Volume 115, Issue 9, 01 September 2001
Index of content:
- Theoretical Methods and Algorithms
115(2001); http://dx.doi.org/10.1063/1.1389291View Description Hide Description
A new low-order scaling algorithm for second-order Møller–Plesset perturbation theory (MP2) is described. The method employs localized orbitals. However, in contrast to other local MP2 schemes reported in the literature, all atomic orbitals with significant contribution to the correlation energy for a given pair or orbitals are retained. Our approach introduces no significant approximation if all significant pairs are taken into account. However, the method is intended for the description of correlation between spatially close (“strong”) pairs; for distant pairs, more economical alternative methods can be used. The algorithm, including a new implementation of the simultaneous two-index integral transformation scheme, is described in detail. Test calculations demonstrate asymptotic linear scaling for large systems. Strong-pair MP2 calculations with more that 1800 contracted basis functions performed on a single PC are reported. As a consequence of its lower scaling, the calculation of the MP2 energy is less expensive than the calculations of the Hartree–Fock energy for large systems. This has been demonstrated for strong pair correlation but is expected to hold also for full MP2 calculations.
115(2001); http://dx.doi.org/10.1063/1.1390511View Description Hide Description
For many-electron atoms, the generalized electron-pair density function represents the probability density function for the magnitude of two-electron vector to be q, where a and b are real-valued parameters. It is pointed out that the second moments associated with are related with several physical properties such as the diamagnetic susceptibility the form factor the incoherent scattering function the minus first moment of the oscillator strength density, and the dipole polarizability The corresponding moments in momentum space are connected with the mass polarization correction the first moment of the oscillator strength density, and the nuclear momentum squared as well as the electronic kinetic energy The average excitation energy is also estimated from and
Nuclear magnetic resonance radiation damping in inhomogeneous radio frequency fields: The toroid cavity detector115(2001); http://dx.doi.org/10.1063/1.1386655View Description Hide Description
A theory is presented for radiation damping (RD) in the toroid cavity nuclear magnetic resonancedetector, a cylindrically symmetric inhomogeneous-rf field detector in which the magnitude of is inversely proportional to the distance from the cylindrical symmetry axis. The equations of motion of the magnetization components are obtained and discussed. Numerical simulations of conventional- and composite-pulse experiments are presented, along with a discussion of the effects of RD on the evolution of magnetization. Preliminary simulations of RD in the presence of inhomogeneous line broadening are also presented. The signature effect of radiation damping in the TCD is the winding or unwinding of magnetization gratings that has recently been observed by other researchers. The observed magnitude of the effect is linked to the effective filling factor, which currently appears to be limited by the stray inductance of the detection circuit. The results are of interest in connection with recent findings regarding the interaction of RD with the dipolar demagnetizing field.
115(2001); http://dx.doi.org/10.1063/1.1389854View Description Hide Description
We develop an efficient multiple time step (MTS) force splitting scheme for biological applications in the AMBER program in the context of the particle-mesh Ewald (PME) algorithm. Our method applies a symmetric Trotter factorization of the Liouville operator based on the position-Verlet scheme to Newtonian and Langevin dynamics. Following a brief review of the MTS and PME algorithms, we discuss performance speedup and the force balancing involved to maximize accuracy, maintain long-time stability, and accelerate computational times. Compared to prior MTS efforts in the context of the AMBER program, advances are possible by optimizing PME parameters for MTS applications and by using the position-Verlet, rather than velocity-Verlet, scheme for the inner loop. Moreover, ideas from the Langevin/MTS algorithm LN are applied to Newtonian formulations here. The algorithm’s performance is optimized and tested on water, solvated DNA, and solvated protein systems. We find CPU speedup ratios of over 3 for Newtonian formulations when compared to a 1 fs single-step Verlet algorithm using outer time steps of 6 fs in a three-class splitting scheme; accurate conservation of energies is demonstrated over simulations of length several hundred ps. With modest Langevin forces, we obtain stable trajectories for outer time steps up to 12 fs and corresponding speedup ratios approaching 5. We end by suggesting that modified Ewald formulations, using tailored alternatives to the Gaussian screening functions for the Coulombic terms, may allow larger time steps and thus further speedups for both Newtonian and Langevin protocols; such developments are reported separately.
Special stability advantages of position-Verlet over velocity-Verlet in multiple-time step integration115(2001); http://dx.doi.org/10.1063/1.1389855View Description Hide Description
We present an analysis for a simple two-component harmonic oscillator that compares the use of position-Verlet to velocity-Verlet for multiple-time step integration. The numerical stability analysis based on the impulse-Verlet splitting shows that position-Verlet has enhanced stability, in terms of the largest allowable time step, for cases where an ample separation of time scales exists. Numerical investigations confirm the advantages of the position-Verlet scheme when used for the fastest time scales of the system. Applications to a biomolecule, a solvated protein, for both Newtonian and Langevin dynamics echo these trends over large outer time-step regimes.
Oxidative addition of Pd to C–H, C–C and C–Cl bonds: Importance of relativistic effects in DFT calculations115(2001); http://dx.doi.org/10.1063/1.1388040View Description Hide Description
To assess the importance of relativistic effects for the quantum chemical description of oxidative addition reactions of palladium to C–H, C–C and C–Cl bonds, we have carried out a systematic study of the corresponding reactions of and with using nonrelativistic (NR), quasirelativistic (QR), and zeroth-order regularly approximated (ZORA) relativistic density functional theory(DFT) at the BP86/TZ(2)P level. Relativistic effects are important according to both QR and ZORA, the former yielding similar but somewhat more pronounced effects than the latter, more reliable method: activation barriers are reduced by 6–14 kcal/mol and reactionenthalpies become 15–20 kcal/mol more exothermic if one goes from NR to ZORA. This yields, for example, 298 K activation enthalpies of −5.0 (C–H), 9.6 (C–C) and −6.0 kcal/mol (C–Cl) relative to the separate reactants at ZORA-BP86/TZ(2)P. In accordance with gas-phase experiments on reactions of Pd with alkanes, we find reaction profiles with pronounced potential wells for reactant complexes (collisionally stabilized and observed in experiments for alkanes larger than at −11.4 −11.6 and relative to separated reactants [ZORA-BP86/TZ(2)P]. Furthermore, we analyze the height of and the relativistic effects on the activation energies in terms of the activation strain of and the transition-state interaction between the reactants in the activated complex, with
Evaluation of the computational methods for electron-impact total ionization cross sections: Fluoromethanes as benchmarks115(2001); http://dx.doi.org/10.1063/1.1388041View Description Hide Description
The experimental electron-impact total ionization cross sections (TICSs, ICSs) of and fluoromethanes reported so far and a new set of data obtained with a linear double focusing time-of-flightmass spectrometer have been compared with the ab initio and (semi)empirical based ICS available methods. TICSs computational methods include: two approximations of the binary-encounter dipole (BED) referred to hereafter as Kim (Kim-BEB) and Khare (Khare-BEB) methods, the Deutsch and Märk (DM) formalism, also requiring atomic and molecular ab initioinformation, the modified additivity rule (MAR), and the Harland and Vallance (HV) methods, both based on semiempirical or empirical correlations. The molecular ab initioinformation required by the Kim, Khare, and DM methods has been computed at a variety of quantum chemistry levels, with and without electron correlation and a comprehensive series of basis sets. The general conclusions are summarized as follows: the Kim method yields TICS in excellent agreement with the experimental method; the Khare method provides TICS very close to that of Kim at low electron-impact energies (<100 eV), but their Mott and Bethe contributions are noticeably different; in the Kim and Khare approximations the electron correlation methods improve the fittings to the experimental profiles in contrast with the large basis sets, that leads to poorer results; the DM formalism yields TICS profiles with shapes similar to the experimental and the BEB methods, but consistently lower and with the profiles maxima shifted towards lower incident electron energies; the MAR method supplies very good ICS profiles, between those of BEB and DM methods; finally, the empirical HV method provides rather poor fittings concomitant with the simplicity and the few empirical parameters used.
115(2001); http://dx.doi.org/10.1063/1.1390513View Description Hide Description
As a test of the time-dependent density-functional theory (TDDFT) for electron–vibration coupling, we apply it to the optical properties of the π–π* transitions in benzene. Quantities calculated are the envelopes of the Franck–Condon factors of the electronic transitions and the oscillator strengths of symmetry-forbidden transitions. The strengths of the π–π* transitions span three orders of magnitude and are reproduced to better than 35% by the theory. Comparable agreement is found for the Franck–Condon widths. We conclude that rather detailed information about the effects of the electron–vibrational coupling can be obtained with the TDDFT.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
115(2001); http://dx.doi.org/10.1063/1.1389308View Description Hide Description
Hydrogen-bonded complexes of the photoacid 1-naphthol with and were investigated by resonanttwo-photonionization,spectralhole burning, and fluorescence spectroscopies. Although the intermolecular vibrations are weak in both absorption and emission, with typical Franck–Condon factors relative to the electronic origin, all six intermolecular modes were identified, namely the hydrogen bond stretch σ, the ammonia torsion τ, two in-plane wags and and two out-of-plane rocking motions and Several ammonia torsional excitations were observed, with spacings in good agreement with the and state effective torsional barriers derived by Humphrey and Pratt [J. Chem. Phys. 104, 8332 (1996)]. The and vibrational excitations exhibit large (2–8 torsional splittings, which indicate strong anharmonic coupling with the ammonia internal rotation. The observed Franck–Condon factors of the intermolecular stretching vibration imply a contraction of the hydrogen bond by Å upon excitation.
Are lithium hydride clusters purely ionic? Study using model potentials and density-functional theory115(2001); http://dx.doi.org/10.1063/1.1389474View Description Hide Description
A study of the and clusters with n up to 7 and using both density-functional theory(DFT) and a model potential is presented. The combined use of these two methods has shown great efficiency. It has enabled us to perform exhaustive explorations of the potential energy surfaces and to study a large number of isomers. Our results show that the structures of the Li–H clusters are very close to typical ionic structures and that the Li–H bond is almost totally ionic. Moreover, the stability of the small clusters is not directly related to the number of ionic bonds formed, and families of structures exist throughout the sizes studied. Our study has also shown that a very simple ionic model potential yields good starting structures and not unreasonable energies. This simple model, however, exhibits two problems: The number of minima in the potential is too large compared to DFT, and its accuracy is by far insufficient to enable one to interpret experimental results. Finally, a good agreement is observed between B3LYP results and the available experimental data.
Computational formulas for symmetry-forbidden vibronic spectra and their application to transition in neat acetone115(2001); http://dx.doi.org/10.1063/1.1386918View Description Hide Description
In this study theoretical expressions are derived to investigate the non-Condon effect for symmetry-forbidden optical transition using displaced–distorted harmonic potential energy surfaces. These expressions can efficiently cope with multipromoting modes and multielectronic states involved in the non-Condon effect at a finite temperature. Ab initio and molecular dynamics calculation results can be directly invoked into the formulas. Based on the proposed formulas, the temperature dependence of the interference effects of multipromoting modes on the non-Condon optical linear spectra is investigated. To demonstrate the computational formulas, the optical absorption and dispersionfluorescence spectra for the forbidden transition of neat acetone, are also studied. Simulation results indicate that the vibrational frequency of torsion mode of acetone plays an important role in the optical spectra. Moreover, the electronic energy gap (adiabatic transition), the Stokes shift caused by environmental interaction, and the average Huang–Rhys factor for intermolecular modes in neat acetone are obtained as 29 900 5400 and 0.607, respectively.
High-resolution energy-selected study of the reaction Accurate thermochemistry for the (X=Br, I) system115(2001); http://dx.doi.org/10.1063/1.1391268View Description Hide Description
Using the high-resolution pulsed field ionization-photoelectron (PFI-PE) and PFI-PE-photoion coincidence (PFI-PEPICO) techniques, we have examined the formation of methyl cation from the dissociation of energy-selected (X=Br and I) near their dissociation thresholds. The breakdown diagrams for thus obtained yield values of 12.834±0.002 eV and 12.269±0.003 eV for the 0 K dissociative threshold or appearance energy (AE) for from and respectively. Similar to the observation in PFI-PE studies of and the PFI-PE spectrum for exhibits a step at the 0 K AE for indicating that the dissociation of excited in high-n (⩾100) Rydberg states at energies slightly above the dissociation threshold occurs in a time scale of The observed step is a confirmation of the 0 K from determined in the PFI-PEPICO study. The adiabatic ionization energies (IEs) for the spin–orbit states were determined by PFI-PE measurements to be 10.5427±0.0010 and 10.8615±0.0010 eV, respectively, yielding the spin–orbit coupling constant to be 2571±4 cm−1. The values from and and the value obtained here, when combined with the known IE of (9.8380±0.0004 eV) and (9.5381±0.0001 eV), have allowed accurate determination of the 0 K bond dissociation energies for (2.996±0.002 eV), (2.291±0.002 eV), (2.431±0.003 eV), and (2.731±0.003 eV). Using the from and together with the known 0 K heats of formation for Br (117.93±0.13 kJ/mol), I (107.16±0.04 kJ/mol), and (1099.05±0.33 kJ/mol), we have obtained more precise values for (−21.30±0.42 kJ/mol) and (22.43±0.50 kJ/mol). This experiment demonstrated that highly reliable values for a range of molecules with error limits comparable to those for some of the most precisely measured values, such as can be obtained by PFI-PE and PFI-PEPICO measurements.
115(2001); http://dx.doi.org/10.1063/1.1385152View Description Hide Description
We recently developed a new method to extract a many-body phase-space dividing surface, across which the transmission coefficient for the classical reaction path is unity. The example of isomerization of a 6-atom Lennard-Jones cluster showed that the action associated with the reaction coordinate is an approximate invariant of motion through the saddle regions, even at moderately high energies, at which most or all the other modes are chaotic [J. Chem. Phys. 105, 10838 (1999); Phys. Chem. Chem. Phys. 1, 1387 (1999)]. In the present article, we propose a new algorithm to analyze local invariances about the transition state of N-particle Hamiltonian systems. The approximate invariants of motion associated with a reaction coordinate in phase space densely distribute in the sea of chaotic modes in the region of the transition state. Using projections of distributions in only two principal coordinates, one can grasp and visualize the stable and unstable invariant manifolds to and from a hyperbolic point of a many-body nonlinear system, like those of the one-dimensional, integrable pendulum. This, in turn, reveals a new type of phase space bottleneck in the region of a transition state that emerges as the total energy increases, which may trap a reacting system in that region.
115(2001); http://dx.doi.org/10.1063/1.1388555View Description Hide Description
Laser-induced fluorescencespectra of the system of recorded on a Fourier transforminterferometer, have allowed 47 vibrational levels of the electronic ground state to be observed. The ground state energies have been fitted to a Dunham polynomial expansion, and also directly to a numerical potential curve. Both fits reproduce the data to within the experimental accuracy of measurement (0.005 cm−1).
115(2001); http://dx.doi.org/10.1063/1.1389838View Description Hide Description
Two-reagent reactions of and with hydrogen/deuterium and ammonia are studied to probe adsorbate-induced cluster structural changes. H/D and bind to the clusters noncompetitively, i.e., to different sites, so simultaneous saturation by the two reagents can be achieved. It is found that H/D adsorption causes a change in from the double icosahedral structure to a face-centered cubic (fcc) or hexagonal close-packed (hcp) one, but that subsequent saturation with converts the cluster back to the double icosahedron. No such structural changes are seen for the triple icosahedral The results for are interpreted in terms of the electron withdrawing or donating character of the ligands and the consequent effect on the extent of d-orbital bonding in the cluster. Possible configurations of the H/D atom binding sites on the icosahedral and clusters and on the fcc/hcp cluster are presented.
115(2001); http://dx.doi.org/10.1063/1.1391264View Description Hide Description
The collision-induced electronic energy transfer that occurs when in the ion-pair electronic state collides with ground electronic state has been investigated. We prepare in single rotational levels in of the E state using two-color double resonance laser excitation. The resulting emission spectrum shows that the nearby electronic state is populated. The cross section for collision-induced energy transfer is found to be A range of D state vibrational levels are populated, consistent with a model in which overlap between the initial and final vibrational wave functions is important, but modulated by propensities for small vibrational energy gaps and those energy gaps that are closely matched to the energy separation in the collision partner.
Direct and indirect methods for studying the energetics and dynamics of the Auger Doppler effect in femtosecond ultra-fast dissociation115(2001); http://dx.doi.org/10.1063/1.1380690View Description Hide Description
Molecules may fragment within a few femtoseconds after core-excitation, a phenomenon known as ultra-fast dissociation. With the aim of providing an understanding of the fundamental phenomenology of the Auger Doppler effect, two methods are presented to study the energetics and dynamics, i.e., the kinetic energy release and the fragment velocities in such processes. The first, direct, method is based on the shifts in kinetic energy of the Auger electrons due to the velocity acquired by the fragment in the ultra-fast dissociation process, i.e., the Auger Doppler effect. The second, indirect, method is based on total-energy arguments in a Born–Haber cycle for excitation, dissociation, and ionization. A combination of the two methods is shown to be able to reproduce experimental spectra well. Based on this, predictions are made for other, yet unstudied, molecular systems. It is also shown that the Auger Doppler effect is not static, but will exhibit dynamicphoton energy dependence. The complete energetics of the three-body dissociation of a molecule into an electron, an ion, and a neutral fragment on a time-scale of a few femtoseconds can thus be accounted for.
Measuring the predissociation and rotational autoionization of the vibrationless Rydberg series in ammonia115(2001); http://dx.doi.org/10.1063/1.1389303View Description Hide Description
A novel method is presented to retrieve the average predissociation rate and the average rotational autoionization rate of a molecule by measuring the field ionizationspectrum only. Both an intuitive picture and a quantitative description are derived for the competition between the three decay channels, field ionization, rotational autoionization, and predissociation.Field ionization spectra of various rotational states of ammonia are presented and fitted. From the fits we found that the average predissociation rate of the Rydberg series converging to the vibrationless ionic state is about equal to the average rotational autoionization rate to the Rydberg series converging to the vibrationless ionic state, namely
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
115(2001); http://dx.doi.org/10.1063/1.1391477View Description Hide Description
We explore an approach to determine the entropy of a liquid in nonequilibrium steady state. Soft-sphere particles interacting with an inverse twelfth-power potential are simulated under the impact of a steady temperature gradient using a realistic algorithm. The thermodynamic relationship between the internal energy and the entropy is integrated in terms of the temperature for identical temperature gradients. Exploiting the scaling property of the interaction, the actual calculations are carried out at different densities starting from dilute systems. The energy of the middle layer is compared to that of an equilibrium system with identical temperature and density. The very small nonequilibrium increase of the energy is connected to the field-induced change in the local structure.
115(2001); http://dx.doi.org/10.1063/1.1391475View Description Hide Description
In this paper, solvation structure and thermodynamic properties of rare gas and alkali impurities in liquid helium-4 have been studied theoretically. A generalized Ornstein–Zernike integral equation for pure quantum fluids [J. Chem. Phys. 114, 7497 (2001)] was extended to the quantum solutions at infinite dilution. Self-correlation function of the solute atom which appears in the integral equation was determined self-consistently with the solvent density fluctuation. Numerical calculations have been performed for the helium-4solutions at 4 K, with Boltzmann statistics being assumed. It was found that all the rare gas species investigated in this study have negative partial molar volumes, owing to the well-defined solvation structure around the impurities. In contrast to this, the alkali atoms have large positive partial molar volumes, primarily coming from the excluded volume contribution. Further, while the rare gas atoms have negative excess chemical potentials, the alkali atoms have large positive values. The former may be dominated by the negative interaction energy between the impurity and surrounding solvent atoms, and the latter by the work done by the volume of the solute to exclude the solvent atoms.