Volume 126, Issue 14, 14 April 2007
 ARTICLES

 Theoretical Methods and Algorithms

Improving the accuracy of densityfunctional theory calculation: The genetic algorithm and neural network approach
View Description Hide DescriptionThe combination of genetic algorithm and neural network approach (GANN) has been developed to improve the calculation accuracy of density functional theory. As a demonstration, this combined quantum mechanical calculation and GANN correction approach has been applied to evaluate the optical absorption energies of 150 organic molecules. The neural network approach reduces the rootmeansquare (rms) deviation of the calculated absorption energies of 150 organic molecules from for the calculation, and the newly developed GANN correction approach reduces the rms deviation to .

Sampling diffusive transition paths
View Description Hide DescriptionThe authors address the problem of sampling doubleended diffusive paths. The ensemble of paths is expressed using a symmetric version of the OnsagerMachlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the wellknown stiffness problem associated with the sampling of infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with the sampling of the coarse features of long paths. The finefeature sampling stiffness is eliminated with the use of the fast sampling algorithm, and the coarsefeature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. The authors use the algorithm to sample the transition path ensemble for the structural interconversion of the 38atom LennardJones cluster at low temperature.

Timereversible ab initio molecular dynamics
View Description Hide DescriptionTimereversible ab initiomolecular dynamics based on a lossless multichannel decomposition for the integration of the electronic degrees of freedom [Phys. Rev. Lett.97, 123001 (2006)] is explored. The authors present a lossless timereversible density matrix molecular dynamics scheme. This approach often allows for stable HartreeFock simulations using only one single selfconsistent field cycle per time step. They also present a generalization, introducing an additional “forcing” term, that in a special case includes a hybrid Lagrangian, i.e., CarParrinellotype, method, which can systematically be constrained to the BornOppenheimer potential energy surface by using an increasing number of selfconsistency cycles in the nuclear force calculations. Furthermore, in analog to the reversible and symplectic leapfrog or velocity Verlet schemes, where not only the position but also the velocity is propagated, the authors propose a Verlettype density velocity formalism for timereversible BornOppenheimer molecular dynamics.

Source and sink potentials for the description of open systems with a stationary current passing through
View Description Hide DescriptionThe authors present a model Hamiltonian for the description of open systems that exchange probability current density with their surroundings. The complex potentials appearing in this Hamiltonian act as source and sink, respectively, of probability current density. The primary applications of the theory of source and sink potentials are molecular electronic devices (MEDs), in the description of which the semiinfinite contacts are replaced by complex potentials. This is done in a rigorous manner, i.e., the exact wave function is recovered in the interior of the MED. To illustrate the approach, certain prototypical molecular conductors are considered in the Hückel approximation. The authors show that, for the examples considered, there exist almost isolated molecular states in the continuum of contact states that manifest themselves as Fano resonances in the transmission probability. The findings are confirmed by density functional theory calculations that also yield the predicted molecular states that are nearly decoupled from the contacts.

Assessment of the efficiency of longrange corrected functionals for some properties of large compounds
View Description Hide DescriptionUsing the longrange correction (LC) density functional theory(DFT) scheme introduced by Iikura et al. [J. Chem. Phys.115, 3540 (2001)] and the Coulombattenuating model (CAMB3LYP) of Yanai et al. [Chem. Phys. Lett.393, 51 (2004)], we have calculated a series of properties that are known to be poorly reproduced by standard functionals: Bond length alternation of conjugated polymers,polarizabilities of delocalized chains, and electronic spectra of extended dyes. For each of these properties, we present cases in which traditional hybrid functionals do provide accurate results and cases in which they fail to reproduce the correct trends. The quality of the results is assessed with regard to experimental values and/or data arising from electroncorrelated wave function approaches. It turns out that (i) both LCDFT and CAMB3LYP provide an accurate bond length alternation for polyacetylene and polymethineimine, although for the latter they decrease slightly too rapidly with chain length. (ii) The LC generalized gradient approximation and MP2 polarizabilities of long polyphosphazene and polymethineimine oligomers agree almost perfectly. In the same way, CAMB3LYP corrects the major part of the B3LYP faults. (iii) LC and CAM techniques do not help in correcting the nonrealistic evolution with chain length of the absorption wavelengths of cyanine derivatives. In addition, though both schemes significantly overestimate the ground to excited state transition energy of substituted anthraquinone dyes, they provide a more consistent picture once a statistical treatment is performed than do traditional hybrid functionals.

Gaussian and finiteelement Coulomb method for the fast evaluation of Coulomb integrals
View Description Hide DescriptionThe authors propose a new linearscaling method for the fast evaluation of Coulomb integrals with Gaussian basis functions called the Gaussian and finiteelement Coulomb (GFC) method. In this method, the Coulomb potential is expanded in a basis of mixed Gaussian and finiteelement auxiliary functions that express the core and smooth Coulomb potentials, respectively. Coulomb integrals can be evaluated by threecenter oneelectron overlap integrals among two Gaussian basis functions and one mixed auxiliary function. Thus, the computational cost and scaling for large molecules are drastically reduced. Several applications to molecular systems show that the GFC method is more efficient than the analytical integration approach that requires fourcenter twoelectron repulsion integrals. The GFC method realizes a near linear scaling for both onedimensional alanine helix chains and threedimensional diamond pieces.

Simple implementation of complex functionals: Scaled selfconsistency
View Description Hide DescriptionWe explore and compare three approximate schemes allowing simple implementation of complex density functionals by making use of selfconsistent implementation of simpler functionals: (i) postlocaldensity approximation (LDA) evaluation of complex functionals at the LDA densities (or those of other simple functionals) (ii) application of a global scaling factor to the potential of the simple functional, and (iii) application of a local scaling factor to that potential. Option (i) is a common choice in densityfunctional calculations. Option (ii) was recently proposed by Cafiero and Gonzalez [Phys. Rev. A71, 042505 (2005)]. We here put their proposal on a more rigorous basis, by deriving it, and explaining why it works, directly from the theorems of densityfunctional theory. Option (iii) is proposed here for the first time. We provide detailed comparisons of the three approaches among each other and with fully selfconsistent implementations for Hartree, localdensity, generalizedgradient, selfinteraction corrected, and metageneralizedgradient approximations, for atoms, ions, quantum wells, and model Hamiltonians. Scaled approaches turn out to be, on average, better than post approaches, and unlike these also provide corrections to eigenvalues and orbitals. Scaled selfconsistency thus opens the possibility of efficient and reliable implementation of density functionals of hitherto unprecedented complexity.

Alternatives to the electron density for describing Coulomb systems
View Description Hide DescriptionStimulated by the difficulty of deriving effective kinetic energy functionals of the electron density, the authors consider using the local kinetic energy as the fundamental descriptor for molecular systems. In this ansatz, the electron density must be expressed as a functional of the local kinetic energy. There are similar results for other quantities, including the local temperature and the KohnSham potential. One potential advantage of these approaches—and especially the approach based on the local temperature—is the chemical relevance of the fundamental descriptor.

Synergistic approach to improve “alchemical” free energy calculation in rugged energy surface
View Description Hide DescriptionThe authors present an integrated approach to “alchemical” free energy simulation, which permits efficient calculation of the free energy difference on rugged energy surface. The method is designed to obtain efficient canonical sampling for rapid free energy convergence. The proposal is motivated by the insight that both the exchange efficiency in the presently designed dualtopology alchemical Hamiltonian replica exchange method (HREM), and the confidence of the free energy determination using the overlap histogramming method, depend on the same criterion, viz., the overlaps of the energy difference histograms between all pairs of neighboring states. Hence, integrating these two techniques can produce a joint solution to the problems of the free energy convergence and conformational sampling in the free energy simulations, in which parameter plays two roles to simultaneously facilitate the conformational sampling and improve the phase space overlap for the free energy determination. Specifically, in contrast with other alchemical HREM based free energy simulation methods, the dualtopology approach can ensure robust conformational sampling. Due to these features (a synergistic solution to the free energy convergence and canonical sampling, and the improvement of the sampling efficiency with the dualtopology treatment), the present approach, as demonstrated in the model studies of the authors, is highly efficient in obtaining accurate free energy differences, especially for the systems with rough energy landscapes.

Direct optimization of nodal hypersurfaces in approximate wave functions
View Description Hide DescriptionThe fixednode variant of the diffusionquantum Monte Carlo method (FNDMC) is capable of obtaining the exact eigenvalues (albeit numerically with statistical error) of a manyelectron Hamilton operator, provided that the nodal hypersurface of the exact wave function is given. The use of nodes of a trial wave function leads to the node location error. The authors have developed local criteria to assess the accuracy of the nodes based on the distances of the nodal hypersurfaces of , , and which coincide for the exact wave function. These criteria are used to develop direct optimization methods for the nodal hypersurface. The optimization of the nodes is demonstrated for simple wave functions of the Be atom and the molecule and verified with FNDMC calculations.

Critical analysis and extension of the Hirshfeld atoms in molecules
View Description Hide DescriptionThe computational approach to the Hirshfeld [Theor. Chim. Acta44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting “HirshfeldI charges” correlate well with electrostatic potential derived atomic charges.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Unusual halogenbonded complex and hydrogenbonded complex formed by interactions between two positively charged atoms of different polar molecules
View Description Hide DescriptionUsing ab initio calculations, the authors’ predicted for the first time that the halogenbonded complex and hydrogenbonded complex formed by the interactions between two positively charged atoms of different polar molecules can be stable in gas phase. It shows that halogen bond or hydrogen bond not only exists between oppositely charged atoms but also between likecharged atoms. That the attraction arising from the special halogen bond or hydrogen bond can exceed the electrostatic repulsion between two contact positively charged atoms stabilizes the complex. Of course, from the point of view of physics they can consider the interactions in and as mainly the sum of the long range molecular interactions, namely, electrostatic, induction, and dispersion with some shortrange repulsion. They found that the intermolecular electron correlation contribution representing dispersion interaction plays a crucial role in the stabilities of seemingly repulsive complexes and .

Photodissociation dynamics of the 2propyl radical,
View Description Hide DescriptionThe photodissociation of 2propyl leading to was investigated with nanosecond time resolution. A supersonic beam of isolated 2propyl radicals was produced by pyrolysis of 2bromopopane. The kinetic energy release of the Hatom photofragment was monitored as a function of excitation wavelength by photofragment Doppler spectroscopy via the Lyman transition. The loss of hydrogen atoms after excitation proceeds in position to the radical center with a rate constant of at . Approximately 20% of the excess energy is deposited as translation in the Hatom photofragment. In contrast 1propyl does not lose H atoms to a significant extent. The experimental results are compared to simple RiceRamspergerKasselMarcus calculations. The possible reaction pathways are examined in hybrid density functional theory calculations.

Study of the state of : Transition probabilities from the ground state, dissociative widths, and Fano parameters
View Description Hide DescriptionThe transition probabilities, the dissociation widths, and the associated Fano parameters for rovibronic lines with of the absorption bands of the state out of the ground state were measured over the complete vibrational progression, showing clearly that only the innerwell state with character can absorb vuv light and predissociate efficiently. The absolute values of these transition probablities, predissociation widths, and Fano parameters were found to agree well with ab initio calculations if one takes into account that the calculations neglect nonadiabatic couplings.

Symmetry segregation of the vibronic levels within the system of thiophosgene, , by opticaloptical double resonance spectroscopy
View Description Hide DescriptionThe first singletsinglet electronic system, , in thiophosgene has been recorded as a laser induced fluorescence(LIF) excitation and an opticaloptical double resonance (OODR) spectrum under jetcooled conditions. In the OODR process, the sum of the frequencies of the pump and probe lasers must be fixed to the energy difference between a pair of vibronic levels in the and states. Detection is through the fluorescence from the state. The blocking of a spectrum into its four possible symmetry components is obtained by adjusting the total energy such that it matches the energy difference between symmetry selected levels in the and electronic states. In this method the pump laser is used to excite a group of “hot” sequence bands that involve combinations of the and antisymmetric vibrations. The additional data that were collected by this method were used to update and refine the analyses of the spectrum. Magnetic dipole transitions are reported for the first time.

JahnTeller effect in tetrahedral symmetry: Largeamplitude tunneling motion and rovibronic structure of and
View Description Hide DescriptionThe energy level structures of the ground vibronic states of , , and have been measured by pulsedfieldionization zerokineticenergy photoelectron spectroscopy. The nuclear spin symmetries of the tunnelingrotational levels have been determined in doubleresonance experiments via selected rotational levels of the and vibrational levels of the ground state of . The energy level structures of , , and have been analyzed with an effective tunnelingrotational Hamiltonian. The analysis together with a group theoretical treatment of the JahnTeller effect in the group prove that the equilibrium geometry of , , and has symmetry and characterize the pseudorotational dynamics in these fluxional cations. The tunneling behavior is discussed in terms of the relevant properties of the potential energy surface, some of which have been recalculated at the CCSD(T)/ccpVTZ level of ab initiotheory.

Most stable structure of fullerene[20] and its novel activity toward addition of alkene: A theoretical study
View Description Hide DescriptionStructures and stabilities of fullerene and have been investigated by the density functional theory and CCSD(T) calculations. In consideration of the JahnTeller distortion of symmetric , possible subgroup symmetries have been used in the full geometry optimization. On the basis of relative energetics, vibrational analyses, and electron affinities,fullerenes and have most stable and structures, respectively. The controversy on the relative stability of fullerene[20] arises from the use of different subgroups in calculation and the basis set dependence in vibrational analysis. Predicted nucleusindependent chemical shift values show that the most stable fullerene and its derivatives and exhibit remarkable aromaticity, while and have no spherical aromaticity. The cage has remarkable activity toward the addition of olefin, and such feasibility of the addition reaction is ascribed to strong bonding interactions among frontier molecular orbitals from and olefin. Calculations indicate that both and have similar features in electronic spectra.

Ab initio calculation of the electronic structures of the ground and excited states of CoH
View Description Hide DescriptionThe electronic structures and the spectroscopic constants of the electronic ground and lowlying electronic excited states of the CoH molecule were studied by multireference single and double excitation configuration interaction ’s correction calculations and sizeconsistent multireference coupled pair approximation (MRCPA) calculations. Calculations were performed under symmetry using Slatertype basis functions. The electronic ground state was confirmed to be the state. It was found that at least four reference configurations were needed to describe the ground state correctly at the level, while the state can be described well by one reference configuration, namely, the HartreeFock configuration. Larger dynamical electron correlation for the lowspin state than that for the highspin state is discussed. Spectroscopic constants, i.e., equilibrium bond lengths , harmonic frequency , and excitation energy, obtained by the method showed good correspondence with experimental values. MRCPA calculations gave a slightly shorter value for than experimental values, but improved and the excitation energy bringing them very close to experimental values.

Coupled cluster study of the energetic properties of
View Description Hide DescriptionAb initio electronic structure calculations are reported for , and its ions and . Geometric parameters are calculated using the singles and doubles coupled cluster method, including a perturbational correction for connected triple excitation, together with systematic sequences of correlation consistent basis sets extrapolated to the complete basis set (CBS) limit. Energetic and structural properties of and the cation and anion are reported. The heat of formation of at in the gas phase is predicted to be from the average of CBS two extrapolation procedures, less than the experimental heat of formation of of . The adiabatic ionization potential and electron affinity are predicted to be 9.37 and , respectively.

Spinforbidden band system of YF
View Description Hide DescriptionOptical spectra of jetcooled diatomic YF have been recorded using resonant twophoton ionization spectroscopy. A vibrational progression corresponding to the system has been identified. The vibrational frequency and anharmonicity of the state are 546.70 and , respectively. The 00, 10, and 20 bands of the system were rotationally resolved and analyzed, allowing the , 1, and 2 levels of the substate to be characterized. From these studies, , , and were obtained ( error limits). For these levels the spinspin coupling constant is identical within experimental error, as . The spinforbidden transition is made allowed by spinorbit interaction between the and the states. Excited state lifetimes of the and the states have been measured as 7.11(41) and , respectively. A spinorbit analysis shows that the state is contaminated with 2% character, which is approximately sufficient to explain the lifetime of the state.