Volume 116, Issue 17, 01 May 2002
 ARTICLES

 Theoretical Methods and Algorithms

Combining semiclassical time evolution and quantum Boltzmann operator to evaluate reactive flux correlation function for thermal rate constants of complex systems
View Description Hide DescriptionThe semiclassical (SC) initial value representation (IVR) provides a way for including quantum effects into classical molecular dynamics simulations. Implementation of the SCIVR to the thermal rate constant calculation, based on the reactive flux correlation function formalism, has two major obstacles: (1) the SC integrand may be highly oscillatory with respect to the initial phase space variables; and (2) matrix elements of the Boltzmannized flux operator, which are crucial in generating the initial (or final) distribution for the SC trajectories, are generally not available in analytic forms. In this paper, we present practical ways of overcoming these two barriers for the SC calculation of thermal rate constants. For the first problem, we show that use of a symmetric flux–flux correlation function, together with the generalized Filinov transformation technique, can significantly smooth the corresponding SC integrand and make the calculation practical for quite large systems. For the second problem, we propose a general method for evaluating matrix elements of the Boltzmannized flux operator “onthefly,” based on the combination of the imaginarytime path integral technique with the Metropolis random walk algorithm. Using these approaches, it is shown that thermal rate constants can be obtained for systems with more than 100 degrees of freedom, as well as for reactions in the deep tunneling regimes where quantum effects are significant.

Multidimensional discrete variable representation bases: Sinc functions and group theory
View Description Hide DescriptionExamples of nontrivial (that is, nonCartesian product) multidimensional discrete variable representation (DVR) basis sets are presented that are generalizations of sinc functions in one dimension. Their use in solving quantum problems in two dimensions is illustrated. Unlike all standard (onedimensional) examples of DVR bases, these bases cannot be created by dividing out the roots of a generatingfunction. It is argued that the difficulty of constructing nontrivial, multidimensional DVR bases is due to the restrictive nature of the DVR conditions, which cannot be satisfied on most subspaces of wave functions. The bases considered in this paper, however, are invariant under translations on a lattice in dimensional space, and the properties of the Abelian group of lattice translations allow the DVR conditions to be satisfied. More generally, the question of the relation between group theory and the conditions necessary to qualify a set of basis functions as a DVR basis is considered. It is shown how to construct orthonormal states that are related by the action of some group, and, in the case of Abelian groups, the extra conditions required to qualify the basis as a DVR set are discussed.

Application of the intermediate Hamiltonian valenceuniversal coupledcluster method to the magnesium atom
View Description Hide DescriptionThe atomically oriented valenceuniversal coupledclusters method in the intermediate Hamiltonian formulation with one and twobody part(s) included in the cluster operator (VUCCSD/R) is applied to describe the ground state and some excited states of the Mg atom. Two Slatertype orbitals (STO) basis sets are employed to see the effect of the basis set on the results. In addition to that, several complete model spaces are used in the calculation starting with and ending with orbitals as active. It has been found that the quality of the description of the ground and excited states depends on the STO basis set used in the calculation. In order to obtain reliable excitation energies, special attention has been paid to the construction of wellbalanced basis sets in which functions necessary for adequate description of both the ground state and excited states under consideration are included. Therefore, in spite of the moderate size of the orbital basis, our results compare quite well in terms of the total energy as well as in energy differences with results of other methods which, in some cases, use significantly larger basis sets.

Polarization consistent basis sets. II. Estimating the Kohn–Sham basis set limit
View Description Hide DescriptionThe performance of the previously proposed polarization consistent basis sets is analyzed at the Hartree–Fock and density functional levels of theory, and it is shown that each step up in basis set quality decreases the error relative to the infinite basis set limit by approximately an order of magnitude. For the largest pc4 basis set the relative energy error is approximately and extrapolation further improves the results by approximately a factor of 2. This provides total atomization energies for molecules with an accuracy of better than 0.01 kJ/mol per atom. The performance of many popular basis sets is evaluated based on 95 atomization energies, 42 ionization potentials and 10 molecular relative energies, and it is shown that the basis sets in all cases provides better accuracy for a similar or a smaller number of basis functions.

Charge transfer in small hydrogen bonded clusters
View Description Hide DescriptionHigh level ab initio and density functional calculations on clusters of water with acetate, methylammonium, and dimethylphosphate show that charge is transferred from the hydrogen bond acceptor to the hydrogen bond donor. The amounts of charge transferred are small, between 0.01 and 0.05 electron per hydrogen bond, but increase nearly linearly with the number of hydrogen bonds. The transfer of charge is not an artifact of the computation, since charge is also transferred in the limit of zero basis set superposition error. Calculations on a number of hydrogen bonded clusters show that the semiempirical AM1 and PM3 methods give excellent agreement with high level MP2 charge transfer effects, especially for AM1. Our results indicate the importance of charge transfer in hydrogen bond interactions.

Selective correlation scheme within diffusion quantum Monte Carlo
View Description Hide DescriptionWe present a selective correlation scheme allowing us to correlate only subsets of electrons, which can be assigned to arbitrary groups of orbitals, within diffusionquantum Monte Carlo calculations. The set of occupied orbitals, obtained from an allelectron meanfield calculation, is divided into two parts: frozen orbitals and explicitly considered orbitals. Electrons residing in frozen orbitals are excluded from the correlation treatment and handled within meanfieldtheory. The effects of such electrons on the remaining correlated electrons are represented by a model potential consisting of Coulomb and exchange parts, combined with a projectionlike operator to ensure orthogonality between the two sets of orbitals. Applying a localization procedure, similar to that used in connection with atomic semilocal pseudopotentials, to the exchange and projectionlike operators, local manyparticle representations of these operators are obtained, which are suitable for use within quantum Monte Carlo calculations. While localizing the exchange part is rather straightforward, special care has to be taken to localize the projectionlike operator properly. As an illustrating example we consider the nitrogen dimer with the triple bond being correlated, while the nonbonding orbitals are kept frozen. By comparison with coupled cluster calculations, we demonstrate that with properly localized operators, the correlation energy of the triple bond can be quantitatively recovered.

New formula for the bulk viscosity constructed from the interatomic potential and the pair distribution function
View Description Hide DescriptionWe provide a physical insight into the mechanism of the bulk viscosity ζ and construct a new formula for ζ directly from microscopic information such as the interatomic potential and the pair distribution function. This is an outstanding advantage when compared to the previously proposed formulas in all of which ζ is expressed only in terms of a macroscopic quantity, i.e., pressure. In other words, our new formula makes it possible for the first time to discuss the relation between the macroscopic quantity ζ and the microscopic properties such as the interatomic potential and the pair distribution function. This new formula is derived by solving the time development equation of the pair distribution function. Among some of the previously proposed formulas, we prove that the Green–Kubo formula and the Heyes formula are both equivalent to our new formula when the macroscopic quantity—pressure—in their expressions is described by means of interatomic potentials and pair distribution functions under appropriate conditions. This fact confirms the validity of our formula, which reinforces the aforementioned advantage. We calculate ζ near the triple point of the LennardJones fluid using our formula, the Green–Kubo formula, and the Heyes formula. The obtained values of ζ are in good agreement with each other.

Extension of the method of moments of coupledcluster equations to excited states: The triples and quadruples corrections to the equationofmotion coupledcluster singles and doubles energies
View Description Hide DescriptionThe recently proposed extension of the method of moments of coupledclusterequations (MMCC) to excited states via the equationofmotion coupledcluster (EOMCC) formalism [K. Kowalski and P. Piecuch, J. Chem. Phys. 115, 2966 (2001)] is developed further. A new approximate variant of the excitedstate MMCC theory, termed the MMCC(2,4) method, is proposed and tested. In the MMCC(2,4) method, relatively simple noniterative corrections due to triples and quadruples are added to the excitedstate energies obtained in the standard EOMCCSD (EOMCC singles and doubles) calculations. The performance of the MMCC(2,4) approach is illustrated by the results of calculations for the excited states of and The MMCC(2,4) energies are compared with the results of the MMCC(2,3) calculations, in which noniterative corrections due to triples only are added to the EOMCCSD energies, and with the results of other EOMCC calculations, including various EOMCC triples schemes.

Nonlinear relaxation of polarization and optical susceptibility of dielectric particles under sudden change of external field direction
View Description Hide DescriptionA dilute suspension of particles with permanent electric dipole moment and additional polarizability is subject to an applied electric field which suddenly changes its magnitude and direction. The time dependent behavior of the polarization and of the optical susceptibility is described by solving the Smoluchowski equation for the orientational distribution function. Because of the change of field direction the problem is not axially symmetric but by the proper choice of coordinate system the dynamical equations can be treated in the same manner as in the case of simple field switching on or field reversal. The two independent components of polarization and the nonvanishing elements of the optical susceptibilitytensor are shown to be superpositions of exponentially decaying functions of time. A fast numerical method is used to calculate the spectrum of decay rates and the amplitudes of the decaying modes. The time dependence of the difference of principal indices of refraction which produces birefringence is calculated from the difference of characteristic values of the susceptibility tensor. The relaxation behavior of polar particles with additional polarizability is compared with that of simpler polar particles.

Solving the Poisson equation for solute–solvent systems using fast Fourier transforms
View Description Hide DescriptionAn iterative algorithm based on fast Fourier transforms is proposed to solve the Poisson equation for systems of heterogeneous permittivity (e.g., solute cavity in a solvent) under periodic boundary conditions. The method makes explicit use of the dipole–dipole interaction tensor, and is thus easily generalizable to arbitrary forms of electrostatic interactions (e.g., Coulomb’s law with straight or smooth cutoff truncation). The convergence properties of the algorithm and the influence of various model parameters are investigated in detail, and a set of appropriate values for these parameters is determined. The algorithm is further tested by application to three types of systems (a single spherical ion, two spherical ions, and small biomolecules), and comparison with analytical results (single ion) and with results obtained using a finitedifference solver under periodic boundary conditions. The proposed algorithm performs very well in terms of accuracy and convergence properties, with an overall speed comparable in the current implementation to that of a typical finitedifference solver. Future developments and applications of the algorithm will include: (i) the assessment of periodicity and cutoffinduced artifacts in explicitsolvent simulations; (ii) the design of new electrostatic schemes for explicitsolvent simulations mimicking more accurately bulk solution; (iii) a faster evaluation of solvation free energies based on continuum electrostatics in cases where periodicityinduced artifacts can be neglected.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Ab initio studies of reactions. I. Kinetics and mechanism for the reaction
View Description Hide DescriptionThe reaction of OH with ClO has been investigated by ab initio molecular orbital and variational transition state theory calculations. Both singlet and triplet potential energy surfaces predicted by the G2M method are presented. The reaction was shown to take place primarily over the singlet surface by two main channels producing and with the former being dominant. The predicted total rate constant, and product branching ratios in the temperature range 200–500 K at agree satisfactorily with experimental values. The computed branching ratios, for and 0.045–0.048 for in the temperature range 200–500 K based on the recent experimental heat of formation for compare closely with the experimental values, and respectively. At higher temperatures (1000–2500 K), the branching ratios increase slightly to 0.084–0.137 and 0.061–0.111 for the OH and OD reactions, respectively. The rate constant for and production from in the temperature range, can be given by and respectively.

Resonances in the reaction due to van der Waals minima
View Description Hide DescriptionWe present extensive exact quantum calculations of the cumulative reaction probability (CRP) for the reaction for a large range of total angular momentum, using the most recent ab initiopotential energy surface of Ramachandran et al. This surface contains van der Waals minima in both the entrance and exit channels that are shown to be responsible for a number of prominent resonances in the CRP in the tunneling region. The evidence for this claim is based on an analysis of the quasibound states of the van der Waals minima and a simple overlap of these states with the region of the saddle point of the reaction. The shift of the CRP with total angular momentum is analyzed in detail, with a focus on the resonances. A rigorous test of the simple shifting approximation is also made both for the total CRP and the thermal rate constant.

Vibrationally resolved threshold photoelectron–photoion coincidence spectra of ArXe
View Description Hide DescriptionHighresolution threshold photoelectron–photoion coincidence spectra of ArXe were measured in the photon energy region 11.9–15.9 eV using the penetrating field technique and synchrotron radiation. Six vibrational progressions were observed and ascribed to the production of the six electronic states of ions 1/2, 3/2, 1/2, 3/2, 1/2, and 1/2) via photoionization of the ground state ArXe dimer. The lowest vibrational level of the ground X 1/2 state and some of the other vibrational levels were observed for the first time in the present measurements. The vibrational constants were obtained from observed vibrational energy levels. The dissociation energy of the ground state 1/2) was obtained as

Infrared–microwave double resonance spectroscopy of OCS in pure and mixed clusters
View Description Hide DescriptionWe have performed microwave–infrared double resonance measurements on OCS in pure and mixed clusters. In contrast to our previous study on OCS in pure cluster, where an asymmetric inhomogeneous linewidth increasing with rotational quantum number j was observed [S. Grebenev, M. Havenith, F. Madeja, J. P. Toennies, and A. F. Vilesov, J. Chem. Phys. 113, 9060 (2000)], we find the lines in the mixed helium cluster to be much narrower, showing a symmetric, probably homogeneous line width. The spectra indicate a significant difference in the rotational relaxation of OCS in mixed clusters as compared to pure cluster. We have applied the model of Lehmann [K. K. Lehmann, Mol. Phys. 97, 645 (1999)], describing the interaction of a molecule with the helium cluster, and modified it in order to describe particle in a box states of OCS in mixed helium clusters. The calculations indicate while in the mixed cluster the OCS is confined to the inner core, the energy of the particle in the box states is increased as compared to the pure cluster. Relaxation mechanisms via these particle in the box states and surface excitations (ripplons) of the cluster are discussed in the text.

Theoretical study of excited state proton transfer in 3,6bis(benzoxazolyl)pyrocatechol (BBPC)
View Description Hide DescriptionAb initiodensity functional theory and approximate instanton methods are used to study proton transfer processes in the first excited electronic state of 3,6bis(benzoxazolyl)pyrocatechol (BBPC). Geometries of dienol, ketoenol, and diketone tautomers as well as transition states for single and double proton transfer processes and the corresponding force fields are obtained with the method and verified with single point calculations. It is shown that ketoenol tautomer is the most stable in the state while the least stable is diketone. The single proton transfer in the state of dienol leads to a somewhat more stable ketoenol tautomer. This result nicely reproduces the experimental assignment stating that BBPC, a symmetric molecule with two equivalent proton transferreaction sites, undergoes a single proton transfer in the state. The excited system has to overcome the barrier of about 9 kcal/mol and proton transfer is therefore dominated by tunneling. Dynamics calculations with the instanton method yield the rate of transfer of again in a very good agreement with the experimental value of [Chem. Phys. Lett. 169, 450 (1990)]. Theory predicts a large kinetic isotope effect on this process. It is also shown that the reverse proton transfer leading back to dienol has the rate strongly dependent on the stabilization energy of ketoenol. It effectively competes with the radiative decay of the latter, resulting in the observed weak dienol fluorescence of BBPC. Finally, the calculations demonstrate why BBPC is not a photochrome unlike many typical Schiff bases.

A theoretical study of the vibrational spectrum of the molecule
View Description Hide DescriptionA theoretical study of the vibrational spectrum of the molecule is carried out. For that purpose, a new Morsecosine potential energy function is determined by fitting to observed vibrational frequencies, using as a starting point an ab initio force field. Highly excited vibrational states for are then calculated up to using a DVR truncationdiagonalization method. Hyperspherical Radau coordinates, which are a set of normal curvilinear coordinates for linear symmetric triatomic molecules, are used in these calculations. The computed vibrational energy levels are shown to present an excellent agreement with the observed values up to Based on these calculations, some unassigned observed vibrational frequencies are identified and the assignments of others are reconsidered. Inspection is made of the vibrational wave functions computed for revealing a persistent regularity up to This regularity is found to be consistent with perturbation theory results for these energies. Van Vleck perturbation theory is used to derive effective Hamiltonians that contain polyad quantum numbers and that provide good agreement with the variational calculations. It is also shown that the asymmetric stretch is practically decoupled from the symmetric stretch and the bend in this range of energies. The nearest neighbor space distribution (NNSD) and the spectral rigidity function show that the calculated vibrational spectrum of up to is essentially regular, in agreement with the most recent statistical analyses made of the spectroscopically observed frequencies.

Theory of stimulated Raman adiabatic passage in a degenerated reaction system: Application to control of molecular handedness
View Description Hide DescriptionWe have developed a new type of stimulated Raman adiabatic passage (STIRAP) that is applicable to a degenerated reactionsystem. The direction of the photonpolarization vector is the adiabatic parameter in the STIRAP. The molecular handedness of a preoriented phosphinotioic acid that has two stable configurations, L and R enantiomers, is used as a model system. The control of molecular handedness in both pure and mixed state cases are considered. In the case of a pure state, a STIRAP with a linearly polarized single laser allows an almost complete transfer from an L (R) enantiomer to the other by adiabatically changing its polarization direction. The adiabatic criterion for changing the polarization direction is clarified. In the case of a mixed state, a STIRAP with two linearly polarized laser pulses allows a selective preparation of pure enantiomers from its racemic mixture. In the low temperature limit, a fivelevel model reduces a threelevel model by setting the direction of the polarization of the pump and Stokes pulses in such a way that only the forward transfer is allowed, while the reverse is forbidden. Furthermore, in the case of mixed state, relaxation effects originating from vibrational mode couplings are taken into account, and the influence of the population decay from intermediate states on the STIRAP is compared with that by a πpulse approach.

Ab initio calculations of lowlying electronic states of vinyl chloride
View Description Hide DescriptionThe equilibrium geometries, vibrational frequencies, excitation energies, and oscillator strengths of vinyl chloride in the ground and five lowestlying excited singlet states have been calculated using MP2, CIS, CASSCF, and MRCI methods with the 6311++G^{*} ^{*} basis set. The geometries and vibrational frequencies of the ground and excited states are utilized to compute Franck–Condon factors. Calculated vibronic spectra for the transitions from the ground state to these five excited states are in agreement with experiment at 52 500–60 000 cm^{−1}, with major contributions from the and transitions. In this study, two spinforbidden transitions of and are calculated to locate in 45 000–54 000 cm^{−1}, and could be responsible for the observed onephoton absorptionspectrum due to an intensity borrowing caused by the spin–orbit coupling of the Cl atom. Based on calculation, we speculate that upon the excitation of vinyl chloride at 193 nm the or excited state, instead of the (π,π^{*}), is initially prepared prior to the subsequent photodissociation processes.

Theoretical characterization of the lowestenergy absorption band of pyrrole
View Description Hide DescriptionThe lowestenergy band of the electronic spectrum of pyrrole has been studied with vibrational resolution by using multiconfigurational secondorder perturbation theory (CASPT2) and its multistate extension (MS–CASPT2) in conjunction with large atomic natural orbitaltype basis sets including Rydberg functions. The obtained results provide a consistent picture of the recorded spectrum in the energy region 5.5–6.5 eV and confirm that the bulk of the intensity of the band arises from a intravalence transition, in contradiction to recent theoretical claims. Computed band origins for the Rydberg electronic transitions are in agreement with the available experimental data, although new assignments are suggested. As illustrated in the paper, the proper treatment of the valence–Rydberg mixing is particularly challenging for ab initio methodologies and can be seen as the main source of deviation among the recent theoretical results as regards the position of the lowlying valence excited states of pyrrole.

Ab initio line shape cross sections: On the need of offtheenergy shell calculation
View Description Hide DescriptionMost of the allquantummechanical calculations of line shape relaxation cross sections that have been previously published were based on the “impact approximation” allowing us to express offdiagonal elements in terms of collision theorySmatrices. Two consequences of that approximation are pointed out. The first is that impact cross sections do not obey detailed balance except in limited cases. The second, which is shown of more severe consequence for line coupling applications, is the loss of a sum rule relating the offdiagonal elements (coupling a given line to all the others) to the diagonal one. Finally, it appears clearly that offtheenergy shell calculations with realistic potential surfaces are absolutely necessary for ab initio computing line shapes of overlapping lines.