Volume 122, Issue 21, 01 June 2005
 ARTICLES

 Theoretical Methods and Algorithms

Gauge invariance of the spinotherorbit contribution to the tensors of electron paramagnetic resonance
View Description Hide DescriptionThe spinotherorbit (SOO) contribution to the tensor of electron paramagnetic resonance arises due to the interaction of electronspin magnetic moment with the magnetic field produced by the orbital motion of other electrons. A similar mechanism is responsible for the leading term in nuclear magneticshielding tensors. We demonstrate that analogous to , paramagnetic contribution exhibits a pronounced dependence on the choice of the magneticfield gauge. The gauge corrections to are similar in magnitude, and opposite in sign, to the paramagnetic SOO term. We calculate gaugeinvariant values using gaugeincluding atomic orbitals and densityfunctional theory. For organic radicals, complete gaugeinvariant values typically amount to less than (ppm), and are small compared to other tensor contributions. For the firstrow transitionmetal compounds, may contribute several thousand ppm to the tensor, but are negligible compared to the remaining deviations from experiment. With popular choices for the magneticfield gauge, the individual gaugevariant contributions may be an order of magnitude higher, and do not provide a reliable estimation of .

Computation of electrostatic forces between solvated molecules determined by the Poisson–Boltzmann equation using a boundary element method
View Description Hide DescriptionA rigorous approach is proposed to calculate the electrostatic forces among an arbitrary number of solvated molecules in ionic solution determined by the linearized Poisson–Boltzmann equation. The variational principle is used and implemented in the frame of a boundary element method(BEM). This approach does not require the calculation of the Maxwell stress tensor on the molecular surface, therefore it totally avoids the hypersingularity problem in the direct BEM whenever one needs to calculate the gradient of the surface potential or the stress tensor. This method provides an accurate and efficient way to calculate the full intermolecular electrostatic interaction energy and force, which could potentially be used in Brownian dynamics simulation of biomolecular association. The method has been tested on some simple cases to demonstrate its reliability and efficiency, and parts of the results are compared with analytical results and with those obtained by some known methods such as adaptive Poisson–Boltzmann solver.

Electron density, exchangecorrelation density, and bond characterization from the perspective of the valencebond theory. I. Two simple analytical cases
View Description Hide DescriptionIn this work, using a valencebond wave function we obtain analytical expressions for the first and secondorder reduced density matrices of two simple, but quite representative, cases of diatomic molecular systems, namely, and LiH. A detailed study of their exchangecorrelation density is performed for both equilibrium and nonequilibrium internuclear distances, discriminating the parallel and antiparallelspin contributions. The results show that the behavior of the exchangecorrelation density clearly changes with the character of the bond, making it possible to obtain a good deal of information regarding the type of the bondinteraction.

Electron density, exchangecorrelation density, and bond characterization from the perspective of the valencebond theory. II. Numerical results
View Description Hide DescriptionIn this work we have analyzed the bond character of a series of representative diatomic molecules, using valence bond and the atoms in molecules points of view. This is done using generalized valencebond calculations. We have also employed more exigent levels, as configuration interaction with single and double excitations and complete active space selfconsistent field calculations, in order to validate the generalized valencebond results. We have explored the possibility that the known delocalization index, and a parameter that measures the excess or defect population within a given atomic basin, can be considered as indicators of the character of bondinteraction. We conclude that for a proper description of the bond character, the global behavior of both the charge and twoelectron densities should be considered.

Transport properties of quantumclassical systems
View Description Hide DescriptionCorrelation function expressions for calculating transport coefficients for quantumclassical systems are derived. The results are obtained by starting with quantum transport coefficient expressions and replacing the quantum time evolution with quantumclassical Liouville evolution, while retaining the full quantum equilibrium structure through the spectral density function. The method provides a variety of routes for simulating transport coefficients of mixed quantumclassical systems, composed of a quantum subsystem and a classical bath, by selecting different but equivalent time evolution schemes of any operator or the spectral density. The structure of the spectral density is examined for a single harmonic oscillator where exact analytical results can be obtained. The utility of the formulation is illustrated by considering the rate constant of an activated quantum transfer process that can be described by a manybody bath reaction coordinate.

Nonlinear instability of densityindependent orbitalfree kineticenergy functionals
View Description Hide DescriptionWe study in this article the mathematical properties of a class of orbitalfree kineticenergy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kineticenergy functionals are not bounded from below. As a matter of illustration, we provide an example of an electronic density of simple shape, the kinetic energy of which is negative.

Extension of renormalized coupledcluster methods including triple excitations to excited electronic states of openshell molecules
View Description Hide DescriptionThe generalpurpose openshell implementation of the completely renormalized equationofmotion coupledcluster approach with singles, doubles, and noniterative triples [CREOMCCSD(T)] is reported. Benchmark calculations for the lowlying doublet and quartet states of the CH radical show that the CREOMCCSD(T) method is capable of providing a highly accurate description of ground and excited states of openshell molecules. This includes states with strong double excitation character, for which the conventional EOMCCSD approach fails.

Characterization of quantum algorithms by quantum process tomography using quadrupolar spins in solidstate nuclear magnetic resonance
View Description Hide DescriptionNMRquantum computing with qubit systems represented by nuclear spins in small molecules in liquids has led to the most successful experimental quantum information processors so far. We use the quadrupolar spinsodium nuclei of a single crystal as a virtual twoqubit system. The large quadrupolar coupling in comparison with the environmental interactions and the usage of strongly modulating pulses allow us to manipulate the system fast enough and at the same time keeping the decoherence reasonably slow. The experimental challenge is to characterize the “calculation” behavior of the quantum processor by process tomography which is here adapted to the quadrupolar spin system. The results of a selection of quantum gates and algorithms are presented as well as a detailed analysis of experimental results.

Symmetryadapted perturbationtheory calculations of intermolecular forces employing densityfunctional description of monomers
View Description Hide DescriptionA symmetryadapted perturbation theory based on Kohn–Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchangecorrelation potentials has been applied to the , , , and dimers. It is shown that SAPT(KS) is able to recover the electrostatic, firstorder exchange, secondorder induction, and exchangeinduction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, firstorder exchange, and secondorder induction energies has been provided.

Stochastic potential switching algorithm for Monte Carlo simulations of complex systems
View Description Hide DescriptionThis paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential . By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential . The validity of the method is illustrated with a simple onedimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A nearcritical LennardJones fluid with more than 20 000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

A quantum wavepacket study of intersystem crossing effects in the reaction
View Description Hide DescriptionWe present for the first time an exact quantum study of spin–orbitinduced intersystem crossing effects in the title reaction. The timedependent wavepacket method, combined with an extended split operator scheme, is used to calculate the finestructure resolved cross section. The calculation involves four electronic potentialenergysurfaces of the state [J. Dobbyn and P. J. Knowles, Faraday Discuss.110, 247 (1998)], the and the two degenerate states [S. Rogers, D. Wang, A. Kuppermann, and S. Wald, J. Phys. Chem. A104, 2308 (2000)], and the spin–orbit couplings between them [B. Maiti, and G. C. Schatz, J. Chem. Phys.119, 12360 (2003)]. Our quantum dynamics calculations clearly demonstrate that the spin–orbit coupling between the triplet states of different symmetries has the greatest contribution to the intersystem crossing, whereas the singlettriplet coupling is not an important effect. A branch ratio of the spin state to of the product OH was calculated to be , with collision energy higher than , when the wave packet was initially on the triplet surfaces. The quantum calculation agrees quantitatively with the previous quasiclassical trajectory surface hopping study.

Effect of relativity on the ionization spectra of the xenon fluorides (, 4, 6)
View Description Hide DescriptionNoble gas compounds exhibit special chemical bonding situations and have been investigated by various spectroscopic and theoretical techniques. In this work we calculate the ionization spectra of the xenon fluorides (, and ) in the valence and subvalence (down to ) areas by application of the recently developed Dirac–Hartree–Fock oneparticle propagator technique. In this technique, the relativistic (fourcomponent) and electron correlationeffects are computed simultaneously. The xenon compounds show considerable spin–orbit splitting strongly influencing the photoelectron spectrum not reproducible in prior calculations. Comparison to onecomponent methods is made and the occurring satellite structures are interpreted. The satellite structures can be attributed either to the breakdown of the oneparticle picture or to a reflection of intraatomic and interatomic Auger decay processes within the molecule.

Product distributions, rate constants, and mechanisms of reactions
View Description Hide DescriptionWe present a quantummechanical investigation of the LiH depletion reaction and of the H exchange reaction. We report product distributions, rate constant, and mechanism of the former, and rate constant and mechanism of the latter reaction. We use the potentialenergy surface by Dunne et al. [Chem. Phys. Lett.336, 1 (2001)], the realwavepacket method by Gray and BalintKurti [J. Chem. Phys.108, 950 (1998)], and the shifting approximation. The nuclearspin statistics and progressions of vibrotational states rule both initialstateresolved and thermal product distributions, which have sawtoothed shapes with odd preferred with respect to even . At high collision energies and temperatures, we obtain a regular 3to1 intensity alternation of rotational states. At low collision energies and temperatures, the degeneracy and density of many levels can, however, give more irregular distributions. During the collision, the energy flows from the reactant translational mode to the product vibration and recoil ones. The rate constants of both reactions are not Arrhenius type because the reactions are barrierless. The lowtemperature, LiH depletion rate constant is larger than the H exchange one, whereas the contrary holds at high temperature. The realtime mechanisms show the nuclear rearrangements of the nonreactive channel and of the reactive ones, and point out that the LiH depletion is preferred over the H exchange at short times. This confirms the rateconstant results.

Vibrational Raman optical activity as a mean for revealing the helicity of oligosilanes: A quantum chemical investigation
View Description Hide DescriptionUsing theoretical simulations based on Hartree–Fock and densityfunctional theory calculations, the simulated vibrational Raman optical activityspectra of helical conformers of heptasilane are shown to present signatures sensitive to the helicity. These signatures are associated with collective wagging, twisting, and rocking motions. These simulated spectra have been obtained by combining analytical and numerical differentiation procedures to evaluate the geometry derivatives of the optical tensors entering into the expressions of the vibrational Raman optical activity intensities. From an investigation of basis set and electron correlation effects, it is shown that, like for local vibrations, diffuse functions are compulsory for evaluating the vibrational Raman optical activity intensities of collective vibrational motions.

On equilibrium structures of the water molecule
View Description Hide DescriptionEquilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born–Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent highquality ab initio semiglobal adiabatic potentialenergy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [Polyansky et al.Science299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born–Oppenheimer approximation suggests that the concept of an isotopeindependent equilibrium structure holds to about and 0.02° for water. The massindependent [Born–Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is and , respectively. The related massdependent (adiabatic) equilibrium bond length and bond angle of is and , respectively, while those of are and . Pure ab initio prediction of and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than (or the lower ones to better than ) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for and . The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and nonBorn–Oppenheimer effects. The spectroscopic(nonadiabatic) equilibrium structural parameters of , obtained from experimentally determined and rotational constants corrected empirically to obtain equilibrium rotational constants, are and .

Analytic calculation of firstorder molecular properties at the explicitly correlated secondorder Møller–Plesset level: Basisset limits for the molecular quadrupole moments of BH and HF
View Description Hide DescriptionThe analytic calculation of firstorder properties has been implemented in the DALTON program at the level of explicitly correlated secondorder MøllerPlesset perturbation theory (MP2R12). The implementation has been accomplished for MP2R12 theory based on standard approximations , , and , using an auxiliary basis for the resolutionoftheidentity approximation, with and without a frozen core. MP2R12 firstorder molecular properties have been calculated analytically for a few small test molecules. For BH and HF, the MP2R12 results were supplemented with explicitly correlated coupledcluster calculations (but at this level from numerical derivatives) including vibrational and relativistic corrections.

Variation of geometries and electron properties along proton transfer in strong hydrogenbond complexes
View Description Hide DescriptionProton transfer in hydrogenbond systems formed by 4methylimidazole in both neutral and protonated cationic forms and by acetate anion are studied by means of ab initio calculations. These two complexes model the histidine (neutral and protonated)aspartate diad present in the active sites of enzymes the catalytic mechanism of which involves the formation of strong hydrogen bonds. We investigate the evolution of geometries, natural bond orbital populations of bonds and electron lone pairs, topological descriptors of the electron density, and spatial distributions of the electron localization function along the process , which represents the stages of the Htransfer. Except for a sudden change in the population of electron lone pairs in N and O at the middle N···H···O stage, all the properties analyzed show a smooth continuous behavior along the covalent hydrogen bond transit inherent to the transfer, without any discontinuity that could identify a formation or breaking of the hydrogen bond. This way, the distinction between covalent or hydrogenbonding features is associated to subtle electron rearrangement at the intermolecular space.

Magnetically induced current densities in and species studied at the coupledcluster level
View Description Hide DescriptionMagnetically induced current densities in the fourmembered rings of and species have been calculated at the coupledcluster singles and doubles (CCSD) level by applying the recently developed gaugeincluding magnetically induced current (GIMIC) method. The strength of the ringcurrent susceptibilities were obtained by numerical integration of the current densities passing through a cross section perpendicular to the ring. The GIMIC calculations support the earlier notion that with formally two electrons sustains a net diatropic ring current. The diatropic contribution to the ringcurrent susceptibility is carried by the electrons in both the and the orbitals. The induced ring current in the compounds, with four electrons, consists of about equally strong diatropic and paratropic currents of about 14 and , respectively. The net current susceptibilities obtained for , , , and at the CCSD level using a triplezeta basis set augmented with polarization functions are 28.1, 28.1, , and , respectively. The corresponding diatropic (paratropic) contributions to the ringcurrent susceptibilities are 32.4 (0.0), 36.7 (0.0), 18.9 , and 18.6 , respectively. For the and species, the net currents circling each cation is estimated to 4.3 and , respectively.

Addition of water, methanol, and ammonia to clusters: Reaction products, transition states, and electron detachment energies
View Description Hide DescriptionProducts of reactions between the book and kite isomers of and three important molecules are studied with electronic structure calculations. Dissociativeadsorption of or is highly exothermic and protontransfer barriers between anionmolecule complexes and the products of these reactions are low. For , the reaction energies are less exothermic and the corresponding barriers are higher. Depending on experimental conditions, coordination complexes or products of dissociativeadsorption may be prepared. Vertical electron detachment energies of stable anions are predicted with ab initio electron propagator calculations and are in close agreement with experiments on and its products with and . Changes in the localization properties of two Alcentered Dyson orbitals account for the differences between the photoelectron spectra of and those of the product anions.

Microwave spectra of the van der Waals complex: A comparison of experiment and theory
View Description Hide DescriptionRotational transitions for the complex were measured in the frequency region from using a pulsednozzle Fouriertransform microwave spectrometer. Twelve (four) type transitions were recorded for the and isotopomers. In addition, the nuclear quadrupolehyperfine structures due to the presence of the (nuclearspin quantum number ) and nuclei were detected and analyzed. Two ab initiopotentialenergysurfaces were calculated at the coupledcluster level of theory with single, double, and pertubatively included triple excitations. Dunning’s augmented correlationconsistent polarized valence triplezeta basis set was used for the nitrogen atoms. For the first surface, a welltempered basis set with additional polarization functions was used for the Xe atom; for the second surface, a newly developed augmented correlationconsistent polarized valence quintuplezeta basis set employing smallcore relativistic pseudopotentials was used for the Xe atom. The basis sets were supplemented with bond functions for the van der Waals bond. The counterpoise correction was applied to reduce the basisset superposition error. The resulting two surfaces both have a single minimum at a Tshaped geometry, with well depths of 122.4 and , respectively. Boundstate energies supported by the potentialenergysurface were determined. The quality of the ab initiopotentialenergysurfaces was evaluated by comparison of the experimental transition frequencies and rotational and centrifugal distortion constants with those derived from the boundstate energies. A scaled potentialenergysurface was obtained which has excellent agreement with the experimental data.