Volume 123, Issue 21, 01 December 2005
Index of content:
- Theoretical Methods and Algorithms
123(2005); http://dx.doi.org/10.1063/1.2121547View Description Hide Description
The use of the spin-dependent pseudopotentials has been shown to markedly enhance the transferability of the commonly used spin-neutral pseudopotential method for the study of the structural and magnetic properties of transition-metal-containing materials. Unfortunately, because the method was based on the rather expensive norm-conserving pseudopotential formalism, the method was limited to the study of fairly small systems. Here we present an extension of the spin-dependent pseudopotential method for the far more computationally advantageous ultrasoft formalism and show that it is very easy to add such a feature to any preexisting computer code. We benchmark our new method by comparing to previously published results and then apply it to the study of several relevant test cases: bulk Ni, Fe, and Co, as well as a Pd atomic wire.
123(2005); http://dx.doi.org/10.1063/1.2135289View Description Hide Description
The Piris natural orbital functional (PNOF) based on a new approach for the two-electron cumulant has been used to predict adiabatic ionization potentials, equilibrium bond distances, and harmonic vibrational frequencies of 18 diatomic molecules. Vertical ionization potentials have been calculated for the same set of diatomic molecules and another set of 20 polyatomic molecules using energy-difference methods as well as the extended Koopman theorem. The PNOF properties compare favorably with the coupled-cluster-doubles results. The calculated PNOF values are in good agreement with the corresponding experimental data, considering the basis sets used .
Intermolecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations123(2005); http://dx.doi.org/10.1063/1.2135288View Description Hide Description
Recently, three of us have proposed a method [Phys. Rev. Lett.91, 33201 (2003)] for an accurate calculation of the dispersion energy utilizing frequency-dependent density susceptibilities of monomers obtained from time-dependent density-functional theory(DFT). In the present paper, we report numerical calculations for the helium, neon, water, and carbon dioxide dimers and show that for a wide range of intermonomer separations, including the van der Waals and short-range repulsion regions, the method provides dispersion energies with accuracies comparable to those that can be achieved using the current most sophisticated wave-function methods. If the dispersion energy is combined with (i) the electrostatic and first-order exchange interactionenergies as defined in symmetry-adapted perturbation theory (SAPT) but computed using monomer Kohn-Sham (KS) determinants, and (ii) the induction energy computed using the coupled KS static response theory, (iii) the exchange-induction and exchange-dispersion energies computed using KS orbitals and orbital energies, the resulting method, denoted by SAPT(DFT), produces very accurate total interaction potentials. For the helium dimer, the only system with nearly exact benchmark values, SAPT(DFT) reproduces the interactionenergy to within about 2% at the minimum and to a similar accuracy for all other distances ranging from the strongly repulsive to the asymptotic region. For the remaining systems investigated by us, the quality of the SAPT(DFT) interactionenergies is so high that these energies may actually be more accurate than the best available results obtained with wave-function techniques. At the same time, SAPT(DFT) is much more computationally efficient than any method previously used for calculating the dispersion and other interactionenergy components at this level of accuracy.
123(2005); http://dx.doi.org/10.1063/1.2133732View Description Hide Description
We generalize antisymmetric geminal products to more than just one generating geminal using an Aufbau Ansatz similar to the Hartree-Fock theory. Investigation of , Be, , LiH, , and shows a very high recovery of electron-correlation energy using this Aufbau Ansatz. The method is inherently multideterminantal and insensitive to symmetry problems. The computational complexity is en par with configuration interaction of singles and doubles.
123(2005); http://dx.doi.org/10.1063/1.2121589View Description Hide Description
The possibilities for the approximate treatment of higher excitations in coupled-cluster (CC) theory are discussed. Potential routes for the generalization of corresponding approximations to lower-level CC methods are analyzed for higher excitations. A general string-based algorithm is presented for the evaluation of the special contractions appearing in the equations specific to those approximate CC models. It is demonstrated that several iterative and noniterative approximations to higher excitations can be efficiently implemented with the aid of our algorithm and that the coding effort is mostly reduced to the generation of the corresponding formulas. The performance of the proposed and implemented methods for total energies is assessed with special regard to quadruple and pentuple excitations. The applicability of our approach is illustrated by benchmark calculations for the butadiene molecule. Our results demonstrate that the proposed algorithm enables us to consider the effect of quadruple excitations for molecular systems consisting of up to 10–12 atoms.
An equation-free probabilistic steady-state approximation: Dynamic application to the stochastic simulation of biochemical reaction networks123(2005); http://dx.doi.org/10.1063/1.2131050View Description Hide Description
Stochastic chemical kinetics more accurately describes the dynamics of “small” chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitraryreaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.
Combining fixed- and moving-grid methods to study direct dissociation processes involving nonadiabatic transitions123(2005); http://dx.doi.org/10.1063/1.2114807View Description Hide Description
We present a novel quantum-dynamics approach suitable for computing direct dissociation processes, including electronic transitions. This approach combines quantum trajectories in the Lagrangian reference frame with standard fixed-grid wave packets in order to overcome the limitations and difficulties of both techniques. As a model application, we consider the ultrafast photodissociation of excited by a femtosecond extreme UV laser pulse.
Relativistic effects on the nuclear magnetic shieldings of rare-gas atoms and halogen in hydrogen halides within relativistic polarization propagator theory123(2005); http://dx.doi.org/10.1063/1.2133729View Description Hide Description
In this work an analysis of the electronic origin of relativistic effects on the isotropic dia- and paramagnetic contributions to the nuclear magnetic shielding for noble gases and heavy atoms of hydrogen halides is presented. All results were obtained within the 4-component polarization propagator formalism at different level of approach [random-phase approximation (RPA) and pure zeroth-order approximation (PZOA)], by using a local version of the DIRAC code. From the fact that calculations of diamagnetic contributions to within RPA and PZOA approaches for and rare-gas atoms are quite close each to other and the finding that the diamagnetic part of the principal propagator at the PZOA level can be developed as a series , it was found that there is a branch of negative-energy “virtual” excitations that contribute with more than 98% of the total diamagnetic value even for the heavier elements, namely, Xe, Rn, I, and At. It contains virtual negative-energy molecular-orbital states with energies between and . This fact can explain the excellent performance of the linear response elimination of small component (LR-ESC) scheme for elements up to the fifth row in the Periodic Table. An analysis of the convergency of and its physical implications is given. It is also shown that the total contribution to relativistic effects of the innermost orbital is by far the largest. For the paramagnetic contributions results at the RPA and PZOA approximations are similar only for rare-gas atoms. On the other hand, if the mass-correction contributions to are expressed in terms of atomic orbitals, a different pattern is found for orbital contributions compared with all other -type orbitals when the whole set of rare-gas atoms is considered.
Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation123(2005); http://dx.doi.org/10.1063/1.2132282View Description Hide Description
The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostaticfree energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, , and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
123(2005); http://dx.doi.org/10.1063/1.2104327View Description Hide Description
The dynamic processes of core-hole excitation in gas-phase molecule have been studied at both Hartree-Fock and hybrid density-functional theory levels. The vibrational structure is analyzed for fully optimized core-excited states. Frank-Condon factors are obtained using the linear coupling model for various potential surfaces. It is found that the vibrational profile of the absorption can be largely described by a summation of two vibrational progressions: a structure-rich profile of stretching mode and a large envelope of congestioned vibrational levels related to the strong (–C–CN) terminal bending bond. Excellent agreement between theoretical and experimental spectra is obtained.
123(2005); http://dx.doi.org/10.1063/1.2128675View Description Hide Description
A recently proposed local Fukui function is used to predict the binding site of atomic hydrogen on siliconclusters. To validate the predictions, an extensive search for the more stable clusters has been done using a modified genetic algorithm. In all cases, the isomer predicted by the Fukui function is found by the search, but it is not always the most stable one. It is discussed that in the cases where the geometricalstructure of the bare siliconcluster suffers a considerable change due to the addition of one hydrogen atom, the situation is more complicated and the relaxation effects should be considered.
123(2005); http://dx.doi.org/10.1063/1.2134703View Description Hide Description
Line oscillator strengths in 16 electric dipole-allowed bands of in the region have been measured at an instrumental resolution of . The transitions terminate on vibrational levels of the , , and Rydberg states and of the and valence states. The dependences of band values derived from the experimental line values are reported as polynomials in and are extrapolated to in order to facilitate comparisons with results of coupled-Schrödinger-equation calculations that do not take into account rotational interactions. Most bands in this study reveal a marked dependence of the values and/or display anomalous -, - and -branch intensity patterns. These patterns should help inform future spectroscopic models that incorporate rotational effects, and these are critical for the construction of realistic atmospheric radiative transfer models. Linewidthmeasurements are reported for four bands. Information provided by the dependences of the experimental linewidths should be of use in the development of a more complete understanding of the predissociation mechanisms in .
Rotational effects in the band oscillator strengths and predissociation linewidths for the lowest transitions of123(2005); http://dx.doi.org/10.1063/1.2134704View Description Hide Description
A coupled-channel Schrödinger equation (CSE) model of photodissociation, which includes the effects of all interactions between the , , and and the and states, is employed to study the effects of rotation on the lowest- band oscillator strengths and predissociationlinewidths. Significant rotational dependences are found which are in excellent agreement with recent experimental results, where comparisons are possible. New extreme-ultraviolet (EUV)photoabsorption spectra of the key transition of are also presented and analyzed, revealing a predissociationlinewidth peaking near . This behavior can be reproduced only if the triplet structure of the state is included explicitly in the CSE-model calculations, with a spin-orbit constant for the diffuse level which accidentally predissociates . The complex rotational behavior of the and other bands may be an important component in the modeling of EUV transmission through nitrogen-rich planetary atmospheres.
123(2005); http://dx.doi.org/10.1063/1.2126972View Description Hide Description
We present an electronic structure and dynamics study of the reaction. CCSD(T)/aug-cc-pVDZ geometry optimizations, harmonic-frequency, and energy calculations indicate that the potential-energysurface is remarkably isotropic near the transition state. In addition, while the saddle-point angle is using MP2 methods, CCSD(T) geometry optimizations predict a bent transition state, with a angle. We use these high-quality ab initio data to reparametrize the parameter-model 3 (PM3) semiempirical Hamiltonian so that calculations with the improved Hamiltonian and employing restricted open-shell wave functions agree with the higher accuracy data. Using this specific-reaction-parameter PM3 semiempirical Hamiltonian (SRP-PM3), we investigate the reactiondynamics by propagating quasiclassical trajectories. The results of our calculations using the SRP-PM3 Hamiltonian are compared with experiments and with the estimates of two recently reported potential-energysurfaces. The trajectory calculations using the SRP-PM3 Hamiltonian reproduce quantitatively the measured vibrational distributions. The calculations also agree with the experimental rotational distributions and capture the essential features of the excitation function. The results of the SRP semiempirical Hamiltonian developed here clearly improve over those using the two prior potential-energysurfaces and suggest that reparametrization of semiempirical Hamiltonians is a promising strategy to develop accurate potential-energysurfaces for reactiondynamics studies of polyatomic systems.
Electron-spin multiplicities and molecular structures of neutral and ionic scandium-benzene complexes123(2005); http://dx.doi.org/10.1063/1.2131867View Description Hide Description
Scandium-benzene complexes, are produced by interactions between the laser-vaporized scandium atoms and benzene vapor in pulsed molecular beams, and identified by photoionization time-of-flight mass spectrometry and photoionization efficiency spectroscopy. The electron-spin multiplicities and geometries of these complexes and their ions are determined by combining pulsed field-ionization zero electron kinetic-energy spectroscopy and density-functional theory calculations. For scandium-monobenzene, a short-range quartet ground state is determined for the neutral complex, and a low-energy triplet state is probed for the ion. For the dibenzene complex, the neutral ground state is a doublet, and two low-energy ion states are singlet and triplet. The quartet and triplet states of scandium-monobenzene and the triplet state of scandium-dibenzene possess sixfold symmetry, whereas the doublet and singlet of the dibenzene complex have twofold symmetry. Moreover, ionization energies and metal-ring stretching wavenumbers are measured for both complexes.
123(2005); http://dx.doi.org/10.1063/1.2133727View Description Hide Description
The four most stable conformers of glycine have been investigated using a variety of quantum-mechanical methods based on Hartree-Fock theory, density-functional theory (B3LYP and statistical average of orbital potential), and electron propagation (OVGF) treatments. Information obtained from these models were analyzed in coordinate and momentum spaces using dual space analysis to provide insight based on orbitals into the bonding mechanisms of glycine conformers, which are generated by rotation of C–O(H) (II), C–C (III), and C–N (IV) bonds from the global minimum structure (I). Wave functions generated from the B3LYP/TZVP model revealed that each rotation produced a unique set of fingerprint orbitals that correspond to a specific group of outer valence orbitals, generally of symmetry. Orbitals , , , and are identified as the fingerprint orbitals for the C–O(H) (II) rotation, whereas fingerprint orbitals for the C–C (III) bond rotation are located as [highest occupied molecular orbital (HOMO)], [next highest molecular occupied molecular orbital (NHOMO)], , and orbitals. Fingerprint orbitals for IV generated by the combined rotations around the C–C, C–O(H), and C–N bonds are found as , , , , and , as well as in orbitals and . Orbital is identified as the fingerprint orbital for all three conformational processes, as it is the only orbital in the outer valence region which is significantly affected by the conformational processes regardless rotation of which bond. Binding energies, molecular geometries, and other molecular properties such as dipole moments calculated based on the specified treatments agree well with available experimental measurements and with previous theoretical calculation.
123(2005); http://dx.doi.org/10.1063/1.2135291View Description Hide Description
The temporal behavior of the photoinduced ion-pair formation process in the ( for and for ) cluster system has been studied via the coupling between the Rydberg and valence states. Comparison of the time constants obtained to those measured in previous experiments for the analogous process in -water clusters, along with a detailed analysis of the signal intensity as a function of laser-pulse power, provides new insight into and confirmation of the previously proposed ion-pair formation mechanism.
123(2005); http://dx.doi.org/10.1063/1.2107648View Description Hide Description
The potassium resonance line centered around 770 nm is a major contributor to the optical extinction in the atmospheres of certain classes of brown dwarfs and extrasolar giant planets. The resonance line is significantly broadened by collisions with He and , and an accurate calculation of the line profile is needed for astrophysical models of these objects. As a first step, we report an accurate ab initio study of the and potential-energy curves correlating to the K and atomic energy levels, together with the dipole moments governing the transitions between these potential-energy curves. The molecular calculations have been carried out using a multireference configuration-interaction method, with the molecular orbitals expanded in a large Gaussian basis set. The transitiondipole moments show significant variation with the molecular geometry. Calculations for the system have been carried out for a range of orientations and internuclear separations, so that the effect of rotation and vibration may be explicitly included in future calculations of the pressure-broadened line profiles.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
123(2005); http://dx.doi.org/10.1063/1.2128706View Description Hide Description
Anomalous x-ray diffraction experiments were carried out on concentrated aqueous solutions of sodium iodide and cesium iodide . Data were gathered at two energies below the absorption edges of the and ions in order to avoid contributions from fluorescence. The statistics and quality of the raw data were improved by the use of a focusing analyzer crystal. Differences were taken between the data sets and used to calculate the hydration structures of and . The structures found are more complex than anticipated for such large ions with relatively low charge densities and show evidence of ion-pair formation in both solutions. A two-Gaussian fit to the data gives information about the and correlations. The central position of the Gaussian representing the was fixed at , that is, the maximum of this contribution. The other parameters were allowed to vary freely, giving a distance of and coordination numbers of 7.9 and 2.7, respectively, for the and correlations. The results on the structure of in the NaI aqueous solution were also fitted to a model based on Gaussians; this gives correlations for and at and with respective coordination numbers of 8.8 and 1.6. The structure of in the CsI solution shows overlapping contributions due to , , and . The best Gaussian fit gives two peaks centered at and and shows that the latter two correlations are unresolved. The hydration structures are compared with those of other alkali and halide ions. The results are also found to be in good agreement with those obtained from standard x-ray diffraction and computer simulation.
Pressure tuning of the Fermi resonance in liquid methanol: Implications for the analysis of high-pressure vibrational spectroscopy experiments123(2005); http://dx.doi.org/10.1063/1.2128671View Description Hide Description
It has been argued that pressure tuning allows for unambiguous assignment of the nonperturbed bands involved in the Fermi coupling of molecular systems in the condensed phase. Here we study the pressure evolution of the Fermi resonance occurring in liquid methanol between the symmetric methyl-stretch fundamental and the methyl-bending overtones. Our analysis is based on Raman experiments in both stretching and bending fundamental regions, which are used to evaluate the effect of pressure on accidental degeneracies occurring in the vibrational spectra of liquid methanol. We emphasize that the difference in frequency of the Fermi doublet constitutes the governing quantity to determine the condition at which the exact degeneracy of the unperturbed modes occurs. Analysis based on the intensity ratio of the Fermi doublet must be disregarded. We confirm the necessity of measuring the full vibrational spectrum under pressure in order to obtain the Fermi coupling parameters unambiguously and to give a correct assignment of the bands involved in the resonance phenomenon. We also analyze the possible occurrence of several simultaneous resonance effects using a multilevel perturbation model. This model provides an appropriate description of the frequencies observed in the experiments over the whole pressure range if we consider that the main resonance occurs between and , in contrast to previous assignments. Our global analysis leads to some general rules concerning measurement and interpretation of high-pressure vibrational spectroscopy experiments.