Volume 109, Issue 11, 15 September 1998
 COMMUNICATIONS


Direct observation of infrared band intensity transfer between coadsorbates having widely separated oscillator frequencies: Intermixed NO/CO adlayers on ordered iridium electrodes
View Description Hide DescriptionThe occurrence of substantial (two–threefold) transfer of infrared band intensity between juxtaposed coadsorbates having widely separated (200–250 cm^{−1}) oscillator frequencies is demonstrated directly for intermixed NO/CO adlayers on ordered Ir(111) and (110) electrodes by selectively removing CO or NO by electrochemicaloxidation and reduction, respectively. The surprisingly large effect is nevertheless semiquantitatively consistent with the predictions of theoretical dipolecoupling models.
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 THEORETICAL METHODS AND ALGORITHMS


The calculation of freeenergy differences by constrained moleculardynamics simulations
View Description Hide DescriptionIn this paper we set out to derive a relation between the constraint force and the derivative of the free energy for a system in which only the reaction coordinate is constrained. Our result differs from the expression by Mülders et al. [J. Chem. Phys. 104, 4869 (1996)] because we take into account the effect of the constraint on the sampled phasespace distribution. The method is illustrated with two prototypical numerical examples.

Analytical energy gradients in secondorder Mo/ller–Plesset perturbation theory for extended systems
View Description Hide DescriptionThe spinrestricted formulas for the analytical gradients of the secondorder Mo/ller–Plesset perturbation (MP2) energy are presented within the framework of ab initio crystal orbital theory of infinite onedimensional lattices (polymers). The coupled perturbed Hartree–Fock equation for polymers is solved iteratively using the atomicorbitalbased algorithms. The MP2 energy and its gradient contributions are evaluated by the diskbased algorithms with the aid of the twoparticle density matrix. The analyticalgradient method at the MP2 level, as well as the analytical first and secondderivative methods at the Hartree–Fock (HF) level, is applied to calculate the equilibrium structures and harmonic vibrational frequencies of alltrans polyacetylene. The deviations of the calculated frequencies from the observed ones for the inphase C=C stretching modes are reduced by about 70% on going from HF/631G to MP2/631G theory.

Approximate oneelectron density matrix functionals for the electron–electron repulsion energy from the hypervirial theorem
View Description Hide DescriptionApplication of the hypervirial theorem to a certain class of twoelectron operators yields the electron–electron repulsion energy as an approximate functional of the Hartree–Fock oneelectron reduced density matrix. This functional is entirely parameterized by a single screening function that, upon the assumption of transferability, can be readily retrieved from the known correlationenergy of the homogeneous electron gas. Invoking the properties of the actual electronic Hamiltonian, the new formalism explicitly incorporates dispersion effects that are not accounted for by the conventional density functional approaches. Even more importantly, it affords analogous functionals for other variational methods such as Monte Carlo selfconsistent field (MC SCF). Since such functionals are bi and trilinear in the occupied orbitals, their fully analytical computation should be feasible with a carefully chosen approximate representation of the screening function.

Liouville’s theorems, Gibbs’ entropy, and multifractal distributions for nonequilibrium steady states
View Description Hide DescriptionLiouville’s bestknown theorem,, describes the incompressible flow of phasespace probability density,. This incompressibleflow theorem follows directly from Hamilton’s equations of motion. It applies to simulations of isolated systems composed of interacting particles, whether or not the particles are confined by a box potential. Provided that the particle–particle and particle–box collisions are sufficiently mixing, the longtimeaveraged value approaches, in a “coarsegrained” sense, Gibbs’ equilibrium microcanonical probability density, from which all equilibrium properties follow, according to Gibbs’ statistical mechanics. All these ideas can be extended to manybody simulations of deterministic open systems with nonequilibrium boundary conditions incorporating heat transfer. Then Liouville’s compressible phasespaceflow theorem—in the original form—applies. I illustrate and contrast Liouville’s two theorems for two simple nonequilibrium systems, in each case considering both stationary and timedependent cases. Gibbs’ distributions for incompressible (equilibrium) flows are typically smooth. Surprisingly, the longtimeaveraged phasespace distributions of nonequilibrium compressibleflow systems are instead singular and “multifractal.” The nonequilibrium analog of Gibbs’ entropy, diverges, to in such a case. Gibbs’ classic remedy for such entropy errors was to “coarsegrain” the probability density—by averaging over finite cells of dimensions Such a coarse graining is effective for isolated systems approaching equilibrium, and leads to a unique entropy. Coarse graining is not as useful for deterministic open systems, constrained so as to describe stationary nonequilibrium states. Such systems have a Gibbs’ entropy which depends, logarithmically, upon the grain size. The two Liouville’s theorems, their applications to Gibbs’ entropy, and to the grainsize dependence of that entropy, are clearly illustrated here with simple example problems.

Energies and analytic gradients for a coupledcluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in
View Description Hide DescriptionWe describe an alternative procedure for obtaining approximate Brueckner orbitals in ab initioelectronic structure theory. Whereas approximate Brueckner orbitals have traditionally been obtained by mixing the orbitals until the coefficients of singly substituted determinants in the manyelectron wave function become zero, we remove singly substituted determinants at the outset and obtain orbitals which minimize the total electronic energy. Such orbitals may be described as variational Brueckner orbitals. These two procedures yield the same set of exact Brueckner orbitals in the full configuration interaction limit but differ for truncated wave functions. We consider the simplest variant of this approach in the context of coupledcluster theory, optimizing orbitals for the coupledcluster doubles (CCD) model. An efficient new method is presented for solving the coupled equations defining the energy, doubles amplitudes, and orbital mixing parameters. Results for several small molecules indicate nearly identical performance between the traditional Brueckner CCD method and the variational Brueckner orbital CCD approach. However, variational Brueckner orbitals offer certain advantages: they simplify analytic gradients by removing the need to solve the coupledperturbed Brueckner coupledcluster equations for the orbital response, and their straightforward extensions for inactive orbitals suggests possible uses in sizeextensive models of nondynamical electron correlation. Application to demonstrates the utility of variational Brueckner orbitals in symmetry breaking cases.

Smoluchowski equation with a sink term: Analytical solutions for the rate constant and their numerical test
View Description Hide DescriptionSmoluchowski equation with a sink term is widely used as a model of a rate process in a slowly relaxing environment. Two approximate solutions for the rate constant obtained for a steeply growing sink are tested numerically using an exponential sink. Both analytical solutions are in a good agreement with the numerical results over a wide range of the problem parameters (environment relaxation rate). They show how the rate constant decreases when the viscosity of the environment increases. If the dependence is approximated by the fractional power law, the exponent is always less than unity and depends on . It tends to zero for fast relaxation of the environment (small and increases when the relaxation slows down grows).

On the semiclassical description of quantum coherence in thermal rate constants
View Description Hide DescriptionAn earlier paper of ours [J. Chem. Phys. 108, 9726 (1998)] used an approximate (linearized) version of the semiclassical initial value representation (SCIVR) to calculate reactive flux correlation functions for a model of unimolecular isomerization, namely a double well potential coupled to an infinite set of harmonic oscillators, obtaining excellent agreement with accurate quantum results for this system. Here we analyze this linearized approximation (LA) further, however, and show that it is not capable of describing quantum interference/coherence effects in the longer time recrossing behavior of the isomerization dynamics. (The recrossing effects seen in our earlier work were due to classical mechanics.) To accentuate quantum effects in the recrossing dynamics, the present article considers the double well potential without the harmonic bath, using both the LA and the full SCIVR. The results of the calculations show that the flux correlation functions given by the LA agrees well with the exact quantum correlation function for times up to meaning that it describes quantum effects in the direct or transition state theory like dynamics accurately. For the longer time recrossing dynamics, however, it agrees with the classical rather than the quantumcorrelation function, i.e., it does not describe quantum coherenceeffects on this time scale. The full SCIVR calculations, however, are in reasonably good agreement with the quantum correlation function for these longer times.

Interfacing relativistic and nonrelativistic methods. II. Investigation of a loworder approximation
View Description Hide DescriptionThe formalism presented in a previous paper for the introduction of relativistic effects into nonrelativistic calculations is used to develop an approximation which is correct to order and is similar to the Breit–Pauli approximation. Although it corresponds to a projection of the Dirac Hamiltonian onto the nonrelativistic (Lévy–Leblond) states which in principle should guarantee a lower bound, the bound depends on the form of the potential. The physical eigenstates correspond to a local minimum in the exponential parameter space which vanishes at large In an extended basis set an approximation to the hydrogenic ground state can always be identified, but the relativistic correction to the energy is grossly overestimated. In molecular calculations, the restriction of the variational space involving the highexponent functions by general contraction did not yield improved numerical stability in a variational scheme. The use of a loworder approximation in a quasivariational method is therefore not expected to yield reliable results.

Analytical evaluation of energy derivatives in extended systems. I. Formalism
View Description Hide DescriptionA method is developed to analytically evaluate energy derivatives for extended systems. Linear dependence among basis functions, which almost always occurs in extended systems and brings instability to the coupledperturbed equations, is automatically eliminated in this method. The remaining independent basis functions are transformed into semiorthogonal orbitals. The derivatives of the orbitals and the overlap matrix over them are obtained via a set of coupledperturbed equations, similar to those of the coupledperturbed HartreeFock (CPHF) equations which are used to calculate the derivatives of the HartreeFock (HF) orbitals and the orbital energies. By introducing symmetrized coordinates, these coupledperturbed equations can be easily solved. Explicit expressions for calculating gradients and Hessians of the HF energy for extended systems are given. With this method, we can calculate energy derivatives with respect to displacements of the nuclei, including those which break the translational symmetry. Therefore, the method not only provides an efficient and accurate approach to calculate energy derivatives of any order, but also enables us to determine the force constants for individual nuclei, the interatomic force constants, and phonon dispersion curves in the whole Brillouin zone. With this method, the computational cost to calculate phonon spectrum with in the Brillouin zone is the same as that needed for the spectrum at
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Initial vibrational level distribution of from the reaction
View Description Hide DescriptionThe reaction of the cyano radical (CN) with hydrogen was studied by timeresolved infrared absorption spectroscopy of individual rovibrational states of HCN. The initial vibrational level distribution of was determined by plotting the time dependence of the fractional population of a vibrational level and extrapolating these curves to the origin of time. The experiments were carried out at two temperatures, 293 and 324 K, with similar results. It was estimated that about 50% of the available reaction exothermicity was deposited as vibrational excitation of the HCN product. Surprisingly, the HCN(101) vibrational level received a significant fraction of the observed vibrational population, implying that the CN vibration was not really a spectator bond in the reaction dynamics. Furthermore, the observed vibrations only account for about 27% of the initial HCN population produced in the title reaction. A significant fraction of the product HCN molecules must have been produced with the bending mode excited, likely in combination with the H–C stretch vibrations.

Collisional removal of by and
View Description Hide DescriptionA statespecific twolaser technique is used to investigate the collisional removal of molecules in the levels, where we directly excite and then probe the populations by resonanceenhanced multiphoton ionization. We find general agreement with earlier 300 K values for removal by and show that removal is slower by a factor of than removal. Only upper limits are obtained for as a collider. For removal of in the atmosphere, is unimportant compared to but it might be competitive for For as a collider, addressing removal in the atmospheres of Mars and Venus, the removal rate coefficients of the vibrationallyexcited levels are similar to that for The significance of the large difference in the and rate coefficients for collisions will be discussed as it relates to the modeling of recent earth nightglow observations.

A selectedionflowdrifttube study of charge transfer processes between atomic, molecular, and dimer ion projectiles and polyatomic molecules ethane, propane, and nbutane
View Description Hide DescriptionCharge transfer processes of and with the alkanes ethane, propane, and nbutane were investigated using the selectedionflowdrifttube (SIFDT) technique. The relative abundances of molecular and fragment hydrocarbon product ions can be explained using the breakdown pattern of the hydrocarbon molecular ion in question and assuming that the recombination energy of the projectile ions is deposited in the quasi continuum of the energy levels of the polyatomic molecular ions in a resonant way. The observed increase of the fragment ion yields with increasing collision energy is due to collision induced excitation up to the dissociation limit of the hydrocarbon ions in collisions with the helium buffer gas atoms rather than to inelastic charge transfer from hyperthermal projectile ions.

A new phosphorus bearing derivative of the methyl radical, studied by microwave spectroscopy and ab initio calculation
View Description Hide DescriptionThe microwave spectrum of the radical in its ground electronic state was detected for the first time using a sourcemodulated microwave spectrometer. The radical was generated in the cell by a dcglow discharge in a mixture of and Fine structure was observed but no hyperfine structure pertaining to the phosphorus and hydrogen nuclei could be resolved. In total 110 spectral lines were measured for the Kstructure and fine structure of eight rotational transitions in the 300–380 GHz region. The rotational, centrifugal distortion, and spinrotation coupling constants were obtained by a leastsquares analysis of the measured frequencies. On the basis of accompanying coupled cluster calculations an accurate equilibrium structure could be established; and The equilibrium dipole moment is predicted to be with the negative end at the phosphorus site.

Solvation of the triple ion in the gas phase
View Description Hide DescriptionFouriertransform ion cyclotron resonance (FTICR) spectrometry was employed to study solvations of the triple ion with oxygendonor Lewis bases in the gas phase. The triple ions were produced in an ICR cell by laser desorptionionization of a lithium chloride/dibenzo18crown6ether matrix pasted on a Teflon substrate. Odonor Lewis bases include 1,4dioxane, 1,3dioxane, tetrahydrofuran (THF), acetone and diethyl ether. All Odonors associate directly with with the maximum solvation numbers of 3 for 1,4dioxane, 1,3dioxane and diethyl ether, and 4 for THF and acetone at room temperature. The rate constants for the stepwise solvations were measured, and the solvent binding energies were determined from van’t Hoff plots. The structures and energetics of and the 1:1 complexes of and with the dioxanes, THF, and acetone were calculated at the HartreeFock (HF) level with a basis set, and those of more highly coordinated complexes were calculated with a basis set. Solvation enthalpies and free energies were calculated, and solvent binding energies were compared with experiments. The mechanisms of stepwise solvations of the triple ion with dioxanes, THF, and acetone are discussed in light of experimental kinetics and binding energies and theoretical structures and solvation energies.

An ab initio study of the monoxides and dioxides of sodium
View Description Hide DescriptionA study of structure and bonding in neutral and cationic sodium monoxides O and dioxides is presented. Structural isomers, adiabatic ionization potentials and sodium bond energies are calculated and the factors leading to “outer shell” sodium are discussed. Monoxide and superoxide properties are investigated using a range of ab initio methods. Density functional theory(DFT) results are found to compare favorably with those from experiment and from more expensive theoretical approaches. DFT is therefore used for all the dioxide calculations. The dioxides are rationalized in terms of the three oxidation states , and , representing three stages in the redox reaction between sodium and oxygen. Superoxide may be reduced by sodium to peroxides , containing stabilized by an equatorial Na cage. O–O cleavage occurs when Na attacks apically, releasing charge stored in this cage and effecting a two electron transfer to . The resulting compounds may be understood as sodiumbridged bismonoxides.

Ab initio potential energy surface by modified Shepard interpolation: Application to the reaction
View Description Hide DescriptionAn ab initiopotential energy surface for the sixatom reaction was constructed, within symmetry, by a modified Shepard interpolation method proposed recently by Collins et al. Selection of data points for the description of the potential energy surface was performed using both the Collins method and the dynamic reaction path (DRP) method. Although the DRP method is computationally more expensive, additional data points can be determined by just one simulation. Analyses of distributions of the data points, reaction probability, and errors in energy and energy gradients determined by the two different methods suggest a slight advantage for the DRP sampling in comparison with the iterative sampling.

Molecularbeam infrared–infrared doubleresonance spectroscopy study of the vibrational dynamics of the acetylenic C–H stretch of propargyl amine
View Description Hide DescriptionThe acetylenic C–H stretch spectrum of propargyl amine near 3330 cm^{−1} has been measured at 0.0002 cm^{−1} (6 MHz) resolution with a tunable colorcenter laser in an electricresonance optothermal spectrometer. The spectrum has been fully assigned through IR–IR double resonance measurements employing a tunable, microwave sideband laser. The 10 μm spectrum of propargyl amine displays splittings in the two nuclear spin symmetry states arising from aminoproton interchange, allowing doubleresonance assignment of the – group resultant proton nuclear spin quantum number in the highly fragmented 3 μm spectrum. The experimental state density is consistent with a increase that is expected if all nearresonant states are coupled. From this Jdependent growth in the state density we determine the density of states at to be 22 states/cm^{−1}. This value is in reasonable agreement with the direct state count result of 16 states/cm^{−1}. The unperturbed transition frequencies for the two different nuclear spin species at a given rotational level do not coincide, differing on average by about 50 MHz. The nonresonant coupling effects which produce effective splittings in the 10 μm spectrum appear to survive into the high state density regime. The measured IVR lifetimes are on the order of 500 ps for the low values studied here and show a dependence with the IVR rate increasing as increases. The statistical properties of the spectrum have been compared to predictions from random matrix theory. The level spacings are not well represented by Wigner statistics as would be expected for underlying chaotic classical dynamics. However, the intensity fluctuations are consistent with a distribution, expected for classically chaotic systems, as measured by Heller’s Fstatistic.

Doorway state enhanced intramolecular vibrational energy redistribution in the asymmetric hydride stretch of methyl vinyl ether
View Description Hide DescriptionThe microwaveinfrared doubleresonance capabilities of an electricresonance optothermal spectrometer have been used to assign the high resolution (5 MHz) infrared spectrum of the asymmetric stretch of the cis conformer of methyl vinyl ether near 3130 cm^{−1}. This vibrational state is anharmonically coupled to a nearresonant bath state by a 0.69 cm^{−1} matrix element resulting in two vibrational bands separated by about 1.44 cm^{−1}. The two mixed states resulting from this interaction are further coupled to other nearresonant bath states with an average matrix element of about 0.01 cm^{−1}. The coupled state density increases weakly with the total angular momentum,, however, the intramolecular vibrational energy distribution (IVR) rate is approximately independent of the total angular momentum quantum number. Therefore, the rotationally mediated coupling mechanisms are weaker than the anharmonic terms in the redistribution process. A twostate analysis of the strong coupling, which includes a phenomenological IVR rate constant, suggests that the IVR rate in the two mixed states is dominated by the contribution from the coupled dark state. From the deconvolution of the IVR rates to remove the contribution from the dark state, the IVR lifetime of the asymmetric stretch is determined to be 660 ps.

Intramolecular vibrational energy redistribution in the acetylenic and hydroxyl stretches of propynol
View Description Hide DescriptionThe highresolution infrared spectra of the acetylenic C–H and O–H stretches of propynol have been measured using an electricresonance optothermal molecular beamspectrometer (EROS). Both spectra display extensive fragmentation of the hydridestretch oscillator strength characteristic of the intramolecular vibrational energy redistribution (IVR) process. The IVR lifetime is strongly modespecific. The IVR lifetime of the acetylenic C–H stretch is approximately 400 ps, with a slight increase in the lifetime with increasing values of the quantum number. The lifetime of the O–H stretch is 60 ps and is independent of the rotational quantum numbers. The experimental upper limit for the anharmonic state densities are 30 and 40 states/cm^{−1} for the acetylenic C–H and O–H stretches, respectively. These values are in good agreement with the values obtained by a direct state count (19 and 32 states/cm^{−1}, respectively). The measured density of states increases with an approximate dependence. These results indicate that all energetically accessible states are involved in the IVR dynamics. However, neither the acetylenic C–H nor the O–H stretch shows a decrease in lifetime as the total angular momentum (J) increases. This result shows that Coriolis coupling of these two hydride stretches to the nearresonant bath states is much weaker than the anharmonic coupling. For the O–H stretch, we are able to obtain the rootmeansquared (rms) matrix element for the Coriolis coupling prefactor, 0.0015(5) cm^{−1}. The rms anharmonic coupling matrix element is 0.03 cm^{−1}. For the low J values measured in the O–H spectrum, the Coriolisinduced IVR rate is much slower than the initial redistribution rate resulting from the stronger anharmonic interactions leading to an IVR process with two distinct time scales.
