Volume 127, Issue 7, 21 August 2007
Index of content:
- Theoretical Methods and Algorithms
Gauge-origin independent calculation of magnetizabilities and rotational tensors at the coupled-cluster level127(2007); http://dx.doi.org/10.1063/1.2755664View Description Hide Description
An implementation of the gauge-origin independent calculation of magnetizabilities and rotational tensors at the coupled-cluster (CC) level is presented. The properties of interest are obtained as second derivatives of the energy with respect to the external magnetic field (in the case of the magnetizability) or with respect to magnetic field and rotational angular momentum (in the case of the rotational tensor), while gauge-origin independence and fast basis-set convergence are ensured by using gauge-including atomic orbitals (London atomic orbitals) as well as their extension to treat rotational perturbations (rotational London atomic orbitals). The implementation within our existing CC analytic second-derivative code is described, focusing on the required modifications concerning integral evaluation and treatment of the unperturbed and perturbed two-particle density matrices. An extensive set of test calculations for LiH and BH (up to the full configuration-interaction limit), for a series of simple hydrides (HF, , , and ) as well as the more challenging molecules CO, , and [employing the CC singles and doubles (CCSD) and the CCSD approximation augmented by a perturbative treatment of triple excitations] demonstrates the importance of electron correlation for high-accuracy predictions of magnetizabilities and rotational tensors.
Automatically generated Coulomb fitting basis sets: Design and accuracy for systems containing H to Kr127(2007); http://dx.doi.org/10.1063/1.2752807View Description Hide Description
For intermediate sized chemical systems the use of an auxiliary basis set (ABS) to fit the charge density provides a useful means of accelerating the performance of various quantum chemical methods. As a consequence much effort has been devoted to the design of various ABSs. This paper explores a fundamentally new approach where the ABS is created dynamically based on the specific orbital basis set (OBS) being used. The new approach includes a parameter that is used to coalesce candidate fitting functions together but which can also be used to provide some coarse grain control over the number of functions in the ABS. The accuracy of the new automatically generated ABS (auto-ABS) is systemically studied for a variety of small systems containing the elements H–Kr. Errors in the Coulomb energy computed using auto-ABS and with a variety of OBSs are shown to be small compared to errors in the Hartree-Fock energy due to incompleteness in the OBS. In contrast to fixed size ABSs, the use of auto-ABS is shown to lead to smaller errors as the size (quality) of the OBS is expanded. The performance of auto-ABS is also compared with the use of the recently proposed universal fitting sets [Weigend, Phys. Chem. Chem. Phys.8, 1057 (2006)] for 180 compounds containing atoms from H to Kr.
Alternative linear-scaling methodology for the second-order Møller-Plesset perturbation calculation based on the divide-and-conquer method127(2007); http://dx.doi.org/10.1063/1.2761878View Description Hide Description
A new scheme for obtaining the approximate correlationenergy in the divide-and-conquer (DC) method of Yang [Phys. Rev. Lett.66, 1438 (1991)] is presented. In this method, the correlationenergy of the total system is evaluated by summing up subsystem contributions, which are calculated from subsystem orbitals based on a scheme for partitioning the correlationenergy. We applied this method to the second-order Møller-Plesset perturbation theory (MP2), which we call DC-MP2. Numerical assessment revealed that this scheme provides a reliable correlationenergy with significantly less computational cost than the conventional MP2 calculation.
Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis127(2007); http://dx.doi.org/10.1063/1.2749505View Description Hide Description
The static and dynamic second hyperpolarizability has been investigated by time-dependent density functional cubic response theory. The third-order coupled perturbed Kohn-Sham equations were solved to obtain the third-order perturbed charge density. Calculations on a number of small molecules (, , , CO, HF, , and ), paradisubstituted oligoacetylene chains, benzene, and eight paradisubstituted benzenes were performed to verify the implementation and to assess the accuracy of the nonhybrid and hybrid time-dependent density functional theory computations. Nitroaniline and a derivative were taken as examples to investigate the distribution of the “ density” and to demonstrate the feasibility of analyzing cubic response functions in terms of contributions from natural bondorbitals (NBOs) and natural localized molecular orbitals (NLMOs). The results highlight the contributions from atoms and bonds on different functional groups to the total value of based on the NBO/NLMO analysis, which might be helpful for new nonlinear optical materials design.
127(2007); http://dx.doi.org/10.1063/1.2761880View Description Hide Description
In this work we present a comprehensive study of analytical electric field gradients in hydrogen halides calculated within the high-order Douglas-Kroll-Hess (DKH) scalar-relativistic approach taking picture-change effects analytically into account. We demonstrate the technical feasibility and reliability of a high-order DKH unitary transformation for the property integrals. The convergence behavior of the DKH property expansion is discussed close to the basis set limit and conditions ensuring picture-change-corrected results are determined. Numerical results are presented, which show that the DKH property expansion converges rapidly toward the reference values provided by four-component methods. This shows that in closed-shell cases, the scalar-relativistic DKH(2,2) approach which is of second order in the external potential for both orbitals and property operator yields a remarkable accuracy. As a parameter-dependence-free high-order DKH model, we recommend DKH(4,3). Moreover, the effect of a finite-nucleus model, different parametrization schemes for the unitary matrices, and the reliability of standard basis sets are investigated.
127(2007); http://dx.doi.org/10.1063/1.2752813View Description Hide Description
With low-order scaling correlated wave functiontheories in mind, we present second quantization formalism as well as biorthonormalization procedures for general—singular or nonsingular—bases. Of particular interest are the so-called projected atomic orbital bases, which are obtained from a set of atom-centered functions and feature a separation of occupied and virtual spaces. We demonstrate the formalism by deriving and implementing second-order Møller-Plesset perturbation theory in it, and discuss the convergence and preconditioning of the iterative amplitude equations in detail.
Quadrupole, octopole, and hexadecapole electric moments of , , , and electronic states: Cylindrically asymmetric charge density distributions in linear molecules with nonzero electronic angular momentum127(2007); http://dx.doi.org/10.1063/1.2755691View Description Hide Description
The number of independent components, , of traceless electric -multipole moments is determined for molecules in , , , and electronic states . Each pole is defined by a rank- irreducible tensor with components proportional to the solid spherical harmonic . Here we focus our attention on poles with (quadrupole, octopole , and hexadecapole ). An important conclusion of this study is that can be 1 or 2 depending on both the multipole rank and state quantum number . For states, all poles have one independent parameter . For spatially degenerate states—, , and —the general rule reads for (when the -pole rank lies below ) but for higher poles with . The second nonzero term is the off-diagonal matrix element . Thus, a state has one dipole but two independent poles for —starting with the quadrupole. A state has for poles but for higher poles—from the hexadecapole up. For states, it holds that for to poles but for all poles. In short, what is usually stated in the literature—that for all possible poles of linear molecules—only applies to states. For degenerate states with , all Cartesian -pole components can be expressed as linear combinations of two irreducible multipoles, and [parallel ( axis) and anisotropy ( plane)]. Our predictions are exemplified by the , , and moments calculated for states of selected diatomics (in parentheses): , , , , , , and . States of symmetry are most affected by the deviation from axial symmetry.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
Submillimeter-wave spectroscopy of in the excited vibrational states: Does the Stark effect cause anomalies in the state?127(2007); http://dx.doi.org/10.1063/1.2766950View Description Hide Description
The lowest two rotational transitions of were not detected in previous investigations. This nonobservation was ascribed to the Stark broadening caused by the electric field in a hollow cathodedischarge and an extended negative glow discharge. However, rotational lines of symmetric-top ions such as and were observed in extended negative glow discharges with no such Stark effect. Also, no anomalies were observed for similar lines for HCN and HNC produced in an extended negative glow discharge. In the present investigation, we extended the measurements of up to . The ions were produced in an extended negative glow discharge in a gas mixture of and CO (a couple of millitorr each) in Ar buffer . The measurements were made mostly at liquid nitrogen temperature. Our observations confirmed that the lowest rotational lines in within our frequency coverage, , were too weak to be detected. However, a most notable result obtained in the present investigation is that the and lines of and the line of have been detected in induced emission. This observation implies that the previous nonobservation of low- lines in may not be due to the Stark effect. The -type splitting in has been observed for the transition and higher. However, the splittings for the and lines that are expected to be large enough have not been resolved. The reason for this “narrowing” has been unexplained at the present stage. The population inversion suggests that, initially, is formed predominantly in stretching vibrational states, and, subsequently, the energy transfer to bending vibrational states takes place through collisional relaxation processes.
127(2007); http://dx.doi.org/10.1063/1.2752162View Description Hide Description
A potential energy surface for the lowest quartet electronic state of lithium trimer is developed and used to study spin-polarized collisions at ultralow kinetic energies. The potential energy surface allows barrierless atom exchange reactions. Elastic and inelastic cross sections are calculated for collisions involving a variety of rovibrational states of . Inelastic collisions are responsible for trap loss in molecule production experiments. Isotope effects and the sensitivity of the results to details of the potential energy surface are investigated. It is found that for vibrationally excited states, the cross sections are only quite weakly dependent on details of the potential energy surface.
The water-oxygen dimer: First-principles calculation of an extrapolated potential energy surface and second virial coefficients127(2007); http://dx.doi.org/10.1063/1.2756524View Description Hide Description
The systematic intermolecular potential extrapolation routine (SIMPER) is applied to the water-oxygen complex to obtain a five-dimensional potential energy surface. This is the first application of SIMPER to open-shell molecules, and it is the first use, in this context, of asymptotic dispersion energy coefficients calculated using the unrestricted time-dependent coupled-cluster method. The potential energy surface is extrapolated to the complete basis set limit, fitted as a function of intermolecular geometry, and used to calculate (mixed) second virial coefficients, which significantly extend the range of the available experimental data.
127(2007); http://dx.doi.org/10.1063/1.2756533View Description Hide Description
Rotationally resolved resonant two-photon ionization (R2PI) spectra of ScCo and YCo are reported. The measured spectra reveal that these molecules possess ground electronic states of symmetry, as previously found in the isoelectronic and CrMo molecules. The ground state rotational constants for ScCo and YCo are and , corresponding to ground statebond lengths of and , respectively. A single electronic band system, assigned as a transition, has been identified in both molecules. In ScCo, the state is characterized by , , and . In YCo, the state has , , and . For YCo, hot bands originating from levels up to are observed, allowing the ground state vibrational constants , , and to be deduced. The bondenergy of ScCo has been measured as from the onset of predissociation in a congested vibronic spectrum. A comparison of the chemical bonding in these molecules to related molecules is presented.
127(2007); http://dx.doi.org/10.1063/1.2762217View Description Hide Description
We applied theoretical models and molecular dynamics simulations to explore extreme multielectron ionization in clusters (, initial cluster radius ) driven by ultraintense infrared Gaussian laser fields (peak intensity , temporal pulse length , and frequency ). Cluster compound ionization was described by three processes of inner ionization, nanoplasma formation, and outer ionization. Inner ionization gives rise to high ionization levels (with the formation of with ), which are amenable to experimental observation. The cluster size and laser intensity dependence of the inner ionization levels are induced by a superposition of barrier suppression ionization (BSI) and electron impact ionization (EII). The BSI was induced by a composite field involving the laser field and an inner field of the ions and electrons, which manifests ignition enhancement and screening retardation effects. EII was treated using experimental cross sections, with a proper account of sequential impact ionization. At the highest intensities inner ionization is dominated by BSI. At lower intensities , where the nanoplasma is persistent, the EII contribution to the inner ionization yield is substantial. It increases with increasing the cluster size, exerts a marked effect on the increase of the ionization level, is most pronounced in the cluster center, and manifests a marked increase with increasing the pulse length (i.e., becoming the dominant ionization channel (56%) for at ). The EII yield and the ionization level enhancement decrease with increasing the laser intensity. The pulse length dependence of the EII yield at establishes an ultraintense laser pulse length control mechanism of extreme ionization products.
Ground states of the , , and CrMo molecules: A second and third order multireference perturbation theory study127(2007); http://dx.doi.org/10.1063/1.2768529View Description Hide Description
The potential energy curves of the molecules , , and CrMo have been studied ab initio using large basis sets and the “-electron valence state perturbation theory” up to the third order in the energy. The third order results for and reproduce the equilibrium distances and the harmonic frequencies in fairly good accordance with the experimental values but tend to underestimate the dissociation energy. The CrMo molecule, for which experimental dissociation energy data do not exist yet, is predicted to have a value for of .
127(2007); http://dx.doi.org/10.1063/1.2768531View Description Hide Description
The second excited state of the hydrogen molecule, the so-called GK state, has a potential energy curve with double minima. At the united atom limit it converges to the configuration of He. At large internuclear distances , it dissociates to two separated atoms, one in the ground state and another in the excited state. Radial pair density calculations and natural orbital analyses reveal unusual effect of electron correlation around the minimum of the potential energy curve. As , a natural orbital of symmetry joins the two natural orbitals of symmetry at smaller . The average interelectronic distance decreases as the internuclear distance increases from Around the singly peaked pair density curve splits into two peaks. The inner peak can be attributed to the formation of the ionic electron configuration , where both electrons are on the same nucleus. As the two electrons run into different nuclei, one of the two electrons is promoted to the state, which results in the outer peak in the pair density curve. The Rydberg configuration persists as the nuclei stretch, and becomes dominant at large where four natural orbitals, two of and two of symmetry, become responsible.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
127(2007); http://dx.doi.org/10.1063/1.2764478View Description Hide Description
The behavior of a two-dimensional neutral Coulomb fluid in the strong association regime (low density, high ionic charge) is explored by means of computer simulation and the hypernetted chain integral equation. The theory reproduces reasonably well the structure and thermodynamics of the system but presents a no-solution region at temperatures well above the computer simulation estimates of the metal-insulator transition. In contrast with hypernetted chain predictions for the three-dimensional Coulomb fluid, here the breakdown of the solution is not accompanied by divergences in any physical quantity.
Solution of the master equation for Wigner’s quasiprobability distribution in phase space for the Brownian motion of a particle in a double well potential127(2007); http://dx.doi.org/10.1063/1.2759486View Description Hide Description
Quantum effects in the Brownian motion of a particle in the symmetric double well potential are treated using the semiclassical master equation for the time evolution of the Wigner distribution function in phase space . The equilibrium position autocorrelation function, dynamic susceptibility, and escape rate are evaluated via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The escape rate so yielded has a quantum correction depending strongly on the barrier height and is compared with that given analytically by the quantum mechanical reaction rate solution of the Kramers turnover problem. The matrix continued fraction solution substantially agrees with the analytic solution. Moreover, the low-frequency part of the spectrum associated with noise assisted Kramers transitions across the potential barrier may be accurately described by a single Lorentzian with characteristic frequency given by the quantum mechanical reaction rate.
Hydration properties of magnesium and calcium ions from constrained first principles molecular dynamics127(2007); http://dx.doi.org/10.1063/1.2768063View Description Hide Description
We studied the solvation structures of the divalent metal cations and in ambient water by applying a Car-Parrinello-based constrained molecular dynamics method. By employing the metal-water oxygen coordination number as a reaction coordinate, we could identify distinct aqua complexes characterized by structural variations of the first coordination shell. In particular, our estimated free-energy profile clearly shows that the global minimum for is represented by a rather stable sixfold coordination in the octahedral arrangement, in agreement with experiments. Conversely, for the free-energy curve shows several shallow local minima, suggesting that the hydration structure of is highly variable. Implications for water exchange reactions are also discussed.
Toward effective and reliable fluorescence energies in solution by a new state specific polarizable continuum model time dependent density functional theory approach127(2007); http://dx.doi.org/10.1063/1.2757168View Description Hide Description
A state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of emission energies has been developed and coded in the framework of the so called polarizable continuum model (PCM). The new model allows for a rigorous and effective treatment of dynamical solvent effects in the computation of fluorescence and phosphorescencespectra in solution, and it can be used for studying different relaxation time regimes. SS and conventional linear response (LR) models have been compared by computing the emission energies for different benchmark systems (formaldehyde in water and three coumarin derivatives in ethanol). Special attention is given to the influence of dynamical solvation effects on LR geometry optimizations in solution. The results on formaldehyde point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents and/or weak transitions. The computed emission energies for coumarin derivatives are very close to their experimental counterparts, pointing out the importance of a proper treatment of nonequilibrium solvent effects on both the excited and the ground state energies. The availability of SS-PCM/TD-DFT models for the study of absorption and emission processes allows for a consistent treatment of a number of different spectroscopic properties in solution.
127(2007); http://dx.doi.org/10.1063/1.2753151View Description Hide Description
In this paper, we consider a dissipative system in which the system is coupled linearly to a harmonic bath. In the continuum limit, the bath is defined via a spectral density and the classical system dynamics is given in terms of a generalized Langevin equation. Using the path integral formulation and factorized initial conditions, it is well known that one can integrate out the harmonic bath, leaving only a path integral over the system degrees of freedom. However, the semiclassical initial value representation treatment of dissipative systems has usually been limited to a discretized treatment of the bath in terms of a finite number of bath oscillators. In this paper, the continuum limit of the semiclassical initial value representation is derived for dissipative systems. As in the path integral, the action is modified with an added nonlocal term, which expresses the influence of the bath on the dynamics. The first order correction term to the semiclassical initial value approximation is also derived in the continuum limit.
127(2007); http://dx.doi.org/10.1063/1.2759484View Description Hide Description
The importance of quantum effects as well as the accuracy of the ab initio-based polarizable TTM2.1-F force field in describing liquid water are quantitatively assessed by a detailed analysis of the temperature dependence of several thermodynamic and dynamical properties computed using the path-integral molecular dynamics and centroid molecular dynamics methods. The results show that quantum effects are not negligible even at relatively high temperatures, and their inclusion in simulations with the TTM2.1-F water model is necessary to achieve a more accurate description of the liquidproperties. Comparison with the results reported in the literature for empirical, nonpolarizable force fields demonstrates that the effects of the nuclear quantization on the dielectric constant are dependent in part on how the electronic polarization is described in the underlying water model, while comparison with other ab initio-based force fields shows that the TTM2.1-F model provides an overall accurate description of liquid water. Analysis of the isotope effect on the dynamical properties does not display significant temperature dependence. This suggests that the contribution of quantum tunneling, which has been proposed as a possible cause for the different orientational dynamics observed for the and systems, appears to be small.