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Computations are presented to describe and analyze the high levels of infrared laser induced vibrational excitation of a monolayer of absorbed 13CO on a NaCl(100) surface. Extending the vibrational site-to-site surface hopping technique of Corcelli and Tully, kinetic Monte Carlo computations are used to incorporate single-quantum vibrational pooling and depooling of the 13CO by phonon excitation to allow up to the n = 45 vibrational state under different lasing conditions. Previously unpredicted pooling peaks at n > 16 are calculated and, under the highest fluence conditions, pooling up to the n = 32 state is found in the calculation. These results lead to the prediction of a secondary local maximum in the dispersed fluorescence of monolayer CO:NaCl(100) under sufficiently high fluence excitation conditions. At times on the order of ms, we recover similar behavior for both high and low fluence results. The calculations confirm that, for situations where the Debye frequency limited n domain restriction approximately holds, the vibrational state population deviates from a Boltzmann population linearly in n, a result that we have derived earlier theoretically for a domain of n restricted to one-phonon transfers. This theoretically understood term, linear in n, dominates the Boltzmann term and is responsible for the inversion of the population of vibrational states, Pn. [ABSTRACT FROM AUTHOR]

In the present paper we provide a statistical theory for the vibrational pooling and fluorescence time dependence observed in infrared laser excitation of CO on an NaCl surface. The pooling is seen in experiment and in computer simulations. In the theory, we assume a rapid equilibration of the quanta in the substrate and minimize the free energy subject to the constraint at any time t of a fixed number of vibrational quanta N(t). At low incident intensity, the distribution is limited to one-quantum exchanges with the solid and the Debye frequency of the solid plays a key role in limiting the range of this one-quantum domain. The resulting inverted vibrational equilibrium population depends only on fundamental parameters of the oscillator (ωe and ωeχe) and the surface (ωD and T). The relation to the Treanor gas phase treatment is discussed. Unlike the solid phase system, the gas phase system has no Debye-constraining maximum. [ABSTRACT FROM AUTHOR]

A theory that describes the non-RRKM (non-Rice-Ramsperger-Kassel-Marcus) effects in the lifetime statistics of activated ozone molecules is derived. The non-RRKM effects are shown to originate due to the diffusive energy exchange between vibrational and rotational degrees of freedom in ozone molecule. The lifetime statistics is found to be intramolecular diffusion controlled at long times. The theoretical results are in good agreement with the direct MD simulations of lifetime statistics. [ABSTRACT FROM AUTHOR]

A classical theory is proposed to describe the non-RRKM effects in activated asymmetric top triatomic molecules observed numerically in classical molecular dynamics simulations of ozone. The Coriolis coupling is shown to result in an effective diffusive energy exchange between the rotational and vibrational degrees of freedom. A stochastic differential equation is obtained for the K-component of the rotational angular momentum that governs the diffusion. [ABSTRACT FROM AUTHOR]

The effect of the large impact parameter near-elastic peak of collisional energy transfer for unimolecular dissociation/bimolecular recombination reactions is studied. To this end, the conventional single exponential model, a biexponential model that fits the literature classical trajectory data better, a model with a singularity at zero energy transfer, and the most realistic model, a model with a near-singularity, are fitted to the trajectory data in the literature. The typical effect of the energy transfer on the recombination rate constant is maximal at low pressures and this region is the one studied here. The distribution function for the limiting dissociation rate constant k0 at low pressures is shown to obey a Wiener–Hopf integral equation and is solved analytically for the first two models and perturbatively for the other two. For the single exponential model, this method yields the trial solution of Troe. The results are applied to the dissociation of O3 in the presence of argon, for which classical mechanical trajectory data are available. The k0’s for various models are calculated and compared, the value for the near-singularity model being about ten times larger than that for the first two models. This trend reflects the contribution to the cross section from collisions with larger impact parameter. In the present study of the near-singularity model, it is found that k0 is not sensitive to reasonable values for the lower bound. Energy transfer values ≤ΔE≥’s are also calculated and compared and can be similarly understood. However, unlike the k0 values, they are sensitive to the lower bound, and so any comparison of a classical trajectory analysis for ≤ΔE≥’s with the kinetic experimental data needs particular care. [ABSTRACT FROM AUTHOR]

The isotopic effects in ozone recombination reactions at low pressures are studied using an approximate theory which yields simple analytic expressions for the individual rate constant ratios, observed under “unscrambled” conditions. It is shown that the rate constant ratio between the two competing channels XYZ→X+YZ and XYZ→XY+Z is mainly determined by the difference of the zero-point energies of diatomic molecules YZ and XY and by the efficiency of the deactivation of the newly formed excited ozone molecules, whereas the mass-independent fractionation depends on a “nonstatistical” symmetry factor η and the collisional deactivation efficiency. Formulas for the pressure effects on the enrichment and on the rate constant ratios are obtained, and the calculated results are compared with experiments and more exact calculations. In all cases, ratios of isotope rates and the pressure dependence of enrichments, the agreement is good. While the initial focus was on isotope effects in the formation of O3, predictions are made for isotope effects on ratios of rate constants in other reactions such as O+CO→CO2, O+NO→NO2, and O+SO→SO2. [ABSTRACT FROM AUTHOR]

The transfer of hydride, proton, or H atom between substrate and cofactor in enzymes has been extensively studied for many systems, both experimentally and computationally. A simple equation for the reaction rate, an analog of an equation obtained earlier for electron transfer rates, is obtained, but now containing an approximate analytic expression for the bond rupture-bond forming feature of these H transfers. A “symmetrization,” of the potential energy surfaces is again introduced [R. A. Marcus, J. Chem. Phys. 43, 679 (1965); J. Phys. Chem. 72, 891 (1968)], together with Gaussian fluctuations of the remaining coordinates of the enzyme and solution needed for reaching the transition state. Combining the two expressions for the changes in the difference of the two bond lengths of the substrate-cofactor subsystem and in the fluctuation coordinates of the protein leading to the transition state, an expression is obtained for the free energy barrier. To this end a two-dimensional reaction space (m,n) is used that contains the relative coordinates of the H in the reactants, the heavy atoms to which it is bonded, and the protein/solution reorganization coordinate, all leading to the transition state. The resulting expression may serve to characterize in terms of specific parameters (two “reorganization” terms, thermodynamics, and work terms), experimental and computational data for different enzymes, and different cofactor-substrate systems. A related characterization was used for electron transfers. To isolate these factors from nuclear tunneling, when the H-tunneling effect is large, use of deuterium and tritium transfers is of course helpful, although tunneling has frequently and understandably dominated the discussions. A functional form is suggested for the dependence of the deuterium kinetic isotope effect (KIE) on ΔG° and a different form for the 13C KIE. Pressure effects on deuterium and 13C KIEs are also discussed. Although formulated for a one-step transfer of a light particle in an enzyme, the results would also apply to single-step transfers of other atoms and groups in enzymes and in solution. [ABSTRACT FROM AUTHOR]

Quantification of energetics and kinetics for the band-edge exciton states of quantum dots and the long-lived dark state is important for better understanding of the underlying mechanism for single-particle intermittency and ensemble fluorescence intensity decay. Based on a multistate diffusion-reaction model by extending our previous studies, we analyze experimental data from ensemble measurements and fluorescence intermittency of single quantum dots and determine important molecular-based quantities such as Stokes shift, free energy gap, activation energy, reorganization energy, and other kinetic parameters. [ABSTRACT FROM AUTHOR]

The dependence of the rate of the reaction CO+OH→H+CO2 on the CO-vibrational excitation is treated here theoretically. Both the Rice-Ramsperger-Kassel-Marcus (RRKM) rate constant kRRKM and a nonstatistical modification knon [W.-C. Chen and R. A. Marcus, J. Chem. Phys. 123, 094307 (2005).] are used in the analysis. The experimentally measured rate constant shows an apparent (large error bars) decrease with increasing CO-vibrational temperature Tv over the range of Tv’s studied, 298–1800 K. Both kRRKM(Tv) and knon(Tv) show the same trend over the Tv-range studied, but the knon(Tv) vs Tv plot shows a larger effect. The various trends can be understood in simple terms. The calculated rate constant kv decreases with increasing CO vibrational quantum number v, on going from v=0 to v=1, by factors of 1.5 and 3 in the RRKM and nonstatistical calculations, respectively. It then increases when v is increased further. These results can be regarded as a prediction when v state-selected rate constants become available. [ABSTRACT FROM AUTHOR]

Light-induced diffusion-controlled electron transfer is proposed as an underlying mechanism for the intermittency (power law and breakdown) of a single quantum dot and ensemble-averaged fluorescence decay. The intensity decay can be approximated to a stretched exponential expression. The physical links to the free energy gap, reorganization energy, electronic coupling, and diffusion correlation times are discussed. A procedure is described for extracting these molecular-based parameters from experiments and is demonstrated with examples using existing data. [ABSTRACT FROM AUTHOR]

The slope of the three-isotope plot for the isotopomer fractionation by direct or nearly direct photodissociation is obtained using a perturbation theoretical analysis. This result, correct to first order in the mass difference, is the same as that for equilibrium chemical exchange reactions, a similarity unexpected a priori. A comparison is made with computational results for N2O photodissociation. This theoretical slope for mass-dependent photolytic fractionation can be used to analyze the data for isotopic anomalies in spin-allowed photodissociation reactions. Earlier work on chemical equilibria is extended by avoiding a high-temperature approximation. [ABSTRACT FROM AUTHOR]

The effect of pressure, temperature, H/D isotopes, and C isotopes on the kinetics of the OH+CO reaction are investigated using Rice-Ramsperger-Kassel-Marcus theory. Pressure effects are treated with a step-ladder plus steady-state model and tunneling effects are included. New features include a treatment of the C isotope effect and a proposed nonstatistical effect in the reaction. The latter was prompted by existing kinetic results and molecular-beam data of Simons and co-workers [J. Phys. Chem. A 102, 9559 (1998); J. Chem. Phys. 112, 4557 (2000); 113, 3173 (2000)] on incomplete intramolecular energy transfer to the highest vibrational frequency mode in HOCO*. In treating the many kinetic properties two small customary vertical adjustments of the barriers of the two transition states were made. The resulting calculations show reasonable agreement with the experimental data on (1) the pressure and temperature dependence of the H/D effect, (2) the pressure-dependent 12C/13C isotope effect, (3) the strong non-Arrhenius behavior observed at low temperatures, (4) the high-temperature data, and (5) the pressure dependence of rate constants in various bath gases. The kinetic carbon isotopic effect is usually less than 10 per mil. A striking consequence of the nonstatistical assumption is the removal of a major discrepancy in a plot of the kOH+CO/kOD+CO ratio versus pressure. A prediction is made for the temperature dependence of the OD+CO reaction in the low-pressure limit at low temperatures. [ABSTRACT FROM AUTHOR]

The light-induced spectral diffusion and fluorescence intermittency (blinking) of semiconductor nanocrystal quantum dots are investigated theoretically using a diffusion-controlled electron-transfer (DCET) model, where a light-induced one-dimensional diffusion process in energy space is considered. Unlike the conventional electron-transfer reactions with simple exponential kinetics, the model naturally leads to a power-law statistics for the intermittency. We formulate a possible explanation for the spectral broadening and its proportionality to the light energy density, the -3/2 power law for the blinking statistics of the fluorescence intermittency, the breakdown of the power-law behavior with a bending tail for the “light” periods, a lack of bending tail for the “dark” periods (but would eventually appear at later times), and the dependence of the bending tail on light intensity and temperature. This DCET model predicts a critical time tc (a function of the electronic coupling strength and other quantities), such that for times shorter than tc the exponent for the power law is -1/2 instead of -3/2. Quantitative analyses are made of the experimental data on spectral diffusion and on the asymmetric blinking statistics for the “on” and “off” events. Causes for deviation of the exponent from the ideal value of -3/2 are also discussed. Several fundamental properties are determined from the present experimental data, the diffusion correlation time, the Stokes shift, and a combination of other molecular-based quantities. Specific experiments are suggested to test the model further, extract other molecular properties, and elucidate more details of the light-induced charge-transfer dynamics in quantum dots. [ABSTRACT FROM AUTHOR]

A major constraint is described for a possible chemical origin for the “mass-independent” oxygen isotope phenomenon in calcium-aluminum rich inclusions (CAIs) in meteorites at high temperatures (∼1500–2000 K). A symmetry-based dynamical η effect is postulated for O atom-monoxide recombination on the surface of growing CAIs. It is the surface analog of the volume-based η effect occurring in a similar phenomenon for ozone in the gas phase [Y. Q. Gao, W. C. Chen, and R. A. Marcus, J. Chem. Phys. 117, 1536 (2002), and references cited therein]: In the growth of CAI grains an equilibrium is postulated between adsorbed species XO (ads)+O (ads)⇋XO2* (ads), where XO2* (ads) is a vibrationally excited adsorbed dioxide molecule and X can be Si, Al, Ti, or other metals and can be C for minerals less refractory than the CAIs. The surface of a growing grain has an entropic effect of many order of magnitude on the position of this monoxide-dioxide equilibrium relative to its volume-based position by acting as a concentrator. The volume-based η effect for ozone in the earlier study is not applicable to gas phase precursors of CAIs, due to the rarity of three-body recombination collisions at very low pressures and because of the high H2 and H concentration in solar gas, which reduces gaseous O and gaseous dioxides and prevents the latter from acting as storage reservoirs for the two heavier oxygen isotopes. A surface η effect yields XO2* (ads) that is mass-independently rich in 17O and 18O, and yields XO (ads)+O (ads) that is mass-independently poor in the two heavier oxygen isotopes. When the XO2* (ads) is deactivated by vibrational energy loss to the grain, it has only one subsequent fate, evaporation, and so undergoes no further isotopic fractionation. After evaporation the XO2 again has only one fate, which is to react rapidly with H and ultimately form 16O-poor H2O. The other species, O (ads)+XO (ads), are 16O rich and react with Ca (ads) and other adsorbed metal atoms or metallic monoxides to form CAIs. The latter are thereby mass-independently poor in 17O and 18O. Some O (ads) used to form the minerals are necessarily in excess of the XO (ads), because of the stoichiometry of the mineral, and modify the fractionation pattern. This effect is incorporated into the mechanistic and mathematical scheme. A merit of this chemical mechanism for the oxygen isotope anomaly is that only one oxygen reservoir is required in the solar nebula. It also does not require a sequestering of intermediate products which could undergo isotopic exchange, hence undoing the original isotopic fractionations. The gas phase source of adsorbed O atoms in this environment is either O or H2O. As inferred from data on the evaporation of Mg2SiO4 taken as an example, the source of O (ads) is primarily H2O rather than O and is accompanied by the evolution of H2. Nonisotopic kinetic experiments can determine more sharply the mechanism of condensed phase growth of these minerals. Laboratory tests are proposed to test the existence of a surface η effect on the growing CAI surfaces at these high temperatures. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A modified ab initio potential energy surface (PES) is used for calculations of ozone recombination and isotopic exchange rate constants. The calculated low-pressure isotopic effects on the ozone formation reaction are consistent with the experimental results and with the theoretical results obtained earlier [J. Chem. Phys. 116, 137 (2002)]. They are thereby relatively insensitive to the properties of these PES. The topics discussed include the dependence of the calculated low-pressure recombination rate constant on the hindered-rotor PES, the role of the asymmetry of the potential for a general X + YZ reaction (Y ≠ Z), and the partitioning to form each of the two recombination products: XYZ and XZY. [ABSTRACT FROM AUTHOR]

A theory for calculating time– and frequency–domain optical spectra of pigment–protein complexes is presented using a density matrix approach. Non-Markovian effects in the exciton–vibrational coupling are included. A correlation function is deduced from the simulation of 1.6 K fluorescence line narrowing spectra of a monomer pigment–protein complex (B777), and then used to calculate fluorescence line narrowing spectra of a dimer complex (B820). A vibrational sideband of an excitonic transition is obtained, a distinct non-Markovian feature, and agrees well with experiment on B820 complexes. The theory and the above correlation function are used elsewhere to make predictions and compare with data on time–domain pump–probe spectra and frequency–domain linear absorption, circular dichroism and fluorescence spectra of Photosystem II reaction centers. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The strange mass-independent isotope effect for the enrichment of ozone and the contrastingly unconventional strong mass-dependent effect of individual reaction rate constants are studied using statistical (RRKM)-based theory with a hindered-rotor transition state. Individual rate constant ratios of recombination reactions and enrichments are calculated. The theory assumes (1) an “η-effect,” 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 zero-point 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 η-effect. 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 low-pressure ozone enrichments, the low-pressure 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 [sup 16]O+[sup 18]O[sup 18]O→[sup 16]O[sup 18]O+[sup 18]O at 130 K and 300 K is used for testin... [ABSTRACT FROM AUTHOR]

Applications of the z-transform were made earlier to interfacial electron transfer involving semi-infinite solids, e.g., semiconductor/liquid and metal/liquid interfaces and scanning tunneling microscopy. It is shown how the method is readily adapted to treat composite materials, such as solid/solid interfaces or “molecular wire”/solid interfaces. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Discusses an intramolecular theory of the unusual mass-independent isotope effect for ozone formation and dissociation. Use of the Rice-Ramsperger-Kessel-Marcus (RKKM) statistical assumption for the quantum states of the energetic molecule; Mechanism for ozone formation; Thermal decomposition of ozone; Ozone formation from heavily enriched oxygen.

Discusses the formulation of a recursion relation for the Green's function for calculating the effective electron coupling in bridge-assisted electronic transfer systems within the framework of the tight-binding Hamiltonian. Recursion expression that is applicable regardless of the number of orbitals per unit.

Expressions are given for a solvent dynamics-modified Rice–Ramsperger–Kassel–Marcus (RRKM) theory for clusters. The role of vibrational assistance across the transition state region is included. The usual differential equation for motion along the slow coordinate X in constant temperature systems is modified so as to apply to microcanonical systems. A negative entropy term, -Sv(X), replaces the (1/T)∂U/∂X or (1/T)∂G/∂X which appears in canonical systems. Expressions are obtained for the RRKM-type rate constant k(X) and for the Sv(X) which appear in the differential equation. An approximate solution for steady-state conditions is given for the case that the ‘‘reaction window’’ is narrow. The solution then takes on a simple functional form. The validity of the assumption can be checked a posteriori. Recrossings of the transition state are included and the condition under which the treatment approaches that in Part I is described. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An expression is obtained for the current in scanning tunneling microscopy (STM) for a single adsorbate molecule. For this purpose the ‘‘Newns–Anderson’’ treatment (a ‘‘discrete state in a continuum’’ treatment) is used to obtain wave functions and other properties of the adsorbate/substrate system. The current is expressed in terms of the adsorbate–tip matrix elements, and an effective local density of states of the adsorbate/substrate system, at the adsorbate. As an example, the treatment is applied to the STM image of adenine adsorbed on a graphite surface, and the results are compared with experiment. The dependence of the image on the position of adenine with respect to the underlying graphite is considered. A discussion is given of the type of experimental STM data needed for suitable comparison of theory and experiment. In an analysis of the calculations, the role of each atom, its neighbors, next nearest neighbors, etc., in an adsorbed molecule is considered. The need for using in the present calculation more orbitals than only the HOMO and the LUMO of the adsorbate is also noted. [ABSTRACT FROM AUTHOR]

The electron transfer rate constant is treated using the spin-boson Hamiltonian model. The spectral density is related to the experimentally accessible data on the dielectric dispersion of the solvent, using a dielectric continuum approximation. On this basis the quantum correction for the ferrous–ferric electron transfer rate is found to be a factor 9.6. This value is smaller than the corresponding result (36) of Chandler and co-workers in their pioneering quantum simulation using a molecular model of the system [J. S. Bader, R. A. Kuharski, and D. Chandler, J. Chem. Phys. 93, 230 (1990)]. The likely reason for the difference lies in use of a rigid water molecular model in the simulation, since we find that other models for water in the literature which neglect the electronic and vibrational polarizability also give a large quantum effect. Such models are shown to overestimate the dielectric dispersion in one part of the quantum mechanically important region and to underestimate it in another part. It will be useful to explore a polarizable molecular model which reproduces the experimental dielectric response over the relevant part of the frequency spectrum. [ABSTRACT FROM AUTHOR]

A treatment of one- or two-photon fluorescence excitation spectra is described using the vibration–rotation coupling of zeroth order states in the excited electronic state and nonadiabatic coupling to the ground state. Using perturbation theory, experimental harmonic frequencies, an anharmonic force field, and various theoretical Coriolis coupling constants, a quasistationary molecular eigenstate in an excited electronic state S1 is first calculated. The S1 eigenstate is then coupled via the nonadiabatic nuclear kinetic energy operator (internal conversion) to rovibronic states in the ground state manifold, the latter states approximated in a simple manner. A search algorithm is used to select the S1 dark states and the S0 states. Both the perturbation theory coefficient and the Franck–Condon factors are employed in the evaluation function used in the search. The results are applied in part II to the channel three problem in benzene. [ABSTRACT FROM AUTHOR]

Rotational lines in the fluorescence excitation spectra of the 14112 band of the first excited singlet state (S1) of benzene are calculated for various J and K. For this purpose, perturbation theory is used to obtain an ‘‘eigenstate’’ in S1. Internal conversion to S0 via Franck–Condon (FC) factors is then calculated. A search procedure is used to obtain the important contributors to this S1 state and to this internal conversion process S1→S0 using the perturbation theory coefficients and the FC factors in the evaluation function. At low J, the calculated lines with K=0 are sharp, other lines being broadened and diminished in intensity. The calculated K=0 lines have a linewidth proportional to J(J+1). For high J, the lines with K=J remain sharp, the other lines being broadened and diminished in intensity. These various results are in general agreement with the experimental findings. The onset of channel three in benzene occurs in the present mechanism via anharmonic-Coriolis coupling in the S1 state plus internal conversion to S0. The calculations suggest that, at low J, parallel Coriolis coupling causes mixing of the in-plane mode-excited ‘‘light state’’ with in-plane modes that are anharmonically coupled to out-of-plane modes.Dark states with certain excited out-of-plane mode contributions possess large FC factors for the internal conversion to S0. At high J, on the other hand, the in-plane modes are coupled directly to these out-of-plane modes by perpendicular Coriolis coupling. Paths involving two perpendicular Coriolis operators are important at high J in the present calculation—their matrix elements are larger at high J and so they become more competitive relative to purely anharmonic coupling operators. Such two-Coriolis paths at high J are expected to yield multiple excitation in the out-of-plane modes and further enhance the internal conversion. The perpendicular Coriolis... [ABSTRACT FROM AUTHOR]

We introduce a point of view for treating the dynamical tunneling splitting of symmetric local mode vibrational states in ABA molecules (A=H typically) which is the one we have employed in treating the vibrational spectroscopy of CH overtones in molecules such as (CX3)3YCCH. Namely, the vibrational coupling corresponding to the dynamical tunneling in semiclassical mechanics via many intermediate off-resonance weak transitions between initial and final states can be treated by a standard high-order perturbation theory. We apply that method to the present simpler problem of tunneling splittings in ABA molecules, and compare the results with those of exact diagonalization, the semiclassical method, and the periodic orbit quantization. Of all the approximate methods, the perturbation theory was found to provide the best approximation to the results of exact diagonalization for the system treated. The relationship between these three methods and application to the problem of vibrational relaxation in polyatomic molecules with tunneling mechanism of intramolecular vibrational relaxation is discussed. [ABSTRACT FROM AUTHOR]

Quantum calculations are reported for the intramolecular vibrational energy redistribution and absorption spectra of the first two excited states of the acetylenic CH stretch vibration in the polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si. Using approximate potential energy surfaces, comparison is made with the corresponding recent experimental spectra. It is found that a model of intramolecular vibrational relaxation based on the assumption of sequential off-resonance transitions via third and fourth order vibrational couplings (as opposed to direct high order couplings) is in agreement with experimental results on spectral linewidths. In a semiclassical limit this type of relaxation corresponds to a dynamic tunneling in phase space. It is shown that the local density of resonances of third and fourth order, rather than the total density of states, plays a central role for the relaxation. It is found that in the Si molecule an accidental absence of appropriate resonances results in a bottleneck in the initial stages of relaxation. As a result, an almost complete localization of the initially prepared excitation occurs. It is shown that an increase of the mass alone of the central atom from C to Si cannot explain the observed difference in the C and Si molecules. The spectral linewidths were calculated with the Golden Rule formula after prediagonalization of the relevant vibrational states which are coupled in the molecule to the CH vibration, directly or indirectly. For the spectral calculations, in addition to the direct diagonalization, a modified recursive residue generation method was used, allowing one to avoid diagonalization of the transformed Lanczos Hamiltonian. With this method up to 30 000 coupled states could be analyzed on a computer with relatively small memory. The efficiency of C programming language for the problem is discussed. [ABSTRACT FROM AUTHOR]

A transform method for treating semi-infinite solids in the tight-binding (TB) approximation is introduced. The difference equations for the TB orbital coefficients are converted, thereby, to convenient algebraic equations. For this purpose, a Dirac delta function normalization for the wave function is also introduced, instead of the usual box one. Single and coupled bands are treated, and the methods are applied elsewhere to electron transfer problems at interfaces. [ABSTRACT FROM AUTHOR]

The CH overtone spectra for vCH=1, 2, and 3 for an intermediate sized molecule, benzene, and the related intramolecular vibrational dynamics are treated theoretically. For this purpose, an artificial intelligence (AI) search technique is employed, using the evaluation function developed in Part II. The curvilinear local-normal mode coordinate system discussed in Part I is also used. The main features of the theoretical spectra are in reasonable accord with those of the experimental ones. Results reflecting the important role of the symmetry of molecules even in their high energy states are described. [ABSTRACT FROM AUTHOR]

The role of resonance centers in obtaining large size matrices via an artificial intelligence (AI) search is discussed. The results are used to develop for an AI search an evaluation function which takes cognizance of isolated internal resonances in these many-state systems. The effect of later-accepted states on resonance centers is included. This evaluation function and one without a resonance factor are used in Part III of this series. A search is made there to select zeroth-order vibrational states of benzene that are used in a diagonalization treatment of CH overtone spectra. When there are many overlapping resonances, as in that case, a comparison of results obtained with those two types of evaluation function is of particular interest. [ABSTRACT FROM AUTHOR]

Avoided crossings between quasidegenerate rovibrational states in the Doppler-free two-photon excitation of the 141 mode in the S1 excited state of benzene are treated theoretically. Two sets of avoided crossings in plots of spectral line frequency vs J at a given K and ΔK have been reported experimentally between an initially prepared ‘‘light’’ state (141 in zeroth order) and dark states, namely, one which in zeroth order is a 51101161 state, the other being in zeroth order a 62111 and/or possibly a 31161 state, implicated earlier by Neusser et al. The identification of these states makes the phenomenon an excellent candidate for treatment of the avoided crossing via a Van Vleck transformation, no other basis set states being needed for the diagonalization in order to extract the important features. Two successive transformations are used for handling direct coupling and coupling via virtual states. The dominant calculated contribution to the coupling is, jointly, Coriolis plus cubic–cubic anharmonic interactions between vibrational modes.Playing less of a role are Coriolis terms in which the inverse moment of inertia tensor is expanded up to quadratic terms in the coordinates. There results a 5×5 (for coupling to 51101161 ) and a 3×3 (for coupling to 62111 or 31161 ) matrix of the transformed Hamiltonian, each of which can also be described, if desired, to a very good approximation by a 2×2 matrix. The coupling element V0 and the difference of the rotational constants for the light and dark states (ΔB) are obtained from the plots of line position vs J(J+1) obtained. For the 141 to 51101161 and for the 141 to 62111 couplings the theoretical results are in reasonable agreement with the experimental results, no adjustable parameters being employed. For a coupling of 141 to 31161 the calculated V0 would be much too high compared with experiment (a factor of 10), the coupling involving the exchange of... [ABSTRACT FROM AUTHOR]

Results on vibrationally-excited ketene photofragment excitation (PHOFEX) spectra of Moore and co-workers are interpreted in terms of a previously described variational implementation of Rice–Ramsberger–Kassel–Marcus (RRKM) theory. At subvibrational excitations, the predictions of this theory reduce to those of phase space theory (PST). However, for excess energies just above the threshold of excitation of a particular vibrational mode of the products, the present theory predicts a significantly greater probability for vibrational excitation, compared with PST, in closer agreement with the experimental results, and predicts an energy dependence of the PHOFEX spectrum that is closer to the observed one. A key feature, to which the present calculations lead, is a two-transition state (TS) description for each vibrational excitation of the products, the PST TS region dominating at the threshold for that excitation and an inner TS region dominating at somewhat higher (∼200 cm-1) energies. The behavior contrasts partly with that of the unimolecular dissociation rate constant kEJ (except at the threshold for kEJ), because of the different focus of the two types of measurements. The theory provides a consistent interpretation of both properties. [ABSTRACT FROM AUTHOR]

A previously described implementation of Rice–Ramsberger–Kassel–Marcus (RRKM) theory for unimolecular dissociation processes involving a highly flexible transition state is applied to the dissociation of CH2CO into CH2 and CO. Results of theoretical calculations for the energy and angular momentum resolved rate constants are presented. Using an added dynamical approximation, the product vibrational–rotational distributions are also calculated. The calculated rate constants are compared with the corresponding experimentally determined quantities where possible. Comparison is also made with phase space theory (PST). The RRKM-based calculations are in good agreement with both the experimentally determined rate constants of Zewail and co-workers and the experimentally determined photofragment excitation spectra of Moore and co-workers. The results on rates are in contrast to the corresponding results from PST calculations. The RRKM-based theory for the product vibrational–rotational distributions predicts a moderately greater probability for vibrational excitations than does PST (particularly for excess energies just above the threshold for excitation of a particular vibrational mode of the products). In other respects the RRKM-based predictions of the ro-vibrational product state distributions are quite similar to those of PST. [ABSTRACT FROM AUTHOR]

Artificial intelligence methods are used to treat the time evolution in intramolecular quantum dynamics. Comparison is made of several AI search algorithms and evaluation functions in an application to the study of quantum intramolecular vibrational redistribution. A combination of a beam search and a best-first search is used, in conjunction with an accumulated evaluation function which encourages both searching and ultimately satisfying the uncertainty principle. The methods developed are applied to an 11-coordinate heavy central mass problem and used to treat both quantum beats and ‘‘dissipative’’ intramolecular energy transfer. Good agreement is obtained with the ‘‘exact’’ quantum dynamics. [ABSTRACT FROM AUTHOR]

The determination of a quantum correction factor for the transitional modes of a unimolecular dissociation/free radical recombination reaction having a transition state of varying looseness is described. The quantum correction factor for the high pressure canonical rate constant is calculated via Monte Carlo path integral evaluation of partition function ratios, and is applied to the recombination reaction 2CH3→C2H6. [ABSTRACT FROM AUTHOR]

We present an algorithm to determine the averaged time evolution of the probability amplitude for a nonstationary state in a quantum mechanical system. The algorithm is based on a low-frequency expansion of the probability amplitude and is related to the generalized moment expansion method which has been applied successfully to the description of dynamic correlation functions in stochastic systems. It is shown that the proposed algorithm gives excellent results for the description of quantum beats in the time evolution of the occupation probability for a nonstationary state in model systems. The relation of the algorithm to other theoretical approaches and the relevance for the description of intramolecular energy transfer processes is discussed. [ABSTRACT FROM AUTHOR]

In part I a reaction–diffusion equation was introduced for the description of electron transfer reactions which are induced by fluctuations in both the solvent polarization and in the intramolecular vibrational coordinates. We analyze the model employing a generalized moment expansion for the time behavior of the survival probability Q(t), i.e., for the fraction of molecules that have not transferred their electron at time t. Numerical and, in the narrow reaction window limit, analytical solutions are given for the average survival times τ. When the contribution of the intramolecular coordinates is appreciable an approximate power-law behavior τ∝ταL, with 0<α≼1, is found for the dependence of τ on the solvent dielectric relaxation time τL, in the large τL regime. Within the framework of the generalized moment description Q(t) is approximated as a superposition of several optimized exponential functions. In the small and intermediate τL regimes it is found that a single- or bi-exponential description, respectively, is sufficient. Simple formulas for such approximations in terms of the average survival times are given. Furthermore it is demonstrated that in the large τL regime a truly multiexponential time behavior for the survival probability is encountered which, over a certain range of time, can appear to be algebraic, i.e., Q(t) ∝t-γ. The relation of these results to experimental data is discussed. [ABSTRACT FROM AUTHOR]

An expression for the distribution of quantum states of the reaction products of unimolecular dissociations is obtained, based on statistical theory. A recently formulated RRKM-type treatment of unimolecular reactions with highly flexible transition states is used to obtain a distribution of quantum states of the products, by introducing an adiabatic approximation for motion from transition state to products. Any impulsive (nonadiabatic) exit channel effects are neglected thereby. Both the final yields of the quantum states of the products and the time evolution of these states are considered. The time evolution of the yield of the products can permit a direct test of non-RRKM effects and, additionally via the long-time component, of other aspects of RRKM theory. The long-time component of the yield of individual quantum states of the products then provides a test of the additional (here, adiabatic) approximation. Such tests are the more definitive the narrower the distribution of initial E’s and J’s of the dissociating molecule. [ABSTRACT FROM AUTHOR]

It is shown how the ‘‘trajectory-close method’’ introduced in earlier papers of this series can be used to treat other resonant systems semiclassically. The method, which does not involve the use of any curvilinear coordinate system, is illustrated for two coupled oscillators which have 3:1, 4:1, 5:1, 3:2, and 5:2 internal resonances. It is readily executed and it is shown how it can be extended to the three-oscillator case. This work supplements our earlier studies of 1:1, 2:1, and 3:1 resonant systems using this technique. Shapes of eigentrajectories and of corresponding quantum mechanical wave functions are compared for each of these systems. The paper also contains a survey of and comparison with other semiclassical methods which have been applied to systems with internal resonances. [ABSTRACT FROM AUTHOR]

A theoretical treatment is given for the effect of intramolecular vibrational and diffusive solvent orientational motions on the rate of electron transfer reactions. Four limiting cases are considered for the two-electronic state problem: slow reaction, wide and narrow reaction window, and nondiffusing limits. With the aid of a decoupling approximation, an expression is derived for the reaction rate which reduces to the appropriate expression for each limiting case when the latter is approached. Under certain conditions the time dependence of the survival probability is multiexponential rather than single exponential. Because of this behavior two average survival times are defined and expressions for each are obtained. Experimental data are considered with the present treatment in mind. One feature of the present work is a more general analysis for the case that both vibrational and solvent diffusive motion contribute to the activation process. The relation to previous works in the literature is described. [ABSTRACT FROM AUTHOR]

Intramolecular charge transfer are considered for the case that the motion of the system is on a single potential energy surface. The case where this motion occurred on two surfaces was considered elsewhere. The former is shown to be much preferable for studies of solvent dynamics. Several aspects of the relation between ‘‘constant charge’’ dielectric relaxation time of the polar solvent and the experimental decay time of emission from the polar excited state of the solute are discussed for hydrogen-bonded systems. [ABSTRACT FROM AUTHOR]

‘‘Adiabatically reduced’’ coupled equations are derived to obtain an approximate quantum mechanical solution for the dynamics of nonstationary states in isolated polyatomic molecules. Under suitable conditions, the number of such equations is considerably less than the number of coupled equations needed in practice for the exact calculation. The relationship of the present technique to several other methods, including the partitioning method, is discussed, and specific applications of the present treatment are given. [ABSTRACT FROM AUTHOR]

Implementation of RRKM theory for unimolecular dissociations having transition states of any degree of looseness is described for reactions involving dissociation into two fragments. The fragments may be atomic, diatomic, or polyatomic species. Action-angle and internal coordinates for the transitional modes of the reaction, transformations to Cartesian coordinates, and other calculational aspects are described. Results for the NO2→NO+O reaction are presented, including the dependence of the microcanonical rate constant on the bond fission and bending potentials for model potential energy surfaces. Illustrative calculations for the C2H6→2CH3 reaction are also given. [ABSTRACT FROM AUTHOR]

Approximate semiclassical solutions are developed for a system of a Morse oscillator coupled to a harmonic oscillator via a nonlinear perturbation. This system serves as a model for the interaction of an excited stretching mode with a bending mode in a polyatomic molecule. Three semiclassical methods are used to treat this model. In particular, a matrix diagonalization, a two-state model, and a uniform semiclassical approximation (USC) based on Mathieu functions are each used to determine the splittings and state mixing involved in these stretch–bend Fermi resonances. For small perturbations, approximate analytic semiclassical expressions are obtained for the system treated. These analytic expressions are given for the splittings using a two-state or USC method and for the overlaps of the zeroth order states with the eigenstates of the molecule using a USC method. [ABSTRACT FROM AUTHOR]

An expression for the scanning tunneling microscopy (STM) current between the tip and sample is presented using first-order perturbation theory for a two-Hamiltonian formalism (‘‘reactants’’ and ‘‘products’’). The calculated STM current depends on the square of the sample-tip matrix elements, averaged over a selection of random points in wave vector space. In the limit of low voltage and temperature, this averaging is over the Fermi surface of the sample. The model is applied to the graphite (0001) and Au(111) surfaces using a simple model (chain) of a tungsten tip and the tight-binding approximation. Comparisons with experiments and with the result for graphite obtained by Tersoff and Lang using a molybdenum tip are given. The theory is applied elsewhere to STM of adsorbates. [ABSTRACT FROM AUTHOR]

A semi-infinite approach (rather than a slab method or finite number of layers) is used to treat surface properties such as wave functions, energy levels, and Fermi surfaces of semi-infinite solids within the tight-binding (TB) approximation. Previous single-band results for the face-centered cubic lattice with a (111) surface and for the simple cubic lattice with a (001) surface are extended to semi-infinite layers, while the extension to calculations of other surfaces is straightforward. Treatment of more complicated systems is illustrated in the calculation of the graphite (0001) surface. Four interacting bands are considered in the determination of the wave functions, energies, and Fermi surface of the graphite (0001) surface. For the TB model used, the matrix elements in the secular determinants for the semi-infinite solid and for the infinite bulk solid obey the same expressions, and the wave functions are closely related. Accordingly, the results for the bulk system can then be directly applied to the semi-infinite one. The main purpose of the present paper is to provide wave functions and other properties used elsewhere to treat phenomena such as scanning tunneling microscopy and electron transfer rates at electrodes. [ABSTRACT FROM AUTHOR]

The Hamiltonian based on curvilinear normal modes and local modes (CNLM) is discussed using Wilson’s exact vibrational Hamiltonian as basis, the CNLM representation diagonalizing only the normal mode block of FG matrix in curvilinear internal coordinates. Using CNLM the kinetic and potential energy operators for benzene are given, including cubic and quartic anharmonicity in the potential energy and cubic and quartic terms in the kinetic energy expansion in curvilinear coordinates. Using symmetrized coordinates and cubic and higher force constants the number and identity of the independent symmetry allowed (A1g) such force constants are obtained. The relation to conventional anharmonic force constants is then given and the allowed contributions of the latter are obtained. The results are applied to CH overtone spectra and intramolecular vibrational dynamics in Part III of this series. [ABSTRACT FROM AUTHOR]

A recently described method for implementing RRKM theory for unimolecular reactions with highly flexible transition states is applied to the calculation of energy and angular momentum resolved rate constants and rotational–vibrational energy distributions for the reaction NCNO→hν NCNO*→NCNO(vib. hot)→NC+NO. The dissociation rate results are compared to the recent experimental results of Khundkar et al., and the vibrational and rotational distribution results are compared to the experimental values of Nadler et al. Comparison is also made with phase space theory calculations. The calculated rotational distributions at energies below the vibrational threshold of the products are the same as those of PST. At energies (2348, 2875 cm-1) above this threshold energy the rovibrational distribution is in better agreement with the data than is that of PST. The need for obtaining more accurate ab initio potential energy surfaces is noted, particularly for treating reactions at still higher energies. [ABSTRACT FROM AUTHOR]

An iterative procedure is proposed for determining increasingly accurate effective Hamiltonians for use in the adiabatically reduced coupled equations approach to intramolecular dynamics calculations [J. Chem. Phys. 84, 2254 (1986)]. The relationships between this iterative determination of the effective Hamiltonian, which is based on an adiabatic approximation, and some other partitioning methods for determining an effective Hamiltonian are discussed. The present iterative procedure provides accurate agreement with the exact dynamics for the two specific model systems studied. [ABSTRACT FROM AUTHOR]

Reactive transition probabilities and Boltzmann-averaged reactive transition probabilities for a slightly off-resonant model H-atom transfer system with an appreciable energy barrier are calculated using the approximate methods of Babamov et al. and of Crothers–Stückelberg. Both are compared with the corresponding quantities obtained from a numerical two-state treatment of the same model system. The method of Babamov et al. is seen to give more accurate results for the transition probabilities at energies below and around the reaction threshold, and much more accurate results for the Boltzmann-averaged probabilities in a wide range of temperatures than the second method. The relative merits of the two formulas are discussed. [ABSTRACT FROM AUTHOR]