is carried out by means of the Variational Monte Carlo method.

Accurate quantum calculations on threebody collisions in recombination and collisioninduced dissociation. I. Converged probabilities for the system
View Description Hide DescriptionThe exact quantum theory of atomic recombination and collisioninduced dissociation (CID) is presented using hyperspherical coordinates. Delves’ coordinates are emphasized, methods for doing numerically exact calculations are discussed and implemented, and fully converged dissociation probabilities are presented for a model system. These are the first accurate CID calculations reported for any atomic system in the full threedimensional physical space.

Should bromoform absorb at wavelengths longer than 300 nm?
View Description Hide DescriptionA theoretical study of the lowlying singlet and triplet electronic states of is presented. Calculations of excitation energies and oscillator strengths are presented using excited statecoupled cluster response methods, as well as the complete active space selfconsistent field method with the full Breit–Pauli spin–orbit operator. These calculations predict that for there is only one singlet state, the that is accessible by wavelengths longer than 234 nm. It is, however, predicted to be very weakly absorbing, but may strongly overlap at shorter wavelengths with a higher state, which itself is predicted to be strongly absorbing. There is one triplet state, the that lies well below the state and has a predicted absorption maximum at about 270 nm. The band origin of the is predicted to lie around 297 nm, but this symmetry minimum is calculated to be a secondorder transition state, ultimately leading to dissociation to

Ultrafast photodissociation of Lasergenerated highharmonic soft xray probing of the transient photoelectron spectra and ionization cross sections
View Description Hide DescriptionThe ultrafast dissociation of gasphase is probed via a 400 nm pump softxray probe scheme at five different highorder harmonic wavelengths (13th, 15th, 17th, 19th, and 21st of an 800 nm Ti:sapphire laser). A series of timeresolved ultrafast photoelectron spectra reveals prompt twophotonionization features, which allow in situmeasurement of the cross correlation between the pump and probe pulses. Transient features are attributed to ionization of the dissociative excited state wave packet, and new spectral peaks are associated with the formation of atomic Br. Deconvolution of timetrace plots of the atomic signals with the crosscorrelation pulse durations reveal similar dissociation times (∼40 fs) at two probe wavelengths (47 and 42 nm). Analysis of the transient wave packet photoelectron signal suggests an ionization process that occurs during dissociation, with a broad electron kinetic energy distribution at an extended Br–Br bond length (R ⩾3 Å). At long delay times (⩾500 fs), an enhancement of the ionization cross section of the Br atom compared to the molecule is observed with each of the probe wavelengths, the ratio increasing from a factor of 21±1 to 56±5 for probe wavelengths of 61.5 to 38 nm, respectively. The intensity of the transient wave packet signal on the dissociative state remains nearly constant between the 17th and 19th harmonic probes, indicating that the ionization cross section of the dissociative state has an entirely different wavelength dependence than the Br atom. The transient wave packet ionization signal is qualitatively 10%–20% of the simultaneous twophoton (400 nm+soft xray) ionization signal. The results are discussed in terms of the transient dynamics of dissociative state photoelectron spectroscopy, the correlation between molecular and atomic ionization probabilities, and above threshold ionization probabilities.

excitation spectrum: Ab initio prediction and spectroscopic manifestation of a linear isomer
View Description Hide DescriptionThe rovibronic excitation spectrum of the van der Waals complex is calculated using an ab initiopotential energy surface for the ground electronic state. The coupledcluster single double triple calculations predict doubleminimum topology (linear and Tshaped wells) for the Xstate potential with a low isomerization barrier. The two lowest vibrational levels, assigned to Tshaped and linear isomers using the localization patterns of the corresponding wave functions, are almost degenerated and lie slightly above the isomerization barrier. This indicates that Tshaped and linear isomers can coexist even at low temperatures and give rise to two separated bands in the excitation spectrum. The main band of the excitation spectrum is assigned to transitions from the Tshaped isomer, whereas the very good agreement between the observed and calculated spectrum, using the ab initio Xstate potential, demonstrates that the unassigned secondary band corresponds to excitation of the linear isomer of the complex. The complete assignment of the spectrum in terms of individual rovibronic transitions is presented.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Electron spin echo envelope modulation theory for high electron spin systems in weak crystal field
View Description Hide DescriptionElectron spin echo envelope modulation (ESEEM) experiments with aqueous complexes of and have shown that a common and unusual feature of the primary ESEEM spectra of such high spin/weak crystal field systems is an extremely low intensity of the sum combination line. Numerical simulations of the ESEEM spectra based on the existing theory [Coffino and Peisach, J. Chem. Phys. 97, 3072 (1992); Larsen and Singel, J. Chem. Phys. 98, 6704 (1993)] could not reproduce these ESEEM spectra. In this work the theoretical description of the ESEEM was revised and corrected, and new expressions were derived for the ESEEM from high electron spin systems in a weak crystal field, interacting with a nuclear spin The corrections primarily affected the shape and intensity of the sum combination line, whose position was found to be sensitive to the product of the crystal field and anisotropic hyperfine interaction constants. These theoretical improvements resulted in a successful simulation of the primary ESEEM from a model system, complex in a frozen glassy water–methanol solution. The results of this work show that the shape and intensity of the sum combination line in ESEEM spectra may be used for evaluating the distribution of crystal field interactions in and similar complexes.

Effective pair potentials in charged molecular systems: Water mediated interactions
View Description Hide DescriptionWe study the effective interactions among ions of various valences immersed in a polar solvent by determining the effective pair potentials (EPPs) obtained after “contracting” (integrating out) the degrees of freedom of the solvent molecules. This is accomplished by extending the framework of the dressed ion theory to describe the formal solution of the reference interaction site model integral equations. It is shown here that these EPPs have in the asymptotic limit the expected Coulomb form, even for finite concentrations of the solute. At shorter distances, the molecular structure of the solvent induces noticeable deviations of the EPPs from the reference potentials corresponding to an analogous model system with a structureless dielectric background. These deviations remain almost invariant over the whole range of concentrations considered here. These EPPs are therefore suitable to be used as the input for computer simulations at the McMillan–Mayer level. We also analyze with some detail the consequences of the short range behavior of the EPPs involving multivalent ions.

Optimal pump–dump control and timefrequency resolved spectroscopy of groundstate wavepacket focusing
View Description Hide DescriptionThe theory of optimal control together with that of transient probe absorption spectroscopy are applied for control and detection of molecular wave packet dynamics in the weak response regime. We obtain a globally optimal pump–dump control field which drives the initial state to the predefined target, focused at the innerturning point region of the electronic ground state potential. As for the detection, we calculate both the integrated and the dispersed transient pump–dump–probe absorption signals and adopt the difference detection schemes to reveal the optimally controlled molecular dynamics.