Volume 121, Issue 16, 22 October 2004
 ARTICLES

 Theoretical Methods and Algorithms

Quantumclassical limit of quantum correlation functions
View Description Hide DescriptionA quantumclassical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantumclassical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a bath of heavy quantum particles. In this limit the time evolution of operators is determined by a quantumclassical Liouville operator, but the full equilibrium canonical statistical description of the initial condition is retained. The quantumclassical correlation function expressions derived here provide a way to simulate the transport properties of quantum systems using quantumclassical surfacehopping dynamics combined with sampling schemes for the quantum equilibrium structure of both the subsystem of interest and its environment.

Accuracy of gates in a quantum computer based on vibrational eigenstates
View Description Hide DescriptionA model is developed to study the properties of a quantum computer that uses vibrational eigenstates of molecules to implement the quantum information bits and shaped laser pulses to apply the quantum logic gates. Particular emphasis of this study is on understanding how the different factors, such as properties of the molecule and of the pulse, can be used to affect the accuracy of quantum gates in such a system. Optimal control theory and numerical timepropagation of vibrational wave packets are employed to obtain the shaped pulses for the gates NOT and Hadamard transform. The effects of the anharmonicity parameter of the molecule, the target time of the pulse and of the penalty function are investigated. Influence of all these parameters on the accuracy of qubit transformations is observed and explained. It is shown that when all these parameters are carefully chosen the accuracy of quantum gates reaches 99.9%.

Accurate calculation of coreelectron binding energies: Multireference perturbation treatment
View Description Hide DescriptionMultireference perturbation theory (MRPT) with multiconfigurational selfconsistent field (MCSCF) reference functions is applied to the calculations of coreelectron binding energies (CEBEs) of atoms and molecules. Orbital relaxations in a coreionized state and electron correlation are both taken into account in a conventional MCSCFMRPT procedure. In the MCSCF calculation, the target core ionized state is directly optimized as an excited state and this treatment can completely prevent a variational collapse. Multireference MøllerPlesset perturbation theory and multiconfigurational selfconsistent field reference quasidegenerated perturbation theory were used to treat electron correlation. The present method quite accurately reproduced the CEBEs of and FH; the average deviation from the experimental data is 0.11 eV using Ahlrichs’ VTZ basis set. The and CEBEs of formic acid and acetic acid were calculated and the results are consistent with the bonding characters of the atoms in these molecules. The present procedure can also be applied to CEBEs of higher angular momentum orbitals by including spinorbit coupling. The calculated CEBEs of and are in reasonable agreement with the available experimental values. In the calculation of the CEBEs, a relativistic correction significantly improves the agreements. The effect of polarization functions is also discussed.

Calculations of static and dynamic polarizabilities of excited states by means of density functional theory
View Description Hide DescriptionWe present density functional theory and calculations for excited state second order, static or dynamic, properties. The excited stateproperties are identified from a double residue of a cubic response function. The performance of various functionals, including the generalized gradient approximation and fractional exact HartreeFock exchange, is compared to coupled cluster calculations. Applications on excited statepolarizabilities of stetrazine and pyrimidine show a good agreement with ab initio correlated, coupled cluster, results.

Spectral implementation of some quantum algorithms by one and twodimensional nuclear magnetic resonance
View Description Hide DescriptionQuantum information processing has been effectively demonstrated on a small number of qubits by nuclear magnetic resonance. An important subroutine in any computing is the readout of the output. “Spectral implementation” originally suggested by Z. L. Madi, R. Bruschweiler, and R. R. Ernst [J. Chem. Phys. 109, 10603 (1999)], provides an elegant method of readout with the use of an extra “observer” qubit. At the end of computation, detection of the observer qubit provides the output via the multiplet structure of its spectrum. In spectral implementation by twodimensional experiment the observer qubit retains the memory of input state during computation, thereby providing correlated information on input and output, in the same spectrum. Spectral implementation of Grover’s search algorithm, approximate quantum counting, a modified version of BersteinVazirani problem, and Hogg’s algorithm are demonstrated here in three and fourqubit systems.

Density functional theory for hyperfine coupling constants with the restrictedunrestricted approach
View Description Hide DescriptionThis work presents derivation, implementation, and the first applications of the restrictedunrestricted approach based on restricted KohnSham formalism for evaluation of hyperfine coupling constants. By using the spinrestricted KohnSham method the wellknown spin contamination problem existing in the unrestricted KohnSham formalism is avoided and a proper description of spin polarization is achieved via the restrictedunrestricted approach without introducing spin contamination into the evaluation of the hyperfine coupling constants. The performance of the proposed formalism is evaluated for a set of organic radicals and transition metalcompounds. The results of this investigation indicate promising accuracy of the restrictedunrestricted approach for calculation of the isotropic hyperfine coupling constants in organic radicals as well as transition metalcompounds.

Triplet instability in doublet systems
View Description Hide DescriptionSome problems associated with unrestricted wave functions for openshell molecules are discussed in the contest of coupledcluster calculation of molecular properties. Particular attention is given to a phenomenon akin to the “triplet instability” of closedshell molecules, where the approximate spin pairing of a nominal pair of electrons in the unrestricted HartreeFock wave function begins to give way to significant spin polarization. This problem—which gives rise to pronounced spin contamination—is discussed from the point of view of orbital instability and occupation numbers of the charge density matrix. The onset, rather than the magnitude of the spin contamination is analyzed in detail for diatomics, especially heteronuclear cases where the transition to significant spin contamination does not occur discontinuously. It is shown that the qualitative description of this phenomenon satisfactorily explains anomalous results for NO and PO, although the magnitude of spin contamination in these molecules is significantly less than in other cases where anomalous results are not observed. It appears that calculations of equilibrium molecular properties using coupledcluster methods based on unrestricted HartreeFock reference should be monitored carefully for any molecule containing a multiple bond, especially when the bonded pair of atoms appear in different rows of the periodic table.

The behavior of density functionals with respect to basis set. I. The correlation consistent basis sets
View Description Hide DescriptionThe accuracy of density functional theory in the description of geometries and atomization energies has been assessed by comparison to experimental data for a series of firstrow closedshell molecules. Six commonly used functionals (B3LYP, B3PW91, B3P86, BLYP, BPW91, BP86) were investigated in combination with the correlationconsistentbasis sets and where T(3), Q(4), 5]. The convergence of molecular properties with respect to increasing basis set size has been examined. A full statistical error analysis has been performed, assessing the success of each functional with respect to each basis set in terms of both accuracy and precision. Overall, there is smooth convergence towards the KohnSham limit for the hybrid functionals B3LYP and B3PW91, whereas the nonlocal functionals are relatively insensitive to basis set choice.

Multiscale quantum propagation using compactsupport wavelets in space and time
View Description Hide DescriptionOrthogonal compactsupport Daubechies wavelets are employed as bases for both space and time variables in the solution of the timedependent Schrödinger equation. Initial value conditions are enforced using special earlytime wavelets analogous to edge wavelets used in boundaryvalue problems. It is shown that the quantum equations may be solved directly and accurately in the discrete wavelet representation, an important finding for the eventual goal of highly adaptive multiresolution Schrödinger equation solvers. While the temporal part of the basis is not sharp in either time or frequency, the Chebyshev method used for pure timedomain propagations is adapted to use in the mixed domain and is able to take advantage of Hamiltonian matrix sparseness. The orthogonal separation into different time scales is determined theoretically to persist throughout the evolution and is demonstrated numerically in a partially adaptive treatment of scattering from an asymmetric Eckart barrier.

Coherent switching with decay of mixing: An improved treatment of electronic coherence for nonBorn–Oppenheimer trajectories
View Description Hide DescriptionThe selfconsistent decayofmixing (SCDM) semiclassical trajectory method for electronically nonadiabatic dynamics is improved by modifying the switching probability that determines the instantaneous electronic state toward which the system decoheres. This method is called coherent switching with decay of mixing (CSDM), and it differs from the previously presented SCDM method in that the electronic amplitudes controlling the switching of the decoherent state are treated fully coherently in the electronic equations of motion for each complete passage through a strong interaction region. It is tested against accurate quantum mechanical calculations for 12 atomdiatom scattering test cases. Also tested are the SCDM method and the trajectory surface hopping method of Parlant and Gislason that requires coherent passages through each strong interaction region, and which we call the “exact complete passage” trajectory surface hopping (ECPTSH) method. The results are compared with previously presented results for the fewest switches with time uncertainty and Tully’s fewest switches (TFS) surface hopping methods and the semiclassical Ehrenfest method. We find that the CSDM method is the most accurate of the semiclassical trajectory methods tested. Including coherent passages improves the accuracy of the SCDM method (i.e., the CSDM method is more accurate than the SCDM method) but not of the trajectory surface hopping method (i.e., the ECPTSH method is not more accurate on average than the TFS method).

Correlation energy of manyelectron systems: A modified Colle–Salvetti approach
View Description Hide DescriptionThe Colle and Salvetti approach [Theo. Chim. Acta 37, 329 (1975)] to the calculation of the correlation energy of a system is modified in order to explicitly include into the theory the kinetic contribution to the correlation energy. This is achieved by deducing from a many electrons wave function, including the correlation effects via a Jastrow factor, an approximate expression of the oneelectron reduced density matrix. Applying the latter to the homogeneous electron gas, an analytic expression of the correlation kinetic energy is derived. The total correlation energy of such a system is then deduced from its kinetic contribution inverting a standard procedure. At variance of the original Colle–Salvetti theory, the parameters entering in both the kinetic correlation and the total correlation energies are determined analytically, leading to a satisfactory agreement with the results of Perdew and Wang [Phys. Rev. B 45, 13244 (1992)]. The resulting (parameterfree) expressions give rise to a modifiedlocaldensity approximation that can be used in selfconsistent densityfunctional calculations. We have performed such calculations for a large set of atoms and ions and we have found results for the correlation energies and for the ionization potentials which improve those of the standard localdensity approximation.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Quantum wavepacket dynamics of scattering: Reaction cross section and thermal rate constant
View Description Hide DescriptionThe channel specific and initial stateselected reaction cross section and temperaturedependent rate constant for the title system is calculated with the aid of a timedependent wavepacket approach and using the ab initiopotential energy surface of Dunne et al. [Chem. Phys. Lett. 336, 1 (2001)]. All partialwave contributions up to the total angular momentum are explicitly calculated within the coupled states (CS) approximation. Companion calculations are also carried out employing the standard as well as the uniform Jshifting (JS) approximation. The overall variation of reaction cross sections corresponds well to the behavior of a barrierless reaction. The hydrogen exchange channel yielding products is seen to be more favored over the HLi depletion channel yielding products at low and moderate collision energies. Sharp resonance features are observed in the crosssection results for the HLi depletion channel at low energies. Resonance features in the reaction cross sections average out with various partialwave contributions, when compared to the same observed in the individual reaction probability curve. Except near the onset of the reaction, the vibrational and rotational excitation of the reagent HLi, in general, does not dramatically influence the reactivity of either channel. The thermal rate constants calculated up to 4000 K show nearly Arrhenius type behavior. The rate constant decreases with vibrational excitation of the reagent HLi, indicating that the cold HLi molecules are efficiently depleted in the reactive encounter with H at relatively low temperatures. The results obtained from the JS approximation are found to agree well qualitatively with the CS results.

Photoelectron spectroscopy and density functional theory of puckered ring structures of Group 13 metalethylenediamine
View Description Hide DescriptionThe ethylenediamine (en) complexes of Al, Ga, and In atoms were prepared in laservaporization supersonic molecular beams and studied with pulsed field ionization zero electron kinetic energy photoelectron spectroscopy and density functional theory. Several conformers of each metal complex are obtained by B3LYP calculations, and a fivemembered cyclic structure is identified by combining the experimental measurements and theoretical calculations. Adiabatic ionization potentials, vibrational frequencies, and bond dissociation energies are determined for the ring structure. The ionization potentials of the Al, Ga, and In species are measured to be 32 784 (5), 33 324 (5), and 33 637 (7) cm^{−1}, respectively, and metalligand dissociation energies of the ionic and neutral complexes are calculated to be and Metalligand stretch and bend as well as a number of ligandbased vibrations are measured. Harmonic frequencies and anharmonicities of the stretch are determined for all three ions and the CCN bend of and In comparison to monodentate methylamine, the bidentate binding of ethylenediamine leads to a significantly lower ionization potential and higher metalligand bond strength of the metal complexes.

Evolution spectrum of isomers in buffer gas
View Description Hide DescriptionThe energy spectrum of nonclassic fullerenes with single heptagon defects calculated by Brenner empirical potential is found to submerge into the spectrum of classic fullerenes. Geometry analysis indicates that these nonclassic fullerene isomers can be more attainable than classic fullerenes at higher StoneWales (SW) stacks. Molecular dynamic simulations of the isomer evolution in He buffer gas at 2500 K demonstrate that nonclassic fullerenes, especially those with heptagon defects, play an important role in the dynamics of annealing, and that the StoneWales stackbystack transition mainly occurs at lower SW stacks. A nonSW multistep rearrangement is first observed in the simulation with its transition sequence and intermediate state presented in detail.

Radial subshell splittings and doublezeta functions in manyelectron atoms
View Description Hide DescriptionWhen the electron–electron interaction is explicitly considered in manyelectron atoms, the average subshell radius splits into two different radii, inner radius and outer radius where n and l are the principal and azimuthal quantum numbers. For the 102 atoms He through Lr in their ground states, the radii and are systematically examined at the Hartree–Fock limit level. For a subshell two exponents and estimated from these radii have good linear correlations with variationally determined exponents and of doubleζ Slatertype functions.

New approximations for calculating dispersion coefficients
View Description Hide DescriptionImproved approaches for finding approximate values of dispersion coefficients are proposed. They are based on scaling the values of timedependent Hartree–Fock (TDHF) dispersion coefficients by factors that use the ratio of the estimated true value and the TDHF value of static dipole polarizabilities. It is shown that for a set of 14 atoms and molecules the average absolutevalue deviation of the estimated twobody isotropic dispersion coefficients with respect to the dipole oscillator strength distribution results is smaller than 1.0% for two of our approaches. For threebody isotropic dispersion coefficients the corresponding deviations are smaller than 1.2%. Our approximations work particularly well compared to approximations proposed by other researchers in cases where the TDHF results differ from the reference values by more than 10%.

The nonmetallicity of molybdenum clusters
View Description Hide DescriptionMolybdenum clusters consisting of 2–55 atoms were investigated using density functional theory calculations with a planewave basis set. The results show that the linear and planar molybdenum clusters have a strong tendency to form dimers. This tendency results in the formation of alternate short and long bonds within a linear cluster, in which the strength of these short bonds is covalent. Therefore, the linear and planar Mo clusters exhibit significant nonmetallic characteristics. Furthermore, the linear and planar Mo clusters show a strong evenodd effect in binding energy with the evennumbered clusters being more stable than their neighboring oddnumbered clusters. On the other hand, the evenodd effect in the energy gap between the highest occupied and the lowest unoccupied molecular orbitals, i.e., the HOMOLUMO energy gap, for the linear and the planar clusters is different. The oddnumbered linear clusters and evennumbered planar clusters have larger HOMOLUMO energy gaps than their corresponding neighboring clusters.

A threedimensional HeNaH potential energy surface for rovibrational energy transfer studies
View Description Hide DescriptionA threedimensional potential energy surface for the HeNaH van der Waals complex is calculated at the coupled cluster singlesanddoubles with noniterative inclusion of connected triples [CCSD(T)] level of theory. Estimates of CCSD(T) interaction energies for an infinitely large basis set is obtained using a basis set extrapolation scheme. The HeNaH potential energy surface is much different than the HeLiH surface. In particular, the HeNaH system has a binding energy of in comparison to for HeLiH. These minima are at the linear geometry where the helium is located at the metal end of the metal hydride. The HeNaH and HeLiH potentials are very similar for the linear geometry. The HeNaH potential energy surface supports one vibrational bound state with Since this energy is smaller than the accuracy of the potential energy surface, the existence of a bound HeNaH complex is questionable.

Electronic spectra of iron monohydride in the infrared near 1.35 and 1.58 μm
View Description Hide DescriptionThe complex, manyline spectrum of FeH, lying in the infrared region between 5500 and 7500 cm^{−1}, has been shown to consist of two separate electronic transitions: and High resolution Fourier transform spectra from thermal emission have been rotationally analyzed in detail. Lambda doubling in both the and states is considerable. The experimentally determined energies and bond lengths of the newly characterized states are in good agreement with theoretical predictions.

Calculated optical and magnetic properties of hexafluorouranate (V) anion:
View Description Hide DescriptionOur ab initio allelectron DiracFock and the corresponding nonrelativistic limit calculations performed at four UF bond distances yield for octahedral the optimized UF bond distance of 2.091 and 2.088 Å, respectively. We have also performed Diracscattered wave calculations at the optimized UF bond distances using the firstorder pertubational procedure to obtain the Zeeman and hyperfine magnetic tensors for the octahedral anion The calculated isotropic Zeemantensor of is in fairly good agreement with the value of obtained in electron spin resonance experiments on the adduct and the unpaired electronspin spends ∼2.5% of its time on the fluorine spinors. The calculated relativistic transition energies of the nearIR and visible absorption bands are also in good agreement with the experimental results. The octahedral uranium hexafluoride anion has a simple crystal field configuration; however, relativistic fourcomponent wave functions are necessary to interpret correctly the available magnetic data, while a relativistic treatment taking into account double group symmetrized basis functions should suffice for the interpretation of the optical data.