Volume 124, Issue 21, 07 June 2006
 ARTICLES

 Theoretical Methods and Algorithms

Frozen local hole approximation
View Description Hide DescriptionThe frozen local hole approximation (FLHA) is an adiabatic approximation which is aimed to simplify the correlation calculations of valence and conduction bands of solids and polymers or, more generally, of the ionization potentials and electron affinities of any large system. Within this approximation correlated local hole states (CLHSs) are explicitly generated by correlating local HartreeFock (HF) hole states, i.e., particle determinants in which the electron has been removed from a local occupied orbital. The hole orbital and its occupancy are kept frozen during these correlation calculations, implying a rather stringent configuration selection. Effective Hamilton matrix elements are then evaluated with the above CLHSs; diagonalization finally yields the desired correlation corrections for the cationic hole states. We compare and analyze the results of the FLHA with the results of a full multireference configuration interaction with single and double excitations calculation for two prototype model systems, ladders and chains. Excellent numerical agreement between the two approaches is found. Comparing the FLHA with a full correlation treatment in the framework of quasidegenerate variational perturbation theory reveals that the leading contributions in the two approaches are identical. In the same way it could be shown that a much less demanding selfconsistent field (SCF) calculation around a frozen local hole fully recovers, up to first order, all the leading single excitation contributions. Thus, both the FLHA and the above SCF approximation are well justified and provide a very promising and efficient alternative to fully correlated wavefunctionbased treatments of the valence and conduction bands in extended systems.

Assessment of a simple correction for the longrange chargetransfer problem in timedependent densityfunctional theory
View Description Hide DescriptionThe failure of the timedependent densityfunctional theory to describe longrange chargetransfer (CT) excitations correctly is a serious problem for calculations of electronic transitions in large systems, especially if they are composed of several weakly interacting units. The problem is particularly severe for molecules in solution, either modeled by periodic boundary calculations with large box sizes or by cluster calculations employing extended solvent shells. In the present study we describe the implementation and assessment of a simple physically motivated correction to the exchangecorrelation kernel suggested in a previous study [O. Gritsenko and E. J. Baerends J. Chem. Phys.121, 655 (2004)]. It introduces the required divergence in the kernel when the transition density goes to zero due to a large spatial distance between the “electron” (in the virtual orbital) and the “hole” (in the occupied orbital). A major benefit arises for solvated molecules, for which many CT excitations occur from solvent to solute or vice versa. In these cases, the correction of the exchangecorrelation kernel can be used to automatically “clean up” the spectrum and significantly reduce the computational effort to determine lowlying transitions of the solute. This correction uses a phenomenological parameter, which is needed to identify a CT excitation in terms of the orbital density overlap of the occupied and virtual orbitals involved. Another quantity needed in this approach is the magnitude of the correction in the asymptotic limit. Although this can, in principle, be calculated rigorously for a given CT transition, we assess a simple approximation to it that can automatically be applied to a number of lowenergy CT excitations without additional computational effort. We show that the method is robust and correctly shifts longrange CT excitations, while other excitations remain unaffected. We discuss problems arising from a strong delocalization of orbitals, which leads to a breakdown of the correction criterion.

Evaluation of pressure tensor in constantvolume simulations of hard and soft convex bodies
View Description Hide DescriptionA method for calculating the pressuretensor in constantvolume Monte Carlo simulations of convex bodies is presented. In contrast to other approaches, the method requires only an isotropic scaling of the simulation box and the counting of simple geometric quantities characterizing overlapping pairs. Nonsphericity presents no special difficulties. The result is expressed as a sum of pairwise contributions and can therefore be used to compute pressuretensor profiles in a conventional way.

The discrete representation correspondence between quantum and classical spatial distributions of angular momentum vectors
View Description Hide DescriptionThis work demonstrates that the quantum mechanical moments of a state described by the density matrix correspond to discrete spherical harmonic moments of the classical multipole expansion of the spatial distribution of the angular momentum vectors. For the diagonal density matrix elements, this work exploits the fact that the quantum mechanical vector coupling (ClebschGordan) coefficients become increasingly accurate discrete representations of spherical harmonics as increases. A Schwingertype basis accounts for nonaxially symmetric angular distributions, which result in nonzero offdiagonal elements of the density matrix. The resulting discrete minimum uncertainty picture of the classical moments has a stringent equivalence with the quantum mechanical one for all and provides an unambiguous connection for the classical and quantum moments in the large limit. The equivalence is numerically tested for simple models, and there is a satisfying equivalence even for small . Applications, implications, and extensions are indicated, and the relevance of this work for the interpretation of classical mechanical simulations of inelastic and reactive molecular collisions will be documented elsewhere.

Exchange energy gradients with respect to atomic positions and cell parameters within the HartreeFock point approximation
View Description Hide DescriptionRecently, linear scaling construction of the periodic exact HartreeFock exchange matrix within the point approximation has been introduced [J. Chem. Phys.122, 124105 (2005)]. In this article, a formalism for evaluation of analytical HartreeFock exchange energy gradients with respect to atomic positions and cell parameters at the point approximation is presented. While the evaluation of exchange gradients with respect to atomic positions is similar to those in the gas phase limit, the gradients with respect to cell parameters involve the accumulation of atomic gradients multiplied by appropriate factors and a modified electron repulsion integral (ERI). This latter integral arises from use of the minimum image convention in the definition of the point HartreeFock approximation. We demonstrate how this new ERI can be computed with the help of a modified vertical recurrence relation in the frame of the ObaraSaika and HeadGordonPople algorithm. As an illustration, the analytical gradients have been used in conjunction with the QUICCA algorithm [K. Németh and M. Challacombe, J. Chem. Phys.121, 2877 (2004)] to optimize periodic systems at the HartreeFock level of theory.

Aspects of quantum coherence in the optical Bloch equations
View Description Hide DescriptionAspects of coherence and decoherence are analyzed within the optical Bloch equations. By rewriting the analytic solution in an alternate form, we are able to emphasize a number of unusual features: (a) despite the Markovian nature of the bath, coherence at long times can be retained; (b) the longtime asymptotic degree of coherence in the system is intertwined with the asymptotic difference in level populations; (c) the traditional populationrelaxation and decoherence times, and , lose their meaning when the system is in the presence of an external field, and are replaced by more general overall time scales; (d) increasing the field strength, quantified by the Rabi frequency , increases the rate of decoherence rather than reducing it, as one might expect; and (e) maximum asymptotic coherence is reached when the system parameters satisfy .

Multipolemultimode Floquet theory of rotational resonance width experiments: distance measurements in uniformly labeled solids
View Description Hide DescriptionA formal description of zeroquantum (ZQ) NMR processes using multipolemultimode Floquet theory is proposed for studying polarization transfer in magic angle spinning experiments. Specifically, we investigate the factors affecting the accuracy and precision of distance measurements that are based on ZQmagnetization exchange processes in rotational resonance width experiments. With suitable examples drawn from measurements in acetyl LvalineLleucine, we substantiate our approach and propose methods for improving the accuracy and reliability of such distance measurements in uniformly , labeled solids. In addition, the theoretical model presented in this article provides a more general framework for describing relaxation phenomena involving multiple decay rate constants in zeroquantum processes.

Charge transfer interaction in the effective fragment potential method
View Description Hide DescriptionAn approximate formula is derived and implemented in the general effective fragment potential (EFP2) method to model the intermolecular charge transferinteraction. This formula is based on second order intermolecular perturbation theory and utilizes canonical molecular orbitals and Fock matrices obtained with preparative selfconsistent field calculations. It predicts charge transferenergies that are in reasonable agreement with the reduced variational space energy decomposition analysis. The formulas for the charge transfer gradients with respect to EFP translational and rotational displacements are also derived and implemented.

Multidimensional reactive scattering with quantum trajectories: Dynamics with 50–200 vibrational modes
View Description Hide DescriptionThe dynamics of ensembles containing thousands of quantum trajectories are studied for multidimensional systems undergoing reactive scattering. The Hamiltonian and equations of motion are formulated in curvilinear reaction path coordinates, for the case of a planar (zerotorsion) reaction path. In order to enhance the computational efficiency, an improved least squares fitting procedure is introduced. This scheme involves contracted basis sets and the use of inner and outer stencils around points where fitting is performed. This method is applied to reactive systems with 50–200 harmonic vibrational modes which are coupled to motion along the reaction coordinate. Dynamical results, including trajectory evolution and timedependent reaction probabilities, are presented and power law scaling of computation time with the number of vibrational modes is described.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photoionization of helium nanodroplets doped with rare gas atoms
View Description Hide DescriptionPhotoionization of He dropletsdoped with rare gas atoms (, Ar, Kr, and Xe) was studied by timeofflight mass spectrometry, utilizing synchrotron radiation from the Advanced Light Source from . High resolution mass spectra were obtained at selected photon energies, and photoion yield curves were measured for several ion masses (or ranges of ion masses) over a wide range of photon energies. Only indirect ionization of the dopant rare gas atoms was observed, either by excitation or charge transfer from the surrounding He atoms. Significant dopantionization from excitation transfer was seen at , the maximum of He absorption band for He droplets, and from charge transfer above , the threshold for ionization of pure He droplets. No or signal from dropletphotoionization was observed, but peaks from and were seen that clearly originated from droplets. For dropletsdoped with or Xe, both and ions were observed. For all rare gases, and were produced by dropletphotoionization. Mechanisms of dopantionization and subsequent dynamics are discussed.

Electronic spectroscopy of the Rydberg states of NO–Rg van der Waals complexes
View Description Hide DescriptionWe have employed resonanceenhanced multiphoton ionization spectroscopy to record electronic absorption spectra of NO–Rg van der Waals complexes. The nitric oxide molecule is the chromophore, and the excitation corresponds to an electron being promoted from the orbital to , , and Rydberg states. We review the ordering of the states of NO and use this as a basis for discussing the components in the NO–Rg complexes, in terms of the interactions between the Rydberg electron, the core, and the Rg atom. Predissociation of the state occurs through the state for NO–Ar and NO–Kr, and this will be considered. We shall also outline problems encountered when trying to record similar spectra for NO–Xe, related to the presence of atomic Xe resonances.

Computed lifetimes of metastable states of
View Description Hide DescriptionHighly correlated internally contracted multireference configuration interaction wave functions are used to calculate the potential energy and spinorbit coupling functions for the lowest electronic states of dication. Using these functions, the positions and lifetimes of the corresponding vibronic states are evaluated by means of logphaseamplitude, stabilization, and complexscaling methods within the framework of a multichannel Schrödinger analysis. For the first time in the literature, the calculated lifetimes are in good agreement with the experiment, thereby proving the reliability of the predicted characteristics and adequacy of the used theory for a theoretical study of other molecular dications.

Are structures with Al–H bonds represented in the photoelectron spectrum of ?
View Description Hide DescriptionPhotoelectron spectra of clusters formed by reactions of with water molecules have been interpreted recently in terms of dissociative absorption products with hydroxide and oxide anions that are coordinated to aluminum cations. Alternative isomers with Al–H bonds have lower energies, but barriers to hydrogen migrations that break O–H bonds and create Al–H bonds are high. Ab initio electron propagator calculations of the vertical electron detachment energies of the anions indicate that the species with hydrides cannot be assigned to the chief features in the photoelectron spectrum. Therefore, the previously studied dissociative absorption products are the structures that are most likely to be probed in the photoelectron spectra.

Vinylideneacetylene cation isomerization investigated by large scale ab initio calculations
View Description Hide DescriptionThe planar isomerization routes of the vinylidene/acetylene cation in the lowest electronic states are accurately examined for the first time, by using large scale MRCI and CCSD(T) calculations in a complementary way. They are compared with the similar calculations performed for the neutral ground stateisomerization. An accurate value of the adiabatic ionization potential of vinylidene is predicted. The vinylidene cation lowest state, , follows an almost flat pathway with a shallow secondary minimum on the potential energy surface, before suddenly dropping to the stable acetylene cation ground state,. It is therefore confirmed to be completely unstable with respect to isomerization. The first excited state of the vinylidene cation, , which also correlates with the ground state of acetylene cation along a isomerization route, has been studied at the same level of calculation. This state is lying only above the state, and exhibits a potential energy barrier of which explains the earlier assignment of this symmetry to the ground state of vinylidene cation. In addition to large scale calculations, a comprehensive description of the important steps of isomerization drawn from a very simple model involving monoconfigurational states is presented. In particular, the behavior of one unique orbital, namely, the outer molecular orbital, is shown to completely govern the molecular geometry and energy evolution along the isomerization route of the ground state cation .

Photoionizationinduced dynamics of ammonia: Ab initio potential energy surfaces and timedependent wave packet calculations for the ammonia cation
View Description Hide DescriptionAn analytical anharmonic sixdimensional threesheeted potential energy surface for the ground and first excited states of the ammonia cation has been developed which is tailored to model the ultrafast photoinduced dynamics. Selected ab initio cuts, obtained by multireference configuration interaction calculations, have been used to determine the parameters of a diabatic representation for this JahnTeller and pseudoJahnTeller system. The model includes higherorder coupling terms both for the JahnTeller and for the pseudoJahnTeller matrix elements. The relaxation to the ground state is possible via dynamical pseudoJahnTeller couplings involving the asymmetric bending and stretching coordinates. The photoelectron spectrum of and the internal conversion dynamics of have been determined by wave packet propagation calculations employing the multiconfigurational timedependent Hartree method. Three different time scales are found in the dynamics calculations for the second absorption band. The ultrafast JahnTellerdynamics of the two excited states occurs on a time scale. The major part of the internal conversion to the ground state takes place within a short time scale of . This fast internal conversion is, however, incomplete and the remaining excited state population does not decay completely even within .

Cross sections and ion kinetic energy analysis for the electron impact ionization of acetylene
View Description Hide DescriptionUsing a Niertype electron impact ion source in combination with a double focusing two sector field mass spectrometer, partial cross sections for electron impact ionization of acetylene are measured for electron energies up to . Discrimination factors for ions are determined using the deflection field method in combination with a threedimensional ion trajectory simulation of ions produced in the ion source. Analysis of the ion yield curves obtained by scanning the deflectors allows the assignment of ions with the same masstocharge ratio to specific production channels on the basis of their different kinetic energy distributions. This analysis also allows to determine, besides kinetic energy distributions of fragment ions, partial cross sections differential in kinetic energy. Moreover a charge separation reaction, the Coulomb explosion of the doubly charged parent ions into the fragment ions and , is investigated and its mean kinetic energy release is deduced.

Multiple photon excitation and ionization of NO in and on helium droplets
View Description Hide DescriptionThe photoexcitation of NO embedded in superfluid nanodroplets having has been examined. Twophoton excitation prepares electronically excited states, most notably, the embedded analog of the state of gas phase NO. Vertical excitation to this low Rydberg state is blueshifted and broadened relative to its gas phase counterpart because of the repulsive electronhelium interaction. Transport to the dropletsurface is believed to be facile in the superfluid. For example, prefers (energetically) to reside at the dropletsurface rather than at the droplet center, in contrast to NO. Photoionization of surfacebound occurs over a significant photon energy range. This yields small cluster ions , with of these clusters having . The variation of ion yield with photon energy displays a precipitous change in the region of for all values of . Possible photoionization mechanisms are discussed and it is suggested that intermediate levels with highRydberg character play a role. This work underscores the important role played by transport in the photophysics of species embedded in the superfluid host.

Effect of additional hydrogen peroxide to , and 2 complexes: Quantum chemical study
View Description Hide DescriptionHydrogen peroxide, , acts as a particularly strong reactant in aqueous environment. It has been demonstrated earlier that agglomerates with a single peroxide interacting with one and two water molecules manifest in several stable conformers within a narrow energy range. In the present study we seek structural changes brought out by adding an extra to these systems at molecular level employing ab initio quantum chemical methods, viz., restricted HartreeFock and the second order MøllerPlesset perturbation theory. These clusters exhibit consistent trends in energy hierarchy at both the levels. Further, a many body interactionenergy analysis quantifies the strength and cooperativity of hydrogen bonding in the , ( and 2) clusters, bringing out structuring/destructuring effects attributed to attachment of water and hydrogen peroxide molecules.

Rotational excitation of water by hydrogen molecules: Comparison of results from classical and quantum mechanics
View Description Hide DescriptionQuasiclassical trajectory calculations are carried out for rotational excitation of water by hydrogen molecules. Statetostate rate coefficients are determined at and are compared to available quantum results. A good agreement between classical and quantum rates is observed for downward transitions, with an average accuracy of classical results better than a factor of 2. It is thus found that the ambiguities described by Faure and Wiesenfeld [J. Chem. Phys.121, 6771 (2004)] can be solved in the particular case of waterlike asymmetrictop molecules.

On the evaluation of quadratic response functions at the fourcomponent HartreeFock level: Nonlinear polarization and twophoton absorption in bromo and iodobenzene
View Description Hide DescriptionThe nonlinear polarization and twophoton absorption parameters have been determined for dibromo and diiodobenzene in their meta and orthoconformations and with relativistic effects accounted for to a varying degree. By exclusion of small component integrals in the calculations of the firstorder hyperpolarizability, results within 1% of fully relativistic fourcomponent HartreeFock values are obtained at a cost of 8.7 times the corresponding nonrelativistic calculations. It is shown that the nonlinear absorption in bromobenzene (and even more so in iodobenzene) is broad banded due to spinorbit interactions among the excited states, and nonrelativistic and scalar relativistic calculations are not to be used in this case.