Volume 124, Issue 19, 21 May 2006
 COMMUNICATIONS


A simple method to selectively scale down the selfinteraction correction
View Description Hide DescriptionThe method of Perdew and Zunger is commonly used to correct the selfinteraction error of approximate density functionals. However, it has been shown that this orbitalbased selfinteraction correction (SIC) tends to overcorrect and often impairs molecular properties. We have recently proposed a method to improve the performance of the SIC by scaling it down in manyelectron regions. In this communication, we present a simplification of this scheme. For every occupied orbital, we introduce a scaling factor determined by the ratio of the orbital density to the total spindensity. Thus, the magnitude of the correction is adjusted depending on how much orbital densities overlap with one another. Such a modification of the PerdewZunger SIC does not add any appreciable time to the computation, but significantly improves the accuracy for a number of benchmark properties.
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 ARTICLES

 Theoretical Methods and Algorithms

Effect of noise on the classical and quantum mechanical nonlinear response of resonantly coupled anharmonic oscillators
View Description Hide DescriptionMultidimensional infrared spectroscopy probes coupled molecular vibrations in complex, condensed phase systems. Recent theoretical studies have focused on the analytic structure of the nonlinear response functions required to calculate experimental observables in a perturbative treatment of the radiationmatter interaction. Classical mechanical nonlinear response functions have been shown to exhibit unbounded growth for anharmonic, integrable systems, as a consequence of the nonlinearity of classical mechanics, a feature that is absent in a quantum mechanical treatment. We explore the analytic structure of the thirdorder vibrational response function for an exactly solvable quantum mechanical model that includes some of the important and theoretically challenging aspects of realistic models of condensed phase systems: anharmonicity, resonant coupling, fluctuations, and a welldefined classical mechanical limit.

Numerical study of the steady state fluctuation relations far from equilibrium
View Description Hide DescriptionA thermostatted dynamical model with five degrees of freedom is used to test the fluctuation relation of Evans and Searles and that of Gallavotti and Cohen . In the absence of an external driving field, the model generates a timeindependent ergodic equilibrium state with two conjugate pairs of Lyapunov exponents. Each conjugate pair sums to zero. The fluctuation relations are tested numerically both near and far from equilibrium. As expected from previous work, near equilibrium the is verified by the simulation data while the is not confirmed by the data. Far from equilibrium where a positive exponent in one of these conjugate pairs becomes negative, we test a conjecture regarding the [Bonetto et al., Physica D105, 226 (1997); Giuliani et al., J. Stat. Phys.119, 909 (2005)]. It was conjectured that when the number of nontrivial Lyapunov exponents that are positive becomes less than the number of such negative exponents, then the form of the needs to be corrected. We show that there is no evidence for this conjecture in the empirical data. In fact, when the correction factor differs from unity, the corrected form of is less accurate than the uncorrected . Also as the field increases the uncorrected appears to be satisfied with increasing accuracy. The reason for this observation is likely to be that as the field increases, the argument of the more and more accurately approximates the argument of the . Since the works for arbitrary field strengths, the uncorrected appears to become ever more accurate as the field increases. The final piece of evidence against the conjecture is that when the smallest positive exponent changes sign, the conjecture predicts a discontinuous change in the “correction factor” for . We see no evidence for a discontinuity at this field strength.

A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows
View Description Hide DescriptionWe present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the SLLOD and SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, nonHamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the wellknown DOLLS tensor Hamiltonian.

A validation of the SLLOD equations of motion for homogeneous steadystate flows
View Description Hide DescriptionA validation of the SLLOD equations of motion for nonequilibrium molecular dynamics simulation under homogeneous steadystate flow is presented. We demonstrate that these equations generate the correct centerofmass trajectory of the system, are completely compatible with (and derivable from) Hamiltonian dynamics, satisfy an appropriate energy balance, and require no fictitious external force to generate the required homogeneous flow. It is also shown that no rigorous derivation of the SLLOD equations exists to date.

The constrained space orbital variation analysis for periodic ab initio calculations
View Description Hide DescriptionThe constrained space orbital variation (CSOV) method for the analysis of the interaction energy has been implemented in the periodic ab initioCRYSTAL03 code. The method allows for the partition of the energy of two interacting chemical entities, represented in turn by periodic models, into contributions which account for electrostatic effects, mutual polarization and charge transfer. The implementation permits one to carry out the analysis both at the HartreeFock and density functional theory levels, where in the latter the most popular exchangecorrelation functionals can be used. As an illustrating example, the analysis of the interaction between CO and the MgO (001) surface has been considered. As expected by the almost fully ionic character of the support, our periodic CSOV results, in general agree with those previously obtained using the embedded cluster approach, showing the reliability of the present implementation.

Canonical transformation theory for multireference problems
View Description Hide DescriptionWe propose a theory to describe dynamic correlations in bonding situations where there is also significant nondynamic character. We call this the canonical transformation (CT) theory. When combined with a suitable description of nondynamic correlation, such as given by a completeactivespace selfconsistent Field (CASSCF) or density matrix renormalization group wave function, it provides a theory to describe bonding situations across the entire potential energy surface with quantitative accuracy for both dynamic and nondynamic correlation. The canonical transformation theory uses a unitary exponential ansatz, is size consistent, and has a computational cost of the same order as a singlereference coupled clustertheory with the same level of excitations. Calculations using the CASSCF based CT method with single and double operators for the potential energy curves for water and nitrogen molecules, the insertion reaction, and hydrogen fluoride and boron hydride bond breaking, consistently yield quantitative accuracies typical of equilibrium region coupled clustertheory, but across all geometries, and better than obtained with multireference perturbation theory.

Elucidating the hard/soft acid/base principle: A perspective based on halfreactions
View Description Hide DescriptionA comprehensive analysis is presented for the acidbase doubleexchange reaction as well as the associated aciddisplacement and basedisplacement “halfreactions” with the goal of elucidating the meaning of the hard/soft acid/base (HSAB) principle and the conditions for its validity. When electrontransfer effects are important and other effects are negligible, the HSAB principle is driven by the surpassing stability of the soft acid/soft base product. When electrostatic effects dominate the reactivity, the HSAB principle is driven by the surpassing stability of the hard acid/hard base product. Because electrontransfer effects favor soft/soft interactions, while electrostatic effects favor hard/hard interactions, acidbase exchange reactions may be used to determine whether a reagent’s reactivity is dominated by electrontransfer or by electrostatic effects. Because electrontransfer and electrostatic considerations separately favor the HSAB principle whenever the electronic chemical potentials of the acids and bases involved in the reaction are similar, our analysis provides strong support for the HSAB principle. The electronic chemical potential measures the intrinsic strength of acids and bases.

Multidimensional spatialspectral holographic interpretation of NMR photography
View Description Hide DescriptionA spectralholographic interpretation arises naturally in nuclear magnetic resonance(NMR)photography from either the intrinsic chemical shift anisotropy of the spin system or the field inhomogeneity due to the applied spatial encoding gradients. We can thus think of NMRphotography as arising from a “diffraction” off a spatialspectral holographic grating. The spatialholographic component arises from a high dielectric constant of the NMR medium at high field strength when the excitation wavelength is commensurate with the size of the NMR sample; otherwise, it is a volume spectralholographic grating. In this paper, the NMR localized spectroscopy(imaging) equation is derived from the principles of spatialspectral holography.Holographic properties of storage and programmable time delay and time reversal are shown to follow naturally from this viewpoint and are experimentally demonstrated in an inhomogeneously broadened NMR sample. These ideas are shown to be extendable to complex signal processing functions such as recognition, correlations, and triple products.

The electronic meanfield configuration interaction method. I. Theory and integral formulas
View Description Hide DescriptionIn this article, we introduce a new method for solving the electronic Schrödinger equation. This new method follows the same idea followed by the meanfieldconfiguration interaction method already developed for molecular vibrations; i.e., groups of electronic degrees of freedom are contracted together in the mean field of the other degrees. If the same partition of electronic degrees of freedom is iterated, a selfconsistent field method is obtained. Making coarser partitions (i.e., including more degrees in the same groups) and discarding the high energy states, the full configuration interaction limit can be approached. In contrast with the usual group function theory, no strong orthogonality condition is enforced. We have made use of a generalized version of the fundamental formula defining a Hopf algebrastructure to derive Hamiltonian and overlap matrix element expressions which respect the group structure of the wave function as well as its fermionic symmetry. These expressions are amenable to a recursive computation.

Elimination of translational and rotational motions in nuclear orbital plus molecular orbital theory: Application of MøllerPlesset perturbation theory
View Description Hide DescriptionThe translation and rotationfree nuclear orbital plus molecular orbital (TRFNOMO) theory was developed to determine the nonadiabatic nuclear and electronic wave functions. This study presents a formulation of TRFNOMO secondorder MøllerPlesset (MP2) perturbation and EpsteinNesbet (EN) theory with the use of the TRF Hamiltonian. Numerical assessment of the TRFNOMO/MP2 and EN is performed for several molecules. We confirm the importance of the elimination of translational and rotational motions in the manybody calculations.

Forward flux samplingtype schemes for simulating rare events: Efficiency analysis
View Description Hide DescriptionWe analyze the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems in or out of equilibrium. We derive analytical expressions for the computational cost of using these methods and for the statistical error in the final estimate of the rate constant for a given computational cost. These expressions can be used to determine which method to use for a given problem, to optimize the choice of parameters, and to evaluate the significance of the results obtained. We apply the expressions to the twodimensional nonequilibrium rare event problem proposed by Maier and Stein [Phys. Rev. E48, 931 (1993)]. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Geometries and magnetisms of the clusters: The density functional investigations
View Description Hide DescriptionThe geometries,stabilities, and electronic and magnetic properties of smallsized clusters with different spin configurations were systematically investigated by using density functional approach. Emphasis is placed on studies that focus on the total energies, equilibrium geometries, growthpattern behaviors, fragmentation energies, and magnetic characteristics of zirconium clusters. The optimized geometries show that the largesized lowlying clusters become threedimensional structures. Particularly, the relative stabilities of clusters in terms of the calculated fragmentation energies and secondorder difference of energies are discussed, exhibiting that the magic numbers of stabilities are , 5, and 7 and that the pentagonal bipyramidal geometry is the most stable isomer and a nonmagnetic ground state. Furthermore, the investigated magnetic moments confirm that the atomic averaged magnetic moments of the display an oddeven oscillation features and the tetrahedron structure has the biggest atomic averaged magnetic moment of In addition, the calculated highest occupied molecular orbitallowest unoccupied molecular orbital gaps indicate that the ( and 7) clusters have dramatically enhanced chemical stabilities.

Broad shape resonance effects in CaF Rydberg states
View Description Hide DescriptionResults of ab initio matrix calculations [S. N. Altunata et al., J. Chem. Phys.123, 084319 (2005)] indicate the presence of a broad shape resonance in electronscattering for the electronic symmetry near the ionization threshold. The properties of this shape resonance are analyzed using the adiabatic partialwave expansion of the scattered electron wave function introduced by Le Dourneuf et al. [J. Phys. B15, L685 (1982)]. The qualitative aspects of the shape resonance are explained by an adiabatic approximation on the electronic motion. Mulliken’s rule for the structure of the Rydberg statewave functions [R. S. Mulliken, J. Am. Chem. Soc.86, 3183 (1964)] specifies that, except for an amplitude scale factor, every excited state wave function within one Rydberg series is built on an innermost lobe that remains invariant in shape and nodal position as a function of the excitation energy. Mulliken’s rule implies a weak energy dependence of the quantum defects for an unperturbed molecular Rydberg series, which is given by the RydbergRitz formula. This zeroorder picture is violated by a single CaF Rydberg series at all Rydberg stateenergies (, more so with increasing ) below the ionization threshold, under the broad width of the shape resonance. Such a violation is diagnostic of a global “scarring” of the Rydberg spectrum, which is distinct from the more familiar local level perturbations.

Frequencyselective homonuclear dipolar recoupling in solid state NMR
View Description Hide DescriptionWe introduce a new approach to frequencyselective homonuclear dipolar recoupling in solid state nuclear magnetic resonance(NMR) with magicangle spinning (MAS). This approach, to which we give the acronym SEASHORE, employs alternating periods of doublequantum recoupling and chemical shift evolution to produce phase modulations of the recoupled dipoledipole interactions that average out undesired couplings, leaving only dipoledipole couplings between nuclear spins with a selected pair of NMR frequencies. In principle, SEASHORE is applicable to systems with arbitrary coupling strengths and arbitrary sets of NMR frequencies. Arbitrary MAS frequencies are also possible, subject only to restrictions imposed by the pulse sequence chosen for doublequantum recoupling. We demonstrate the efficacy of SEASHORE in experimental NMR measurements of frequencyselective polarization transfer in uniformly , labeled Lvaline powder and frequencyselective intermolecular polarization transfer in amyloidfibrils formed by a synthetic decapeptide containing uniformly , labeled residues.

Theoretical investigation of intramolecular vibrational energy redistribution in highly excited HFCO
View Description Hide DescriptionThe present paper is devoted to the simulations of the intramolecular vibrational energy redistribution (IVR) in HFCO initiated by an excitation of the outofplane bending vibration . Using a full sixdimensional ab initiopotential energy, the multiconfiguration timedependent Hartree (MCTDH) method was exploited to propagate the corresponding sixdimensional wave packets. This study emphasizes the stability of highly excited states of the outofplane bending mode which exist even above the dissociation threshold. More strikingly, the structure of the IVR during the first step of the dynamics is very stable for initial excitations ranging from to . This latter result is consistent with the analysis of the eigenstates obtained, up to , with the aid of the Davidson algorithm in a foregoing paper [Iung and Ribeiro, J. Chem. Phys.121, 174105 (2005)]. The present study can be considered as complementary to this previous investigation. This paper also shows how MCTDH can be used to predict the dynamical behavior of a strongly excited system and to determine the energies of the corresponding highly excited states.

Size and charge effects on the binding of CO to late transition metal clusters
View Description Hide DescriptionWe report on the size and charge dependence of the C–O stretching frequency, , in complexes of CO with gas phase anionic, neutral, and cationic cobalt clusters , anionic, neutral, and cationic rhodium clusters , and cationic nickel clusters for up to 37. We develop models, based on the established vibrational spectroscopy of organometallic carbonyl compounds, to understand how cluster size and charge relate to in these complexes. The dominating factor is the available electron density for backdonation from the metal to the CO orbital. Electrostatic effects play a significant but minor role. For the charged clusters, the size trends are related to the dilution of the charge density at the binding site on the cluster as increases. At large , approaches asymptotes that are not the same as found for on the single crystalmetal surfaces, reflecting differences between binding sites on medium sized clusters and the more highly coordinated metal surface sites.

Experimental and theoretical ionization cross sections for a hydrogen target at incident energy in a coplanar asymmetric geometry
View Description Hide DescriptionVery recently it was shown that the molecular threebody distorted wave (M3DW) approach gives good agreement with the shape of the experimental data for electronimpact ionization of in a coplanar symmetric geometry, providing the incident electrons have an energy of or greater. One of the weaknesses of these studies was that only the shape of the cross section could be compared to experiment, since there was no absolute or relative normalization of the data. Here we report a joint experimental/theoretical study of electronimpact ionization of in a coplanar asymmetric geometry where the energy of the incident electron was fixed, and different pairs of final state electron energies were used. In this case, the experimental data can be normalized such that only one renormalization factor is required. It is shown that the M3DW is pretty good in agreement with experiment. However, a better treatment of polarization and exchange between the continuum and bound state electrons is required before quantitative agreement between experiment and theory is achieved.

Extensive ab initio study of the valence and lowlying Rydberg states of BBr including spinorbit coupling
View Description Hide DescriptionThe electronic states of the BBr molecule, including 12 valence states and 12 lowlying Rydberg states, have been studied at the theoretical level of with allelectron augccpVQZ basis sets and DouglasKroll [Ann. Phys. (N.Y.)82, 89 (1974)] scalar relativistic correction. The spinorbit coupling effect in the valence states was calculated by the state interaction approach with the full BreitPauli Hamiltonian. This is the first multireference ab initio study of the excited electronic states of BBr. Potential energy curves of all states were plotted with the help of the avoided crossing rule between electronic states of the same symmetry. The structural properties of these states were analyzed. Computational results reproduced most experimental data well. The transition properties of the , , and states to the ground state transitions were obtained, including the transition dipole moments, the FranckCondon factors, and the radiative lifetimes. The evaluated radiative lifetime of the , and states are near , much longer than that of the state.

Nonadiabatic response of molecules to strong fields of picosecond, femtosecond, and subfemtosecond duration: An experimental study of the methane dication
View Description Hide DescriptionThe double ionization of methane has been accomplished using strong optical fields that are generated using moderately intense lasers, and by strong fields that are induced by fastmoving, highly charged ions. In the former case laser intensities in the range generate fields whose durations are of and while in the latter case equivalent fields last for only . The dynamics of the fieldionized electrons are different in the two temporal regimes, fast (picoseconds), and ultrafast (few tens of femtoseconds and subfemtoseconds). Our experiments show that nonadiabatic effects come into play in the ultrafast regime; we directly monitor such effects by measuring the kinetic energy that is released when a specific bond in the doubly charged methane molecular ion breaks.