Volume 128, Issue 12, 28 March 2008
 COMMUNICATIONS


Phase control of molecular fragmentation with a pair of femtosecondlaser pulses
View Description Hide DescriptionWe demonstrate the control of molecular fragmentation of oxylene on a femtosecond time scale in twopulse measurements with a pair of femtosecondlaser pulses. Parent and fragmention yields were recorded as a function of interpulse delays, i.e., different relative phases of the excitation pulses. The experiments revealed different fragmentation mechanisms in the temporal region of direct overlapping pulses and for separated pulses. For overlapping pulses all ion yields followed the excitation intensity which oscillated as a function of interpulse delay due to the change of constructive and destructive interference of the light fields. For larger delays, in particular, the oscillations of the and fragmention yield showed a significant deviation from each other. The results are interpreted as a manifestation of optical phasedependent electronic excitations mapped onto the nuclear fragmentation dynamics.

Charge patching method for electronic structure of organic systems
View Description Hide DescriptionThe development of the charge patching method for the calculation of the electronic structure of organic systems containing a large number of atoms was presented. The method was tested on a range of systems including alkane and alkene chains, polyacenes, polythiophenes, polypyrroles, polyfuranes, polyphenylene vinylene, and poly(amidoamine) dendrimers. The results obtained by the method are in very good agreement with direct calculations based on density functional theory, since the eigenstate errors are typically of the order of a few tens of meV.
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 ARTICLES

 Theoretical Methods and Algorithms

Born–Oppenheimer approximation and beyond for timedependent electronic processes
View Description Hide DescriptionExplicit computations of electronic motion in time and space are gradually becoming feasible and available. The knowledge of this motion is of relevance by itself but is also important for understanding available and predicting future experiments on the electronic time scale. In electronic processes of interest, usually several and even many stationary electronic states participate and the obvious question arises on how to describe the accompanying quantum nuclear dynamics at least on the time scale of the process. In this work, we attempt to study the nuclear dynamics in the framework of a fully timedependent Born–Oppenheimer approximation. Additionally, we attempt to go beyond this approximation by introducing the coupling of several electronic wavepackets by the nuclear wavepackets. In this context, we also discuss a timedependent transformation to diabatic electronic wavepackets. A simple but critical model of charge transfer is analyzed in some detail on various levels of approximation and also solved exactly.

Simulating prescribed particle densities in the grand canonical ensemble using iterative algorithms
View Description Hide DescriptionWe present two efficient iterative Monte Carlo algorithms in the grand canonical ensemble with which the chemical potentials corresponding to prescribed (targeted) partial densities can be determined. The first algorithm works by always using the targeted densities in the (ideal gas) terms and updating the excess chemical potentials from the previous iteration. The second algorithm extrapolates the chemical potentials in the next iteration from the results of the previous iteration using a first order series expansion of the densities. The coefficients of the series, the derivatives of the densities with respect to the chemical potentials, are obtained from the simulations by fluctuation formulas. The convergence of this procedure is shown for the examples of a homogeneous LennardJones mixture and a electrolyte mixture in the primitive model. The methods are quite robust under the conditions investigated. The first algorithm is less sensitive to initial conditions.

Solving the Schrödinger and Dirac equations of hydrogen molecular ion accurately by the free iterative complement interaction method
View Description Hide DescriptionThe nonrelativistic Schrödinger equation and the relativistic fourcomponent Dirac equation of were solved accurately in an analytical expansion form by the free iterative complement interaction (ICI) method combined with the variational principle. In the nonrelativistic case, we compared the free ICI wave function with the socalled “exact” wave function as two different expansions converging to the unique exact wave function and found that the free ICI method is much more efficient than the exact method. In the relativistic case, we first used the inverse Hamiltonian to guarantee Ritztype variational principle and obtained accurate result. We also showed that the ordinary variational calculation also gives a nice convergence when the function is appropriately chosen, since then the free ICI calculation guarantees a correct relationship between the large and small components of each adjacent order, which we call ICI balance. This is the first application of the relativistic free ICI method to molecule. We calculated both ground and excited states in good convergence, and not only the upper bound but also the lower bound of the groundstate energy. The error bound analysis has assured that the present result is highly accurate.

Triple excitations in statespecific multireference coupled cluster theory: Application of MkMRCCSDT and methods to model systems
View Description Hide DescriptionWe report the first implementation with correct scaling of the Mukherjee multireference coupled cluster method with singles, doubles, and approximate iterative triples (, ) as well as full triples (MkMRCCSDT). These methods were applied to the classic H4, P4, , and H8 model systems to assess the ability of the schemes to accurately account for triple excitations. In all model systems the inclusion of triples via the various approaches greatly reduces the nonparallelism error (NPE) and the mean nonparallelism derivative diagnostics for the potential energy curves, recovering between 59% and 73% of the full triples effect on average. The most complete triples approximation, MkMRCCSDT3, exhibits the best average performance, reducing the mean NPE to below , compared to for MkMRCCSD. Both linear and quadratic truncations of the MkMRCC triples coupling terms are viable simplifications producing no significant errors. If the offdiagonal parts of the occupiedoccupied and virtualvirtual blocks of the Fock matrices are ignored, the storage of the triples amplitudes is no longer required for the methods introduced here. This proves to be an effective approximation that gives results almost indistinguishable from those derived from full consideration of the Fock matrices.

A unified densityfunctional treatment of dynamical, nondynamical, and dispersion correlations. II. Thermochemical and kinetic benchmarks
View Description Hide DescriptionIn a previous work [J. Chem. Phys.127, 124108 (2007)] we introduced an exactexchangebased densityfunctional methodology incorporating dynamical, nondynamical, and dispersion correlations, called DF07. In this work, the performance of the DF07 method is assessed on a variety of thermochemical and kinetic benchmark data including ionization potentials,electron affinities,proton affinities, isomerization energies, bond dissociationenthalpies, and barrier heights of radical reactions. DF07 gives uniform accuracy over all our benchmark data without any refitting of parameters. The importance of the exactexchange character of DF07 is highlighted through comparison with a threeparameter hybrid metageneralizedgradientapproximation functional.

Interference and quantization in semiclassical response functions
View Description Hide DescriptionApplication of the Herman–Kluk semiclassical propagator to the calculation of spectroscopic response functions for anharmonic oscillators has demonstrated the quantitative accuracy of these approximate dynamics. In this approach, spectroscopic response functions are expressed as multiple phasespace integrals over pairs of classical trajectories and their associated stability matrices. Here we analyze the Herman–Kluk semiclassical approximation to a linear response function and determine the origin of the capacity of this method to reproduce quantum effects in a response function from classical dynamical information. Our analysis identifies those classical trajectories that contribute most significantly to the response function on different time scales. This finding motivates a procedure for computing the linear response function in which the interference between pairs of classical trajectories is treated approximately, resulting in an integral over a single average trajectory, as in a purely classical calculation.

Interpreting ultrafast molecular fragmentation dynamics with ab initio electronic structure calculations
View Description Hide DescriptionHighlevel ab initio electronic structure calculations are used to interpret the fragmentation dynamics of , following excitation with an intense ultrafast laser pulse. The potential energy surfaces of the ground and excited cationic states along the dissociativebond have been calculated using multireference second order perturbation theory methods. The calculations confirm the existence of a charge transfer resonance during the evolution of a dissociative wave packet on the ground state potential energy surface of the molecular cation and yield a detailed picture of the dissociation dynamics observed in earlier work. Comparisons of the ionic spectrum for two similar molecules support a general picture in which molecules are influenced by dynamic resonances in the cation during dissociation.

Poissontransformed density fitting in relativistic fourcomponent Dirac–Kohn–Sham theory
View Description Hide DescriptionWe present recent developments in the implementation of the density fitting approach for the Coulomb interaction within the fourcomponent formulation of relativistic density functional theory [Belpassi et al., J. Chem. Phys.124, 124104 (2006)]. In particular, we make use of the Poisson equation to generate suitable auxiliary basis sets and simplify the electron repulsion integrals [Manby and Knowles, Phys. Rev. Lett.87, 163001 (2001)]. We propose a particularly simple and efficient method for the generation of accurate Poisson auxiliary basis sets, based on already available standard Coulomb fitting sets. Just as is found in the nonrelativistic case, we show that the number of standard auxiliary fitting functions that need to be added to the Poissongenerated functions in order to achieve a fitting accuracy equal or, in some cases, better than that of the standard procedure is remarkably small. The efficiency of the present implementation is demonstrated in a detailed study of the spectroscopic properties and energetics of several gold containing systems, including the Au dimer and the CsAu molecule. The extraction reaction of a molecule from a cluster is also calculated as an example of mixed heavylightatom molecular systems. The scaling behavior of the algorithm implemented is illustrated for some closed shell gold clusters up to . The increased sparsity of the Coulomb matrices involved in the Poisson fitting is identified, as are potential computational applications and the use of the Poisson fitting for the relativistic exchangecorrelation problem.

A new approach for efficient simulation of Coulomb interactions in ionic fluids
View Description Hide DescriptionWe propose a simplified version of local molecular field (LMF) theory to treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on splitting the Coulomb potential into a shortranged part that combines with other shortranged core interactions and is simulated explicitly. The averaged effects of the remaining longranged part are taken into account through a selfconsistently determined effective external field. The theory contains an adjustable length parameter that specifies the cutoff distance for the shortranged interaction. This can be chosen to minimize the errors resulting from the meanfield treatment of the complementary longranged part. Here we suggest that in many cases an accurate approximation to the effective field can be obtained directly from the equilibrium charge density given by the Debye theory of screening, thus eliminating the need for a selfconsistent treatment. In the limit , this assumption reduces to the classical Debye approximation. We examine the numerical performance of this approximation for a simple model of a symmetric ionic mixture. Our results for thermodynamic and structural properties of uniform ionic mixtures agree well with similar results of Ewald simulations of the full ionic system. In addition, we have used the simplified theory in a grandcanonical simulation of a nonuniform ionic mixture where an ion has been fixed at the origin. Simulations using shortranged truncations of the Coulomb interactions alone do not satisfy the exact condition of complete screening of the fixed ion, but this condition is recovered when the effective field is taken into account. We argue that this simplified approach can also be used in the simulations of more complex nonuniform systems.

NMR implementation of adiabatic SAT algorithm using strongly modulated pulses
View Description Hide DescriptionNMR implementation of adiabatic algorithms face severe problems in homonuclear spin systems since the qubit selective pulses are long and during this period, evolution under the Hamiltonian and decoherence cause errors. The decoherence destroys the answer as it causes the final state to evolve to mixed state and in homonuclear systems, evolution under the internal Hamiltonian causes phase errors preventing the initial state to converge to the solution state. The resolution of these issues is necessary before one can proceed to implement an adiabatic algorithm in a large system where homonuclear coupled spins will become a necessity. In the present work, we demonstrate that by using “strongly modulated pulses” (SMPs) for the creation of interpolating Hamiltonian, one can circumvent both the problems and successfully implement the adiabatic SAT algorithm in a homonuclear three qubit system. This work also demonstrates that the SMPs tremendously reduce the time taken for the implementation of the algorithm, can overcome problems associated with decoherence, and will be the modality in future implementation of quantum information processing by NMR.

Improvement of the coupledcluster singles and doubles method via scaling same and oppositespin components of the double excitation correlation energy
View Description Hide DescriptionThere has been much interest in costfree improvements to secondorder Møller–Plesset perturbation theory (MP2) via scaling the same and oppositespin components of the correlationenergy (spincomponent scaled MP2). By scaling the same and oppositespin components of the double excitation correlationenergy from the coupledcluster of single and double excitations (CCSD) method, similar improvements can be achieved. Optimized for a set of 48 reactionenergies, scaling factors were determined to be 1.13 and 1.27 for the same and oppositespin components, respectively. Preliminary results suggest that the spincomponent scaled CCSD (SCSCCSD) method will outperform all MP2 type methods considered for describing intermolecular interactions. Potential energy curves computed with the SCSCCSD method for the sandwich benzene dimer and methane dimer reproduce the benchmark CCSD(T) potential curves with errors of only a few hundredths of for the minima. The performance of the SCSCCSD method suggests that it is a reliable, lower cost alternative to the CCSD(T) method.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

On the generalized equipartition theorem in molecular dynamics ensembles and the microcanonical thermodynamics of small systems
View Description Hide DescriptionWe consider various ensemble averages within the molecular dynamics (MD) ensemble, corresponding to those states sampled during a MD simulation in which the application of periodic boundary conditions imposes a constraint on the momentum of the center of mass. As noted by Shirts et al. [J. Chem. Phys.125, 164102 (2006)] for an isolated system, we find that the principle of equipartition is not satisfied within such simulations, i.e., the total kinetic energy of the system is not shared equally among all the translational degrees of freedom. Nevertheless, we derive two different versions of Tolman’s generalized equipartition theorem, one appropriate for the canonical ensemble and the other relevant to the microcanonical ensemble. In both cases, the breakdown of the principle of equipartition immediately follows from Tolman’s result. The translational degrees of freedom are, however, still equivalent, being coupled to the same bulk property in an identical manner. We also show that the temperature of an isolated system is not directly proportional to the average of the total kinetic energy (in contrast to the direct proportionality that arises between the temperature of the external bath and the kinetic energy within the canonical ensemble). Consequently, the system temperature does not appear within Tolman’s generalized equipartition theorem for the microcanonical ensemble (unlike the immediate appearance of the temperature of the external bath within the canonical ensemble). Both of these results serve to highlight the flaws in the argument put forth by Hertz [Ann. Phys.33, 225 (1910); 33, 537 (1910)] for defining the entropy of an isolated system via the integral of the phase space volume. Only the Boltzmann–Planck entropy definition, which connects entropy to the integral of the phase space density, leads to the correct description of the properties of a finite, isolated system. We demonstrate that the use of the integral of the phase space volume leads to unphysical results, indicating that the property of adiabatic invariance has little to do with the behavior of small systems.

The adsorption of CO on charged and neutral Au and : A comparison between wavefunction based and density functional theory
View Description Hide DescriptionQuantum theoretical calculations are presented for CO attached to charged and neutral Au and with the aim to test the performance of currently applied density functional theory(DFT) by comparison with accurate wavefunction based results. For this, we developed a compact sized correlationconsistent valence basis set which accompanies a smallcore energyconsistent scalar relativistic pseudopotential for gold. The properties analyzed are geometries, dissociation energies, vibrational frequencies, ionization potentials, and electron affinities. The important role of the basisset superposition error is addressed which can be substantial for the negatively charged systems. The dissociation energies decrease along the series , Au–CO, and and as well as along the series , , and . As one expects, a negative charge on gold weakens the carbon oxygen bond considerably, with a consequent redshift in the CO stretching frequency when moving from the positively charged to the neutral and the negatively chargedgold atom or dimer. We find that the different density functional approximations applied are not able to correctly describe the rather weak interaction between CO and gold, thus questioning the application of DFT to CO adsorption on larger goldclusters or surfaces.

Modeling of clusters. II. Calculation of vibrational spectrum
View Description Hide DescriptionWe have computed the vibrational spectrum of the helium ionized trimer using three different potential energy surfaces [D. T. Chang and G. L. Gellene, J. Chem. Phys.119, 4694 (2003); E. Scifoni et al., ibid.125, 164304 (2006); I. Paidarová et al., Chem. Phys.342, 64 (2007)]. Differences in the details of these potential energy surfaces induce discrepancies between bound state energies of the order of . The effects of the geometric phase induced by the conical intersection between the ground electronic potential energy surface and the first excited one are studied by computing vibrational spectra with and without this phase. The six lowest vibrational bound states are negligibly affected by the geometric phase. Indeed, they correspond to wavefunctions localized in the vicinity of the linear symmetric configurations and can be assigned well defined vibrational quantum numbers. On the other hand, higher excited states are delocalized, cannot be assigned definite vibrational quantum numbers, and the geometric phase shifts their energies by approximately .

Formation of hydrogenated boron clusters in an external quadrupole static attraction ion trap
View Description Hide DescriptionWe report the formation of icosahedral through ionmolecule reactions of the decaborane ion [ ] with diborane molecules in an external quadrupole static attraction ion trap. The hydrogen content of is determined by the analysis of the mass spectrum. The result reveals that is the main product. Ab initio calculations indicate that preferentially forms an icosahedral structure rather than a quasiplanar structure. The energies of the formationreactions of and between ions, which are considered to be involved in the formation of , and a molecule are calculated. The calculations of the detachment pathway of molecules and H atoms from the product ions, and , indicate that the intermediate state has a relatively low energy, enabling the detachment reaction to proceed owing to the sufficient reactionenergy. This autodetachment of accounts for the experimental result that is the most abundant product, even though it does not have the lowest energy among .

Ab initio potential energy surfaces and nonadiabatic interactions in the collision system
View Description Hide DescriptionAb initio calculations on the system have been carried out in Jacobi coordinates at the multireference configuration interaction level employing Dunning’s correlationconsistent polarized valence triple zeta basis set to analyze the role of lowlying electronic excited states in influencing the collision dynamics relevant to the experimental collision energy range of . The lowest two adiabatic potential energy surfaces, asymptotically correlating to and , have been obtained. Using ab initio procedures, the (radial) nonadiabatic couplings and the mixing angle between the lowest two electronic states ( and ) have been obtained to yield the corresponding quasidiabatic potential energy matrix. The strengths of the computed vibrational coupling matrix elements reflect a similar trend, as has been observed experimentally in the magnitudes of the statetostate transition probability for the inelastic vibrational excitations [J. Krutein and F. Linder, J. Chem. Phys.71, 559 (1979); F. A. Gianturco et al., J. Phys. B14, 667 (1981)].

Quantum dynamics of inelastic excitations and charge transfer processes in the collisions
View Description Hide DescriptionStateresolved differential cross section, integral cross section, average vibrational energy transfer, and the relative transition probability are computed for the system using our newly obtained ab initio potential energy surfaces (PES) at the multireference configuration interaction level of accuracy employing the correlation consistent polarized valence triple zeta basis set. The quantum dynamics is treated within the vibrational closecoupling rotational infiniteorder sudden approximation using the coupled ground state and first excited stateab initio quasidiabatic PES. The computed collision attributes for the inelastic vibrational excitation are compared with the statetostate scattering data available at and and are found to be in overall good agreement with those of the experiments. The results for the vibrational charge transfer processes at these collisionenergies are also presented.

Automatic generation of active coordinates for quantum dynamics calculations: Application to the dynamics of benzene photochemistry
View Description Hide DescriptionA new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space selfconsistent field method. At the FranckCondon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments.