Volume 126, Issue 11, 21 March 2007
 COMMUNICATIONS


Effect of fluorination on the electronic structure and optical excitations of conjugated molecules
View Description Hide DescriptionFluorination of conjugated organic molecules is a strategy to obtain possible type conducting and airstable materials due to the lowering of the frontier molecular orbitals (MOs) by the high electronegativity of fluorine. Nevertheless, the resulting optical gaps may be widened or narrowed, depending on the molecular backbone and/or the number and position of the fluorine atoms. The authors have performed timedependent density functional theory calculations to address the subtle influence of fluorine substitution on the absolute MO energies and the subsequent impact on the optical transitions in homologous conjugated oligomers based on thiophene and acene units.

Equilibrium theory for a particle pulled by a moving optical trap
View Description Hide DescriptionThe viscous drag on a colloidal particle pulled through solution by an optical trap is large enough that on experimentally relevant time scales the mechanical force exerted by the trap is equal and opposite the viscous drag force. The rapid mechanical equilibration allows the system to be modeled using equilibrium theory where the effects of the energy dissipation (thermodynamic disequilibrium) show up only in the coordinate transformations that map the system from the laboratory frame of reference, relative to which the particle is moving, to a frame of reference in which the particle is, on average, stationary and on which the stochastic dynamics is governed by a canonical equilibrium distribution function. The simple equations in the stationary frame can be analyzed using the OnsagerMachlup theory for stochastic systems and provide generalizations of equilibrium and near equilibrium concepts such as detailed balance and fluctuationdissipation relations applicable to a wide range of systems including molecular motors, pumps, and other nanoscale machines.
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 ARTICLES

 Theoretical Methods and Algorithms

General excitations in timedependent density functional theory
View Description Hide DescriptionA general framework within timedependent density functional theory is presented for the calculation of excitations to states of arbitrary multiplicity in molecular systems with a nonsinglet ground state. The proposed approach combines generalized orbital excitation operators designed to generate excited states which have welldefined multiplicities and the noncollinear formulation of density functional theory and it can be straightforwardly implemented in currently existing density functional programs.

Reduced dynamics of coupled harmonic and anharmonic oscillators using higherorder perturbation theory
View Description Hide DescriptionSeveral techniques to solve a hierarchical set of equations of motion for propagating a reduced density matrix coupled to a thermal bath have been developed in recent years. This is either done using the path integral technique as in the original proposal by Tanimura and Kubo [J. Phys. Soc. Jpn.58, 101 (1998)] or by the use of stochastic fields as done by Yan et al. [Chem. Phys. Lett.395, 216 (2004)]. Based on the latter ansatz a compact derivation of the hierarchy using a decomposition of the spectral density function is given in the present contribution. The method is applied to calculate the time evolution of the reduced density matrix describing the motion in a harmonic, an anharmonic, and two coupled oscillators where each system is coupled to a thermal bath. Calculations to several orders in the systembath coupling with two different truncations of the hierarchy are performed. The respective density matrices are used to calculate the time evolution of various system properties and the results are compared and discussed with a special focus on the convergence with respect to the truncation scheme applied.

Geometry optimization using improved virtual orbitals: A complete active space numerical gradient approach
View Description Hide DescriptionThe improved virtual orbitalcomplete active space configuration interaction (IVOCASCI) method is extended to enable geometry optimization and the calculation of vibrational frequencies for ground and excited states using numerical energy gradients. Applications consider the ground state geometries and vibrational frequencies of the , LiF, , and HCN molecules, as well as excited state properties for HCN, systems that are sufficiently complex to access the efficacy of the method. Comparisons with other standard approaches (selfconsistent field, second order MöllerPlesset perturbation theory, complete active space selfconsistent field, and coupled cluster singles and doubles methods) demonstrate that the numerical gradient version of the IVOCASCI approach generally fares comparable to or better for all systems studied. The accurate estimates for the bond length and vibrational frequency are notable since many other computationally facile methods produce poor results.

Sampling enhancement for the quantum mechanical potential based molecular dynamics simulations: A general algorithm and its extension for free energy calculation on rugged energy surface
View Description Hide DescriptionAn approach is developed in the replica exchange framework to enhance conformational sampling for the quantum mechanical (QM) potential based molecular dynamics simulations. Importantly, with our enhanced sampling treatment, a decent convergence for electronic structure selfconsistentfield calculation is robustly guaranteed, which is made possible in our replica exchange design by avoiding direct structure exchanges between the QMrelated replicas and the activated (scaled by low scaling parameters or treated with high “effective temperatures”) molecular mechanical (MM) replicas. Although the present approach represents one of the early efforts in the enhanced sampling developments specifically for quantum mechanical potentials, the QMbased simulations treated with the present technique can possess the similar sampling efficiency to the MM based simulations treated with the Hamiltonian replica exchange method (HREM). In the present paper, by combining this sampling method with one of our recent developments (the dualtopology alchemical HREM approach), we also introduce a method for the sampling enhanced QMbased free energy calculations.

Probing the limits of accuracy in electronic structure calculations: Is theory capable of results uniformly better than “chemical accuracy”?
View Description Hide DescriptionCurrent limitations in electronic structure methods are discussed from the perspective of their potential to contribute to inherent uncertainties in predictions of molecular properties, with an emphasis on atomization energies (or heats of formation). The practical difficulties arising from attempts to achieve high accuracy are illustrated via two case studies: the carbon dimer and the hydroperoxyl radical . While the wave function is dominated by a single configuration, the carbon dimer involves considerable multiconfigurational character. In addition to these two molecules, statistical results will be presented for a much larger sample of molecules drawn from the Computational Results Database. The goal of this analysis will be to determine if a combination of coupled clustertheory with large 1particle basis sets and careful incorporation of several computationally expensive smaller corrections can yield uniform agreement with experiment to better than “chemical accuracy” . In the case of , the best current theoretical estimate of the zeropointinclusive, spinorbit corrected atomization energy and the most recent Active Thermochemical Table (ATcT) value are in excellent agreement. For the agreement is only slightly poorer, with theory almost encompassing the most recent ATcT value . For a larger collection of , a mean absolute deviation of was found. The same high level of theory that produces good agreement for atomization energies also appears capable of predicting bond lengths to an accuracy of .

Gradients for twocomponent quasirelativistic methods. Application to dihalogenides of element 116
View Description Hide DescriptionThe authors report the implementation of geometry gradients for quasirelativistic twocomponent HartreeFock and density functional methods using either the zeroorder regular approximation Hamiltonian or spindependent effective core potentials. The computational effort of the resulting program is comparable to that of corresponding nonrelativistic calculations, as it is dominated by the evaluation of derivative twoelectron integrals, which is the same for both types of calculations. Besides the implementation of derivatives of matrix elements of the oneparticle Hamiltonian with respect to nuclear displacements, the calculation of the derivative exchangecorrelation energy for the open shell case involves complicated expressions because of the noncollinear approach chosen to define the spin density. A pilot application to dihalogenides of element 116 shows how spinorbit coupling strongly affects the chemistry of the superheavy block elements. While these molecules are bent at a scalarrelativistic level, spinorbit coupling is so strong that only the atomic orbitals of element 116 are involved in bonding, which favors linear molecular geometries for dihalogenides with heavy terminal halogen atoms.

Quasirelativistic theory. II. Theory at matrix level
View Description Hide DescriptionThe Dirac operator in a matrix representation in a kinetically balanced basis is transformed to the matrix representation of a quasirelativistic Hamiltonian that has the same electronic eigenstates as the original Dirac matrix (but no positronic eigenstates). This transformation involves a matrix , for which an exact identity is derived and which can be constructed either in a noniterative way or by various iteration schemes, not requiring an expansion parameter. Both linearly convergent and quadratically convergent iteration schemes are discussed and compared numerically. The authors present three rather different schemes, for each of which even in unfavorable cases convergence is reached within three or four iterations, for all electronic eigenstates of the Dirac operator. The authors present the theory both in terms of a nonHermitian and a Hermitian quasirelativistic Hamiltonian. Quasirelativistic approaches at the matrix level known from the literature are critically analyzed in the frame of the general theory.

New coarsegraining procedure for the dynamics of charged spherical nanoparticles in solution
View Description Hide DescriptionA multiscale strategy based on the Brownian dynamics (BD) simulation method is presented here. It leads to an approximate but realistic reproduction of the dynamics of charged nanoparticles in suspension. This method is particularly suited to systems containing highly dissymmetric electrolytes with added salts, such as micellar suspensions or protein solutions. The coarsegraining procedure leads to a description where only the translational degrees of freedom of the nanoparticles are left, all the degrees of freedom related to the smallest solutes being rigorously averaged out. The authors’ contribution aims at quantitatively evaluating the influence of the eliminated forces on the dynamics of the nanoparticles. For this purpose, an effective diffusion coefficient has to be calculated. In practice, this effective diffusion coefficient is taken as an input of a coarsegrained simulation that uses the potential of mean force between nanoparticles. The procedure has been validated by the quantitative comparison between the coarsegrained calculations and BD simulations at the “microscopic” level of description (which explicitly include microions). For a model of aqueous solutions of 101 electrolyte with a 11 added salt, the agreement is found to be excellent. This new method allows us to compute the diffusion coefficients of nanoparticles with a computation time at least one order of magnitude lower than with explicit BD.

Decoherence and quantumclassical master equation dynamics
View Description Hide DescriptionThe conditions under which quantumclassical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantumclassical subsystem interacting with a classical bath are considered. Starting with an exact nonMarkovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. One contribution to this equation contains the bath average of a memory kernel that accounts for all coherences in the system. It is shown to be a rapidly decaying function, motivating a Markovian approximation on this term in the evolution equation. The resulting subsystem density matrix equation is still nonMarkovian due to the fact that bath degrees of freedom have been projected out of the dynamics. Provided the computation of nonequilibrium average values or correlation functions is considered, the nonMarkovian character of this equation can be removed by lifting the equation into the full phase space of the system. This leads to a trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results are illustrated by computations of the rate constant of a modelnonadiabatic chemical reaction.

Linearscaling implementation of molecular electronic selfconsistent field theory
View Description Hide DescriptionA linearscaling implementation of HartreeFock and KohnSham selfconsistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the RoothaanHall (RH) energy function and solving the Newton equations using the preconditioned conjugategradient (PCG) method. For rapid PCG convergence, the Löwdin orthogonal atomic orbital basis is used. The resulting linearscaling trustregion RoothaanHall (LSTRRH) method works by the introduction of a levelshift parameter in the RH Newton equations. A great advantage of the LSTRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the levelshifted Newton equations. For density averaging, the authors use the trustregion densitysubspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linearscaling evaluation of the Fock/KohnSham matrix (including a boxed fitting of the electron density), LSTRRH and TRDSM methods constitute the linearscaling trustregion SCF (LSTRSCF) method. The LSTRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LSTRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electronic structures and electron detachment energies of halogen substituted acetate anions,
View Description Hide DescriptionThe electronic structures and the halogen inductive effects on the acetate anion were investigated in by photoelectron spectroscopy (PES) and ab initio calculations. The PES spectra indicated that the electron binding energies increased in the order of , contradictory to the known electron affinities of the halogen atoms. The measured adiabatic detachment energies (ADEs) are 3.80, 3.93, and and the vertical detachment energies (VDEs) are 3.96, 4.10, and for the F, Cl, and Brsubstituted species, respectively. Structures of these anions and their neutral species were obtained by full geometry optimizations at the CCSD(T)/augccpVDZ level of theory, and final energies were calculated at the CCSD(T)/augccpVTZ level. The calculated ADEs (3.76, 3.88, and for F, Cl, Br, respectively) and VDEs (4.14, 4.29, and , respectively) are in good agreement with the corresponding experimental results. Theoretical analysis shows that the increase of ADE/VDE from F to Cl to Br is related to that the matching of the orbital energy of X with the group is better for Br than that of Cl and F. For comparison, additional calculations were carried out to include halogen substituted ethanol,. Similar trend on electron binding energies was also found. In contrast, the ionization potentials (IPs) of both and decrease in the order of . These systematic changes of detachment energy and IPs were explained by examining the charge redistributions upon detaching electrons.

Excited state radiationless decay process with Duschinsky rotation effect: Formalism and implementation
View Description Hide DescriptionDuschinsky rotation effect is a simple and effective way to characterize the difference between the ground state and excited statepotential energy surfaces. For complex molecules, harmonic oscillator model is still the practical way to describe the dynamics of excited states. Based on the firstorder perturbation theory à la Fermi golden rule, the authors have applied the path integral of Gaussian type for the correlation function to derive an analytic formalism to calculate the internal conversion rate process with Duschinsky rotation effect being taken into account. The validity of their formalism is verified through comparison with previous work, both analytically for the case of neglecting Duschinsky rotation and numerically for the ethylene molecules with twomode mixing. Their expression is derived for multimode mixing.

Vibrationrotation energy pattern in acetylene: up to
View Description Hide DescriptionAll known vibrationrotation absorption lines of accessing levels up to were gathered from the literature. They were fitted simultaneously to dependent Hamiltonian matrices exploiting the well known vibrational polyad or cluster block diagonalization, in terms of the pseudoquantumnumbers and , and accounting also for parity and symmetry properties. The anharmonic interaction coupling terms known to occur from a pure vibrational fit in this acetylene isotopologue [Robert et al., J. Chem. Phys.123, 174302 (2005)] were included in the model. A total of 12 703 transitions accessing 158 different vibrational states was fitted with a dimensionless standard deviation of 0.99, leading to the determination of 216 vibrationrotation parameters. The experimental data included very weak vibrationrotation transitions accessing 18 previously unreported states, some of them forming branches with very irregular patterns.

Ab initio and analytical intermolecular potential for
View Description Hide DescriptionIn recent years, the ClO free radical has been found to play an important role in the ozone removal processes in the atmosphere. In this work, the authors present a potential energy surface scan of the system with highlevel ab initio methods. Because of the existence of lowlying excited states of the complex and their potential impact on the chemical behavior of the ClO radical in the atmosphere, the authors perform the potential energy surface scan at the CCSD(T)/augccpVTZ level of theory of both the first excited and ground states. Analytical potentials for both ground and excited states, with the ClO and units held fixed at their optimized geometries and with anisotropic atomic polarizabilities modeling the physics of the unpaired electron in the ClO radical, were built based on a Tholetype model. The two minima of the complex are recovered by the analytical potential.

The rotational spectra, potential function, BornOppenheimer breakdown, and magnetic shielding of SnSe and SnTe
View Description Hide DescriptionThe pure rotational spectra of 27 isotopic species of SnSe and SnTe have been measured in the frequency range of using a FabryPérottype resonator pulsedjet Fouriertransform microwave spectrometer. Gaseous samples of both chalcogenides were prepared by laser ablation of suitable target rods and were stabilized in supersonic jets of Ar. Global multiisotopolog analyses of all available highresolution data produced spectroscopic Dunham parameters , , , , , and for both species, as well as BornOppenheimer breakdown (BOB) coefficients for Sn, Se, and Te. A direct fit of the same data sets to an appropriate radial Hamiltonian yielded analytic potential energy functions and BOB radial functions for the electronic state of both SnSe and SnTe. Additionally, the magnetic hyperfine interaction produced by the dipolar nuclei , , , and was observed, yielding first determinations of the corresponding spinrotation coupling constants.

High harmonic generation and molecular orbital tomography in multielectron systems
View Description Hide DescriptionHigh harmonic radiation is produced when atoms or molecules are ionized by an intense femtosecond laser pulse. The radiated spectrum has been shown experimentally to contain information on the electronic structure of the molecule, which can be interpreted as an image of a single molecular orbital. Previous theory for high harmonic generation has been limited to the singleactiveelectron approximation. Utilizing semisudden approximation, the authors develop a theory of the recombination step in high harmonic generation and tomographic reconstruction in multielectron systems, taking into account electron spin statistics and electronelectron correlations within the parent molecule and the ion. They show that the resulting corrections significantly modify the theoretical predictions, and bring them in a better agreement with experiment. They further show that exchange contributions to harmonic radiation can be used to extract additional information on the electronic wave function.

Quantum instanton evaluation of the thermal rate constants and kinetic isotope effects for reaction in full Cartesian space
View Description Hide DescriptionThe quantum instanton calculations of thermal rate constants for the gasphase reaction and its deuterated analogs are presented, using an analytical potential energy surface. The quantum instanton approximation is manipulated by full dimensionality in Cartesian coordinate path integral Monte Carlo approach, thereby taking explicitly into account the effects of the whole rotation, the vibrotational coupling, and anharmonicity of the reaction system. The rates and kinetic isotope effects obtained for the temperature range of show good agreements with available experimental data, which give support to the accuracy of the underlying potential surface used. In order to investigate the sole quantum effect to the rates, the authors also derive the classical limit of the quantum instanton and find that it can be exactly expressed as the classical variation transition state theory. Comparing the quantum quantities with their classical analogs in the quantum instanton formula, the authors demonstrate that the quantum correction of the prefactor is more important than that of the activation energy at the transition state.

Rotational fluctuation of molecules in quantum clusters. I. Path integral hybrid Monte Carlo algorithm
View Description Hide DescriptionIn this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys.120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurationalbias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed.