Volume 126, Issue 20, 28 May 2007
 COMMUNICATIONS


Anisotropy of the angular distribution of fragment ions in dissociative double photoionization of molecules in the energy range
View Description Hide DescriptionThe double photoionization of molecules by linearly polarized light in the energy range has been studied by coupling ion imaging technique and electronionion coincidence. For the two possible dissociative processes, leading to and , angular distributions of ionic fragments have been measured, finding an evident anisotropy. This indicates that the molecules ionize when their axis is parallel to the light polarization vector and the fragments are separating in a time shorter than the dication rotational period. The analysis of results provides, in addition to the total kinetic energy of ionic fragments, crucial information about the double photoionization dynamics.

Role of the exchangecorrelation potential in ab initio electron transport calculations
View Description Hide DescriptionThe effect of the exchangecorrelation potential in ab initio electron transport calculations is investigated by constructing optimized effective potentials using different energy functionals or the electron density from secondorder perturbation theory. The authors calculate electron transmission through two atomic chain systems, one with charge transfer and one without. Dramatic effects are caused by two factors: changes in the energy gap and the selfinteraction error. The error in conductance caused by the former is about one order of magnitude while that caused by the latter ranges from several times to two orders of magnitude, depending on the coupling strength and charge transfer. The implications for accurate quantum transport calculations are discussed.

Completeness of a kinetically balanced Gaussian basis
View Description Hide DescriptionIt is shown that the exact relativistic wave function of the ground state of Hlike ions can be expanded in a kinetically balanced eventempered Gaussian basis. The error of the overlap integral between exact and approximate wave function depends as , with , on the size of the basis, both for the large and the small components. Even the error of the energy has essentially the same dependence on and decays only slightly slower than its nonrelativistic counterpart, which goes as .

Lagrangian approach to molecular vibrational Raman intensities using timedependent hybrid density functional theory
View Description Hide DescriptionThe authors propose a new route to vibrational Raman intensities based on analytical derivatives of a fully variational polarizabilityLagrangian. The Lagrangian is constructed to recover the negative frequencydependent polarizability of timedependent HartreeFock or adiabatic (hybrid) density functional theory at its stationary point. By virtue of the variational principle, firstorder polarizability derivatives can be computed without using derivative molecular orbital coefficients. As a result, the intensities of all Ramanactive modes within the double harmonic approximation are obtained at approximately the same cost as the frequencydependent polarizability itself. This corresponds to a reduction of the scaling of computational expense by one power of the system size compared to a force constant calculation and to previous implementations. Since the Raman intensity calculation is independent of the harmonic force constant calculation more, computationally demanding density functionals or basis sets may be used to compute the polarizability gradient without much affecting the total time required to compute a Raman spectrum. As illustrated for fullerene , the present approach considerably extends the domain of molecular vibrational Raman calculations at the (hybrid) density functional level. The accuracy of absolute and relative Raman intensities of benzene obtained using the PBE0 hybrid functional is assessed by comparison with experiment.
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 ARTICLES

 Theoretical Methods and Algorithms

Vibrational excitation energies from vibrational coupled cluster response theory
View Description Hide DescriptionResponse theory in the context of vibrational coupled cluster (VCC) theory is introduced and used to obtain vibrational excitation energies. The relation to the vibrational configuration interaction (VCI) approach is described, and the increase in accuracy of VCC response energies relative to VCI energies is discussed theoretically in terms of a perturbational order expansion and demonstrated numerically. To illustrate the theory, a pilot implementation is used to obtain anharmonic vibrational frequencies for fundamental, first overtone and combination excitations of formaldehyde as well as for the fundamental transitions of ethylene.

Anharmonic properties of the vibrational quantum computer
View Description Hide DescriptionWe developed an efficient approach to study the coherent control of vibrational statetostate transitions. The approximations employed in our model are valid in the regime of the low vibrational excitation specific to the vibrational quantum computer. Using this approach we explored how the vibrational properties of a twoqubit system affect the accuracy of subpicosecond quantum gates. The optimal control theory and numerical propagation of laserdriven vibrational wave packets were employed. The focus was on understanding the effect of the three anharmonicity parameters of the system. In the threedimensional anharmonicity parameter space we identified several spots of high fidelity separated by low fidelity planar regions. The seemingly complicated picture is explained in terms of interferences between different statetostate transitions. Very general analytic relationships between the anharmonicity parameters and the frequencies are derived to describe the observed features. Geometrically, these expressions represent planes in the threedimensional anharmonicity parameter space. Results of this work should help to choose a suitable candidate molecule for the practical implementation of the vibrational twoqubit system.

A simple and efficient evolution operator for timedependent Hamiltonians: the Taylor expansion
View Description Hide DescriptionNo compact expression of the evolution operator is known when the Hamiltonian operator is time dependent, like when Hamiltonian operators describe, in a semiclassical limit, the interaction of a molecule with an electric field. It is well known that Magnus [N. Magnus, Commun. Pure Appl. Math.7, 649 (1954)] has derived a formal expression where the evolution operator is expressed as an exponential of an operator defined as a series. In spite of its formal simplicity, it turns out to be difficult to use at high orders. For numerical purposes, approximate methods such as “RungeKutta” or “split operator” are often used usually, however, to a small order , so that only small time steps, about onetenth or onehundredth of the field cycle, are acceptable. Moreover, concerning the latter method, split operator, it is only very efficient when a diagonal representation of the kinetic energy operator is known. The Taylor expansion of the evolution operator or the wave function about the initial time provides an alternative approach, which is very simple to implement and, unlike split operator, without restrictions on the Hamiltonian. In addition, relatively large time steps (up to the field cycle) can be used. A twolevel model and a propagation of a Gaussian wave packet in a harmonic potential illustrate the efficiency of the Taylor expansion. Finally, the calculation of the timeaveraged absorbed energy in fluoroproprene provides a realistic application of our method.

Monte Carlo approach to the decay rate of a metastable system with an arbitrarily shaped barrier
View Description Hide DescriptionA path integral Monte Carlo method based on the fastFourier transform technique combined with the important sampling method is proposed to calculate the decay rate of a metastable quantum system with an arbitrary shape of a potential barrier. The contribution of all fluctuation actions is included which can be used to check the accuracy of the usual steepestdescent approximation, namely, the perturbation expansion of potential. The analytical approximation is found to produce the decay rate of a particle in a cubic potential being about larger than the Monte Carlo data at the crossover temperature. This disagreement increases with increasing complexity of the potential shape. We also demonstrate via Langevin simulation that the postsaddle potential influences strongly upon the classical escape rate.

Derivatives of the polarization propagator including orbital relaxation effects
View Description Hide DescriptionIn this article, we relate derivatives of the polarization propagator used in manybody theory to the nonlinear (quadratic) polarization propagator, and we relate derivatives of the quadratic polarization propagator to the nonlinear propagator of the next higher order, the cubic polarization propagator. We restrict the analysis to differentiation with respect to parameters for which the derivative of the Hamiltonian can be written as a sum of oneelectron operators. Geometrical derivatives are obtained by specializing to the parameter to the coordinate of nucleus I. We treat orbital relaxation explicitly by allowing for the dependence of creation and annihilation operators in the propagators. This treatment entails an extension of the geometrical derivative relations among response functions proven by Olsen and Jørgensen [J. Chem. Phys.82, 3235 (1985)], because the propagator derivatives may involve changes in the oneelectron orbitals that do not appear in the susceptibility derivatives. These results underlie the relations between Raman intensities and electricfield shielding tensors, which have been explained in terms of nonlocal polarizability and hyperpolarizability densities. The results suggest an alternative computational route to geometrical or other derivatives of both linear and nonlinearresponse functions: these derivatives can be evaluated without numerical differentiation, directly from the propagator of the next higher order.

Local effective potential theory: Nonuniqueness of potential and wave function
View Description Hide DescriptionIn local effective potential energy theories such as the HohenbergKohnSham density functional theory (HKSDFT) and quantal density functional theory (QDFT), electronic systems in their ground or excited states are mapped to model systems of noninteracting fermions with equivalent density. From these models, the equivalent total energy and ionization potential are also obtained. This paper concerns (i) the nonuniqueness of the local effective potential energy function of the model system in the mapping from a nondegenerate ground state, (ii) the nonuniqueness of the local effective potential energy function in the mapping from a nondegenerate excited state, and (iii) in the mapping to a model system in an excited state, the nonuniqueness of the model systemwave function. According to nondegenerate ground state HKSDFT, there exists only one local effective potential energy function, obtained as the functional derivative of the unique ground state energy functional, that can generate the ground state density. Since the theorems of ground state HKSDFT cannot be generalized to nondegenerate excited states, there could exist different local potential energy functions that generate the excited state density. The constrainedsearch version of HKSDFT selects one of these functions as the functional derivative of a bidensity energy functional. In this paper, the authors show via QDFT that there exist an infinite number of local potential energy functions that can generate both the nondegenerate ground and excited state densities of an interacting system. This is accomplished by constructing model systems in configurations different from those of the interacting system. Further, they prove that the difference between the various potential energy functions lies solely in their correlationkinetic contributions. The component of these functions due to the Pauli exclusion principle and Coulomb repulsion remains the same. The existence of the different potential energy functions as viewed from the perspective of QDFT reaffirms that there can be no equivalent to the ground state HKSDFT theorems for excited states. Additionally, the lack of such theorems for excited states is attributable to correlationkinetic effects. Finally, they show that in the mapping to a model system in an excited state, there is a nonuniqueness of the model systemwave function. Different wave functions lead to the same density, each thereby satisfying the sole requirement of reproducing the interacting system density. Examples of the nonuniqueness of the potential energy functions for the mapping from both ground and excited states and the nonuniqueness of the wave function are provided for the exactly solvable Hooke’s atom. The work of others is also discussed.

Hydrogen bonding definitions and dynamics in liquid water
View Description Hide DescriptionXray and neutron diffractions, vibrational spectroscopy, and xray Raman scattering and absorption experiments on water are often interpreted in terms of hydrogen bonding. To this end a number of geometric definitions of hydrogen bonding in water have been developed. While all definitions of hydrogen bonding are to some extent arbitrary, those involving one distance and one angle for a given water dimer are unnecessarily so. In this paper the authors develop a systematic procedure based on twodimensional potentials of mean force for defining cutoffs for a given pair of distance and angular coordinates. They also develop an electronic structurebased definition of hydrogen bonding in liquid water, related to the electronic occupancy of the antibonding OH orbitals. This definition turns out to be reasonably compatible with one of the distanceangle geometric definitions. These two definitions lead to an estimate of the number of hydrogen bonds per molecule in liquid simple point charge∕extended (SPC∕E) water of between 3.2 and 3.4. They also used these and other hydrogenbond definitions to examine the dynamics of local hydrogenbond number fluctuations, finding an approximate longtime decay constant for SPC∕E water of between 0.8 and , which corresponds to the time scale for local structural relaxation.

Canonical averaging in the second order quantized Hamilton dynamics by extension of the coherent state thermodynamics of the harmonic oscillator
View Description Hide DescriptionA conceptually simple approximation to quantum mechanics, quantized Hamilton dynamics (QHD) includes zeropoint energy, tunneling, dephasing, and other important quantum effects in a classicallike description. The hierarchy of coupled differential equations describing the time evolution of observables in QHD can be mapped in the second order onto a classical system with double the dimensionality of the original system. While QHD excels at dynamics with a single initial condition, the correct method for generating thermal initial conditions in QHD remains an open question. Using the coherent state representation of thermodynamics of the harmonic oscillator (HO) [Schnack, Europhys. Lett.45, 647 (1999)], we develop canonical averaging for the second order QHD [Prezhdo, J. Chem. Phys.117, 2995 (2002)]. The methodology is exact for the free particle and HO, and shows good agreement with quantum results for a variety of quartic potentials.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Ab initio potential energy surface and spectrum of the state of the complex
View Description Hide DescriptionThe threedimensional interaction potential for is computed using accurate ab initio methods and a large basis set. Scalar relativistic effects are accounted for by largecore relativistic pseudopotentials for the iodine atoms. Using multireference configuration interaction calculations with subsequent treatment of spinorbit coupling, it is shown for linear and perpendicular structures of the complex that the interaction potential for is very well approximated by the average of the and interaction potentials obtained without spinorbit coupling. The threedimensional and interaction potentials are computed at the unrestricted openshell coupledcluster level of theory using large basis sets.Bound state calculations based on the averaged surface are carried out and binding energies, vibrationally averaged structures, and frequencies are determined. These results are found to be in excellent accord with recent experimental measurements from laserinduced fluorescence and action spectra of . Furthermore, in combination with a recent state potential, the spectral blueshift is obtained and compared with available experimental values.

branch linewidths of perturbed by : Experiments and quantum calculations from an ab initio potential
View Description Hide DescriptionIn this work the authors present an experimental and theoretical study about the branch lines’ broadening coefficients of perturbed by . Experimental values for these parameters have been obtained at 440 and , and quantum calculations have been performed using a new ab initiopotential energy surface, obtained by quantum chemistry methods. The results of these calculations are compared to experimental data obtained previously at 77 and [L. Gomez et al., Mol. Phys.104, 1869 (2006)] and to the present measurements. A satisfactory agreement is obtained for the whole range of temperatures used in the experiments.

Analytic functions for the threebody potential of the helium trimer
View Description Hide DescriptionThe threebody potential for the ground state of the helium trimer is determined by an extended geminal model. The basis set for the calculation is an uncontracted set of Gaussiantype functions. Three different types of configurations were considered: (i) equilateral triangles, (ii) linear configurations with , and (iii) a set of pseudorandom configurations. The interatomic distances were selected within the interval . The computed points have been fitted to global potential functions. The fit is characterized by a maximum absolute error equal to and a mean error equal to .

Fivedimensional ab initio potential energy surface and predicted infrared spectra of van der Waals complexes
View Description Hide DescriptionThe authors present a new fivedimensional potential energy surface for including the normal mode for the antisymmetric stretching vibration of the molecule. The potential energies were calculated using the supermolecular approach with the full counterpoise correction at the CCSD(T) level with an augccpVTZ basis set supplemented with bond functions. The global minimum is at two equivalent Tshaped coplanar configurations with a well depth of . The rovibrational energy levels for four species of (, , , and ) were calculated employing the discrete variable representation (DVR) for radial variables and finite basis representation (FBR) for angular variables and the Lanczos algorithm. Our calculations showed that the offdiagonal intra and intermolecular vibrational coupling could be neglected, and separation of the intramolecular vibration by averaging the total Hamiltonian with the wave function of a specific vibrational state of should be a good approximation with high accuracy. The calculated band origin shift in the infrared spectra in the region of is for and for , which agrees well with the observed values of and . The calculated rovibrational spectra for are consistent with the available experimental spectra. For , it is predicted that only type transitions occur for , while both type and type transitions are significant for .

Macroscopic evidences for nonRiceRamspergerKassel effects in the reaction between and : The occurrence of nonstatistical isotopic branching ratio
View Description Hide DescriptionThe dynamics of the isotopic scrambling in the energized and metastable complex has been studied using classical molecular dynamics (MD) trajectories starting from regions of phase space corresponding to an already formed collisional complex. The simulations cover the range of internal energies spanned by gas phase collision experiments. Rate constants for the isotopic exchange and the complex dissociation have been computed; the isotopic branching ratio has also been obtained from MD simulations and found to deviate substantially from an equivalent prediction based on a previously proposed kinetic scheme. This finding suggests the possibility that details of the reactiondynamics play a role in defining the isotopic branching ratio. The analysis of trajectory results indicated a relatively long lifetime for the collisional complex and the presence of multiple time scales for the exchange process, with a large fraction of the exchange events being separated only by a single oxygenoxygen vibration or half of it. The occurrence of these fast consecutive jumps and their different probabilities as a function of the relative direction between first and second jumps suggest the presence of ballistic motion in the complex following each reactive event. This can be explained on the basis of overlapping regions in phase space and it is used to provide an explanation of the difference between kinetic and MD branching ratios.

Electronic anisotropy between open shell atoms in first and second order perturbation theory
View Description Hide DescriptionThe interaction between two atoms in states with nonzero electronic orbital angular momenta is anisotropic and can be represented by a spherical tensor expansion. The authors derive expressions for the first order (electrostatic) and second order (dispersion and induction) anisotropicinteraction coefficients in terms of the multipole moments and dynamic polarizabilities of the atoms and show that a complete description of the second order interaction requires odd rank or “outofphase” polarizabilities. The authors relate the tensorial expansion coefficients to the adiabatic BornOppenheimer potentials of the molecule and show that there are linear, and in some cases nonlinear, constraints on the van der Waals coefficients of these potentials.

On the helixcoil transition in alanine based polypeptides in gas phase
View Description Hide DescriptionUsing multicanonical simulations, the authors study the effect of charged end groups on helix formation in alanine based polypeptides. They confirm earlier reports that neutral polyalanine exhibits a pronounced helixcoil transition in gas phase simulations. Introducing a charged at the C terminal stabilizes the helix and leads to a higher transition temperature. On the other hand, adding the at the N terminal inhibits helix formation. Instead, a more globular structure was found. These results are in agreement with recent experiments on alanine based polypeptides in gas phase. They indicate that present force fields describe accurately the intramolecular interactions in proteins.

Reagents for electrophilic amination: A quantum Monte Carlo study
View Description Hide DescriptionElectrophilic amination is an appealing synthetic strategy to construct carbonnitrogen bonds. The authors explore the use of the quantum Monte Carlo method and a proposed variant of the electron pair localization function—the electron pair localization function density—as a measure of the nucleophilicity of nitrogen lone pairs as a possible screening procedure for electrophilic reagents.