Volume 121, Issue 3, 15 July 2004
 COMMUNICATIONS


Kinetic isotope effect in hydrogen transfer arising from the effects of rotational excitation and occurrence of hydrogen tunneling in molecular systems
View Description Hide DescriptionHydrogen kinetic isotope effect with values of which are generally ascribed to quantum tunneling of hydrogen are shown to arise in O+HCl(DCl,TCl) reactions due to the effects of rotational excitation on the distribution of encounters with the critical dividing surface. At higher rotational excitations these distributions are shifted towards the regions of the critical dividing surface with low barrier energies which can lead to a large enhancement of the barrier crossing. This effect depends strongly on the hydrogen isotope involved in the reaction and, at some temperatures, gives rise to α much larger than 3.3. It can be readily seen that the effect should arise also in condensed molecular systems, due to internal rotations or other vibrations »perpendicular« to the reaction coordinate.
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 ARTICLES

 Theoretical Methods and Algorithms

Plane wave packet formulation of atomplusdiatom quantum reactive scattering
View Description Hide DescriptionWe recently interpreted several reactive scattering experiments using a plane wave packet (PWP) formulation of quantum scattering theory [see, e.g., S. C. Althorpe, F. FernándezAlonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper presents the first derivation of this formulation for atomplusdiatom reactive scattering, and explains its relation to conventional timeindependent reactive scattering. We generalize recent results for sphericalparticle scattering [S. C. Althorpe, Phys. Rev. A 69, 042702 (2004)] to atomrigidrotor scattering in the spacefixed frame, atomrigidrotor scattering in the bodyfixed frame, and finally rearrangement scattering. The reactive scattering is initiated by a plane wave packet, describing the reagents in centerofmass scattering coordinates, and is detected by projecting onto a series of (or plane wave “probe” packets. The plane wave packets are localized at the closest distance from the scattering center at which the interaction potential can be neglected. The time evolution of the initial plane wave packet provides a clear visualization of the scattering into space of the reaction products. The projection onto the probe packets yields the timeindependent, statetostate scattering amplitude, and hence the differential cross section. We explain how best to implement the PWP approach in a numerical computation, and illustrate this with a detailed application to the reaction.

Efficient hybrid density functional calculations in solids: Assessment of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional
View Description Hide DescriptionThe present work introduces an efficient screening technique to take advantage of the fast spatial decay of the short range Hartree–Fock (HF) exchange used in the Heyd–Scuseria–Ernzerhof (HSE) screened Coulomb hybrid density functional. The screened HF exchange decay properties and screening efficiency are compared with traditional hybrid functional calculations on solids. The HSE functional is then assessed using 21 metallic, semiconducting, and insulating solids. The examined properties include lattice constants, bulk moduli, and band gaps. The results obtained with HSE exhibit significantly smaller errors than pure density functional theory(DFT) calculations. For structural properties, the errors produced by HSE are up to 50% smaller than the errors of the local density approximation, PBE, and TPSS functionals used for comparison. When predicting band gaps of semiconductors, we found smaller errors with HSE, resulting in a mean absolute error of 0.2 eV (1.3 eV error for all pure DFT functionals). In addition, we present timing results which show the computational time requirements of HSE to be only a factor of 2–4 higher than pure DFT functionals. These results make HSE an attractive choice for calculations of all types of solids.

Mapping potential energy surfaces
View Description Hide DescriptionA recently proposed dynamical method [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)] allows us to globally sample the free energysurface. This approach uses a coarsegrained nonMarkovian dynamics to bias microscopic atomic trajectories. After a sufficiently long simulation time, the global free energysurface can be reconstructed from the nonMarkovian dynamics. Here we apply this scheme to study the free energysurface, i.e., the potential energy surface in coarsegrained space. We show that the accuracy of the reconstructedpotential energy surface can be dramatically improved by a simple postprocessing procedure with only minor computational overhead. We illustrate this approach by conducting conformational analysis on a small organic molecule, demonstrating its superiority over traditional unbiased approaches in sampling potential energy surfaces in coarsegrained space.

Perturbation theory corrections to the twoparticle reduced density matrix variational method
View Description Hide DescriptionIn the variational 2particlereduceddensitymatrix (2RDM) method, the groundstateenergy is minimized with respect to the 2particle reduced density matrix, constrained by Nrepresentability conditions. Consider the Nelectron Hamiltonian as a function of the parameter λ where we recover the Fock Hamiltonian at λ=0 and we recover the fully correlated Hamiltonian at λ=1. We explore using the accuracy of perturbation theory at small λ to correct the 2RDM variational energies at λ=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2RDM method will capture a fairly constant percentage of the correlation energy for λ∈(0,1] because the nonperturbative 2RDM approach depends more significantly upon the nature rather than the strength of the twobody Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2RDM energies in the equilibrium bonding region, while the 2RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2RDM energies are similar in accuracy to those from coupledcluster singles and doubles (CCSD), but at nonequilibrium geometries the 2RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen.

Singular value decomposition applied to the compression of amplitude for the coupled cluster method
View Description Hide DescriptionWe apply the singular value decomposition to compress the degrees of freedom of amplitude for the CCSDT1 method (compressed CCSDT1). This method enables us to make the number of the amplitudes less than that of the amplitudes, making CCSDT1 calculations much less expensive without losing accuracy. We perform test calculations on some atoms and molecules to investigate the applicability of this method. Computational results for the electronic energies as well as timings of these calculations are presented.

Secondorder Møller–Plesset theory with linear R12 terms (MP2R12) revisited: Auxiliary basis set method and massively parallel implementation
View Description Hide DescriptionAb initioelectronic structure approaches in which electron correlation explicitly appears have been the subject of much recent interest. Because these methods accelerate the rate of convergence of the energy and properties with respect to the size of the oneparticle basis set, they promise to make accuracies of better than 1 kcal/mol computationally feasible for larger chemical systems than can be treated at present with such accuracy. The linear R12 methods of Kutzelnigg and coworkers are currently the most practical means to include explicit electron correlation. However, the application of such methods to systems of chemical interest faces severe challenges, most importantly, the still steep computational cost of such methods. Here we describe an implementation of the secondorder Møller–Plesset method with terms linear in the interelectronic distances (MP2R12) which has a reduced computational cost due to the use of two basis sets. The use of two basis sets in MP2R12 theory was first investigated recently by Klopper and Samson and is known as the auxiliary basis set (ABS) approach. One of the basis sets is used to describe the orbitals and another, the auxiliary basis set, is used for approximating matrix elements occurring in the exact MP2R12 theory. We further extend the applicability of the approach by parallelizing all steps of the integraldirect MP2R12 energy algorithm. We discuss several variants of the MP2R12 method in the context of parallel execution and demonstrate that our implementation runs efficiently on a variety of distributed memory machines. Results of preliminary applications indicate that the twobasis (ABS) MP2R12 approach cannot be used safely when small basis sets (such as augmented double and tripleζ correlation consistent basis sets) are utilized in the orbital expansion. Our results suggest that basis set reoptimization or further modifications of the explicitly correlated ansatz and/or standard approximations for matrix elements are necessary in order to make the MP2R12 method sufficiently accurate when small orbital basis sets are used. The computer code is a part of the latest public release of Sandia’s Massively Parallel Quantum Chemistry program available under GNU General Public License.

Continuum equations for magnetic and dielectric fluids with internal rotations
View Description Hide DescriptionSeveral authors have attempted with varying success to derive a complete set of basic equations for the motion of polar fluids having internal rotations and hence in a state of polarization disequilibrium. This work develops a complete set of governing equations derived on the basis of dynamic balance relationships with the dissipation function determined from thermodynamic consideration. The magnetization relaxationequation is thereby determined from requirement of positive entropy production along with a complete set of constitutive laws including antisymmetric terms of the total stress tensor. The analysis employs the Minkowski expression of electromagnetic momentum and assumes that the product of electromagnetic stress and velocity contributes to the energy balance on the same footing as contact stresses of pressure and viscous origin. The work refines the treatment of our earlier effort carrying out the analysis to first order in the ratio of fluid velocity to light speed throughout.

A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. IV. The short time behavior of the memory function
View Description Hide DescriptionUsing a recently developed diagrammatic formulation of the kinetic theory of fluctuations in liquids, we investigate the short time behavior of the memory function for density fluctuations in a classical atomic fluid. At short times, the memory function has a large contribution that is generated by the repulsive part of the interatomic potential. We introduce a small parameter that is a measure of the softness of the repulsive part of the potential. The diagrams in the memory function that contribute to lowest order in that small parameter are identified and summed to give an explicit expression for the dominant contribution to the memory function at short times. The result leads to a theory for fluids with continuous potentials that is similar to the Enskog theory for hard sphere fluids.

Perturbational relativistic theory of electron spin resonance tensor
View Description Hide DescriptionWe carry out a complete treatment of the leadingorder relativistic oneelectron contributions, arising from the Breit–Pauli Hamiltonian, to the tensor of electron spin resonance spectroscopy. We classify the different terms and discuss their interpretation as well as give numerical ab initio estimates for the and series, using analytical response theory calculations with a multiconfigurational selfconsistent field reference state. The results are compared to available experimental data.

LocalSCF method for semiempirical quantumchemical calculation of ultralarge biomolecules
View Description Hide DescriptionA linearscaling semiempirical method, LocalSCF, has been proposed for the quantumchemical calculations of ultralarge molecular systems by treating the largescale molecular task as a variational problem. The method resolves the selfconsistent field task through the finite atomic expansion of weakly nonorthogonal localized molecular orbitals. The inverse overlap matrix arising from the nonorthogonality of the localized orbitals is approximated by preserving the firstorder perturbation term and applying the secondorder correction by means of a penalty function. This allows for the separation of the orbital expansion procedure from the selfconsistent field optimization of linear coefficients, thereby maintaining the localized molecular orbital size unchanged during the refinement of linear coefficients. Orbital normalization is preserved analytically by the variation of virtual degrees of freedom, which are orthogonal to the initial orbitals. Optimization of linear coefficients of localized orbitals is performed by a gradient procedure. The computer program running on a commodity personal computer was applied to the GroELGroES chaperonin complex containing 119 273 atoms.

Sixdimensional vibrational analysis of coupled intermolecular vibrations in a binary cluster
View Description Hide DescriptionWe report on full (six) dimensional calculations of the intermolecular vibrations of a binary aromaticsolvent cluster. An exact Hamiltonian for this kind of interaction is modified in a general manner in order to perform calculations of molecules without symmetry. The binary cluster phenol is used as a test case since its intermolecular vibrations are anharmonic and highly coupled. The formulation of the Schrödinger equation leads to a complexvalued eigenvalue problem with a dimension larger than two million, which is solved by filter diagonalization to obtain both eigenvalues and eigenvectors. With the knowledge of the eigenvectors, an interpretation of all eigenvalues is possible by a characterization with pseudoquantum numbers that are related to the widely used nomenclature of intermolecular normal motions in aromatic(solvent) clusters.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Absolute intensities of Raman trace scattering from bicyclo[1.1.1]pentane
View Description Hide DescriptionOur previous theoretical studies have identified the Raman intensity parameter for the bridgehead C–H stretch in bicyclo[1.1.1]pentane as the largest for any saturated hydrocarbon yet considered, while the methylene C–H parameter is predicted to be ordinary. Theoretical methods including selfconsistent field, static and time dependent density functional theory, and coupled cluster, all predict a large bridgehead intensity parameter, but differ widely in the actual value. We have synthesized bicyclo[1.1.1]pentane and recorded the absolute intensity Raman trace scatteringspectra. The recorded intensity of a resonance polyad in the C–H stretching region has been resolved and distributed onto the fundamental modes through an anharmonic resonance analysis from a computed quartic force field. The experimental internal coordinate intensity parameters have been obtained and compared with those computed. Although the static and dynamic density functional values overestimate the parameter by 10%–18%, the values predicted at the coupledcluster level are found to be correct to within experimental error.

Reactions of with and its deuterated isotopomers, a wave packet study
View Description Hide DescriptionUsing a Chebyshev wave packet method, total and stateresolved reaction probabilities were calculated for the reactions of with various hydrogen isotopomers and HD, on a recent ab initiopotential energy surface. For all the isotopic variants, it was found that the initial state specified reaction probabilities have no energy threshold and are strongly oscillatory, indicative of the involvement of longlived resonances in this barrierless reaction. The product vibrational and rotational distributions for all three isotopic reactions, and the CH/CD branching ratio for the reaction, show strong dependence on the collision energy, further underscoring the important role played by the resonances. The generally decaying vibrational distributions and highly excited rotational distributions, which corroborate an insertion mechanism, and the dominance of the channel in the reaction are consistent with existing experimental observations. Initial state specified integral cross sections and rate constants were estimated using a capture model. The estimated rate constants were found to be close and in the order Finally, a method to calculate branching ratio in the reaction is proposed.

Photodissociation of HCl and small complexes in and on large clusters
View Description Hide DescriptionPhotodissociation experiments were carried out at 193 nm for single HCl molecules which are adsorbed on the surface of large clusters and small complexes which are embedded in the interior of these clusters. For the surface case the size dependence is measured for the average sizes No cage exit events are observed in agreement with the substitutional position of the molecule deeply buried in the outermost shell. This result is confirmed by a molecular dynamics simulation of the pickup process under realistic conditions concerning the experiment and the interaction potentials. The calculations of the dissociation process employ the surface hopping model. For the embedded case the average sizes covered are and 6 and The kinetic energy of the H atom fragments is measured exhibiting peaks at zero and around 2.0 eV which mark completely caged and unperturbed fragments, respectively. The ratio of theses peaks strongly depends on the cluster size and agrees well with theoretical predictions for one and two closed icosahedral shells, in which the nonadiabatic coupling of all states was accounted for.

Electron attachment on HI and DI in a uniform supersonic flow: Thermalization of the electrons
View Description Hide DescriptionIn order to check the electron thermalization in the CRESU technique (Cinétique de Réaction en Ecoulement Supersonique Uniforme, e.g., “reaction kinetics in a uniform supersonic flow”), electron attachment on HI and DI has been studied in the 48–170 K range. Attachment to HI is exothermic and the reaction is expected to be fast and to proceed at a rate close to the capture limit. On the contrary, attachment to DI is slightly endothermic, and a strong positive temperature dependence of the measured rate coefficient is expected if the electrons are thermal. This dependence is not observed, and we conclude that the electrons are not in thermal equilibrium with the neutrals in the afterglow. A model, based on electron heating by superelastic collisions with the buffer gas, is proposed to explain this fact and implications for previously published results are discussed.

Infrared–infrared double resonance spectroscopy of cyanoacetylene in helium nanodroplets
View Description Hide DescriptionInfrared–infrared double resonancespectroscopy is used as a probe of the vibrational dynamics of cyanoacetylene in helium droplets. The C–H stretching vibration of cyanoacetylene is excited by an infrared laser and subsequent vibrational relaxation results in the evaporation of approximately 660 helium atoms from the droplet. A second probe laser is then used to excite the same C–H stretching vibration downstream of the pump, corresponding to a time delay of approximately 175 μs. The hole burned by the pump laser is narrower than the single resonance spectrum, owing to the fact that the latter is inhomogeneously broadened by the droplet size distribution. The line width of the hole is characteristic of another broadening source that depends strongly on droplet size.

Theoretical analysis of singlet and triplet excited states of nickel porphyrins
View Description Hide DescriptionLocal density and generalized gradient approximation timedependent density functional methods have been used for calculation of the singlet and triplet excited states of nickel–porphine, Ni–tetraphenyloporphine, and Ni–octaethyloporphyrine. Special attention is paid to metal–ligand transitions and transitions. It is shown that the lowest exited singlet states of the three compounds can be described as a transfer of an electron from the porphine ring to the orbital of the nickel atom. On the other hand, the lowest excited triplet state arises from promotion of an electron between two nickeld orbitals, an occupied and an empty It is proposed that a rapid quenching of the excited singlet states is due to an ultrafast intersystem crossing between and or states.

New ab initio potential energy surface for the van der Waals complex
View Description Hide DescriptionA threedimensional potential energy surface has been calculated for the ground electronic state of the system. The calculations were performed at the coupled electron pair approximation level with an extended basis set which ensures a balance between accuracy and feasability. The validity of the method and of the basis set was tested through calculations of the polarizability of the He atom and of the spectroscopic constants of the ion. The calculated potential energy surface has been fitted to a spherical harmonic expansion to facilitate calculations of rotational excitation of by collisions with He.

Rotational isomerism of acetic acid isolated in raregas matrices: Effect of medium and isotopic substitution on IRinduced isomerization quantum yield and tunneling rate
View Description Hide DescriptionRotational isomerization of acetic acid is studied in Ar, Kr, and Xe matrices. The lightinduced reaction is promoted using resonant excitation of a number of modes in the 3500–7000 cm^{−1} region, and the quantum yields for this process are measured for various acetic acid isotopologues and matrix materials. For excitation of acetic acid at energiesabove the predicted isomerizationenergy barrier (⩾4400 cm^{−1}), the measured quantum yields are in average 2%–3%, and this is one order of magnitude smaller than the corresponding values known for formic acid (HCOOH). This difference is interpreted in terms of the presence of the methyl group in acetic acid, which enhances energy relaxation channels competing with the rotational isomerization. This picture is supported by the observed large effect of deuteration of the methyl group on the photoisomerization quantum yield. The reaction quantum yields are found to be similar for Ar, Kr, and Xe matrices, suggesting similar energy relaxation processes for this molecule in the various matrices. The IRinduced process, studied for acetic acid deuterated in the hydroxyl group, shows reliably larger quantum yields as compared with the process. For pumping of acetic acid at energiesbelow the predicted isomerization barrier, the reaction quantum yields decrease strongly when the photonenergy decreases, and tunneling is the most probable mechanism for this process. For the dark reaction, the observed temperature and medium effects indicate the participation of the lattice phonons in the tunnelinginduced process.