Volume 121, Issue 19, 15 November 2004
 COMMUNICATIONS


The ground state tunneling splitting of malonaldehyde: Accurate full dimensional quantum dynamics calculations
View Description Hide DescriptionBenchmark calculations of the tunneling splitting in malonaldehyde using the full dimensional potential proposed by Yagi et al. [J. Chem. Phys. 115, 10647 (2001)] are reported. Two exact quantum dynamics methods are used: the multiconfigurational timedependent Hartree (MCTDH) approach and the diffusionMonte Carlo based projection operator imaginary time spectral evolution (POITSE) method. A ground statetunneling splitting of is calculated using POITSE. The MCTDH computation yields converged to about 10% accuracy. These rigorous results are used to evaluate the accuracy of approximate dynamical approaches, e.g., the instanton theory.
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 ARTICLES

 Theoretical Methods and Algorithms

Full configuration interaction potential energy curves for the and states of A challenge for approximate methods
View Description Hide DescriptionThe molecule exhibits unusual bonding and several lowlying excited electronic states, making the prediction of its potential energy curves a challenging test for quantum chemical methods. We report full configuration interaction results for the and states of which exactly solve the electronic Schrödinger equation within the space spanned by a basis set. Within the subgroup used by most electronic structure programs, these states all have the same symmetry and all three states become energetically close for interatomic distances beyond 1.5 Å. The quality of several singlereference ab initio methods is assessed by comparison to the benchmark results. Unfortunately, even coupledcluster theory through perturbative triples using an unrestricted Hartree–Fock reference exhibits large nonparallelity errors for the ground state. The excited states are not accurately modeled by any commonly used singlereference method, nor by configuration interaction including full quadruple substitutions. The present benchmarks will be helpful in assessing theoretical methods designed to break bonds in ground and excited electronic states.

An efficient method for calculating maxima of homogeneous functions of orthogonal matrices: Applications to localized occupied orbitals
View Description Hide DescriptionWe present here three new algorithms (one purely iterative and two DIISlike [Direct Inversion in the Iteractive Subspace]) to compute maxima of homogeneous functions of orthogonal matrices. These algorithms revolve around the mathematical lemma that, given an invertible matrix A, the function has exactly one local (and global) maximum for U special orthogonal [i.e., and This is proved in the Appendix. One application of these algorithms is the computation of localized orbitals, including, for example, Boys and EdmistonRuedenberg (ER) orbitals. The Boys orbitals are defined as the set of orthonormal orbitals which, for a given vector space of orbitals, maximize the sum of the distances between orbital centers. The ER orbitals maximize total selfinteraction energy. The algorithm presented here computes Boys orbitals roughly as fast as the traditional method (Jacobi sweeps), while, for large systems, it finds ER orbitals potentially much more quickly than traditional Jacobi sweeps. In fact, the required time for convergence of our algorithm scales quadratically in the region of a few hundred basis functions (though cubicly asymptotically), while Jacobi sweeps for the ER orbitals traditionally scale as the number of occupied orbitals to the fifth power. As an example of the utility of the method, we provide below the ER orbitals of nitrated and nitrosated benzene, and we discuss the chemical implications.

Coping with the node problem in quantum hydrodynamics: The covering function method
View Description Hide DescriptionA conceptually simple approach, the covering function method (CFM), is developed to cope with the node problem in the hydrodynamic formulation of quantum mechanics. As nodes begin to form in a scattering wave packet (detected by a monitor function), a nodeless covering wave function is added to it yielding a total function that is also nodeless. Both local and global choices for the covering function are described. The total and covering functions are then propagated separately in the hydrodynamic picture. At a later time, the actual wave function is recovered from the two propagated functions. The results obtained for Eckart barrier scattering in one dimension are in excellent agreement with exact results, even for very long propagation times The capability of the CFM is also demonstrated for multidimensional propagation of a vibrationally excited wave packet.

Density functional response theory calculations of threephoton absorption
View Description Hide DescriptionThreephoton absorption probabilities have been calculated through application of a recently derived method for cubic response functions within density functional theory(DFT). Calculations are compared with Hartree–Fock (HF) and with a coupled cluster hierarchy of models in a benchmarking procedure. Except for cases having intermediate states near resonance, density functional theory is demonstrated to be in sufficient agreement with the highly correlated methods in order to qualify for predictions of For the larger systems addressed, a set of acceptor A and donor D substituted πconjugated systems formed by transstilbene and dithienothiophene (DTT), we find noticeable differences in the magnitude of between HF and DFT, although similar trends are followed. It is shown that the dipolar structures, TSAD and DTTAD, have substantially larger than other types of modifications which is in accordance with observations for twophoton absorption. This is the first application of density functional theory to threephoton absorption beyond the use of fewstate models.

Quantum statistical mechanics with Gaussians: Equilibrium properties of van der Waals clusters
View Description Hide DescriptionThe variational Gaussian wavepacket method for computation of equilibrium density matrices of quantum manybody systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time starting at the classical limit For an particle system a Gaussian is represented by its center the width matrix and the scale all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at notverylow temperatures the method is surprisingly accurate for a range of model systems including the case of doublewell potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with degrees of freedom. Furthermore, an approximation based on a direct product of singleparticle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of LennardJones cluster. Our results agree very well with the available pathintegral Monte Carlo calculations.

Calculation of excitedstate properties using general coupledcluster and configurationinteraction models
View Description Hide DescriptionUsing stringbased algorithms excitation energies and analytic first derivatives for excited states have been implemented for general coupledcluster (CC) models within CC linearresponse (LR) theory which is equivalent to the equationofmotion (EOM) CC approach for these quantities. Transition moments between the ground and excited states are also considered in the framework of linearresponse theory. The presented procedures are applicable to both singlereferencetype and multireferencetype CC wave functions independently of the excitation manifold constituting the cluster operator and the space in which the effective Hamiltonian is diagonalized. The performance of different LRCC/EOMCC and configurationinteraction approaches for excited states is compared. The effect of higher excitations on excitedstate properties is demonstrated in benchmark calculations for and As a first application, the stationary points of the surface of acetylene are characterized by highaccuracy calculations.

Cooperating or fighting with control noise in the optimal manipulation of quantum dynamics
View Description Hide DescriptionThis paper investigates the impact of control field noise on the optimal manipulation of quantum dynamics. Simulations are performed on several multilevel quantum systems with the goal of population transfer in the presence of significant control noise. The noise enters as runtorun variations in the control amplitude and phase with the observation being an ensemble average over many runs as is commonly done in the laboratory. A genetic algorithm with an improved elitism operator is used to find the optimal field that either fights against or cooperates with control field noise. When seeking a high control yield it is possible to find fields that successfully fight with the noise while attaining good quality stable results. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with the noise and thereby drive the dynamics more efficiently. In general, noise reduces the coherence of the dynamics, but the results indicate that population transfer objectives can be met by appropriately either fighting or cooperating with noise, even when it is intense.

An extension of the quasicontinuum treatment of multiscale solid systems to nonzero temperature
View Description Hide DescriptionCovering the solid lattice with a finiteelement mesh produces a coarsegrained system of mesh nodes as pseudoatoms interacting through an effective potential energy that depends implicitly on the thermodynamic state. Use of the pseudoatomic Hamiltonian in a Monte Carlo simulation of the twodimensional LennardJones crystal yields equilibrium thermomechanical properties (e.g., isotropic stress) in excellent agreement with “exact” fully atomistic results.

Multidimensional density operator propagations in open systems: Model studies on vibrational relaxations and surface sticking processes
View Description Hide DescriptionAn efficient method for the numerical treatment of multidimensional dynamics of open systems is presented: the multiconfiguration timedependent Hartree (MCTDH) method extended to the propagation of density operators. With this method we investigate the relaxation process of a CO molecule adsorbed on a coppersurface, i.e., CO/Cu(100), after the excitation with an infrared (IR) pulse. The interaction potential was taken from the literature [J. C. Tully and M. Gomez, J. Vac. Sci. Technol. A 11, 1914 (1993)]. Lifetime estimations and thermalization studies were performed on the IR excited CO molecule. We were able to treat this system with all six degrees of freedom (DOF) and thus 12 dynamical variables, but most of our studies used a two or four DOF model. Finally, we demonstrate the applicability of MCTDH to the analysis of scattering processes in an open environment. We calculate sticking coefficients of a scattered particle to a modelsurface, the latter acting as heat bath. The surface corrugation and the initial particle energy have been varied, and six different relaxation strengths have been studied. These calculations were done under the inclusion of three DOFs: the two surface coordinates and the distance between the particle and the surface.

Frame transformation relations for fluxional symmetric rotor dimers
View Description Hide DescriptionThe theory of frame transformation relation connecting body oriented angular momentum states and lab weakly coupled momentum states have been extended from rotorelectron to rotordimer systems. Coupling schemes are analyzed for weak and strong cases of correlation between lab and two different rotor body frames. It is shown that the frame transformation relation is a purely quantum effect at low angular momentum but an approach to a classical limit for high J. Symmetry analysis of frame transformation is compared to eigensolutions of model coupling Hamiltonian.

Efficient calculation of potential energy surfaces for the generation of vibrational wave functions
View Description Hide DescriptionAn automatic procedure for the generation of potential energy surfaces based on high level ab initio calculations is described. It allows us to determine the vibrational wave functions for molecules of up to ten atoms. Speedups in computer time of about four orders of magnitude in comparison to standard implementations were achieved. Effects due to introduced approximations—within the computation of the potential—on fundamental modes obtained from vibrational selfconsistent field and vibrational configuration interaction calculations are discussed. Benchmark calculations are provided for formaldehyde and 1,2,5oxadiazole (furazan).

Atomic spectral methods for molecular electronic structure calculations
View Description Hide DescriptionTheoretical methods are reported for ab initio calculations of the adiabatic (Born–Oppenheimer) electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbationtheoretical treatments of longrange interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectralproduct basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrödinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomicenergy and pairwiseatomic interactionenergy matrices, providing a basis for molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectralproduct basis is shown to contain the totally antisymmetric irreducible representation of the symmetric group of aggregate electron coordinate permutations once and only once, but to also span other (nonPauli) symmetric group representations known to contain unphysical discrete states and associated continua in which the physically significant Schrödinger eigenstates are generally embedded. These unphysical representations are avoided by isolating the physical block of the Hamiltonian matrix with a unitary transformation obtained from the metric matrix of the explicitly antisymmetrized spectralproduct basis. A formal proof of convergence is given in the limit of spectral closure to wave functions and energy surfaces obtained employing conventional prior antisymmetrization, but determined without repeated calculations of Hamiltonian matrix elements as integrals over explicitly antisymmetric aggregate basis states. Computational implementations of the theory employ efficient recursive methods which avoid explicit construction the metric matrix and do not require storage of the full Hamiltonian matrix to isolate the antisymmetric subspace of the spectralproduct representation. Calculations of the lowestlying singlet and triplet electronic states of the covalent electron pair bond illustrate the various theorems devised and demonstrate the degree of convergence achieved to values obtained employing conventional prior antisymmetrization. Concluding remarks place the atomic spectralproduct development in the context of currently employed approaches for ab initio construction of adiabatic electronic eigenfunctions and potential energy surfaces, provide comparisons with earlier related approaches, and indicate prospects for more general applications of the method.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dynamics of collisions: A timedependent quantum mechanical investigation on a new ab initio potential energy surface
View Description Hide DescriptionA global analytical potential energy surface for the ground state of has been constructed by fitting an analytic function to the ab initiopotential energy values computed using coupled cluster singles and doubles with perturbative triples [CCSD(T)] method and Dunning’s augmented correlation consistent polarized valence triple zeta basis set. Using this potential energy surface, timedependent quantum mechanical wave packet calculations were carried out to calculate the reaction probabilities for the exchange reaction for different initial vibrational and rotational (j) states of for total angular momentum equal to zero. With increase in the number of oscillations in the plot increases and the oscillations become more pronounced. While increases with increase in rotational excitation from to 1, it decreases with further increase in j to 2 over a wide range of energies. In addition, rotational excitation quenches the oscillations in plots.

Nonadiabatic energy transfer studies of by timedependent wave packet
View Description Hide DescriptionThreedimensional timedependent quantum calculations have been performed on two/three coupled potential surfaces, including the singlet surface and two triplet surfaces and for the electronic quenching process of An extended splitoperator scheme was employed to study this nonadiabatic process. Two types of singlet surface namely, double many body expansion (DMBE2) [Nakamura and Kato, J. Chem. Phys. 110, 9937 (1999)] and ZPM2 [Zahr, Preston, and Miller, J. Chem. Phys. 62, 1127 (1975)] were used in the calculations, along with spin–orbit couplings of Nakamura–Kato and with a constant value of 80 cm^{−1}. All the calculated probabilities are resonance dominated, with a general decreasing trend within the investigated collision energy range. The probability involving three potential energy surfaces is approximately two times as high as that on two potential energy surfaces. At low collision energies, the calculations on the ZPM2 surface produced much larger probability than that on the DMBE2 surface, but the difference was diminishing as the collision energy became high. The behavior of the probability on DMBE2/ZPM2 surfaces at low energies indicates that the ZPM2 surface dominates over the DMBE2 surface in the description of the process. However, the DMBE2 surface has been modified by removing the unreasonable barrier. The estimated quenching cross sections both on the ZPM2 surface and on the modified DMBE2 surface in the threecoupledsurface calculations agree with the experimental measurement. Also, a rather insensitive characteristic of the probability relative to the analytical function form of spin–orbit coupling is revealed.

The ability of silylenes to bind excess electrons: Electron affinities of and species
View Description Hide DescriptionRecently, Ishida and coworkers [J. Am. Chem. Soc. 125, 3212 (2003)] have isolated silylene radical anions via the oneelectron reduction of isolable cyclic dialkylsilylenes, discovering these corresponding radical anions to be relatively stable at low temperatures. Herein we report theoretical predictions of the adiabatic electron affinities (AEA), vertical electron affinities, and vertical detachment energies of a series of methyl, silyl, and halosubstituted silylene compounds. This research utilizes the carefully calibrated [J. C. RienstraKiracofe, G. S. Tschumper, H. F. Schaefer, S. Nandi, and G. B. Ellison, Chem. Rev. (Washington, DC) 102, 231 (2002)] DZP++ basis with the combination of the popular nonhybrid and hybrid DFT functionals, BLYP, B3LYP, and BHHLYP. The level of theory employed and the ensemble of species under study confirm the ability of silylenes to bind excess electrons with being the most effective, having a predicted AEA of 1.95 eV. While it is known that methyl substituents have a diminishing effect on the computed electron affinities (EAs), it is shown that fluorine shows an analogous negative effect. Similarly, previous suggestions that will not bind an electron appear incorrect, with predicted here to be 0.46 eV.

Photodissociation of CCH: Classical trajectory calculations involving seven electronic states
View Description Hide DescriptionThe photodissociation dynamics of ethynyl radical, involving seven electronic states is studied by classical trajectory calculations. Initial values of the trajectories are selected based on relative absorption intensities calculated by Mebel et al. The energies and the derivatives are interpolated by threedimensional cubic spline interpolator using an extended data pool. Mean square errors and standard deviations in interpolation of energies for 450 data points are found to be in the range and respectively. The photofragments of and H are produced mainly in the electronic states of as product. The avoided crossings do not appear to be in the main dissociation pathways. The internal distributions are in good accord with the experimental results where comparison is possible, suggesting that the fragmentation mechanism of into and H is a two step process involving radical as an intermediate with a life time long enough to allow complete collection of the phase space in the experiments.

Application of direct potential fitting to line position data for the and states of LiH
View Description Hide DescriptionA collection of 9089 spectroscopic LiH line positions, of widely varying precision, which sample 84.9% and 98.6% of the A and X state well depths, respectively, have been employed in a direct leastsquares fit of the effective potential energy and BornOppenheimer breakdown functions for the two states. For the four isotopomers and the data comprise both pure rotational and vibrationrotational transitions within the ground state, as well as rotationally resolved transitions in the system. Despite the unusual shape and associated anomalous properties of the A state potential, no special features or considerations were required in the direct potential fitting approach. The reduced standard deviation of the fit was close to unity, indicating that the quantum mechanical eigenvalues calculated from the fully analytical functions of the Hamiltonians of the two states, which are characterized by a total of only 53 fitted parameters, represent the line positions, on average, to within the estimated uncertainties. A quantum mechanical calculation of the molecular constants and from the fitted potential for the A state of confirms that the usual polynomial expansion in is an unsatisfactory representation for the rotational terms of the lowest vibrational levels.

On the ultraviolet photodissociation of
View Description Hide DescriptionThe photodissociation of through excitation in the first absorption band is investigated by means of multireference spinorbit configuration interaction (CI) calculations. Bending potentials for lowlying electronic states of are obtained in symmetry for TeH distances fixed at the ground state equilibrium value of as well as for the minimum energy path constrained to Asymmetric cuts of potential energy surfaces for excited states (at and θ=90.3°) are obtained for the first time. It is shown that vibrational structure in the 380–400 nm region of the long wavelength absorption tail is due to transitions to which has a shallow minimum at large HTeH separations. Transitions to this state are polarized in the molecular plane, and this state converges to the excited limit. These theoretical data are in accord with the selectivity toward relative to that has been found experimentally for 355 nm photodissociation. The calculated transition dipole moment increases rapidly with HTeH distance; this explains the observation of vibrational structure for low vibrational levels, despite unfavorable Franck–Condon factors. According to the calculated vertical energies and transition moment data, the maximum in the first absorption band at ≈245 nm is caused by excitation to which has predominantly in symmetry) character.

Fine structure of the band origins of phthalocyanine molecules in helium droplets
View Description Hide DescriptionThe laserinduced fluorescence(LIF) excitation spectra of free base phthalocyanine (Pc), MgPc, and ZnPc molecules in superfluidheliumdroplets at have been studied. The spectra reveal the rich vibronic structure of the electronic transitions. The band origins of the transitions consist of zero phonon lines accompanied by phonon wings, which originate from simultaneous electronic excitation of the molecule and excitation of the collective modes of the helium surrounding it. The phonon wings have discrete structures suggesting localization of some helium atoms in the neighborhood of the molecules. Zero phonon lines of MgPc and ZnPc molecules are split into three components, which are separated by 0.2–0.4 cm^{−1}. Possible mechanism of splitting involves static or dynamic Jahn–Teller interaction of metalphthalocyanine molecules in the twofold degenerate state with the helium shell.