Index of content:
Volume 126, Issue 10, 14 March 2007
- Theoretical Methods and Algorithms
Langevin stabilization of molecular-dynamics simulations of polymers by means of quasisymplectic algorithms126(2007); http://dx.doi.org/10.1063/1.2464095View Description Hide Description
Algorithms for the numerical integration of Langevin equations are compared in detail from the point of view of their accuracy, numerical efficiency, and stability to assess them as potential candidates for molecular-dynamics simulations of polymeric systems. Some algorithms are symplectic in the deterministic frictionless limit and prove to stabilize long time-step integrators. They are tested against other popular algorithms. The optimal algorithm depends on the main goal: accuracy or efficiency. The former depends on the observable of interest. A recently developed quasisymplectic algorithm with great accuracy in the position evaluation exhibits better overall accuracy and stability than the other ones. On the other hand, the well-known BrünGer-Brooks-Karplus [Chem. Phys. Lett.105, 495 (1982)] algorithm is found to be faster with limited accuracy loss but less stable. It is also found that using higher-order algorithms does not necessarily improve the accuracy. Moreover, they usually require more force evaluations per single step, thus leading to poorer performances.
Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for , , , and126(2007); http://dx.doi.org/10.1063/1.2566637View Description Hide Description
The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers are found on the dissociation products. An “-electron self-interaction-free” functional for positive integer is one that produces a realistic linear variation of total energy with in the range of , and so can avoid these errors. This desideratum is a natural generalization to all of the more familiar one of one-electron self-interaction freedom. The intent of this paper is not to advocate for any functional, but to understand what is required for a functional to be -electron self-interaction-free and thus correct even for highly stretched bonds. The original Perdew-Zunger self-interaction correction (SIC) and our scaled-down variant of it are exactly one- and nearly two-electron self-interaction-free, but only the former is nearly so for atoms with . Thus all these SIC’s produce an exact binding energy curve for , and an accurate one for , but only the unscaled Perdew-Zunger SIC produces an accurate one for , where there are more than two electrons on each fragment . We also discuss , which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly -electron self-interaction-free for atoms of all stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system.
126(2007); http://dx.doi.org/10.1063/1.2698467View Description Hide Description
We show the possibility to accelerate—in a resonant way—a nonlinear chemical reaction by imposing a small temperature modulation. This classical resonance, which happens for particular modulation frequencies, is illustrated on the athermic cubic Schlögl model, which allows us to get analytical expressions for both the reactionrelaxation time and the frequency-resonant delay.
126(2007); http://dx.doi.org/10.1063/1.2646940View Description Hide Description
A simple symmetry adapted search algorithm (SASS) exploiting point group symmetry increases the efficiency of systematic explorations of complex quantum mechanical potential energy surfaces. In contrast to previously described stochastic approaches, which do not employ symmetry, candidate structures are generated within simple point groups, such as , , and . This facilitates efficient sampling of the Pople's dimensional configuration space and increases the speed and effectiveness of quantum chemical geometryoptimizations. Pople's concept of framework groups [J. Am. Chem. Soc.102, 4615 (1980)] is used to partition the configuration space into structures spanning all possible distributions of sets of symmetry equivalent atoms. This provides an efficient means of computing all structures of a given symmetry with minimum redundancy. This approach also is advantageous for generating initial structures for global optimizations via genetic algorithm and other stochastic global search techniques. Application of the SASS method is illustrated by locating 14 low-lying stationary points on the cc-pwCVDZ ROCCSD(T) potential energy surface of . The global minimum structure is identified, along with many unique, nonintuitive, energetically favorable isomers.
Interpolating moving least-squares methods for fitting potential energy surfaces: An application to the unimolecular reaction126(2007); http://dx.doi.org/10.1063/1.2698393View Description Hide Description
Classical trajectories have been used to compute rates for the unimolecular reaction on a fitted ab initio potential energy surface (PES). The ab initio energies were obtained from CCSD(T)/aug-cc-pvtz electronic structure calculations. The ab initio energies were fitted by the interpolating moving least-squares (IMLS) method. This work continues the development of the IMLS method for producing ab initio PESs for use in molecular dynamics simulations of many-atom systems. A dual-level scheme was used in which the preliminary selection of data points was done using a low-level theory and the points used for fitting the final PES were obtained at the desired higher level of theory. Classical trajectories were used on various low-level IMLS fits to tune the fit to the unimolecular reaction under study. Procedures for efficiently picking data points, selecting basis functions, and defining cutoff limits to exclude distant points were investigated. The accuracy of the fitted PES was assessed by comparing interpolated values of quantities to the corresponding ab initio values. With as little as 330 ab initio points classical trajectory rate constants were converged to 5%–10% and the rms error over the six-dimensional region sampled by the trajectories was a few tenths of a kcal/mol.
126(2007); http://dx.doi.org/10.1063/1.2647227View Description Hide Description
A diffusionMonte Carlo algorithm employing “on the fly” extrapolation with respect to the time step is implemented and demonstrated simulating realistic systems. Significant advantages are obtained when using on the fly extrapolation, leading to reduced systematic and statistical errors. The sound theoretical basis of extrapolation on the fly is discussed and compared to justifications for the a posteriori extrapolation.
Efficient vector potential method for calculating electronic and nuclear response of infinite periodic systems to finite electric fields126(2007); http://dx.doi.org/10.1063/1.2711202View Description Hide Description
The response of periodic systems to external electric fields is a challenging theoretical problem. The authors show how the vector potential approach yields a numerically efficient treatment of the combined electronic and nuclear response to a finite static field. Their method is based on a self-consistent reformulation of the charge flow term in the single particle Hamiltonian. Careful numerical implementation yields a treatment whose computational needs are only marginally larger than those of a conventional field-free calculation. To prove the method exemplary polymer calculations are done for a model Hamiltonian. The latter contains all essential elements of an ab initio Kohn-Sham or Hartree-Fock Hamiltonian but allows for extensive testing. The extension to three-dimensional systems is described.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
126(2007); http://dx.doi.org/10.1063/1.2698320View Description Hide Description
The static electric dipole polarizabilities of rhodium clusters , , have been measured via a molecular beam deflection method. Uniform high-field beam deflections, indicative of induced polarization, were observed for all except and which by contrast exhibited beam broadening and anomalously high effective polarizabilities. Analysis of the beam deflection profile of indicates that it possesses a permanent dipole moment of . Unlike the other clusters in the size range, the polarizability of is observed to decrease with increasing source temperature. We attribute this temperature dependence to paraelectric behavior, suggesting that is a fluxional molecule possessing a dipole moment that spatially fluctuates, uncorrelated with overall rotation.
126(2007); http://dx.doi.org/10.1063/1.2709880View Description Hide Description
The bound state properties of the ground state and the lowest triplet state of the , , and helium atoms are determined to very high accuracy from the results of direct numerical computations. To compute the bound state properties of these atoms the author applied his exponential variational expansion in relative/perimetric three-body coordinates. For the ground state and the lowest triplet state of the , , and atoms the author also determined the lowest order QED corrections and the field component of isotopic shift ( shift). For the state of the atom the hyperfine structure splitting is evaluated. The considered properties of the ground state and the lowest state in the and atoms are of great interest in a number of applications.
126(2007); http://dx.doi.org/10.1063/1.2567235View Description Hide Description
We study the statistics of photon emission from three-level single molecule systems. The generating function method [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett.90, 238305 (2003)] is used to calculate steady state absorption line shapes and Mandel’s parameter as a function of excitation frequency, as well as the time dependence associated with approach to the steady state. The line shape calculations confirm known results derived via other methods, while the parameter results display complex frequency dependences not amenable to simple interpretation. This study confirms the applicability of the generating function formalism to multilevel quantum systems, including the proper modeling of quantum coherence effects.
126(2007); http://dx.doi.org/10.1063/1.2713107View Description Hide Description
The authors compared circularly and linearly polarized lights in the ionization and fragmentation of anthracene, using femtosecond laser pulses at intensities of . Singly and doubly charged intact molecular ions as well as numerous fragment ions were observed in the mass spectra, which were investigated as a function of laser intensity and polarization. At comparable intensities above the saturation threshold for complete ionization, the fragmentation pathways are enhanced with a circularly polarized field compared to a linearly polarized field. Resonant excitation of the molecular cation through the transition is proposed to be the initial step to ion fragmentation. The circularly polarized field interacts with a larger fraction of the randomly oriented molecules than the linearly polarized field, and this is considered to be the reason for the enhanced fragmentation brought about by circularly polarized light.
Role of the electric dipole moment in positron binding to the ground and excited states of the BeO molecule126(2007); http://dx.doi.org/10.1063/1.2711203View Description Hide Description
Self-consistent-field and multireference single- and double-excitation configuration interaction (CI) calculations have been carried out for various electronic states of the beryllium oxide molecule and their positron-attached counterparts. Particular emphasis is placed on the correlation between the polarity of a given BeO state and the magnitude of the positron binding energy as the internuclear distance is varied. Potential curves are computed for all BeO states that correlate with the first three atomic limits for this system and good agreement is found between the experimental and calculated spectroscopic constants in all cases. The present level of CI treatment is known to underestimate the positron affinities of atoms by at least several tenths of an eV, and this fact needs to be taken into account in evaluating the results for positron binding to molecules. The lowest BeO excited states are not found to bind with a positron in the Franck-Condon region due to their comparatively small dipole moments caused by O to Be charge transfer relative to the ground state, which in turn does have a fairly sizeable positron affinity. The situation changes significantly as dissociation proceeds, however, with both and positronic states lying several tenths of an eV lower than their neutral counterparts over a broad range of internuclear distance.
126(2007); http://dx.doi.org/10.1063/1.2646899View Description Hide Description
Experimental crossed-beam studies carried out previously have indicated that the dynamics of the Rydberg-atom-molecule reaction are very similar to those of the corresponding ion-molecule reaction. The equivalence of the cross sections for these related systems would open up a new approach to the experimental study of ion-molecule reactions. However, a recent experimental and theoretical study has brought to light some important qualitative differences between the Rydberg-atom reaction and the ion-molecule reaction; in particular, the experimental cross section for the Rydberg-atom reaction exhibits a higher degree of forward-backward scattering asymmetry than predicted by a quasiclassical trajectory study of the ion-molecule reaction. In this paper, the authors consider the dynamics of the Rydberg-electron over the course of a reactive collision and the implications of these dynamics for the Rydberg-atom-molecule crossed-beam experiment. Using an approach based on perturbation theory, they estimate the attenuation of the experimental signal due to the Rydberg-electron dynamics as a function of the scattering angle. They show that at least part of the experimental asymmetry can be ascribed to this angle dependent attenuation. Their results offer general insight into the practical aspects of the experimental study of ion-molecule reactions by means of their Rydberg-atom counterparts.
Theoretical investigation of the alkaline-earth dihydrides from relativistic all-electron, pseudopotential, and density-functional study126(2007); http://dx.doi.org/10.1063/1.2437213View Description Hide Description
Highly precise ground state geometries, harmonic vibrational frequencies and force constants of alkaline-earth dihydrides from to are obtained using relativistic small-core energy-consistent effective core potentials at the coupled-cluster level. The results are compared with all-electron as well as density functional calculations. All-electron results, in particular, clearly show the importance of relativistic effects in the properties considered in this paper. The monotonic trends in the geometries are explained in terms of second-order perturbation theory. Trends in the force constants are monotonic except for the bending mode where an anomaly occurs from to . It is rationalized in terms of reduced hybridization due to relativity, which is shown to be an energy effect attributed to the stabilization of the orbital. The pseudopotentials show an excellent performance in comparison with all-electron methods and are therefore successfully transferred to molecular cases. The density functional methods, however, suffer from functional dependencies with B3LYP performing the best in this case.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
126(2007); http://dx.doi.org/10.1063/1.2434969View Description Hide Description
The authors present results from molecular dynamics simulations on the effect of smooth and rough probes on the dynamics of a supercooled Lennard-Jones (LJ) mixture. The probe diameter was systematically varied from one to seven times the diameter of the large particles of the LJ mixture. Mean square displacements show that in the presence of a large smooth probe the supercooled liquid speeds up, while in the presence of a large rough probe, the supercooled liquid slows down. Non-Gaussian parameters indicate that with both smooth and rough probes, the heterogeneity of the supercooled system increases. From the analysis of local Debye-Waller factors, it is evident that the change in the dynamics of the LJ system is heterogeneous, with the largest perturbations close to the probes. Large smooth and rough probes appear to set up heterogeneities in these supercooled systems that would otherwise not occur, and these heterogeneities persist for long times.
126(2007); http://dx.doi.org/10.1063/1.2464081View Description Hide Description
General expressions are obtained for the thermodynamic properties of nonideal gases of arbitrary composition. These include the equation of state and solvation thermodynamic functions of mixtures with any number of components, expanded to first order in total number density. The results are expressed in terms of binary second virial coefficients which are in turn related to binary interaction potential energy functions. Solvation thermodynamic functions (at both constant pressure and constant volume) are decomposed into solute-solvent and solvent-reorganization contributions, thus indicating how each of the latter quantities may be experimentally measured. Moreover, the results are used to identify solute-induced changes in solventthermodynamic functions, as well as nonideal (excess) contributions to chemical reaction equilibria and solvation heat capacities. The effects of a solute on the reorganization energy and chemical potential of a nonideal solvent are shown to differ qualitatively from both the corresponding ideal gas and high density fluid results.
126(2007); http://dx.doi.org/10.1063/1.2539105View Description Hide Description
Dielectric relaxation and dynamic heat capacity measurements are compared for 2-ethyl-1-hexanol near its glass transition temperature in order to further clarify the origin of the prominent Debye-type loss peak observed in many monohydroxy alcohols and other hydrogen-bonding liquids. While the dielectric spectrum displays two distinct polarization processes that are separated by a factor of 2000 in terms of the peak frequency, the heat capacity shows only a single peak. The dielectric process with lower amplitude and higher peak frequency coincides with the calorimetric signal, whereas the large dielectric Debye signal is not associated with calorimetric modes. The authors conclude that the Debye process corresponds to a transition among states which differ in energy only in the case of an external electric field.
Effects of a constant electric field on the diffusional instability of cubic autocatalytic reaction fronts126(2007); http://dx.doi.org/10.1063/1.2566796View Description Hide Description
An electric field applied in the direction of propagation of a chemical reaction-diffusion front can affect the stability of this front with regard to diffusive instabilities. The influence of an applied constant electric field is investigated by a linear stability analysis and by nonlinear simulations of a simple chemical system based on the cubic autocatalytic reaction. The diffusional stability of the front is seen to depend on the intensity and sign of the applied field, and , the ratio diffusion coefficients of the reactant species. Depending on , the front can become more or less diffusively unstable for a given value of . Above a critical value of , which depends on , electrophoretic separation of the two fronts is observed.
126(2007); http://dx.doi.org/10.1063/1.2566868View Description Hide Description
First principles simulations of the hydration shells surrounding ions are reported for temperatures near . The predicted six water molecules in the octahedral first hydration shell were found to be trigonally coordinated via hydrogen bonds to shell water molecules in agreement with the putative structure used to analyze the x-ray data, but in disagreement with the results reported from conventional molecular dynamics using two-and three-body potentials. Bond lengths and angles of the water molecules in the first and second hydration shells and the average radii of these shells also agreed very well with the results of the x-ray analysis. Water transfers into and out of the second solvation shell were observed to occur on a picosecond time scale via a dissociative mechanism. Beyond the second shell the bonding pattern substantially returned to the tetrahedral structure of bulk water. Most of the simulations were done with 64 solvating water molecules . Limited simulations with 128 water molecules were also carried out. Results agreed as to the general structure of the solvation region and were essentially the same for the first and second shell. However, there were differences in hydrogen bonding and Al–O radial distribution function in the region just beyond the second shell. At the end of the second shell a nearly zero minimum in the Al–O radial distribution was found for the 128 water system. This minimum is less pronounced minimum found for the 64 water system, which may indicate that sizes larger than 64 may be required to reliably predict behavior in this region.
126(2007); http://dx.doi.org/10.1063/1.2672734View Description Hide Description
The observation of a very sharp low frequency spike in the hyper-Rayleigh spectrum (HRS) of strongly dipolar fluids, such as acetonitrile and water, has been interpreted as reflecting a very slowly relaxing component in the transverse dipole density. This suggestion is at variance with the expectation of the dielectric theory for an isotropic fluid and has led to the speculation that the slow relaxation is associated with the reorganization of ferroelectric domains. Very large-scale molecular-dynamics simulation ( molecules) have been carried out using a three-site potential model of acetonitrile. The simulated fluid shows no suggestion of strong dipole correlations and domain structure. The dipole density correlations behave as predicted by the normal dielectric theory and their spectra do not show the low-frequency feature seen in the HRS. In order to examine the characteristics of the spectra which would be seen in a ferroelectric domain, the acetontrile model was transmuted to more closely resemble a Stockmayer-type fluid with the same dipole density and a ferroelectric phase was observed. In this phase the dielectricspectra show (i) a high-frequency spectral feature due to librational motion of the molecules within a domain, and (ii) slowly-relaxing longitudinal and transverse polar modes, again at variance from the experimental HRS characteristics.