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Volume 116, Issue 1, 01 January 2002
 ARTICLES

 Theoretical Methods and Algorithms

An adaptive, kinkbased approach to path integral calculations
View Description Hide DescriptionA kinkbased expression for the canonical partition function is developed using Feynman’s path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on the 3×3 Hubbard model and overcomes the sign problem seen in traditional path integral studies of fermion systems. Kinks correspond to transitions between different Nelectron states, much in the same manner as occurs in configuration interaction calculations in standard ab initio methods. The different Nelectron states are updated, based on which states occur frequently during a Monte Carlo simulation, giving better estimates of the true eigenstates of the Hamiltonian.

Quantumclassical dynamics including continuum states using quantum trajectories
View Description Hide DescriptionWe apply the MQCB (mixed quantum/classical mechanics based on Bohmian trajectories) [E. Gindensperger, C. Meier, and J. A. Beswick, J. Chem. Phys. 113, 9369 (2000)] to the case where the quantum degree of freedom contains both bound and continuum states. The quantum degree of freedom is treated by a wave packet that is propagated on a spatial grid with a Hamiltonian that depends parametrically on the classical degrees of freedom, while the classical degrees of freedom themselves are coupled to the wave function via quantum trajectories. The method is applied to a simple model of a light particle colliding with a heavy (classical) particle absorbed on a surface, which has been used by other authors to develop methods to combine quantum degrees of freedom including continuum states with classical mechanics. The results are compared to the Ehrenfest meanfield method as well as to full quantum results.

How well do Car–Parrinello simulations reproduce the Born–Oppenheimer surface? Theory and examples
View Description Hide DescriptionWe derive an analytic expression for the average difference between the forces on the ions in a Car–Parrinello simulation and the forces obtained at the same ionic positions when the electrons are at their ground state. We show that for common values of the fictitious electron mass, a systematic bias may affect the Car–Parrinello forces in systems where the electron–ion coupling is large. We show that in the limit where the electronic orbitals are rigidly dragged by the ions the difference between the two dynamics amounts to a rescaling of the ionic masses, thereby leaving the thermodynamics intact. We study the examples of crystalline magnesium oxide and crystalline and molten silicon. We find that for crystalline silicon the errors are very small. For crystalline MgO the errors are very large but the dynamics can be quite well corrected within the rigidion model. We conclude that it is important to control the effect of the electron mass parameter on the quantities extracted from Car–Parrinello simulations.

bond as dihydrogen bond acceptor: Some theoretical observations and predictions
View Description Hide Descriptiondimer and complexes of methane, hydrogen cyanide, ammonia, water, methanol, and hydrogen fluoride, are studied using the Møller–Plesset secondorder perturbation theory and the 631++G^{*} ^{*} basis set to understand the features of dihydrogen bond. Complex binding energy is corrected for the basis set superposition error with the counterpoise method and for the zero point energy. Natural bond orbital analysis is used to discuss the charge transfer. Computed results indicate that dihydrogen bond does not occur in both and complexes. Apart from the hydrogen bond(H bond) found previously in the crystal, the B–H…H–X (X=C,O,F) H bonds have been observed in and complexes. As for the complexes in which only dihydrogen bonds appear the strength of dihydrogen bonds ranges from −13.9 to −20.5 kJ/mol. While the formation of complexes, the weakest B–N bond of contracts (its stretch appears blueshifted), and both B–H and X–H bonds in the B–H…H–X H bonds elongate slightly owing to the charge transfer from σ(B–H) to σ^{*}(X–H), and the B–H…H tends to be bent. The charge transfer is generally proportional to the secondorder perturbation energy lowering due to the interaction of frontier orbitals in σ→σ^{*} and cases, and the threshold value (1.5 kcal/mol) of as one of the indices for judging the existence of dihydrogen bonds is recommended.

Generalized form of the conserved quantity in constanttemperature molecular dynamics
View Description Hide DescriptionA generalized form of the conserved quantity in the constanttemperature molecular dynamics (MD) simulation is proposed as a measure of accuracy of MD simulations. This quantity is defined as the deviation of the distribution functions, or the Jacobian determinant, generated by the MD trajectory, from the ideal canonical value. For the Nosé–Hoover equations, this has the same form as the Hamiltonian of Nosé’s extended system. We calculated the conserved quantities for a series of constanttemperature simulations of a small protein, crambin, in water, and used them to evaluate the accuracy of the simulations under various conditions; i.e., with the Gaussian isokinetic or Nosé–Hoover equations, with flexible or rigidbody water, and with a single or multipletimestep algorithm. New integrators, based on the decomposition of the exponential Liouville operators, were developed for the simulation with rigidbody water. The comparison of the conserved quantities showed that the Gaussian isokinetic equations produced almost the same degree of accuracy as the Nosé–Hoover equations, and that the rigidbody treatment of water and the multipletimestep algorithm greatly improved the accuracy.

Periodic density functional embedding theory for complete active space selfconsistent field and configuration interaction calculations: Ground and excited states
View Description Hide DescriptionWe extend our recently reported embedding theory [J. Chem. Phys. 110, 7677 (1999)] to calculate not only improved descriptions of ground states, but now also localized excited states in a periodically infinite condensed phase. A local region of the solid is represented by a small cluster for which high quality quantum chemical calculations are performed. The interaction of the cluster with the extended condensed phase is taken into account by an effective embedding potential. This potential is calculated by periodic density functional theory(DFT) and is used as a oneelectron operator in subsequent cluster calculations. Among a variety of benchmark calculations, we investigate a CO molecule adsorbed on a Pd(111) surface. By performing complete active space selfconsistent field, configuration interaction (CI), and Møller–Plesset perturbation theory of order n we not only were able to obtain accurate adsorption energies via local corrections to DFT, but also vertical excitation energies for an internal (5σ→2π^{*}) excitation within the adsorbed CO molecule. We demonstrate that our new scheme is an efficient and accurate approach for the calculation of local excited states in bulk metals and on metal surfaces. Additionally, a systematic means of improving locally on ground state properties is provided.

Constant pressure hybrid Molecular Dynamics–Monte Carlo simulations
View Description Hide DescriptionNew hybrid Molecular DynamicsMonte Carlo methods are proposed to increase the efficiency of constantpressure simulations. Two variations of the isobaric Molecular Dynamics component of the algorithms are considered. In the first, we use the extendedensemble method of Andersen [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)]. In the second, we arrive at a new constantpressure Monte Carlo technique based on the reversible generalization of the weakcoupling barostat [H. J. C. Berendsen et al., J. Chem. Phys. 81, 3684 (1984)]. This latter technique turns out to be highly effective in equilibrating and maintaining a target pressure. It is superior to the extendedensemble method, which in turn is superior to simple volumerescaling algorithms. The efficiency of the proposed methods is demonstrated by studying two systems. The first is a simple LennardJones fluid. The second is a mixture of polyethylene chains of 200 monomers.

A polynomial expansion of the quantum propagator, the Green’s function, and the spectral density operator
View Description Hide DescriptionOne of the methods for calculating time propagators in quantum mechanics uses an expansion of in a sum of orthogonal polynomial. Equations involving Chebychev, Legendre, Laguerre, and Hermite polynomials have been used so far. We propose a new formula, in which the propagator is expressed as a sum in which each term is a Gegenbauer polynomial multiplied with a Bessel function. The equations used in previous work can be obtained from ours by giving specific values to a parameter. The expression allows analytic continuation from imaginary to real time, transforming thus results obtained by evaluating thermal averages into results pertaining to the time evolution of the system. Starting from the expression for the time propagator we derive equations for the Green’s function and the density of states. To perform computations one needs to calculate how the polynomial in the Hamiltonian operator acts on a wave function. The high order polynomials can be obtained from the lower ordered ones through a three term recursion relation; this saves storage and computer time. As a numerical test, we have computed the bound state spectrum of the Morse oscillator and the transmission coefficient for tunneling through an Eckart barrier. We have also studied the evolution of a Gaussian wave packet in a Morse potential well.

Classical phasespace analysis of vibronically coupled systems
View Description Hide DescriptionBased on a recently introduced mapping formulation [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997)], a classical phasespace description of vibronically coupled molecular systems is developed. In this formulation the problem of a classical treatment of discrete quantum degrees of freedom such as electronic states is bypassed by transforming the discrete quantum variables to continuous variables. Here the mapping formalism is applied to a spinbosontype system with a single vibrational mode, e.g., representing the situation of a photoinduced electron transfer promoted by a highfrequency vibrational mode. Studying various Poincaré surfacesofsection, a detailed phasespace analysis of the mapped twostate problem is given, showing that the model exhibits mixed classical dynamics. Furthermore, a number of periodic orbits (PO’s) of the nonadiabatic system are identified. In direct extension of the usual picture of trajectories propagating on a single BornOppenheimer surface, these vibronic PO’s describe nuclear motion on several coupled potentialenergysurfaces. A quasiclassical approximation is derived that expresses timedependent quantities of a vibronically coupled system in terms of the PO’s of the system. As an example, it is demonstrated that vibronic PO’s may be used to calculate the timedependent population probability of the initially excited electronic state. For the system under consideration, already two PO’s are sufficient to qualitatively describe the shorttime evolution of the nonadiabatic process.

Theoretical studies of the spin dynamics of quadrupolar nuclei at rotational resonance conditions
View Description Hide DescriptionA theory of the spin dynamics of quadrupolar nuclei in the suddenpassage limit is discussed in relation to the recently observed rotational resonance (RR) effects on the excitation and conversion of triplequantum coherence in the FASTER multiplequantum magicangle spinning (MQMAS) experiments [T. Vosegaard, P. Florian, D. Massiot, and P. J. Grandinetti, J. Chem. Phys. 114, 4618 (2001)]. A novel interaction frame, which combines the quadrupolar interaction with the central transition radio frequency irradiation, is shown to be useful in understanding the complex spin dynamics at and away from RR conditions. Analytical expressions for the Hamiltonian obtained from bimodal Floquet theory are included in order to provide insight into the spin dynamics observed in the FASTER MQMAS experiments. Numerical simulations have been performed and were found to support the theoretical formalism.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Torsion–rotation analysis of OH stretch overtone–torsion combination bands in methanol
View Description Hide DescriptionWe report rotationally resolved spectra of jetcooled methanol for the OH stretch overtones, and and for the torsional combinations, and The spectra are obtained by direct excitation from the vibrational ground state with an infrared laser pulse. Population in the resulting upper state levels is detected by infrared laser assisted photofragment spectroscopy (IRLAPS). Global fits of the spectra to the Herbst Hamiltonian yield the torsional and rotational parameters, including F, ρ, and for each OH stretch excited state. For each quantum of OH stretch excitation, we find that the torsional barrier height increases by and the torsional inertial F decreases by With reference to ab initio calculations, we explain the increase in in terms of changes in the electronic structure of methanol as the OH bond is elongated. For we observe only transitions with and for we observe only We present a Franck–Condon model to explain these apparent selection rules and the overall pattern of intensity.

Multiple surface longrange interaction potentials between C and closedshell molecules
View Description Hide DescriptionA method for calculating multiple longrange interaction potentials between an atom (C in this particular case), and closedshell molecules is described. This method was recently utilized by Bettens and Collins [J. Chem. Phys. 114, 10342 (2001)] for determining capture rate coefficients for collisions of C and Ge with unsaturated hydrocarbons. The method takes account of the physical size of the molecule and exactly treats the electrostaticinteraction between the quadrupole of the atom and all electrostatic moments of the molecule. This method requires a molecular density matrix, which can be obtained from an ab initio calculation.

Calculation of the Si–H stretching–bending overtones in employing ab initio potential energy and dipole moment surfaces
View Description Hide DescriptionThe Si–H stretching–bending overtones in were investigated employing theoretically calculated potential energy surfaces (PES) and dipole momentsurfaces (DMS). The coupled cluster method CCSD(T) was utilized to generate both onedimensional (1D) and threedimensional (3D) surfaces. An empirical 3D PES was also taken into consideration. The computed energy levels and band intensities agree reasonably well with observation for most of the bands. Comparison of CCSD(T) and density functional results for the very weak band shows that it is essential to calculate the DMS at a high level of quantumchemical theory when cancellation of linear and quadratic contributions to the DMS is significant. The 3D ab initio PES yields more accurate band intensities than the empirical PES and therefore appears to be more realistic.

Three versus fourcoordinate phosphorus in the gas phase and in solution: Treacherous relative energies for phosphine oxide and phosphinous acid
View Description Hide DescriptionPrevious ab initio studies have consistently predicted phosphine oxide to be less stable than its nearly isoenergetic cis and transphosphinous acid isomers However, complete basis set extrapolations employing the coupledcluster series show that phosphine oxide is actually ca. 1.0 kcal/mol more stable than its acid forms in the gas phase. Incorporation of tight d functions via Dunning’s corevalence (ccpCVXZ) or newly constructed “plus d” basis sets is essential for rapid convergence of core polarization effects which are evident even at the SCF level. The precision to which the phosphorus hybridization is described in the three and fourcoordinate environments ultimately determines the predicted gasphase relative energy orderings. Focalpoint analyses demonstrate that this system represents a disturbing case where use of a conventional valence quadrupleζ quality basis set (ccpVQZ)—even at the CCSD(T) level—fails to provide the correct relative energy ordering for simple closedshell species which do not exhibit appreciable multireference character. Thus, we underscore the importance of using phosphorus basis sets which have the flexibility to describe core polarization adequately. In addition, Monte Carlo(MC)freeenergyperturbation simulations in solution clearly demonstrate that the small energy gap significantly increases in favor of the oxide (10.0 kcal/mol) upon solvation due to stronger hydrogen bonding with the highly polar bond.

Collisioninduced absorption in the fundamental band of II. Dependence on the perturber gas
View Description Hide DescriptionThe integrated intensities of the collisioninduced enhancement spectra of the band of perturbed by rare gases and linear molecules and are calculated theoretically using the quadrupoletransition moment obtained from an analysis of spectra. In addition to the isotropic quadrupole mechanism responsible for the enhancement in rare gases, there is additional absorption arising from the anisotropicquadrupole mechanism in the case of molecular perturbers. This latter effect involves the matrix element of the anisotropicpolarizability for the transition in that is available from the analysis of the depolarized Raman intensity measurements. Overall, the theoretical values for the slope of the enhancement spectra with respect to the perturber density are in reasonably good agreement with the experimental results, thus confirming that the collisioninduced absorption arises primarily through the quadrupolar induction mechanism.

Formation of various types of metallofullerenes by laser ablation of externally doped fullerenes (M=Sm, Pt, Ni, La, Y, and Rh)
View Description Hide DescriptionA photofragmentation study of metal fullerides (M=Sm, Pt, Ni, La, Y, and Rh) by excimer laser ablationTOF mass spectrometry shows that many kinds of metallofullerenes have been observed in both the positive and negative ionic modes. For (M=Sm, Pt, and Ni), the metal atom is incorporated into the network of the fullerene cage to replace one carbon atom of the cage forming substitutional metallofullerene. While in the case of metal fullerides (M=La, Y), evidence of the encapsulation of La and Y atoms in fullerene cages forming endohedral fullerenes has been observed. Different from the above two cases, the laser ablation of rhodium fulleride produces two sequences of rhodiumcontaining fullerene clusters and Oddnumbered allcarbon clusters in the fullerene regime are observed in our laser ablation study of all the metal fullerides in the negative ion channel. The structures of metallofullerenes and with an even and odd number of total atoms, respectively, are discussed. Formation mechanisms with the participation of oddnumbered allcarbon fullerene clusters as intermediates are supposed.

On the theory of the strange and unconventional isotopic effects in ozone formation
View Description Hide DescriptionThe strange massindependent isotope effect for the enrichment of ozone and the contrastingly unconventional strong massdependent effect of individual reaction rate constants are studied using statistical (RRKM)based theory with a hinderedrotor transition state. Individual rate constant ratios of recombination reactions and enrichments are calculated. The theory assumes (1) an “ηeffect,” which can be interpreted as a small deviation from the statistical density of states for symmetric isotopomers, compared with the asymmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. A partitioning effect controls the recombination rate constant ratios. It arises from small differences in zeropoint energies of the two exit channels of dissociation of an asymmetric ozone isotopomer, which are magnified into large differences in numbers of states in the two competing exit channel transition states. In enrichment experiments, in contrast, this partitioning factor disappears exactly [Hathorn and Marcus, J. Chem. Phys. 112, 9497 (2000)], and what remains is the ηeffect. Both aspects can be regarded as “symmetry driven” isotopic effects. The two experiments, enrichments and rate constant ratios, thus reveal markedly different theoretical aspects of the phenomena. The calculated lowpressure ozone enrichments, the lowpressure recombination rate constant ratios, the effects of pressure on the enrichment, on the individual recombination rate constant ratios, and on the recombination rate constant are consistent with the experimental data. The temperature dependence of the enrichment and of the recombination rate constant ratios is discussed and a variety of experimental tests are proposed. The negative temperature dependence of the isotopic exchange rate constant for the reaction at 130 K and 300 K is used for testing or providing information on the nature of a variationally determined hinderedrotor transition state. The theory is not limited to ozone formation but is intended to apply to other reactions where a symmetrical stable or unstable gas phase molecule may be formed.

The application of a vacuum ultraviolet Fourier transform spectrometer and synchrotron radiation source to measurements of: IV. The and bands of NO
View Description Hide DescriptionThe and bands of NO have been recorded using a vacuum ultraviolet Fourier transformspectrometer with synchrotron radiation as light source. The analysis of the and bands of NO provides accurate rotational line positions and term values. Molecular constants of the level of the and level of the have been determined. Accurate rotational line strengths have also been obtained. The band oscillator strength of the and bands are determined to be and respectively.

Dopplerfree twophoton absorption spectroscopy and the Zeeman effect of the band of benzene
View Description Hide DescriptionA Dopplerfree absorptionspectrum and the Zeeman effect of the transition of benzene have been measured by means of twophoton absorptionspectroscopy with counterpropagating light beams of identical wavelength within an external cavity. Rotational lines were fully resolved, and 647 lines of have been assigned. The molecular constants of the state have been determined as and The Zeeman splittings for lines of a given J were observed to increase regularly with K and reach a maximum at This demonstrates that the magnetic moment lies along the c axis (perpendicular to the molecular plane). The magnetic moment of the level was determined to be The Zeeman splittings of the levels were observed to increase with increasing J. Via analysis of the rotationally resolved Zeeman spectra, it is concluded that the state is mixed with the state. This new finding suggests that vibronic interactions between and and between and through the mixed component, contribute to the and intersystem crossings, respectively.

Fully relativistic coupledcluster static dipole polarizabilities of the positively charged alkali ions from to
View Description Hide DescriptionThe static dipole polarizabilities of the positively charged alkali atoms from to (ekaFr) were obtained from relativistic coupledcluster theory using a scalar relativistic Douglas–Kroll Hamiltonian. Spin–orbit coupling effects were obtained from a fully relativistic fourcomponent Dirac–Hartree–Fock scheme followed by a secondorder manybody perturbation treatment to account for electron correlation. Electron correlationeffects are found to be small for all ions, but become more sizable as the nuclear charge increases. Scalar relativistic effects dominate over electron correlation for and Spin–orbit coupling is nonnegligible for the heaviest elements and where they dominate over both electron correlation and scalar relativistic effects. Breit interactions obtained for and can safely be neglected. A relationship between dipole polarizabilities and second ionization potentials is established. The use of a basis set limit oneelectron description and a high level treatment of electron correlation and relativistic effects makes our results the most accurate available for the stable dipole polarizabilities (1.00±0.04 a.u. for 5.52±0.04 a.u. for 9.11±0.04 a.u. for 15.8±0.1 a.u. for 20.4±0.2 a.u. for and 32±1 a.u. for