Volume 125, Issue 6, 14 August 2006
 COMMUNICATIONS


Enhancement of molecular modes by electronically resonant multipulse excitation: Further progress towards mode selective chemistry
View Description Hide DescriptionWe show that molecular vibrations induced by resonant excitation pulses can be enhanced by pulse trains, compared to Fourierlimited pulses of equal pulse energy. As a proofofprinciple, a low frequency mode of Nile Blue at is observed and amplified in a pump and probe experiment. In addition to previous experiments in our group, an increased population transfer to the excited electronic state is identified as an important element of the underlying physical mechanism. These results suggest an enhancement on the level of individual molecules rather than a macroscopic effect.

Rotational dynamics of a diatomic solute in the roomtemperature ionic liquid 1ethyl3methylimidazolium hexafluorophosphate
View Description Hide DescriptionReorientational time correlation functions for a diatomic solute in 1ethyl3methylimidazolium hexafluorophosphate are analyzed via molecular dynamicscomputer simulations, where denotes an equilibrium ensemble average, the th order Legendre polynomial and the angle between the solute orientation at time and its initial direction. Overall results are indicative of heterogeneous dynamics in . For a small nondipolar solute, are welldescribed as stretched exponential functions in wide time ranges. One striking feature is that after rapid initial relaxation, decays more slowly than . As a result, the correlation time associated with the former is considerably longer than that with the latter. This is ascribed to solvent structural fluctuations, which allow largeamplitude solute rotations. As the solute size grows, relaxation of approaches exponential decay.
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 ARTICLES

 Theoretical Methods and Algorithms

The electronic groundstate energy problem: A new reduced density matrix approach
View Description Hide DescriptionWe present here a formulation of the electronic groundstate energy in terms of the second order reduced density matrix, using a duality argument. It is shown that the computation of the groundstate energy reduces to the search of the projection of some twoelectron reduced Hamiltonian on the dual cone of representability conditions. Some numerical results validate the approach, both for equilibrium geometries and for the dissociation curve of .

The origin of molecular distortions: A proposed experimental test
View Description Hide DescriptionBersuker and coworkers [Vibronic Interactions in Molecules and Crystals (SpringerVerlag, Berlin, 1989);Chem. Rev.101, 1067 (2001);The JahnTeller Effect (Cambridge University Press, Cambridge, England, 2005);J. Chem. Phys.124, 044321 (2006)] showed that the source of distortions from high symmetry configurations in molecules is vibrationalelectronic (vibronic). It is here suggested that if one induces transitions by two consecutive operations (vibrational and electronic) performed in a given and in the reverse order, then the vibronic scenario gives different probabilities for the two orders, while an alternative scenario gives the same probability. The entanglement measure of the vibronic description is noted, and the broader aspect of the suggestion for experimentally testing state entanglements is discussed.

Generalized coarsegrained model based on point multipole and GayBerne potentials
View Description Hide DescriptionThis paper presents a general coarsegrained molecular mechanics model based on electric point multipole expansion and GayBerne [J. Chem. Phys.74, 3316 (1981)] potential. Coarse graining of van der Waals potential is achieved by treating molecules as soft uniaxial ellipsoids interacting via a generalized anisotropic GayBerne function. The charge distribution is represented by point multipole expansion, including point charge, dipole, and quadrupole moments placed at the center of mass. The GayBerne and point multipole potentials are combined in the local reference frame defined by the inertial frame of the allatom counterpart. The coarsegrained model has been applied to rigidbody molecular dynamics simulations of molecular liquids including benzene and methanol. The computational efficiency is improved by several orders of magnitude, while the results are in reasonable agreement with allatom models and experimental data. We also discuss the implications of using point multipole for polar molecules capable of hydrogen bonding and the applicability of this model to a broad range of molecular systems including highly charged biopolymers.

Using a family of dividing surfaces normal to the minimum energy path for quantum instanton rate constants
View Description Hide DescriptionOne of the outstanding issues in the quantum instanton (QI) theory (or any transitionstatetype theory) for thermal rate constants of chemical reactions is the choice of an appropriate “dividing surface” (DS) that separates reactants and products. (In the general version of the QI theory, there are actually two dividing surfaces involved.) This paper shows one simple and general way for choosing DSs for use in QI theory, namely, using the family of (hyper) planes normal to the minimum energy path on the potential energy surface at various distances along it. Here the reaction coordinate is not one of the dynamical coordinates of the system (which will in general be the Cartesian coordinates of the atoms), but rather simply a parameter which specifies the DS. It is also shown how this idea can be implemented for an atom system in threedimensional space in a way that preserves overall translational and rotational invariance. Numerical application to a simple system (the collinear reaction) is presented to illustrate the procedure.

Wigner molecules: Natural orbitals of strongly correlated twoelectron harmonium
View Description Hide DescriptionExplicit asymptotic expressions for natural orbitals and their occupancies are derived for the harmonium atom at the strongcorrelation limit at which the confinement strength tends to zero. Unlike in systems with moderate correlation effects, the occupancies at the limit (derived from occupation amplitudes with alternating sign patterns) are vanishingly small and asymptotically independent of the angular momentum, forming a geometric progression with the scale factor proportional to and the common ratio of ca. 0.0186. The radial components of the natural orbitals are given by products of polynomials and Gaussian functions that, as expected, peak at approximately half of the equilibrium interelectron distance.

Wigner molecules: The strongcorrelation limit of the threeelectron harmonium
View Description Hide DescriptionAt the strongcorrelation limit, electronic states of the threeelectron harmonium atom are described by asymptotically exact wave functions given by products of distinct Slater determinants and a common Gaussian factor that involves interelectron distances and the centerofmass position. The Slater determinants specify the angular dependence and the permutational symmetry of the wave functions. As the confinement strength becomes infinitesimally small, the states of different spin multiplicities become degenerate, their limiting energy reflecting harmonic vibrations of the electrons about their equilibrium positions. The corresponding electron densities are given by products of angular factors and a Gaussian function centered at the radius proportional to the interelectron distance at equilibrium. Thanks to the availability of both the energy and the electron density, the strongcorrelation limit of the threeelectron harmonium is well suited for testing of density functionals.

Mean field linear response within the elimination of the small component formalism to evaluate relativistic effects on magnetic properties
View Description Hide DescriptionThe linear response within the elimination of the small component formalism is aimed at obtaining the leading order relativistic corrections to magnetic molecular properties in the context of the elimination of the small component approximation. In the present work we extend the method in order to include twobody effects in the form of a mean field onebody operator. To this end we consider the fourcomponent DiracHartreeFock operator as the starting point in the evaluation of the second order relativistic expression of magnetic properties. The approach thus obtained is the fully consistent leading order approximation of the random phase approximation fourcomponent formalism. The mean fieldeffect on the relativistic corrections to both the diamagnetic and paramagnetic terms of magnetic properties taking into account both the Coulomb and Breit twobody interactions is considered.

Highaccuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification
View Description Hide DescriptionThe recently developed highaccuracy extrapolated ab initiothermochemistry method for theoretical thermochemistry, which is intimately related to other highprecision protocols such as the Weizmann3 and focalpoint approaches, is revisited. Some minor improvements in theoretical rigor are introduced which do not lead to any significant additional computational overhead, but are shown to have a negligible overall effect on the accuracy. In addition, the method is extended to completely treat electron correlation effects up to pentuple excitations. The use of an approximate treatment of quadruple and pentuple excitations is suggested; the former as a pragmatic approximation for standard cases and the latter when extremely high accuracy is required. For a test suite of molecules that have rather precisely known enthalpies of formation {as taken from the active thermochemical tables of Ruscic and coworkers [Lecture Notes in Computer Science, edited by M. Parashar (Springer, Berlin, 2002), Vol. 2536, pp. 25–38; J. Phys. Chem. A108, 9979 (2004)]}, the largest deviations between theory and experiment are 0.52, , and for the latter three methods, respectively. Some perspective is provided on this level of accuracy, and sources of remaining systematic deficiencies in the approaches are discussed.

Hybrid exchangecorrelation functional for core, valence, and Rydberg excitations: CorevalenceRydberg B3LYP
View Description Hide DescriptionThe corevalenceRydberg Becke’s threeparameter exchange (LYP) correlation functional (CVRB3LYP) is proposed as a means to improve descriptions of Rydberg excitations of corevalence B3LYP (CVB3LYP). CVB3LYP describes excitations from both core and occupied valence orbitals to unoccupied valence orbitals with high accuracy but fails to describe those to Rydberg orbitals. CVRB3LYP, which adopts the appropriate portions of HartreeFock exchange for unoccupied valence and Rydberg regions separately, overcomes the disadvantage of CVB3LYP. Numerical assessment confirms that timedependent density functional theory calculations with CVRB3LYP succeed in describing not only core excitations but also Rydberg excitations with reasonable accuracy.

Relative Boltzmann entropy, evolution equations for fluctuations of thermodynamic intensive variables, and a statistical mechanical representation of the zeroth law of thermodynamics
View Description Hide DescriptionGeneralized thermodynamics or extended irreversible thermodynamics presumes the existence of thermodynamic intensive variables (e.g., temperature, pressure, chemical potentials, generalized potentials) even if the system is removed from equilibrium. It is necessary to properly understand the nature of such intensive variables and, in particular, of their fluctuations, that is, their deviations from those defined in the extended irreversible thermodynamic sense. The meaning of temperature is examined by means of a kinetic theory of macroscopic irreversible processes to assess the validity of the generalized (or extended) thermodynamic method applied to nonequilibrium phenomena. The Boltzmann equation is used for the purpose. Since the relative Boltzmannentropy has been known to be intimately related to the evolution of the aforementioned fluctuations in the intensive thermodynamic variables, we derive the evolution equations for such fluctuations of intensive variables to lay the foundation for investigating the physical implications and evolution of the relative Boltzmannentropy, so that the range of validity of the thermodynamictheory of irreversible processes can be elucidated. Within the framework of this work, we examine a special case of the evolution equations for the aforementioned fluctuations of intensive variables, which also facilitate investigation of the molecular theory meaning of the zeroth law of thermodynamics. We derive an evolution equation describing the relaxation of temperature fluctuations from its local value and present a formula for the temperature relaxation time.

Extensions of corrections to CC2R12 for excited states
View Description Hide DescriptionAs known since about two decades, R12 methods, which include terms linear in the interelectronic distance in the wave function, improve substantially the basis set convergence of the ground statecorrelationenergy. In a previous study, however, it was found that the same approach does not give a similar systematic improvement if applied to excited states in the framework of coupled cluster response theory. In the present work, we examine the reason for this behavior and show that the inclusion of additional orbitals in the construction of the pair functions leads to an enhanced basis set convergence (and thus a balanced description) also for the excited states.

Multidimensional reactive scattering with quantum trajectories: Dynamics with Morse vibrational modes
View Description Hide DescriptionThe reactive scattering of a wave packet is studied by the quantum trajectory method for a model system with up to 25 Morse vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates with the restriction to a planar reaction path. Spatial derivatives are evaluated by the least squares method using contracted basis sets. Dynamical results, including trajectory evolution and timedependent reaction probabilities, are presented and analyzed. For the case of one Morse vibrational mode, the results are in good agreement with those derived through direct numerical integration of the timedependent Schrödinger equation.

Origin invariant approaches to the calculation of twophoton circular dichroism
View Description Hide DescriptionThe origin dependence of the expression of twophoton circular dichroism in the length formulation employed by the authors in a recent computational study [B. Jansík et al., Chem. Phys. Lett.414, 461 (2005)] is discussed in detail, and some inherently origin invariant alternative formulations are introduced. Extensive computational tests on a small reference chiral system, namely, a chiral form of , are performed at the density functional theory (DFT)/B3LYP level of theory with large diffuse correlation consistent basis sets. The results indicate that the velocity formulation originally proposed by Tinoco, Jr. [J. Chem. Phys.62, 1006 (1975)] provides the most convenient approach for an origin invariant calculation of twophoton circular dichroism.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

The nuclear electric quadrupole moment of antimony from the molecular method
View Description Hide DescriptionRelativistic DiracCoulomb (DC) HartreeFock calculations are employed to obtain the analytic electric field gradient (EFG) on the antimony nucleus in the SbN, SbP, SbF, and SbCl molecules. The electronic correlation contribution to the EFGs is included with the DCCCSD(T) and DCCCSDT approaches, also in the fourcomponent framework, using a finitedifference method. The total EFG results, along with the experimental nuclear quadrupole coupling constants from microwave spectroscopy, allow to derive the nuclear quadrupole moments of and , respectively, as and .

High resolution laser induced fluorescence spectroscopy of the (0,0) band of cobalt monofluoride
View Description Hide DescriptionThe fine and hyperfine interaction parameters in the and states of cobalt monofluoride, CoF, have been determined from an analysis of highresolution laser induced fluorescencespectra of the and band systems. The previously reported pure rotational transitions of the state [T. Okabayashi and M. Tanimoto, J. Mol. Spectrosc.221, 149 (2003)] were included in the data set. The hyperfine parameters for and have been interpreted using atomic data together with a proposed molecular orbital description for the and states. A comparison of the hyperfine parameters in the state of cobalt monohydride, CoH, with those of the state of CoF reveals that the bonding in the two molecules is significantly different. It is shown that, in a situation where the substates of a multiplet degenerate electronic state are analyzed separately, the Fermi contact parameter can be determined with fair accuracy from the apparent centrifugal distortion of the hyperfine structure.

A new approximation for atomdiatom rotationalrelaxation cross sections
View Description Hide DescriptionA semiclassical approximation to the matrix of the infiniteordersudden approximation is introduced. This is employed to yield for the energytransfer effective cross section a purely classical approximation, analogous to the MasonMonchick approximation [J. Chem. Phys.36, 1622 (1962)] for traditional collision integrals. Constraints on energy and on angular momentum transfer are included. Numerical evaluation of this new approximation can readily be performed alongside that for traditional collision integrals. The new result is tested against full classical trajectory calculations for six potential energy surfaces for the collision systems , , He–CO, and . Differences of no more than 15% from the classical trajectory calculations have been obtained.

Direct dynamics study on the hydrogen abstraction reactions
View Description Hide DescriptionWe present a direct ab initio dynamics study on the hydrogen abstraction reactions , which are predicted to have six possible reaction channels for abstraction and four for abstraction caused by the different isomers and various attacking orientations of foreign radical to . The structures and frequencies at the stationary points and the points along the minimum energy paths (MEPs) of all reaction channels are obtained at the level of theory. Energetic information of stationary points and the points along the MEPs is further refined by means of MCQCISD method. The rate constants of these channels are calculated using the improved canonical variational transitionstate theory with the smallcurvature tunneling correction (ICVT/SCT) method. The calculated results show that the favorable reaction channels are channels (n1) and (n4) as well as (c1) and (c3) (refer to Scheme 1) in the whole temperature range. The total ICVT/SCT rate constants of all channels for the two reactions at the level are both in good agreement with the available experimental data, and corresponding threeparameter expressions of in are fitted as for abstraction and for abstraction. Additionally, the long range interaction between the H atom of bond in foreign radicals and the lone pair on the nonreactive N atom of the transition states is further discussed to explain the various transitionstate numbers of the two similar hydrogen abstraction reactions.

Interaction potentials for : Spectroscopy and transport coefficients
View Description Hide DescriptionHighlevel ab initio CCSD(T) calculations are performed in order to obtain accurate interaction potentials for the anion interacting with each rare gas (Rg) atom. For the Rg atoms from He to Ar, two approaches are taken. The first one implements a relativistic core potential and an augccpVQZ basis set for bromine, an augccpV5Z basis set for Rg, and a set of bond functions placed at the midpoint of the Rg–Br distance. The second one uses the allelectron approximation with augccpV5Z bases further augmented by an extra diffuse function in each shell. Comparison reveals close similarity between both sets of results, so for Rg atoms from Kr to Rn only the second approach is exploited. Calculated potentials are assessed against the previous empirical, semiempirical, and ab initio potentials, and against available beam scattering data, zero electron kinetic energy spectroscopic data, and various sets of the measured ion mobilities and diffusion coefficients. This multiproperty analysis leads to the conclusion that the present potentials are consistently good for the whole series of pairs over the whole range of internuclear distances covered.