Volume 111, Issue 13, 01 October 1999
 COMMUNICATIONS


Single molecule thermal rotation and diffusion: Acetylene on Cu(001)
View Description Hide DescriptionA variable temperature scanning tunneling microscope was used to directly observe the thermally induced rotation of a single acetylene molecule between two equivalent orientations on Cu(001) above 68 K. Measurements of the rotation rate as a function of temperature yielded an energy barrier of meV and a preexponential factor of Thermal diffusion of individual acetylene molecules was monitored above 178 K by single molecule tracking. A diffusion barrier of eV and a preexponential factor of were determined by measuring the hopping rate as a function of temperature.

Glass transition of onedimensional molecular chains of pnitroaniline confined in nanopores revealed by dielectric spectroscopy
View Description Hide DescriptionThe dynamics of molecular chains of hydrogenbonded pnitroaniline (pNA), confined in the onedimensional pore system of was studied by broadband dielectricspectroscopy Hz). Two relaxation processes were observed. A fast process (the process) shows above a Vogel–Fulcher–Tammann behavior typical of glassforming materials, indicating cooperative dynamics of the “condensed” pNA chains. Below the glass temperature the relaxation peak broadens significantly and obeys an Arrhenius law. Both observations imply a change in length scale of cooperativity from a temperaturecontrolled to a chainlengthdependent one. The second relaxation process is tentatively assigned to structuralrelaxations of the host lattice itself, since it is also present in calcined (empty) crystals.

The influence of polymer on the diffusion of a spherical tracer
View Description Hide DescriptionWe analyze how the addition of a small number of polymer molecules influences the diffusion constant of a spherical tracer, whose radius is small compared to the size of the polymer. We show that the polymer chain can be regarded as a twodimensional object which is an impenetrable obstacle for the tracer. It is also shown that the diffusion constant of the tracer, in contrast to the solutionviscosity, is independent of chain length, depending only on the monomer concentration.
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 THEORETICAL METHODS AND ALGORITHMS


A combination of Kohn–Sham density functional theory and multireference configuration interaction methods
View Description Hide DescriptionAn effective Hamiltonian in a basis of spin and spacesymmetry adapted configuration state functions (CSF), which includes information from Kohn–Sham density functional theory(DFT), is used to calculate configuration interaction (CI) wave functions for the electronic states of molecules. The method emphasizes on states of multiconfigurational character which cannot be represented by conventional DFT. The CI matrix elements are constructed empirically by using the exact operator and corrections from DFT. Both the optimized KS orbitals from the parent determinant and the corresponding KS potential from the parent state density are used. Depending on their energy gap the CI offdiagonal elements between CSF are exponentially scaled to zero to avoid double counting of electron correlation. The selection of the most important CSF describing nondynamical correlation effects and the use of an approximate resolution of the identity (RI) for the evaluation of the twoelectron integrals allows a very efficient DFT/MRCI treatment of molecules with several hundreds of electrons. As applications, the prediction of excitation energies for singlet and triplet states of organic molecules and transition metal complexes, the calculation of electronic circular dichroism spectra and investigations of the energetics of diradicals are presented. It is found, that the new DFT/MRCI approach gives results of high accuracy (rms errors for relative energies <0.2 eV) comparable to those from sophisticated ab initio treatments.

A reexamination of exchange energy functionals
View Description Hide DescriptionConventional exchange functionals are examined through the oneparameter progressive (OP) correlation functional from physical and numerical points of view. With an exchange functional that obeys the fundamental conditions of the exact exchange functional, the OP functional has been proved to satisfy all fundamental conditions of the exact correlation functional. In this paper, we discuss whether conventional exchange functionals satisfy these conditions or not, and propose some strict conditions for exchange functionals that are required to obey the fundamental conditions. By combining the exchange functionals with the OP correlation functional, we also evaluate chemical properties for the G2 set of molecules, and confirm that the correction for exchange functionals obviously contributes to the improvement of calculated results.

Slippage of initial conditions for the Redfield master equation
View Description Hide DescriptionFor a slow open quantum subsystem weakly coupled to a fast thermal bath, we derive the general form of the slippage to be applied to the initial conditions of the Redfield master equation. This slippage is given by a superoperator which describes the nonMarkovian dynamics of the subsystem during the shorttime relaxation of the thermal bath. We verify in an example that the Redfield equation preserves positivity after the slippage superoperator has been applied to the initial density matrix of the subsystem. For δcorrelated baths, the Redfield master equation reduces to the Lindblad master equation and the slippage of initial conditions vanishes consistently.

NonMarkovian stochastic Schrödinger equation
View Description Hide DescriptionWe report a study of a stochastic Schrödinger equation corresponding to the Redfield master equation with slipped initial conditions, which describes the dynamics of a slow subsystem weakly coupled to a fast thermal bath. Using the projectionoperator method of Feshbach, we derive a nonMarkovian stochastic Schrödinger equation of the generalized Langevin type, which simulates the time evolution of the quantum wave functions of the subsystem driven by the fluctuating bath. For δcorrelated baths, the nonMarkovian stochastic Schrödinger equation reduces to the previously derived Markovian one. Numerical methods are proposed to simulate the time evolution under our nonMarkovian stochastic Schrödinger equation. These methods are illustrated with the spinboson model.

Loworder scaling local electron correlation methods. I. Linear scaling local MP2
View Description Hide DescriptionA new implementation of local secondorder Mo/llerPlesset perturbation theory (LMP2) is presented for which asymptotically all computational resources (CPU, memory, and disk) scale only linearly with the molecular size. This is achieved by (i) using orbital domains for each electron pair that are independent of molecular size; (ii) classifying the pairs according to a distance criterion and neglecting very distant pairs; (iii) treating distant pairs by a multipole approximation, and (iv) using efficient prescreening algorithms in the integral transformation. The errors caused by the various approximations are negligible. LMP2 calculations on molecules including up to 500 correlated electrons and over 1500 basis functions in symmetry are reported, all carried out on a single lowcost personal computer.

Coulomb energies of icosahedral h orbitals
View Description Hide DescriptionMatrix elements of all twoelectron and threeelectron operators that are scalar with respect to the icosahedral group have been tabulated for the icosahedral configurations These operators represent the Coulomb interaction between electrons occupying orbitals, and also the effects (to the lowest orders of perturbation theory) of configuration interaction on the levels of States and operators are labelled by the irreducible representations (irreps) of the continuous groups and in addition to the irreps of An alternative scheme is introduced in which the irreps of are retained, but the orbital angularmomentum quantum numbers associated with are replaced by the irreps of the permutation groups and the latter corresponding to the interchanges (possibly nonfeasible) of the six fivefold axes of an icosahedron among themselves. The kaleidoscope operator K, which rotates the weight space of by is an element of and and can be used to characterize the operators. The energy matrices in the second scheme are particularly simple, the scalar or pseudoscalar nature of the operators with respect to leading to block forms either on the diagonal or off the diagonal, respectively. Operators of the former kind are invariant under the K operation and, in the hypothetical absence of the pseudoscalars, would lead to every level of icosahedral type being degenerate with a level of type

Prediction of electron paramagnetic resonance gtensors of transition metal complexes using density functional theory: First applications to some axial systems
View Description Hide DescriptionWe applied the recently developed densityfunctional (DFT) formulation of the electron paramagnetic resonance(EPR)gtensor to a series of axially symmetric transition metal complexes where Cr, Mo, W, Tc, and Re; and N; Cl, and Br). Values for the gtensor components are determined by an interplay between three contributions arising due to magnetic fieldinduced coupling between the following orbitals: (a) The singly occupied molecular orbital (αSOMO) and a metalbased vacant d orbital [either or depending on the tensor component]; (b) the bonding counterparts of the metal’s type d orbitals and the vacant βSOMO; and (c) ligandbased occupied MOs (molecular orbitals) of the appropriate symmetry and the βSOMO. The first contribution (which is the only term accounted for in the simple ligand fieldtheory) is usually negative, and decreases the gtensor components relative to the free electron value, while contributions (b) and (c) are positive. Either of the three terms may dominate, so that values both below and above the free electron are obtained naturally. Calculated gtensors exhibit only a moderate dependence on the molecular geometry. Quasirelativistic VWN (Vosko–Wilk–Nusair) LDA(local density approximation) geometries are in a good agreement with the available experimental data, and are satisfactory for calculation of gtensors.Tensor components obtained with VWN LDA and gradientcorrected BP86 functionals are essentially identical, and always too positive compared to experiment. The residual errors in both components exhibit strong correlation with the position of the transition metal center in the periodic table. Trends in gtensor components within the same transition row are correctly reproduced by both functionals, so that a simple additive correction brings and results into a good agreement with experiment. The deficiencies in the calculated g values may be traced back to the overestimation of the covalent character of bonds formed by metal d orbitals in popular approximate functionals. Calculations of EPRgtensor thus provide a very stringent quality test for approximate density functionals.

Transition state wave packet study of hydrogen diffusion on Cu(100) surface
View Description Hide DescriptionThe transition state wave packet (TSWP) approach to the thermal rate constant based on the fluxflux autocorrelation function is used to investigate the diffusiondynamics of an H atom on the Cu(100) surface in the uncorrelated hopping regime. The high efficiency of the approach makes it feasible to include up to eight Cu modes explicitly in the time dependent quantum simulation. This is necessary since on the rigid surface the fluxflux autocorrelation function never decays to a negligibly small value to give a converged rate constant. For short times, the Cu modes included dynamically merely have a zeropointenergy effect on the fluxflux autocorrelation function. For longer times, however, the Cu modes absorb the activation energy of the H atom and effectively suppress recrossing of the transition state surface, resulting in convergence of the autocorrelation function and the hopping rate. For this system, recrossing of the transition state surface is minimal with the medium damping present, and the converged hopping rate can be well approximated by the short time behavior of the correlation function on the rigid surface. In addition, we find that the contributions of the excited Cu modes to the hopping rate may be accurately modeled by thermal “transition state” factors. Based on this, a new quantum transition state theory (QTST) is derived. The new theory provides a general way to calculate the approximate quantum correction to the traditional TST. It also provides a systematic and flexible tool to calculate the rate constant at any desired level of accuracy between the traditional TST level and the exact result. Finally, since the surface relaxation due to the presence of the H atom lowers both the energies of H atom in the binding well and on the saddle point almost equally, it only minimally affects the hopping rate, provided the configuration of the surface atoms is fully relaxed initially.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Direct observation of rotational transitions of the CO–CO dimer
View Description Hide DescriptionMeasurements of five pure rotational transitions of a mixed isotopomer of the CO–CO van der Waals dimer with a Fourier transformmicrowave spectrometer in the frequency range from 3 to 19 GHz are reported. For symmetry reasons, pure rotational transitions in the vibrational ground state are not accessible in the symmetric species, and the mixed isotopomer was studied instead. The observed lines were identified as belonging to the dimer by isotopomeric variation of the sample composition, monitoring of the microwave excitation pulse conditions, and comparison of the measured frequencies with those predicted in a recent infrared study. [M. D. Brookes and A. R. W. McKellar, J. Chem. Phys. (submitted).]

Collisional dynamics of I. Quantumresolved vibrational energy transfer for
View Description Hide DescriptionVibrationaltotranslational energy transfer between the lowest vibrational levels of the state of has been investigated using spectrally resolved, laserinduced fluorescence techniques. The small vibrational spacing leads to highly nonadiabatic conditions, particularly for the collision pair. However, the transition probabilities for collisions with the rare gases range from 0.75% to 1.75% per collision, considerably lower than would be anticipated from standard vibrational energy transfertheory. Multiquantum transfer rates are low, consistent with the low anharmonicity of the state. The rates for transitions scale linearly with vibrational quantum number as expected near the bottom of this nearly harmonic potential.

The structure and ground state dynamics of Ar–IH
View Description Hide DescriptionThe structure and ground state dynamics of the atom–diatom dimer interaction between Ar and HI has been investigated by microwave and near infrared supersonic jet spectroscopy.Ab initio molecular orbital calculations were used to provide greater insight into the nature of the interaction. The ground state is shown to be in the isomeric form Ar–IH with for the normal isotopomer and for Ar–ID. The potential surface from an ab initio molecular orbital calculation was scaled and shifted to yield a nonlinear leastsquares fit of the rovibrational state energies to the experimental data. The ground statepotential energy surface obtained in this manner has a barrier between the Ar–IH and Ar–HI isomers of 88.5 cm^{−1} with respect to the global minimum. Such calculations are also used to predict the presence of localized states in the secondary minimum associated with isomers Ar–HI and Ar–DI. Attempts to experimentally identify transitions associated with the latter were unsuccessful. The ground state, Ar–IH isomeric structure, contrasts with the corresponding ground state of the other members of the homologous series Ar–HX ( Cl, and Br) in which the Ar is bound to the proton.

Photodissociation dynamics of studied using resonance enhanced multiphoton ionization (REMPI) with timeofflight mass spectrometry
View Description Hide DescriptionThe photodissociation dynamics of have been studied using resonanceenhanced multiphoton ionization with timeofflight mass spectrometry.Polarization dependent timeofflight profiles were collected for a range of wavelengths from 248 to 268 nm, corresponding to the red wing of the absorptionspectrum. Forward convolution fits to the data have provided translational energy distributions and anisotropy parameters over the entire wavelength range for both and The average translational energies for the Br and channels are 20 and 23 kcal/mol, respectively. The measured anisotropy parameters indicate that both channels arise preferentially from a parallel transition and that the relative contribution of this transition increases with decreasing wavelength. Nonadiabatic transitions appear to play a smaller role in dissociation than in its monohalogenated analogues, specifically We suggest that this difference is the result of the intrinsic symmetry and lower radial velocity of and it is discussed in terms of a onedimensional Landau–Zener model. A C–Br bond dissociation energy of 67.5 kcal/mol in was also calculated using ab initio methods at the MP2/ccpVtz//MP2/ccpVdz level.

A coupledcluster study of the HOBr→HBrO transition state
View Description Hide DescriptionThe structural and energetic properties of the HOBr→HBrO transition state are examined using the single and doubles coupledcluster method that includes a perturbational estimate of the effect of connected triple excitations [CCSD(T)]. The energy change for the isomerizationreaction is best estimated to be 56.5 endothermic, and the activation energy for the process is 75.0

Magnetic and microwave field effects for single rotational levels of the band of oxalylfluoride in cooled jet conditions
View Description Hide DescriptionFluorescence intensity and decay in oxalylfluoride vapors excited to single rotational levels (SRLs) of the state of the transition, were measured as a function of an external magnetic field. On excitation to these levels, dynamics in zero field may be described in the smallmolecule limit, with fluorescence exhibiting an almost exponential decay. However, at increased field strength B the initial fluorescence decay becomes faster, the decay profile becoming biexponential at higher fields. Thus, a magnetic fieldinduced change of dynamics occurs in the state, from that of a small molecule, to the intermediate case. The decay rate constant of the fast component was measured for different SRLs, being independent on the magnetic field strength, while the slow component lifetime is field dependent, increasing at higher fields. Both the fast and slow decay lifetimes depend on the studied SRL. At higher fields, the slow component amplitude decreases, while that of the fast component increases with subsequent saturation at high fields. Halfwidth value of the field dependence of the slow component amplitude increases linearly with Structure of the OD EPR spectrum of excited to the level was resolved. Experimental data are interpreted using the indirect mechanism theory in the low level density limit.

Nuclear spin relaxation in paramagnetic complexes of Electron spin relaxation effects
View Description Hide DescriptionElectron spin relaxation for an system and its field dependence in the presence of static zerofield splitting (ZFS) has been described and incorporated in a model for nuclear spinlattice relaxation in paramagnetic complexes in solution, proposed earlier by the group in Florence. Slow reorientation is assumed and the electron spin energy level structure (at any orientation of the molecule with respect to the laboratory frame) is described in terms of the Zeemaninteraction and of the static ZFS. The electron spin relaxation is assumed to be caused by a transient ZFS modulated by the deformation of the complex described as a distortional (or pseudorotational) motion and the Redfield theory is used to derive the electron spin relaxation matrices. In the description of the electron spin relaxation we neglect any contribution from mechanisms involving modulation by reorientation, such as those of the static ZFS and the less important Zeemaninteraction, as we limit ourselves to the slowrotation limit (i.e., This in general covers the behavior of proteins and macromolecules. The decomposition (DC) approximation is used, which means that the reorientational motion and electron spin dynamics are assumed to be uncorrelated. This is not a serious problem, due to the slowrotation condition, since reorientational and distortional motions are timescale separated. The resulting nuclear magnetic relaxation dispersion (NMRD) profiles obtained using the Florence model are calculated and compared with the calculations of the Swedish approach, which can be considered essentially exact within the given set of assumed interactions and dynamic processes. That theory is not restricted by the Redfield limit and can thus handle electron spin relaxation in the slowmotion regime, which is a consequence of not explicitly defining any electron spin relaxation times. Furthermore, the DC approximation is not invoked, and in addition, the electron spin relaxation is described by reorientationally modulated static ZFS and Zeemaninteraction besides the distortionally modulated transient ZFS. The curves computed with the Florence model show a satisfactory agreement with these more accurate calculations of the Swedish approach, in particular for the axially symmetric static ZFS tensor, providing confidence in the adequacy of the electron spin relaxationmodel under the condition of slow rotation. The comparison is also quite instructive as far as the physical meaning of the electron spin relaxation and of its interplay with the nuclear spin system are concerned.

Modified BornOppenheimer basis for nonadiabatic coupling: Application to the vibronic spectrum of
View Description Hide DescriptionNonadiabatic matrix elements, when computed using a BornOppenheimer (BO) basis, do not vanish asymptotically because the motion of the electrons with the nuclei at large internuclear separations is not taken into account. We apply a method suggested by Delos [Rev. Mod. Phys. 53, 287 (1981)] to include the effect of electron translation factors in a quantummechanical framework, thus correcting the BO basis to incorporate proper boundary conditions. We calculate the nonadiabatic matrix elements for and its isotopic variants. We focus our calculations on for which experimental results exist, and calculate its vibronic spectrum. This is the first application of this method to calculate high precision spectroscopic information for molecular systems.

A failing of coupledstates calculations for inelastic and pressurebroadening cross sections: Calculations on –Ar
View Description Hide DescriptionFully quantal benchmark calculations of pressurebroadening cross sections for infrared and Raman lines of perturbed by Ar are carried out using both closecoupling (CC) and coupledstates (CS) calculations. CS calculations are found to underestimate the cross sections by up to 15%. The effect occurs even for isotropic Raman cross sections, which are not affected by reorientation contributions. The discrepancy arises mostly for collisions with large orbital angular momenta occurring on the longrange part of the potential. It may be attributed to collisions that are adiabatic rather than sudden in nature. A hybrid computational method, employing CS calculations for low and decoupled dominant (DLD) calculations for high offers a promising solution.
