Volume 124, Issue 12, 28 March 2006
 COMMUNICATIONS


Formation of capillary bridges in twodimensional atomic force microscopelike geometry
View Description Hide DescriptionWe discuss the phase diagram of a fluid confined in a twodimensional atomic force microscopelike geometry which allows the formation of liquid bridges connecting the opposite walls. The corresponding phase behavior of the fluid is influenced by the phenomenon of complete filling of a wedge.

Toward uniform nanotubular compounds: Synthetic approach and ab initio calculations
View Description Hide DescriptionWe propose to synthesize a new class of singlewalled nanotubular compounds (SWNCs) and investigate the interplay between their structural and electronic properties using ab initiodensity functional calculations. SWNCs are composed of cyclacenes of variable diameter interconnected by various linker compounds. Cyclacenes map directly onto and can be viewed as the shortest segments of zigzag carbon nanotubes. We focus on cyclacenes with –12 fused benzene rings interconnected by biphenyl, tetrazine, or acetylene linkers. Depending upon the nature and the orientation of the linkers, we find it possible to change the systems from narrowgap to widegap semiconductors, and to modulate the band dispersion, suggesting the possibility of band gap engineering.
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 ARTICLES

 Theoretical Methods and Algorithms

SPOCK.CI: A multireference spinorbit configuration interaction method for large molecules
View Description Hide DescriptionWe present SPOCK.CI, a selecting direct multireference spinorbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spinfree density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys.111, 5645 (1999)] and includes spinorbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective oneelectron spinorbit atomic meanfield Hamiltonian, the application of a resolutionoftheidentity approximation to computationally expensive spinfree fourindex integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spindependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Secondorder properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sumoverstate approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on pyran4thione, dithiosuccinimide, and freebase porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of freebase porphin, MRSOCI calculations can easily be run on a singleprocessor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.

Full configuration interaction approach to the fewelectron problem in artificial atoms
View Description Hide DescriptionWe present a new high performance configuration interaction code optimally designed for the calculation of the lowestenergy eigenstates of a few electrons in semiconductorquantum dots (also called artificial atoms) in the strong interaction regime. The implementation relies on a singleparticle representation, but it is independent of the choice of the singleparticle basis and, therefore, of the details of the device and configuration of external fields. Assuming no truncation of the Fock space of Slater determinants generated from the chosen singleparticle basis, the code may tackle regimes where Coulomb interaction very effectively mixes many determinants. Typical strongly correlated systems lead to very large diagonalization problems; in our implementation, the secular equation is reduced to its minimal rank by exploiting the symmetry of the effectivemass interacting Hamiltonian, including square total spin. The resulting Hamiltonian is diagonalized via parallel implementation of the Lanczos algorithm. The code gives access to both wave functions and energies of first excited states. Excellent code scalability in a parallel environment is demonstrated; accuracy is tested for the case of up to eight electrons confined in a twodimensional harmonic trap as the density is progressively diluted up to the Wigner regime, where correlations become dominant. Comparison with previous quantum Monte Carlo simulations in the Wigner regime demonstrates power and flexibility of the method.

Cooperative effects in photon statistics of molecular dimers with spectral diffusion
View Description Hide DescriptionThe twopoint fluorescence intensity correlation function and the Mandel parameter are calculated for a strongly pumped dimer of twolevel molecules undergoing GaussianMarkovian frequency fluctuations. The effects of detuning and saturation are examined. All fluctuation time scale regimes are explored using a continued fraction solution of the stochastic Liouville equation for the generating function. Bunching and antibunching are observed for slow and fast fluctuations, respectively. The shorttime antibunching dip in and its variation with intermolecular coupling, the exciton annihilation rate, and laser detuning are studied.

Electron density fitting for the Coulomb problem in relativistic densityfunctional theory
View Description Hide DescriptionA density fitting approach for the Coulomb matrix representation within the fourcomponent formulation of relativistic densityfunctional theory is presented. Our implementation, which uses spinor basis sets, shares all the advantages of those found in nonrelativistic quantum chemistry. We show that very accurate Coulomb energies may be obtained using a modest number of scalar auxiliary basis functions for molecules containing heavy atoms. The efficiency of this new implementation is demonstrated in a detailed study of the spectroscopic properties of the gold dimer, and its scaling behavior has been tested by calculations of some closedshell gold clusters . The algorithm is found to scale as , just as it does in the nonrelativistic case, and represents a dramatic improvement in efficiency over the conventional approach in the calculation of the Coulomb matrix, with computation times that are reduced to less than 3% for and up to 1% in the case of .

Towards a spinadapted coupledcluster theory for highspin openshell states
View Description Hide DescriptionA spinadapted coupledcluster (SACC) scheme based on the additional consideration of spin constraints is proposed for the quantum chemical treatment of highspin openshell cases. Its computational feasibility is demonstrated via a pilot implementation within the singles and doubles approximation. Test calculations indicate that the suggested SACC scheme provides results of similar accuracy as the more traditional schemes without spin adaptation.

Computation of methodologyindependent ionic solvation free energies from molecular simulations. I. The electrostatic potential in molecular liquids
View Description Hide DescriptionThe computation of ionic solvation free energies from atomistic simulations is a surprisingly difficult problem that has found no satisfactory solution for more than . The reason is that the charging free energies evaluated from such simulations are affected by very large errors. One of these is related to the choice of a specific convention for summing up the contributions of solvent charges to the electrostatic potential in the ionic cavity, namely, on the basis of point charges within entire solvent molecules ( scheme) or on the basis of individual point charges ( scheme). The use of an inappropriate convention may lead to a chargeindependent offset in the calculated potential, which depends on the details of the summation scheme, on the quadrupolemoment trace of the solvent molecule, and on the approximate form used to represent electrostatic interactions in the system. However, whether the or scheme (if any) represents the appropriate convention is still a matter of ongoing debate. The goal of the present article is to settle this longstanding controversy by carefully analyzing (both analytically and numerically) the properties of the electrostatic potential in molecular liquids (and inside cavities within them). Restricting the discussion to real liquids of “spherical” solvent molecules (represented by a classical solvent model with a single van der Waals interaction site), it is concluded that (i) for Coulombic (or straightcutoff truncated) electrostatic interactions, the scheme is the appropriate way of calculating the electrostatic potential; (ii) for nonCoulombic interactions deriving from a continuously differentiable function, both and schemes generally deliver an incorrect result (for which an analytical correction must be applied); and (iii) finitetemperature effects, including intermolecular orientation correlations and a preferential orientational structure in the neighborhood of a liquidvacuum interface, must be taken into account. Applications of these results to the computation methodologyindependent ionic solvation free energies from molecular simulations will be the scope of a forthcoming article.

Gridbased ThomasFermiAmaldi equation with the molecular cusp condition
View Description Hide DescriptionFirst, the ThomasFermiAmaldi (TFA) equation was formulated with a newly derived condition to remove the singularities at the nuclei, which coincided with the molecular cusp condition. Next, the collocation method was applied to the TFA equation using the gridbased density functional theory. In this paper, the electron densities and the radial probabilities for specific atoms (He, Be, Ne, Mg, Ar, Ca) were found to agree with those from the ThomasFermiDirac (TFD) method. Total energies for specific atoms (He, Ne, Ar, Kr, Xe, Rn) and molecules were also found to be close to those from the HartreeFock method using the Pople basis set 6311G relative to the TFD method. In addition, the computational expense to determine the electron density and its corresponding energy for a large scale structure, such as a carbon nanotube, is shown to be much more efficient compared to the conventional HartreeFock method using the 631G Pople basis set.

Development of a latticesum method emulating nonperiodic boundary conditions for the treatment of electrostatic interactions in molecular simulations: A continuumelectrostatics study
View Description Hide DescriptionArtifacts induced by the application of periodic boundary conditions and latticesum methods in explicitsolvent simulations of (bio)molecular systems are nowadays a major concern in the computersimulation community. The present article reports a first step toward the design of a modified latticesum algorithm emulating nonperiodic boundary conditions, and therefore exempt of such periodicityinduced artifacts. This result is achieved here in the (more simple) context of continuum electrostatics. It is shown that an appropriate modification of the periodic Poisson equation and of its boundary conditions leads to a continuumelectrostatics scheme, which, although applied under periodic boundary conditions, exactly mimics the nonperiodic situation. The possible extension of this scheme to explicitsolvent simulations is outlined and its practical implementation will be described in more details in a forthcoming article.

On the characterization of three state conical intersections: A quasianalytic theory using a group homomorphism approach
View Description Hide DescriptionIn this work, degenerate perturbation theory through second order is used to characterize the vicinity of a three state conical intersection. This report extends our recent demonstration that it is possible to describe the branching space (in which the degeneracy is lifted linearly) and seam space (in which the degeneracy is preserved) in the vicinity of a two state conical intersection using second order perturbation theory. The general analysis developed here is based on a group homomorphism approach. Second order perturbation theory, in conjunction with high quality ab initioelectronic structure data, produces an approximately diabatic Hamiltonian whose eigenenergies and eigenstates can accurately describe the three adiabatic potential energy surfaces, the interstate derivative couplings, and the branching and seam spaces in their full dimensionality. The application of this approach to the minimum energy three state conical intersection of the pyrazolyl radical demonstrates the potential of this method. A Hamiltonian comprised of the ten characteristic (linear) parameters and over order parameters is constructed to describe the branching space associated with a point of conical intersection. The second order parameters are determined using data at only 30 points. In the vicinity of the conical intersection the energy and derivative couplings are well reproduced and the singularity in the derivative coupling is analyzed.

Counterdiabatic suppression of background state population in resonance leaking by controlling intermediate branching
View Description Hide DescriptionThe counterdiabatic principle [M. Demirplak and S. A. Rice, J. Phys. Chem. A107, 9937 (2003)] is used in a pragmatic way to formulate a practical control strategy for perturbed population transfer. Interpreting the appearance of population in undesirable intruder or background states as phenomenological consequences of diabatic perturbations, such branching is suppressed as soon as it arises. By invoking a penalty term that is sensitive to any transitional population in undesirable levels, a correction field is created which effectively prevents diabatic behavior. This strategy is applied to the control of background state population in multiphoton excitations. For a model fivelevel system we show that leaking of a resonant threephoton transition to a background state can readily be suppressed by simple correction fields obtained from our intermediatebranching driven implementation of counterdiabatic control.

Moleculardynamics evaluation of fluidphase equilibrium properties by a novel freeenergy perturbation approach: Application to gas solubility and vapor pressure of liquid hexane
View Description Hide DescriptionA novel freeenergyperturbation method is developed for the computation of the free energy of transferring a molecule between fluid phases. The methodology consists in drawing a freeenergy profile of the target molecule moving across a binaryphase structure built in the computer. The novelty of the method lies in the difference of the definition of the freeenergy profile from the common definition. As an important element of the method, the process of making a correction to the transfer free energy with respect to the cutoff of intermolecular forces is elucidated. In order to examine the performance of the method in the application to fluidphase equilibrium properties, moleculardynamics computations are carried out for the evaluation of gas solubility and vapor pressure of liquid hexane at . The gas species treated are methane, ethane, propane, and butane, with the gas solubility expressed as Henry’s constant. It is shown that the method works fine and calculated results are generally in good agreement with experiments. It is found that the cutoff correction is strikingly large, constituting a dominant part of the calculated transfer free energy at the cutoff of .

Assessing a new nonempirical density functional: Difficulties in treating conjugation effects
View Description Hide DescriptionThe reliability of the TaoPerdewStaroverovScuseria (TPSS) exchangecorrelation functional for the description of conjugation effects in modelconjugated systems has been thoroughly assessed through the calculation of torsion energy profiles. The functional reproduces qualitatively the shape of torsional potentials but, interestingly, the mixing of TPSS and exact exchange governs the quantitative results: thus, welldefined hybrid extensions of the functional are consistently employed to improve the results. The hybrid approaches led to more accurate descriptions of conjugation effects but, however, the finest performance along the whole range of dihedral angles was obtained by a customized mixing of pure or hybrid TPSS functionals and wave function methods in a multicoefficient fashion. Despite the successful construction of this nonempirical functional, higher rungs of the ladder of methods in which TPSS is based are hoped to reduce the errors with respect to reference data for conjugated systems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

An opticaloptical double resonance probe of the lowest triplet state of jetcooled thiophosgene: Rovibronic structures and electronic relaxation
View Description Hide DescriptionThe vibrational structure, rotational structure, and electronic relaxation of the “dark” state of jetcooled thiophosgene have been investigated by twocolor opticaloptical double resonance (OODR) spectroscopy, which monitors the fluorescence generated by excitation. This method is capable of isolating the vibrational structure into , , and symmetry blocks. The fluorescencedetected vibrational structure of the spin state of shows that the CS stretching frequency as well as the barrier height for pyramidal deformation are significantly greater in the state than in the corresponding state. The differing vibrational parameters of the thiophosgene relative to the thiophosgene can be attributed to the motions of unpaired electrons that are better correlated when they are in the excited singlet state than when they are in the triplet state of same electron configuration. A set of structural parameters and the information concerning the spin states have been obtained from leastsquare fittings of the rotationally resolved excitation spectrum. The nearly degenerate and spin states are well removed from spin component, indicating that thiophosgene is a good example of case (ab) coupling. The decay of the spin state of thiophosgene, obtained from timeresolved OODR experiment, is characteristic of strongcoupling intermediatecase decay in which an initial rapid decay is followed by recurrences and/or a longlived quasiexponential decay.

A study of the ground state of manganese dimer using quasidegenerate perturbation theory
View Description Hide DescriptionWe study the electronic structure of the ground state of the manganese dimer using the stateaveraged complete active space selfconsistent field method, followed by secondorder quasidegenerate perturbation theory. Overall potential energy curves are calculated for the , , and states, which are candidates for the ground state. Of these states, the state has the lowest energy and we therefore identify it as the ground state. We find values of , , and for the bond length, dissociation energy, and vibrational frequency, in good agreement with the observed values of , , and in raregas matrices. These values show that the manganese dimer is a van der Waals molecule with antiferromagnetic coupling.

Theoretical investigation of twophoton absorption allowed excited states in symmetrically substituted diacetylenes by ab initio molecularorbital method
View Description Hide DescriptionSymmetrically substituted diacetylene compounds, which shows large twophoton absorption(TPA) cross sections, have been theoretically investigated by the ab initio molecularorbital method employing several theoretical models including the configuration interaction with single excitation (CIS), random phase approximation (RPA), and timedependent densityfunctional theory (TDDFT) methods. The calculated excited energies are overestimated by CIS or RPA, whereas underestimated by TDDFT with the B3LYP parametrization for both onephoton absorption (OPA) and TPA allowed states. The lowest OPA state is well described by the highest occupied molecular orbital (HOMO)lowest unoccupied molecular orbital (LUMO) transition. On the other hand, lower TPA allowed states can be represented as the superposition of the and transitions, giving rise to two TPA allowed states. The absorption intensity for the lower TPA state of the diacetylenes molecules is discussed in terms of the alternancy symmetry and its breaking. The symmetry property is differently manifested for neutral and dicationic diacetylenes. Introduction of charges breaks the alternancy symmetry, which gives rise to an increase in the TPA cross sections at the lower frequency. The upper TPA state is calculated to show huge TPA cross sections, which reproduces the enhancement of the TPA cross section experimentally observed for one of the diacetylenes at the higherfrequency region. The enhancement is discussed employing an index defined as the ratio of the transitionpolarizability and its static limit, which represents the degree of influence of onephoton resonance on the TPA intensity. The huge TPA cross sections are found to be due to a nearresonance effect. The present theoretical calculation approves the previously proposed assumption based on the fourstate (dual threestate) model, which consists of the ground, one OPA allowed, and two TPA allowed states.

How strong is the interaction between a noble gas atom and a noble metal atom in the insertion compounds ( and Ag, and , Kr, and Xe)?
View Description Hide DescriptionAb initio molecular orbital calculations have been carried out to investigate the structure and the stability of noble gas insertion compounds of the type ( and Ag, and , Kr, and Xe) through second order MøllerPlesset perturbation method. All the species are found to have a linear structure with a noble gas–noble metal bond, the distance of which is closer to the respective covalent bond length in comparison with the relevant van der Waals limit. The dissociation energies corresponding to the lowest energy fragmentation products, , have been found to be in the range of to . The respective barrier heights pertinent to the bent transition states ( bending mode) are quite high for the CuXeF and AgXeF species, although for the Ar and Kr containing species the same are rather low. Nevertheless the bond length in compounds reported here is the smallest bond ever predicted through any experimental or theoretical investigation, indicating strongest interaction. All these species (except AgArF) are found to be metastable in their respective potential energy surface, and the dissociation energies corresponding to the fragments have been calculated to be . Indeed, in the present work we have demonstrated that the noble metal–noble gas interaction strength in species (with and Ag, and and Xe) is much stronger than that in systems. Bader’s [Atoms in moleculesA Quantum Theory (Oxford University Press, Oxford, 1990)] topological theory of atoms in molecules (AIM) has been employed to explore the nature of interactions involved in these systems. Geometric as well as energetic considerations along with AIM results suggest a partial covalent nature of bonds in these systems. The present results strengthen our earlier work and further support the proposition on the possibility of experimental identification of this new class of insertion compounds of noble gas atoms containing noble gas–noble metal bond.

On the structure and chemical bonding of and in upon coordination
View Description Hide DescriptionPhotoelectron spectroscopy was combined with ab initio calculations to elucidate the structure and bonding in and . Wellresolved electronic transitions were observed in the photoelectron spectra of and at three photon energies (355, 266, and ). The spectra of were observed to be similar to those of except that the electron binding energies of the former are lower, suggesting that the motif in is structurally and electronically similar to that in . The electron affinities of and were measured fairly accurately to be and , respectively. Global minimum structure searches for and were performed using gradient embedded genetic algorithm followed by B3LYP, MP2, and CCSD(T) calculations. Vertical electron detachment energies were calculated for the lowest and structures at the CCSD(T)/, ROVGF/, UOVGF/, and timedependent B3LYP/ levels of theory. Experimental vertical detachment energies were used to verify the global minimum structure for . Though the octahedral , analogous to the closo form of borane , is the most stable form for the bare hexasilicon dianion, it is not the kernel for the global minimum. The most stable isomer of is based on a motif, which is distorted into symmetry similar to the ground state structure of . The octahedral coordinated by a is a lowlying isomer and was also observed experimentally. The chemical bonding in and was understood using natural bond orbital, molecular orbital, and electron localization function analyses.

Potential energy surface, kinetics, and dynamics study of the reaction
View Description Hide DescriptionA modified and recalibrated potential energy surface for the gasphase reaction is reported and tested. It is completely symmetric with respect to the permutation of the four methane hydrogen atoms and is calibrated with respect to updated experimental and theoretical stationary point properties and experimental forward thermal rate constants. From the kinetics point of view, the forward and reverse thermal rate constants and the activation energies were calculated using the variational transitionstate theory with semiclassical transmission coefficients over a wide temperature range of . The theoretical results reproduce the available experimental data, with a small curvature of the Arrhenius plot which indicates the role of tunneling in this hydrogen abstraction reaction. A dynamics study was also performed on this PES using quasiclassical trajectory(QCT) calculations, including corrections to avoid zeropoint energy leakage along the trajectories. First, we found a noticeable internal energy in the coproduct methyl radical, both in the groundstate and vibrationally excited reactions. This internal energy was directly precluded in some experiments or oversimplified in previous theoretical studies using pseudotriatomic models. Second, our QCT calculations give HCl rotational distributions slightly hotter than those in experiment, but correctly describing the experimental trend of decreasing the HCl product rotation excitation in going from to for the reaction. Third, the state specific scattering distributions present a reasonable agreement with experiment, although they tend to make the reaction more forward and backward scattered than found experimentally probably because of the hotter rotational distribution and the deficiencies of the QCT methods.