Index of content:
Volume 126, Issue 18, 14 May 2007
- Theoretical Methods and Algorithms
Two-electron reduced density matrices from the anti-Hermitian contracted Schrödinger equation: Enhanced energies and properties with larger basis sets126(2007); http://dx.doi.org/10.1063/1.2723115View Description Hide Description
Two-electron reduced density matrices (2-RDMs) have recently been directly determined from the solution of the anti-Hermitian contracted Schrödinger equation (ACSE) to obtain 95%–100% of the ground-statecorrelationenergy of atoms and molecules, which significantly improves upon the accuracy of the contracted Schrödinger equation (CSE) [D. A. Mazziotti, Phys. Rev. Lett.97, 143002 (2006)]. Two subsets of the CSE, the ACSE and the contraction of the CSE onto the one-particle space, known as the 1,3-CSE, have two important properties: (i) dependence upon only the 3-RDM and (ii) inclusion of all second-order terms when the 3-RDM is reconstructed as only a first-order functional of the 2-RDM. The error in the 1,3-CSE has an important role as a stopping criterion in solving the ACSE for the 2-RDM. Using a computationally more efficient implementation of the ACSE, the author treats a variety of molecules, including , , HCN, and , in larger basis sets such as correlation-consistent polarized double- and triple-zeta. The ground-stateenergy of neon is also calculated in a polarized quadruple-zeta basis set with extrapolation to the complete basis-set limit, and the equilibrium bond length and harmonic frequency of are computed with comparison to experimental values. The author observes that increasing the basis set enhances the ability of the ACSE to capture correlation effects in ground-stateenergies and properties. In the triple-zeta basis set, for example, the ACSE yields energies and properties that are closer in accuracy to coupled cluster with single, double, and triple excitations than to coupled cluster with single and double excitations. In all basis sets, the computed 2-RDMs very closely satisfy known -representability conditions.
Effective method to compute vibrationally resolved optical spectra of large molecules at finite temperature in the gas phase and in solution126(2007); http://dx.doi.org/10.1063/1.2721539View Description Hide Description
The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky rotation of the normal modes and the effect of thermal excitation. The method automatically selects the relevant vibronic contributions to the spectrum, independently of their frequency, and it is able to provide fully converged spectra with moderate computational times, both in vacuo and in solution. By describing the electronic states in the frame of the density functional theory and its time-dependent extension, they computed the room temperature absorption spectra of coumarin C153 and trans-stilbene in cyclohexane and the phosphorescencespectrum of porphyrazine in gas phase, showing that the method is fast and efficient. The comparison with experiment for trans-stilbene and coumarin C153 is very satisfactory, confirming the progress made toward a reliable method for the computation and interpretation for the optical spectra of large molecules.
126(2007); http://dx.doi.org/10.1063/1.2730507View Description Hide Description
Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by Gillespie about three decades ago [J. Phys. Chem.81, 2340 (1977)]. Since then, intensive work has been done to make the algorithm more efficient in terms of running time. All accelerated versions of the algorithm are aimed at minimizing the running time required to produce a stochastic trajectory in state space. In these simulations, a necessary condition for reliable statistics is averaging over a large number of simulations. In this study the author presents a new accelerating approach which does not alter the stochastic algorithm, but reduces the number of required runs. By analysis of collected data the author demonstrates high precision levels with fewer simulations. Moreover, the suggested approach provides a good estimation of statistical error, which may serve as a tool for determining the number of required runs.
126(2007); http://dx.doi.org/10.1063/1.2723118View Description Hide Description
Density-functional calculations on transition-metal atoms are problematic due to the numerous possible ways, having inequivalent densities, of occupying the orbitals. The problem is compounded by the issue of real orbitals versus complex orbitals. In this work we systematize the application of density-functional theories to transition-metal atoms using a current-density-dependent functional. For all the single-determinantal angular momentum eigenstates of ground-state terms, we obtain near degeneracy for the energies as we should. Also, we find a simple rule for occupying the real orbitals that reproduces the energies of the (complex) angular momentum eigenstate results. Thus the long-standing confusion over how to compute transition-metal atom reference energies is resolved.
Quantum effect of intramolecular high-frequency vibrational modes on diffusion-controlled electron transfer rate: From the weak to the strong electronic coupling regions126(2007); http://dx.doi.org/10.1063/1.2735323View Description Hide Description
The Sumi-Marcus theory is extended by introducing two approaches to investigate electron transferreactions from weak-to-strong electronic coupling regime. One of these approaches is the quantum -matrix theory, useful for dealing with the intramolecular vibrational motions in the whole electronic coupling domain. The other is the split operator approach that is employed to solve the reaction-diffusion equation. The approaches are then applied to electron transfer in the Marcus inverted regime to investigate the nuclear tunneling effect on the long time rate and the survival probabilities. The numerical results illustrate that the adiabatic suppression obtained from the -matrix approach is much smaller than that from the Landau-Zener theory whereas it cannot be predicted by the perturbation theory. The jointed effects of the electronic coupling and solventrelaxation time on the rates are also explored.
Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities126(2007); http://dx.doi.org/10.1063/1.2733666View Description Hide Description
The authors present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency-dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, they implemented it in a real-space (basis-set-free) code and applied it to benchmark molecules, namely, CO, , and para-nitroaniline. Their results are in agreement with experimental and previous theoretical studies and fully validate their approach.
126(2007); http://dx.doi.org/10.1063/1.2731779View Description Hide Description
The authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem of heavier atoms. The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem. This follows from recent work by one of them, showing how one can calculate corrections to approximate evolution schemes, even when the Hamiltonian that corresponds to these approximate schemes is unknown. Then, they take the limit in which the width of the frozen Gaussians approaches zero, which makes the corrections to the evolution of the quantum subsystem depend only on classical bath coordinates. The test calculations they present use low-dimensional systems, in which comparison to exact quantum dynamics is feasible.
Interpolating moving least-squares methods for fitting potential energy surfaces: Computing high-density potential energy surface data from low-density ab initio data points126(2007); http://dx.doi.org/10.1063/1.2730798View Description Hide Description
A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for one-dimensional model potentials as well as for three-dimensional (HCN) and six-dimensional (HOOH) molecular PESs.
126(2007); http://dx.doi.org/10.1063/1.2724823View Description Hide Description
The authors consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. They show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, they obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtleties of kinetic theory in the derivation of dynamical density functional theory.
Enveloping distribution sampling: A method to calculate free energy differences from a single simulation126(2007); http://dx.doi.org/10.1063/1.2730508View Description Hide Description
The authors present a method to calculate free energy differences between two states and “on the fly” from a single molecular dynamics simulation of a reference state . No computer time has to be spent on the simulation of intermediate states. Only one state is sampled, i.e., the reference state which is designed such that the subset of phase space important to it is the union of the parts of phase space important to and . Therefore, an accurate estimate of the relative free energy can be obtained by construction. The authors applied the method to four test systems (dipole inversion, van der Waals interactionperturbation, charge inversion, and water to methanol conversion) and compared the results to thermodynamic integration estimates. In two cases, the enveloping distribution sampling calculation was straightforward. However, in the charge inversion and the water to methanol conversion, Hamiltonian replica-exchange molecular dynamics of the reference state was necessary to observe transitions in the reference state simulation between the parts of phase space important to and , respectively. This can be explained by the total absence of phase space overlap of and in these two cases.
126(2007); http://dx.doi.org/10.1063/1.2730511View Description Hide Description
The authors propose a new algorithm for molecular dynamics simulation. The method includes a Monte Carlo scheme for incrementing the dilation rate in the equations of motion. The new algorithm needs no extra computation and the dynamics of the system preserves its continuity. Application of this approach is very advantageous for models where the derivation and the computation of the pressure is time consuming. The authors present results of model calculations.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
Experimental and theoretical studies of the electronic structure and the ionization and dissociation processes of trifluoromethyl peroxynitrate126(2007); http://dx.doi.org/10.1063/1.2734971View Description Hide Description
In this work, we present a complete study of the ionization and dissociation processes for trifluoromethyl peroxynitrate . was generated by UV photolysis of a mixture of , , and . The product was detected and characterized by the photoelectron spectroscopy (PES) and photoionization mass spectroscopy (PIMS). The geometric and electronic structures of were investigated by the combination of experiments and the density functional and ab initio calculations. It is worthwhile mentioning that drastic changes occur in the geometry of after ionization. Due to the removal of one electron from the O–N bond, the COON dihedral angle changes to 180° and as a result, the nonplanar structure becomes planar. And the O–N single bond length increases remarkably, with the positive charge most localized on the moiety. The experimental first vertical ionization potential is . Based on the calculated bonddissociation energies, the dissociation pathway was predicted. The calculated results explain the ion intensities observed in the photoionization mass spectrum. The dissociation of O–N single bond is found to be the most favored of the possible dissociation paths for .
126(2007); http://dx.doi.org/10.1063/1.2723109View Description Hide Description
The authors report the first theoretical study on the hexa-atomic molecules at the , , and (single point) levels. Three low-lying isomers (within ) can be formally viewed as constructed by one interacting with the planar at the side Al–X bond (X-1), side Al–Al bond (X-2), and central C atom (X-3). The isomers X-1 and X-2 both have planar structures that include the planar tetracoordinate carbon,aluminum, and silicon/germanium, while the three-dimensional isomer X-3 has the pentacoordinate carbon. The planarity of X-1 and X-2 is ascribed to the ligand five-center two-electron bonding molecular orbital, similar to the orbital responsible for the planarity of . Kinetically, the two planar structures X-1 and X-2 can be easily interconverted to each other via the intermediate X-3, indicative of their coexistence. Of particular interest, isomer X-1 represents the first example that simultaneously contains three types of planar centers in a single molecule, to the best of our knowledge. The three low-lying and structurally interesting isomers X-1, X-2, and X-3 await future experimental verification. The present results could enrich the planar chemistry.
126(2007); http://dx.doi.org/10.1063/1.2732751View Description Hide Description
The authors present quantum scattering calculations of rate coefficients for the spin-orbit relaxation of atoms in a gas of molecules and atoms in a gas of and molecules. Their calculation of the thermally averaged rate coefficient for the electronic relaxation of chlorine in agrees very well with an experimental measurement at room temperature. It is found that the spin-orbit relaxation of chlorine atoms in collisions with hydrogen molecules in the rotationally excited state is dominated by the near-resonant electronic-to-rotational energy transfer accompanied by rotational excitation of the molecules. The rate of the spin-orbit relaxation in collisions with molecules increases to a great extent with the rotational excitation of the molecules. They have found that the isotope effect in the relaxation of is very sensitive to temperature due to the significant role of molecular rotations in the nonadiabatic transitions. Their calculation yields a rate ratio of 10 for the electronic relaxation in and at room temperature, in qualitative agreement with the experimental measurement of the isotope ratio of about 5. The isotope effect becomes less significant at higher temperatures.
126(2007); http://dx.doi.org/10.1063/1.2730829View Description Hide Description
The pulsed field ionization-photoelectron (PFI-PE) spectrum of bromochloromethane in the region of has been measured using vacuum ultraviolet laser. The vibrational structure resolved in the PFI-PE spectrum was assigned based on ab initio quantum chemical calculations and Franck-Condon factor predictions. At energies above the adiabatic ionizationenergy (IE) of , the Br–C–Cl bending vibration progression of is well resolved and constitutes the major structure in the PFI-PE spectrum, whereas the spectrum at energies above the is found to exhibit complex vibrational features, suggesting perturbation by the low lying excited state. The assignment of the PFI-PE vibrational bands gives the and the bending frequencies for . We have also examined the dissociativephotoionization process, , in the energy range of using the synchrotron based PFI-PE-photoion coincidence method, yielding the threshold or appearance energy. Combining the and values obtained in this study, together with the known , we have determined the bond dissociation energies for and . We have also performed CCSD(T, full)/complete basis set (CBS) calculations with high-level corrections for the predictions of the , , , , and . The comparison between the theoretical predictions and experimental determinations indicates that the CCSD(T, full)/CBS calculations with high-level corrections are highly reliable with estimated error limits of .
126(2007); http://dx.doi.org/10.1063/1.2735298View Description Hide Description
The electric field gradient (EFG) at the gold nucleus is calculated using a finite field approach, to make the extraction of the nuclear quadrupole moment from experimental nuclear quadrupole coupling constants possible. The four-component Dirac-Coulomb Hamiltonian serves as the framework, 51 of the 79 electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the contribution of the Gaunt term, the main part of the Breit interaction, is evaluated. Large basis sets (up to uncontracted Gaussians) are employed. Energy splittings of the and levels, rather than level shifts, are used to extract the EFG constants, as the former remain linear with up to , whereas the latter display significant nonlinearity even at Larger values lead to larger energy changes and better precision. Excellent agreement (0.1%) is obtained between values derived from and data. Systematic errors connected with neglecting triple and higher excitations, truncating the basis and orbital active space, and approximating the Gaunt contribution are evaluated. The final value of is . It is lower than the muonic and agrees within error bounds with the recent value of obtained from molecular calculations.
126(2007); http://dx.doi.org/10.1063/1.2723087View Description Hide Description
Photoelectron spectra of neutral silver trimers, grown in ultracold helium nanodroplets, are recorded after ionization with laser pulses via a strong optical resonance of this species. Varying the photon energy reveals that direct vertical two-photonionization is hindered by a rapid relaxation into the lower edge of a long-living excited state manifold. An analysis of the ionization threshold of the embedded trimer yields an ionization potential of consistent with the value found in the gas phase. The asymmetrical form of the electron energy spectrum, which is broadened toward lower kinetic energies, is attributed to the influence of the matrix on the photoionization process. The lifetime of the excited state was measured in a two-color pump-probe experiment to be .
126(2007); http://dx.doi.org/10.1063/1.2730832View Description Hide Description
We report a new ab initio study of the acetylene potential energy surface, which clarifies the nature of its energy minimum, and present computed equilibrium geometries and diabatic frequencies. This information enables the computation of harmonic vibrational overlap integrals of vibrational levels with the state. The results of this calculation support the interpretation of two local perturbations of , revealed in ultraviolet laser-induced fluorescence/surface electron ejection by laser excited metastables spectroscopy and Zeeman anticrossing measurements, respectively, as arising from two rotational submanifolds of a single vibrational state. We present plausible assignments for this state as a guide for future experimental work.
126(2007); http://dx.doi.org/10.1063/1.2731788View Description Hide Description
First quasiclassical trajectory calculations have been carried out for the reaction using a recent ab initio potential energy surface for the ground electronic state, , of . Total and state-specific integral cross sections have been determined for a wide range of collision energies . Then, thermal and state-specific rate constants have been calculated in the temperature range. The thermal rate constant varies from at down to at with a maximum value of obtained at . Cross sections and rate constants are found to be almost independent of the rovibrational state of OH.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
Vibronic and spin-orbit coupling of a transition-metal ion encapsulated in an icosahedral cage: The Jahn-Teller problem126(2007); http://dx.doi.org/10.1063/1.2730504View Description Hide Description
Interplay between the vibronic and spin-orbit coupling in the Jahn-Teller problem, where and are the quartet and sextet spin representation, and and denote the fourfold and fivefold degenerate vibrational modes in icosahedral symmetry, respectively, is studied. A or transition-metal ion in an icosahedral field may provide a realization of this system.