Volume 121, Issue 12, 22 September 2004
 ARTICLES

 Theoretical Methods and Algorithms

Optical properties of singly charged conjugated oligomers: A coupledcluster equation of motion study
View Description Hide DescriptionWe have implemented a coupledclusterequation of motion approach combined with the intermediate neglect of differential overlap parametrization and applied it to study the excited states and optical absorptions in positively and negatively charged conjugated oligomers. The method is found to be both reliable and efficient. The theoretical results are in very good agreement with experiments and confirm that there appear two subgap absorption peaks upon polaron formation. Interestingly, the relative intensities of the polaroninduced subgap absorptions can be related to the extent of the lattice geometry relaxations.

Phasespace invariants for aggregates of particles: Hyperangular momenta and partitions of the classical kinetic energy
View Description Hide DescriptionRigorous definitions are presented for the kinematicangular momentum of a system of classical particles (a concept dual to the conventional angular momentum the angular momentum associated with the moments of inertia, and the contributions to the total kinetic energy of the system from various modes of the motion of the particles. Some key properties of these quantities are described—in particular, their invariance under any orthogonal coordinate transformation and the inequalities they are subject to. The main mathematical tool exploited is the singular value decomposition of rectangular matrices and its differentiation with respect to a parameter. The quantities introduced employ as ingredients particle coordinates and momenta, commonly available in classical trajectory studies of chemical reactions and in molecular dynamics simulations, and thus are of prospective use as sensitive and immediately calculated indicators of phase transitions,isomerizations, onsets of chaotic behavior, and other dynamical critical phenomena in classical microaggregates, such as nanoscale clusters.

Generalized simulated tempering realized on expanded ensembles of nonBoltzmann weights
View Description Hide DescriptionA generalized version of the simulated tempering operated in the expanded ensembles of nonBoltzmann weights has been proposed to mitigate a quasiergodicity problem occurring in simulations of rough energy landscapes. In contrast to conventional simulated tempering employing the Boltzmann weight, our method utilizes a parametrized, generalized distribution as a workhorse for stochastic exchanges of configurations and subensembles transitions, which allows a considerable enhancement for the rate of convergence of Monte Carlo and molecular dynamics simulations using delocalized weights. A feature of our method is that the exploration of the parameter space encouraging subensembles transitions is greatly accelerated using the dynamic update scheme for the weight via the average guide specific to the energy distribution. The performance and characteristic feature of our method have been validated in the liquidsolidtransition of LennardJones clusters and the conformational sampling of alanine dipeptide by taking two types of Tsallis [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] expanded ensembles associated with different parametrization schemes.

Geometric view of the thermodynamics of adsorption at a line of threephase contact
View Description Hide DescriptionWe consider three fluid phases meeting at a line of common contact and study the linear excesses per unit length of the contact line (the linear adsorptions of the fluid’s components. In any plane perpendicular to the contact line, the locus of choices for the otherwise arbitrary location of that line that makes one of the linear adsorptions, say vanish, is a rectangular hyperbola. Two of the adsorptions and then both vanish when the contact line is chosen to pass through any of the intersections of the two corresponding hyperbolas and There may be two or four such real intersections. It is found most surprisingly, and confirmed in a numerical example, that the adsorption of component 1 in a frame of reference in which the adsorptions and are both 0, depends on which intersection of the hyperbolas and is chosen for the location of the contact line. This implies that what had long been taken to be the line analog of the Gibbs adsorptionequation is incomplete; there must be additional, previously unanticipated terms in the relation, consistent with the invariance of the line tension to choice of location of the contact line. It is then not by itself but a related expression containing it that must be invariant, and this invariance is also confirmed in the numerical example. The presence of the additional terms in the adsorptionequation is further confirmed and their origin clarified in a meanfield densityfunctional model. The supplemental terms vanish at a wetting transition, where one of the contact angles goes to 0.

Finite size scaling for the atomic Shannoninformation entropy
View Description Hide DescriptionWe have developed the finite size scaling method to treat the criticality of Shannoninformation entropy for any given quantum Hamiltonian. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we present a study to estimate the critical exponents of the Shannoninformation entropy the electronic energy and the correlation length for atoms with the variable which is the inverse of the nuclear charge This was realized by approximating the multielectron atomic Hamiltonian with a oneelectron model Hamiltonian. This model is very accurate for describing the electronic structure of the atoms near their critical points. For several atoms in their ground electronic states, we have found that the critical exponents for He C N F and Ne respectively, are (1, 0, 0). At the critical points the bound state energies become absorbed or degenerate with continuum states and the entropies reach their maximum values, indicating a maximal delocalization of the electronic wave function.

Relativistically corrected hyperfine structure constants calculated with the regular approximation applied to correlation corrected ab initio theory
View Description Hide DescriptionThe infiniteorder regular approximation (IORA) and IORA with modified metric (IORAmm) is used to develop an algorithm for calculating relativistically corrected isotropic hyperfine structure (HFS) constants. The new method is applied to the calculation of alkali atoms Li–Fr, coinage metal atoms Cu,Ag, and Au, the radical ion, and the mercury containing radicals HgH, HgCN, and HgF. By stepwise improvement of the level of theory from Hartree–Fock to secondorder Møller–Plesset theory and to quadratic configuration interaction theory with single and double excitations, isotropic HFS constants of high accuracy were obtained for atoms and for molecular radicals. The importance of relativistic corrections is demonstrated.

Degeneracy in discrete variable representations: General considerations and application to the multiconfigurational timedependent Hartree approach
View Description Hide DescriptionProblems appear in discrete variable representations (DVRs) based on general basis sets when the coordinate matrix has degenerate eigenvalues. Then the DVR is not uniquely defined. This paper shows that this problem can be caused by symmetry. Taking the symmetry into account when constructing the DVR solves the problem. The symmetry effect can be particularly important for the timedependent DVR used in multiconfigurational timedependent Hartree calculations employing the correlation DVR (CDVR) approach. Problems reported previously for the initialstate selected treatment of the reaction can be attributed to this symmetry effect. They can be solved by using a symmetryadapted approach to construct the timedependent DVR. Thus, the present paper shows that the CDVR scheme can be employed also in initialstate selected scattering calculations if the symmetry of the system is properly taken into account in the construction of the timedependent DVR.

Truncation of the correlation consistent basis sets: An effective approach to the reduction of computational cost?
View Description Hide DescriptionThe systematic reduction of commonly used basis sets as a means to reduce computational cost is examined for a small test set of molecules, which includes HF, and HCN. Coupled cluster with single, double, and quasiperturbative triple excitations calculations were performed using both the correlation consistent basis sets, and a set of systematically reduced basis sets to examine both the impact of the reduction upon the accuracy of the structures and energies, and the computational cost savings achieved. The effect of several truncation scenarios upon basis set convergence is also examined. Overall, for the systems studied, a reduction can occur which preserves the wellestablished systematic convergence behavior of the correlation consistent basis sets.

Using molecular similarity to construct accurate semiempirical electronic structure theories
View Description Hide DescriptionAb initioelectronic structure methods give accurate results for small systems, but do not scale well to large systems. Chemical insight tells us that molecular functional groups will behave approximately the same way in all molecules, large or small. This molecular similarity is exploited in semiempirical methods, which couple simple electronic structuretheories with parameters for the transferable characteristics of functional groups. We propose that highlevel calculations on small molecules provide a rich source of parametrization data. In principle, we can select a functional group, generate a large amount of ab initio data on the group in various smallmolecule environments, and “mine” this data to build a sophisticated model for the group’s behavior in large environments. This work details such a model for electron correlation: a semiempirical, subsystembased correlation functional that predicts a subsystem’s twoelectron density matrix as a functional of its oneelectron density matrix. This model is demonstrated on two small systems: chains of linear, minimalbasis treated as a sum of four overlapping subsystems; and the aldehyde group of a set of molecules. The results provide an initial demonstration of the feasibility of the approach.

Normal mode analysis using the driven molecular dynamics method. II. An application to biological macromolecules
View Description Hide DescriptionThe driven moleculardynamics (DMD) method, recently proposed by Bowman, Zhang, and Brown [J. Chem. Phys. 119, 646 (2003)], has been implemented into the TINKER molecular modeling program package. The DMD method yields frequencies and normal modes without evaluation of the Hessian matrix. It employs an external harmonic driving term that can be used to scan the spectrum and determine resonant absorptions. The molecular motions, induced by driving at resonant frequencies, correspond to the normalmode vibrations. In the current work we apply the method to a 20residue protein, Trpcage, that has been reported by Neidigh, Fesinmeyer, and Andersen [Nature Struct. Biol. 9, 425 (2002)]. The structural and dynamical properties of this molecule, such as Bfactors, rootmean square fluctuations,anisotropies, vibrational entropy, and crosscorrelations coefficients, are calculated using the DMD method. The results are in very good agreement with ones calculated using standard normalmode analysis method. Thus, the DMD method provides a viable alternative to the standard Hessianbased method and has considerable potential for the study of large systems, where the Hessianbased method is not feasible.

A semiempirical generalized gradient approximation exchangecorrelation functional
View Description Hide DescriptionWe describe our attempts to improve upon the quality of the KT1 and KT2 generalized gradient approximation (GGA) exchangecorrelation functionals [T. W. Keal and D. J. Tozer, J. Chem. Phys. 119, 3015 (2003)], through the introduction of additional gradientcorrected exchange and correlation terms. A GGA functional, denoted KT3, is presented, which maintains the high quality maingroup nuclear magnetic resonance shielding constants obtained with KT1 and KT2; results are 2–3 times more accurate than conventional GGA and hybrid functionals. For the extensive range of systems considered in this study, KT3 also provides atomization energies, ionization potentials,electron affinities,proton affinities, bond angles, and electronic polarizabilities that are comparable to, or that surpass, those of the best presentday GGAs. Furthermore, it provides equilibrium molecular bond lengths and diatomic harmonic vibrational wave numbers that are as accurate as those from the best hybrid functionals. Further improvements are required in the description of classical chemical reaction barriers.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Ab initio study of f–f spectroscopy and chemical binding
View Description Hide DescriptionA valence full configuration interaction study with a polarized doubleζ quality basis set has been carried out for the lowest 49 electronic states of The calculations use a pseudopotential treatment for the core electrons and incorporate a oneelectron spin–orbit interaction operator. Electrons in the valence s, p, d, and f subshells were included in the active space. The resulting electronic potential energy curves are largely repulsive. The chemical bonding is ionic in character with negligible participation of 5felectrons. The molecular spectroscopy of arises essentially from an in situ core with states slightly redshifted by the presence of chloride ion. asymptotes which give rise to the few attractive potential energy curves can be predicted by analysis of the spectroscopy of isolated and The attractive curves have substantial binding energies, on the order of 75–80 kcal/mol, and are noticeably lower than recent indirect measurements on the isovalent An independent empirical correlation supports the predicted reduction in binding energy. The energies of the repulsive curves are strongly dependent on the selection of the underlying atomic orbitals while the energies of the attractive curves do not display this sensitivity. The calculations were carried out using our recently developed parallel spin–orbit configuration interaction software.

Femtosecond study of dynamics
View Description Hide DescriptionThe shorttime nuclear dynamics of is investigated using femtosecond photodetachmentphotoionization spectroscopy and timedependent quantum wave packet calculations. The dynamics is initiated in the electronic ground state of the complex by electron photodetachment from the complex, where hydrogen atoms are oriented toward Cu. Several timeresolved resonant multiphoton ionization schemes are used to probe the ensuing reorientation and dissociation. Immediately following photodetachment, the neutral complex is far from its minimum energy geometry and possesses an internal energy comparable to the dissociation energy and undergoes both largeamplitude motion and dissociation.Dissociation is observed to occur on three distinct time scales: 0.6, 8, and 100 ps. These results are compared to the results of timedependent wave packet calculations, propagating the initial anion vibrational wave functions on the groundstate potential of the neutral complex. An excellent agreement is obtained between the experimental results and the ionization signals derived from the calculated probability amplitudes. Related experiments and calculations are carried out on the complex, with results very similar to those of

A theoretical and computational study of the anion, neutral, and cation complexes
View Description Hide DescriptionAn ab initio investigation of the potential energy surfaces and vibrational energies and wave functions of the anion, neutral, and cation complexes is presented. The equilibrium geometries and harmonic frequencies of the three charge states of are calculated at the MP2 level of theory. CCSD(T) calculations predict a vertical electron detachment energy for the anion complex of 1.65 eV and a vertical ionization potential for the neutral complex of 6.27 eV. Potential energy surfaces are calculated for the three charge states of the copperwater complexes. These potential energy surfaces are used in variational calculations of the vibrational wave functions and energies and from these, the dissociation energies of the anion, neutral, and cation charge states of are predicted to be 0.39, 0.16, and 1.74 eV, respectively. In addition, the vertical excitation energies, that correspond to the transition of the copper atom, and ionization potentials of the neutral are calculated over a range of configurations. In hydrogenbonded, CuHOH configurations, the vertical excitation and ionizationenergies are blueshifted with respect to the corresponding values for atomic copper, and in configurations where the copper atom is located near the oxygen end of water, both quantities are redshifted.

Dissociative recombination cross section and branching ratios of protonated dimethyl disulfide and Nmethylacetamide
View Description Hide DescriptionDimethyl disulfide (DMDS) and Nmethylacetamide are two first choice model systems that represent the disulfide bridge bonding and the peptide bonding in proteins. These molecules are therefore suitable for investigation of the mechanisms involved when proteins fragment under electron capturedissociation (ECD). The dissociative recombination cross sections for both protonated DMDS and protonated Nmethylacetamide were determined at electron energies ranging from 0.001 to 0.3 eV. Also, the branching ratios at 0 eV centerofmass collision energy were determined. The present results give support for the indirect mechanism of ECD, where free hydrogen atoms produced in the initial fragmentation step induce further decomposition. We suggest that both indirect and direct dissociations play a role in ECD.

Structure of the clusters via ab initio genetic algorithm and photoelectron spectroscopy
View Description Hide DescriptionThe application of the ab initio genetic algorithm with an embedded gradient has been carried out for the elucidation of global minimum structures of a series of anionic sodium chloride clusters, produced in the gas phase using electrospray ionization and studied by photoelectron spectroscopy. These are all superhalogen species with extremely high electron binding energies. The vertical electron detachment energies for were measured to be 5.6, 6.46, 6.3, and 7.0 eV, for respectively. Our ab initio gradient embedded genetic algorithm program detected the linear global minima for and and threedimensional structures for the larger species. was found to have symmetry, which can be viewed as a cube missing a corner cation, whereas was found to have symmetry, close to a 3×3 planar structure. Excellent agreement between the theoretically calculated and the experimental spectra was observed, confirming the obtained structures and demonstrating the power of the developed genetic algorithm technique.

High level ab initio study of the structure and vibrational spectra of
View Description Hide DescriptionA highlevel ab initio study has been performed on the conformational structure and vibrational spectra of Calculations carried out with coupledcluster methods using a series of Pople and Dunning basis sets reveal that there is a significant basis set dependence on the predicted ab initio structure. Higher angular momentumbasis sets are shown to be necessary in order to bring the calculated structure into agreement with experimental rotational constants. Harmonic vibrational frequencies of are computed at the CCSD(T)/augccpVTZ level of theory while the corresponding vibrational anharmonicities are calculated at the MP2/ccpVTZ level. In addition, the absorption cross sections of OH stretching overtones in are calculated using a dipole function computed at the QCISD level of theory and found to be in good agreement with the available experimental data.

A computational study of the dihydrogen bonded complexes HBeH⋯HArF and HBeH⋯HKrF
View Description Hide DescriptionWe report an ab initio computational study of the properties of two linear dihydrogenbonded complexes of HBeH with the recently discovered rare gas compounds HArF and HKrF at the level of theory. The HBeH⋯HArF and HBeH⋯HKrF complexes were found to have zeropoint energy corrected binding energies of 27 and 12 kJ mol^{−1}, respectively. Large red shifts of the HRg vibrational stretching frequency in both complexes were also predicted. The electron density rearrangement of the rare gas compounds on complexation was also examined. We also consider the relative stabilities of Dcontaining isotopomers of the complexes by comparison of their computed zeropoint vibrational energies.

Core excitations of naphthalene: Vibrational structure versus chemical shifts
View Description Hide DescriptionHighresolution xray photoelectron emission (XPS) and nearedge xray absorption fine structure(NEXAFS)spectra of naphthalene are analyzed in terms of the initial state chemical shifts and the vibrational fine structure of the excitations. Carbon atoms located at peripheral sites experience only a small chemical shift and exhibit rather similar chargevibrational coupling, while the atoms in the bridging positions differ substantially. In the XPSspectra, CH stretching modes provide important contributions to the overall shape of the spectrum. In contrast, the NEXAFS spectrum contains only vibrational progressions from particular CC stretching modes. The accuracy of ab initio calculations of absolute electronic transition energies is discussed in the context of minute chemical shifts, the vibrational fine structure, and the state multiplicity.

A timedependent wave packet study of the vibronic and spinorbit interactions in the dynamics of reaction
View Description Hide DescriptionWe investigate the vibronic and spinorbit (SO) coupling effects in the stateselected dynamics of the title reaction with the aid of a timedependent wave packet approach. The ab initiopotential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the atom to the molecule splits the degeneracy of the state and gives rise to and electronic states. These two surfaces form a conical intersection at this geometry. These states transform as and respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into and components at the linear geometry. The groundstate reagent correlates with and where as the SO excited reagent correlates with at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial stateselected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a timedependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled twostate model and for the total angular momentum (neglecting the electronic orbitalangular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled threestate model comprising six diabatic surfaces for the total angular momentum neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.