Volume 113, Issue 9, 01 September 2000
Index of content:
- Theoretical Methods and Algorithms
113(2000); http://dx.doi.org/10.1063/1.1287424View Description Hide Description
The fluctuationtheorem gives an analytical expression for the probability of observing second law violating dynamical fluctuations in nonequilibrium systems. At equilibrium, statistical mechanical fluctuations are known to be ensemble dependent. In this paper we generalize the transient and steady-state fluctuationtheorems to various nonequilibrium dynamical ensembles. The transient and steady-state fluctuationtheorem for an isokinetic ensemble of isokinetic trajectories is tested using nonequilibrium molecular dynamics simulations of shear flow.
113(2000); http://dx.doi.org/10.1063/1.1287837View Description Hide Description
A simplified approach to quantum control of chemical reactiondynamics based on a classical, local control theory was developed. The amplitude of the control pulse is proportional to the linear momentum of the reactionsystem within the dipole approximation for the system-radiation field interaction. The kinetic energy of the system is the controlling parameter. That is, the reaction is controlled by accelerating the representative point on a potential energy surface before crossing over a potential barrier and then by deaccelerating it to the target after passing over the potential barrier. The classical treatment was extended to control of wave packet dynamics by replacing the classical momentum by a quantum mechanically averaged momentum on the basis of the Ehrenfest theorem. The present method was applied to a quantum system of a simple one-dimensional, double-well potential for checking its validity. A restriction of the applicability of the simplified method was also discussed. An isomerization of HCN was treated as a model system for wave packet control of a two-dimensional reaction.
Structure optimization via free energy gradient method: Application to glycine zwitterion in aqueous solution113(2000); http://dx.doi.org/10.1063/1.1287785View Description Hide Description
The free energy gradient method was applied to the multidimensional geometry optimization of glycine zwitterion (ZW) in aqueous solution in order not only to demonstrate its applicability, but also to examine its efficiency. The method utilizes force on the free energysurface that can be directly calculated by the molecular dynamics method and the free energyperturbation theory. Then, the most stable ZW structure in aqueous solution was obtained within the tolerance assumed, and it was found that the free energy (FE) and enthalpy changes of stabilization from the initial geometry optimized in the gas phase are −0.9 and −3.5 kcal/mol, respectively, and the amino and carboxyl groups are spatially separated by each other due to their solvating with water molecules. Comparing the contributions of enthalpy and entropy to FE, the former is attributed to the main origin of FE stabilization during the optimization procedure, and it was found that solvation entropy prevents water molecules from solvating the ZW more strongly.
113(2000); http://dx.doi.org/10.1063/1.1287786View Description Hide Description
We discuss the application of Monte Carlo methods to the self-consistent calculation of a Ginzburg–Landau free energy functional for Lennard-Jones systems in three dimensions. Following this discussion, we demonstrate that the parameters in the coarse-grained free energy can be extracted from a multivariate distribution of energies and particle densities which, when suitably reweighted, permit one to extrapolate the results to other nearby points in the thermodynamic parameter space. For the purposes of illustration, both single-phase and liquid–gas coexistence are considered here with the aim of describing various regions of the phase diagram with a single function and, in doing so, providing a link between atomistic and mesoscopic length scales.
Nuclear magnetic resonance spin–spin coupling constants from coupled perturbed density functional theory113(2000); http://dx.doi.org/10.1063/1.1286806View Description Hide Description
For the first time, a complete implementation of coupled perturbed density functional theory (CPDFT) for the calculation of NMR spin–spin coupling constants (SSCCs) with pure and hybrid DFT is presented. By applying this method to several hydrides, hydrocarbons, and molecules with multiple bonds, the performance of DFT for the calculation of SSCCs is analyzed in dependence of the XC functional used. The importance of electron correlation effects is demonstrated and it is shown that the hybrid functional B3LYP leads to the best accuracy of calculated SSCCs. Also, CPDFT is compared with sum-over-states (SOS)DFT where it turns out that the former method is superior to the latter because it explicitly considers the dependence of the Kohn–Sham operator on the perturbed orbitals in DFT when calculating SSCCs. The four different coupling mechanisms contributing to the SSCC are discussed in connection with the electronic structure of the molecule.
Second-order perturbation corrections to singles and doubles coupled-cluster methods: General theory and application to the valence optimized doubles model113(2000); http://dx.doi.org/10.1063/1.1286597View Description Hide Description
We present a general perturbative method for correcting a singles and doubles coupled-cluster energy. The coupled-clusterwave function is used to define a similarity-transformed Hamiltonian, which is partitioned into a zeroth-order part that the reference problem solves exactly plus a first-order perturbation. Standard perturbation theory through second-order provides the leading correction. Applied to the valence optimized doubles (VOD) approximation to the full-valence complete active space self-consistent field method, the second-order correction, which we call (2), captures dynamical correlation effects through external single, double, and semi-internal triple and quadruple substitutions. A factorization approximation reduces the cost of the quadruple substitutions to only sixth order in the size of the molecule. A series of numerical tests are presented showing that VOD(2) is stable and well-behaved provided that the VOD reference is also stable. The second-order correction is also general to standard unwindowed coupled-cluster energies such as the coupled-cluster singles and doubles (CCSD) method itself, and the equations presented here fully define the corresponding CCSD(2) energy.
113(2000); http://dx.doi.org/10.1063/1.1287833View Description Hide Description
A gauge-origin invariant formulation of the frequency-dependent Verdet constant of magneto-optical rotation and of the Faraday B term of magnetic circular dichroism for coupled-clusterwave functions is derived within the framework of variational response theory. Working expressions suitable for implementation in ab initio program packages are presented. These expressions have a structure similar to that of the expressions for the first hyperpolarizability and the two-photon transition moment, respectively, for the Verdet constant and the B term. The approach is general and can easily be extended to other similar frequency-dependent properties as well as to other wavefunction models. Pilot results at the CCSD level are presented for of HF and
Development of reference states for use in absolute free energy calculations of atomic clusters with application to 55-atom Lennard-Jones clusters in the solid and liquid states113(2000); http://dx.doi.org/10.1063/1.1286808View Description Hide Description
In this paper four reference states allowing computation of the absolute internal free energies of solid and liquid clusters are introduced and implemented. Three of these are introduced for the first time. Two of these references are useful for highly fluctional liquidlike clusters while the other two are appropriate for more rigid solidlike clusters. These reference states are combined with a finite time variational method to obtain upper and lower bounds to the absolute free energies of clusters of Lennard-Jones (LJ) atoms, and allowing the efficiency of each of the four reference states to be elucidated. The optimal references are then applied to obtain upper and lower bounds to the internal free energies (the absolute free energy in the cluster center of mass frame) of over a series of fixed temperatures including the solid–liquid coexistence regime. The reversible scaling method, recently introduced by de Koning, Antonelli, and Yip, is then used to extend the results over a continuous range of temperatures. Estimation of the rotational free energy allows comparisons to free energies of in the nonrotating center of mass frame as estimated by Doye and Wales.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
113(2000); http://dx.doi.org/10.1063/1.1287401View Description Hide Description
The (0,0,0)–(0,0,0) bands of the and systems of three isotopomers of yttrium imide and have been studied by laser-induced fluorescence in a molecular beam apparatus. Rotational, fine, and nuclear magnetic hyperfine structures have been resolved and analyzed. The previously studied (0,0,0)–(0,0,0) bands of the three isotopomers have been reanalyzed. Global fits of all observed bands, in which the ground state has been fitted to a Hamiltonian model, while the excited states have been represented by term values, have been performed for the three isotopomers. Subsequently, the individual bands have been fitted. The ground state parameters have been fixed at the values obtained in the global fits, while the upper states have been fitted to the Hamiltonian models. The (0,0,0) state of and is severely perturbed. Even though the nature of these perturbing states can only be speculated upon, the introduction of effective perturbers made it possible to deperturb the state successfully. The state is unperturbed. The spectra can be reproduced to better than 120 MHz (0.004 The analyses confirm that the molecule is linear in all four states with the nuclear arrangement Y–N–H. The bond lengths structure) in the ground state and the and excited states have been derived to be and respectively. The electronic configurations for the ground state and the and excited states are discussed and compared with calculations whenever possible.
113(2000); http://dx.doi.org/10.1063/1.1287400View Description Hide Description
We report on the low-energy electron induced production of CO within thin solid films of acetone condensed at low temperature on a solid Ar substrate. The CO fragments, which remain trapped within the bulk of the acetone film, are detected in situ via their first electronic state using high-resolution electron-energy-lossspectroscopy. The production of CO is studied as a function of the electron energy (2–25 eV), electron dose, and film thickness. The energy dependence of CO production is calibrated in terms of an electron scattering cross section It is characterized by an energy threshold at 8 eV, a strong rise up to about 14 eV, and a broad maximum of at 16 eV followed by a relatively small and monotonous decrease up to 25 eV. The production of CO is discussed in terms of the formation of several core-excited electron resonances, which may lead directly to the fragmentation of the molecule via dissociative electron attachment or indirectly by decaying into an entirely repulsive part of the corresponding neutral excited state and positive ion states.
113(2000); http://dx.doi.org/10.1063/1.1287718View Description Hide Description
A bound-to-free transition initiated by femtosecond excitation of diatomic molecules results in photofragments with a distribution of kinetic energies. A measurement of the kinetic-energy distribution yields the modulus squared of the asymptotic momentum-space wave packet prepared in the laser excitation process. On the other hand, the coordinate-space density of the wave packet entering the interaction-free region can be determined from pump–probe integrated fluorescence spectroscopy. We provide several numerical examples to show that this information can be used to determine the phase of the asymptotic wave packet so that this particular quantum-mechanical wave function can be characterized completely. To achieve this aim we use an iteration scheme (Gerchberg–Saxton algorithm) which does not require any further information about the system or the laser pulses.
113(2000); http://dx.doi.org/10.1063/1.1287831View Description Hide Description
Ab initio post Hartree–Fock studies were performed on the title species. Their structures consist of a tightly bound core ion which generates progressively weaker bonded distinct shells of Ar atoms. The predicted structures of clusters explain the experimental pattern of changes in the stepwise enthalpies and entropies of dissociation. The subtle changes in thermodynamic properties reproduced by calculations indicate an accurate location of the global minimum geometries of the clusters and the proper determination of the shells for coordinating argon atoms. The nature of chemical bonding is studied based on the interaction energy decomposition. The importance of the covalent component in the interaction forces is revealed.
113(2000); http://dx.doi.org/10.1063/1.1287616View Description Hide Description
Emission, absorption, and excitation spectroscopy has been used for a detailed analysis of the optical transitions of trapped in cryogenic matrices. Upon excitation of electronic states correlating to the or the asymptote, fast nonradiative relaxation leads to emission from the lowest excited state in all matrices, which decays monoexponentially in 1 ms in Ne, 280 μs in Ar, and 12 μs in Xe. In addition, electronically unrelaxed emission of is reported in neon and in xenon matrices and attributed to the state in neon and to the state and the or states in xenon. The results are rationalized by assuming: (a) that population of the excited states occurs mainly close to the asymptotic limit, where branching is determined by nonadiabatic coupling and energetics, that are strongly environment dependent, and (b) that in Xe matrices the states correlating to the and asymptotic limits are stabilized in different configurations, as a result of the very different solvation properties of the atomic and the state. Further emission bands are found in the vicinity of the dimer transitions, which we attribute to and to site effects on In particular, electronically unrelaxed emission from excited states of is reported.
113(2000); http://dx.doi.org/10.1063/1.1287840View Description Hide Description
Complementary to our recent report on the F+HD reaction, the reactive excitation functions for the other isotopomers are presented. Through analysis of the differential cross section data, the collisional energy dependencies of product vibrational branchings for F+HD are also reported here. Several important conclusions can be drawn from this work. First, the transition-state properties, in particular the barrier height, of this reaction are well-characterized by the SW PES, despite its neglect of spin–orbit couplings. Second, contrary to the theoretical conclusion in recent literatures, an experimental observation is presented which seems to suggest that a resonance may indeed exist for the reaction in support of the original interpretation proposed by Lee and co-workers. Third, the vibrational branching for the F+HD→HF+D reaction elucidates another facet of resonance effects in the integral cross sections. Finally, the nonadiabatic reactivity of the spin–orbit excited atom is found to be small, which is in line with the conclusion inferred from a most recent, full quantum mechanical multisurface calculation.
Infrared absorption spectra by collisional complexes: The effect of the anisotropy of the interaction potential113(2000); http://dx.doi.org/10.1063/1.1287822View Description Hide Description
As an extension of previous work which was based on the isotropic interaction approximation, absorption spectra in the rotational and fundamental bands of induced by collisions with He, are calculated by numerical integration of the close-coupled Schrödinger equation to account for the anisotropy of the interaction potential. A refined quantum chemical dipole surface of interacting pairs is also obtained with an extended grid of molecular geometries. This dipole surface agrees generally well with previous results, but is smaller by about 5% in the isotropic overlap term which is significant only in the fundamental band. The effects of the anisotropy of the interaction are to reduce the peak intensities of the Q and S lines by roughly 10% and to increase absorption in the far wings by a similar amount. The accuracy of the dipole surface as well as that of the ab initiointeraction potential that enters the calculations of the spectra are believed to permit the prediction of absolute spectral intensities with an accuracy of about Comparisons with the available measurements show very good agreement of the shapes of the spectral profiles, but the absolute intensities differ by up to 10% in some cases. These remaining differences between theory and measurements appear to be random and are generally smaller than the differences among comparable measurements. Our results should therefore provide a reliable basis for predicting absorption by pairs for temperatures and frequencies for which no laboratory measurements exist. This fact is of a special interest, for example, for the spectroscopic analyses of the atmospheres of the outer planets.
113(2000); http://dx.doi.org/10.1063/1.1287394View Description Hide Description
Photodissociation of acetone cations, at 355 nm has been studied by means of the ion velocity imaging technique. Acetone cations are produced via direct photoionization of a supersonic beam of acetone at 118 nm generated by frequency tripling the 355 nm laser. Only the acetyl cation, could be detected as a dissociation product in the time-of-flightmass spectrometer. The acetyl ion signal depends upon the fifth power of the 355 nm laser energy, while the acetone ion signal depends upon the third power. This suggests that the fragment ion is produced via two-photon absorption of 355 nm photons by the acetone cation. The total translational energy distribution and angular distribution of acetyl cation were derived from the 2D images of for the reaction The translational energy distribution suggests that methyl radicals are produced in two electronically excited states, the Rydberg and the valence states. The anisotropy parameter β shows that the Rydberg state is formed via a perpendicular excitation and the valence state via a parallel transition.
Toluene: Structure, dynamics, and barrier to methyl group rotation in its electronically excited state. A route to IVR113(2000); http://dx.doi.org/10.1063/1.1287392View Description Hide Description
Rotationally resolved fluorescence excitation spectra of several torsionally active bands in the electronic transitions of toluene and toluene- have been recorded in the collision-free environment of a molecular beam.Analyses of these data provide accurate values of the internal rotor constants F; the barrier heights the frame rotational constants the overall rotational constantsB and C; and the torsion-rotation coupling constants in the and levels of the state and the ±1, and 3+ levels of the state. Comparison of the B, and C values in the levels of the two states shows that toluene is quinoidal in form, with shorter ring “parallel” C–C bonds than “perpendicular” ones, unlike the state. The preferred conformation of the methyl group is staggered in both states, but the values are significantly different; and Comparison of the F, and values in the different torsional levels of the state shows that, below the barrier, the methyl group tilts and the ring bond lengths change with increasing displacements along the torsional coordinate. Above the barrier, the precessional motion of the is quenched but larger ring distortions are observed. Thus, the data are consistent with an enhanced hyperconjugative interaction between the benzene ring and the methyl group in the state. This interaction is substantially modulated by the relative motion of the two attached groups, providing a facile route to IVR.
113(2000); http://dx.doi.org/10.1063/1.1287398View Description Hide Description
State-to-state reactive scattering of is studied using crossed supersonic jets and high-resolution IR laser direct absorption techniques. Rovibrational state-resolved HF column-integrated absorption profiles are obtained under single collision conditions and converted to populations via appropriate density-to-flux transformation. Nascent rovibrational distributions in each state are reported. Summed over all product rotational levels, the nascent vibrational quantum state populations for 2σ error bars] are in agreement with previous flow cell studies by Setser, Heydtmann, and co-workers [Chem. Phys. 94, 109 (1985)]. At the rotational state level, however, the current studies indicate nascent distributions for that are significantly hotter than previously reported, ostensibly due to reduced collisional relaxation effects under supersonic jet conditions. Final HF rotational states from are observed near the maximum energetically accessible J values in both the and vibrational manifolds, which provides experimental support for a bent F–H–C transition state structure.
113(2000); http://dx.doi.org/10.1063/1.1287823View Description Hide Description
The forward–backward semiclassical dynamics methodology [J. Phys. Chem. 103, 7753, 9479 (1999)] is reformulated in the interaction representation. The new version of the method allows for a fully quantum mechanical description of a low-dimensional subsystem of interest, along with a semiclassical forward–backward treatment of the solvent coordinates and their coupling to the reference subsystem. Application to the long-time tunneling dynamics in a symmetric double-well system coupled to a harmonic bath shows that the interaction FBSD is capable of capturing quantitatively the tunneling and decoherence effects induced by weakly dissipative environments.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
113(2000); http://dx.doi.org/10.1063/1.1287421View Description Hide Description
Hydrogen bonding plays an enormous role in determining the solution properties of liquid water. In the present study, the translational diffusion and the reorientational correlation times of isolated water molecules dissolved in nitromethane were studied using NMRmeasurements in the temperature range of 260–314 K. It was found that the water diffusion coefficient was considerably faster than in pure water at the same temperature. Further, the activation energy for the translational motion of the water was about 10 kJ mol−1, which was the same as that of the (solvent) nitromethane. However, the activation energy for the reorientational motion of the water was significantly less at 7.7 kJ mol−1. In this study we show that the motions of the isolated water molecules behave significantly different than water molecules in pure water due to the absence of hydrogen bonding to nearby water molecules.