Trends in Quantum Chemistry

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    TrendsinQuantumChemistry

    Program

    Abstracts

    Participants

    December1214,2008

    DepartmentofChemistry

    AarhusUniversity

    LarsKristensensDetNaturligeSystem

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    Aarhus 2008-12-11

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    Trends in Quantum ChemistryA meeting on the future purposes and methods

    Lundbeck Foundation Center for Theoretical Chemistry atAarhus University December 12 - 14 2008

    Organization and scientific committee:

    Jan Linderberg (chair), Poul Jrgensen, Mikkel Bo Hansen, Hanne Kirkegaard

    This meeting is open to all interested persons. There will be a nominal fee, not more than DKK1000, for participation, coffees, and Saturday meals. Those who choose only the dinner on Sat-

    urday will be charged DKK250. Submit your intention to take part tojan@chem.au.dk.A poster session is being held and additional contributors are encouraged to reserve their slotas soon as possible by e-mail tojan@chem.au.dk.

    Pictures of historical interest can be contributed, electronically or otherwise.

    Program with confirmed speakers.

    Time Function: person

    December 12, 2008

    Friday, 13.15 - 14.35 Chair: Berta Fernandez Rodrigues

    Friday, 13.15 - 13.25 Welcome address: Ove Christiansen

    Friday, 13.25 - 14.00 Lecture: Josef Michl:From Molecular Rotors to Molecular Bubbles

    Friday, 14.00 - 14.35 Lecture: Henrik Koch:

    Cholesky decompositions in quantum chemistry: Theway it could have happened and should have happened,but did not happen

    Friday, 14.35 - 14.45 Refreshments

    Friday, 14.45 - 14.40 Chair: Micha Jaczuski

    Friday, 14.45 - 15.20 Lecture: Kurt Mikkelsen:To QM/MM or Not to QM/MM

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    Aarhus 2008-12-11

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    Time Function: person

    Friday, 15.20 - 15.55 Lecture: Mary Jo Ondrechen:Theoretical Chemistry Meets Genomics: Predicting andUnderstanding Protein Function at the Molecular Level

    Friday, 15.55 - 16.30 Lecture: Branislav Jansik:Multilevel minimization of the Kohn-Sham energy

    Friday, 16.30 - 18.30 Chair: Jens OddershedePoster session. Refreshments available.

    December 13, 2008

    Saturday, 9.00 - 10.40 Chair: Jens Spanget-Larsen

    Saturday, 9.00 - 9.35 Lecture: Jack Simons:

    Electron Propagator Studies of Electron TransferDissociation of Peptides

    Saturday, 9.35 - 10.10 Lecture: Nelson H. F. Beebe:Computer arithmetic and the MathCW library

    Saturday, 10.10 - 10.45 Lecture: Danny Yeager:Investigation of electron-atom/molecule scatteringresonances using a complex multiconfigurationalself-consistent field method (CMCSCF)

    Saturday, 10.45 -11.00 Cakes and coffee/tea

    Saturday, 11.00 - 12.10 Chair: Pekka Pyykk

    Saturday, 11.00 - 11.35 Lecture: Mark Ratner:Still Green after 38 years: Approaching Junction Trans-port Problems

    Saturday, 11.35 - 12.10 Lecture: Sren Berg Padkjr:Modeling of Biopharmaceutical drugs

    Saturday, 12.10 - 13.30 Lunch, Kemisk Kantine

    Saturday, 13.30 - 15.15 Chair: Antonio Rizzo

    Saturday, 13.30 - 14.05 Lecture: Rodney J. Bartlett:Some Approaches to Large Scale Coupled-ClusterApplications.

    Saturday, 14.05 - 14.40 Lecture: Hans Jrgen Aa. Jensen:Combining the best of wave function theory with the bestof density functional theory

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    Time Function: person

    Saturday, 14.40 - 15.15 Lecture: Thomas Bondo Pedersen:From Cholesky decomposition to density fitting

    Saturday, 15.15 - 15.45 Refreshments.

    Saturday, 15.45 - 17.10 Chair: Yngve hrn

    Saturday, 15.45 - 16.20 Lecture: Trygve Helgaker:Molecules in Strong Magnetic Fields

    Saturday, 16.20 - 16.55 Lecture: Sonia Coriani:In silico determination of magnetic circular dichroismparameters and spectra

    Saturday, 16.55 - 17.10 Chairmans concluding remarks

    Saturday, 17.10 - 18.00 Pause.

    Saturday, 18.00 19.00 Lars Kristensen presents his painting The naturalsystem in the Chemistry Auditorium and glgg isserved.

    Saturday, 19.00 ???? Luciadinner, Kemisk Kantine

    December 14, 2008

    Sunday, 11.00 - ???? Brunch at Musikhusets bistro

    Posters to be presented Friday:Pekka Pyykk, Jens Spanget-Larsen, Eduard Matito Gras, Thomas Kjrgaard, Kasper Kris-tensen, Jan Linderberg, Jeppe Olsen, Toms Rocha-Rinza, Kristian Sneskov, Manuel Sparta,Christof Httig, Stephan Sauer, John R. Sabin, Marcin Ziolokowski.

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    Abstracts

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    Computer arithmetic and the MathCW libraryNelson H. F. Beebe- University of Utah- Department of Mathematics, 110 LCB Internet e-mail: beebe@math.utah.edu- Salt Lake City, UT 84112-0090, USA URL: http://www.math.utah.edu/~beebe/

    -Abstract

    This talk describes the significance of specific features ofinteger and floating-point arithmetic for computation. Itdiscusses the impact of the recent introduction of support fordecimal floating-point arithmetic in software and hardware.It sketches the development of a large portable mathematicalfunction library that is a superset of the C99 library, and

    smoothes the path to future support of octuple precision

    (256-bit 70D) floating-point software arithmetic on currentplatforms.

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    Solving the eigenvalue equations of correlated vibrational structure methods:

    preconditioning and targeting strategies

    W. Gyorffy, P. Seidler, and O. Christiansen

    (Dated: December 3, 2008)

    We present various preconditioners and eigenvector targeting strategies in combination with Olsen

    method (See e.g. section 11.5.3 in [1]) for solving the eigenvalue equations encountered in vibrational

    configuration interaction method [26], vibrational configuration interaction, and vibrational coupled clus-

    ter response theory [710]. These iterative subspace methods allow significant flexibility and robustness in

    computing selected vibrational states, which is particular important in the often occurring but non-trivial

    cases of near-degeneracies and strong resonance interactions. Well-separated states are easily obtained in a

    few iterations, and at low cost. Target states with nearly-degenerate and interacting neighboring states are

    treated in a dynamic way such that both the state best matching the original target and states strongly cou-

    pled to this state are simultaneously obtained. The strategy described scales favorably with the number of

    target states and the dimension of the eigenvalue problem. The algorithm may reach cubic convergence rate

    by stepwise improvement of the quality of the mode excitation level-based preconditioning. Features of the

    methods are demonstrated in calculations of overtone vibrational states of formaldehyde, and fundamental

    states of vinyl-fluoride, vinyl-chloride, and vinyl-bromide molecules.

    [1] T. Helgaker, P. Jrgensen, and J. Olsen, Molecular Electronic-Structure Theory (John Wiley & Sons, Chichester,

    2000).

    [2] J. M. Bowman, K. Christoffel, and F. Tobin, J. Phys. Chem. 83, 905 (1979).

    [3] T. C. Thompson and D. G. Truhlar, Chem. Phys. Lett. 75, 87 (1980).

    [4] K. M. Christoffel and J. M. Bowman, Chem. Phys. Lett. 85, 220 (1982).

    [5] O. Christiansen, J. Chem. Phys. 120, 2140 (2004).

    [6] O. Christiansen, J. Chem. Phys. 120, 2149 (2004).

    [7] O. Christiansen, J. Chem. Phys. 122, 194105 (2005).

    [8] O. Christiansen, J. Kongsted, M. J. Paterson, and J. M. Luis, J. Chem. Phys. 125, 214309 (2006).

    [9] P. Seidler and O. Christiansen, J. Chem. Phys. 126, 204101 (2007).

    [10] P. Seidler, M. B. Hansen, and O. Christiansen, J. Chem. Phys. 128, 154113 (2008).

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    An efficient way to explicit inclusion of anharmonicity in thermal

    averages and thermochemical properties

    Mikkel Bo Hansen, Ove Christiansen, and Danielle Toffoli

    The Lundbeck Foundation Center for Theoretical Chemistry and

    Center for Oxygen Microscopy and Imaging,

    Department of Chemistry, University of Arhus,

    Langelandsgade 140,

    DK-8000 Arhus C, Denmark

    Jacob Kongsted

    Department of Theoretical Chemistry, Chemical Center, University of Lund, P.O.

    Box 124, S-221 00 Lund, Sweden

    December 10, 2008

    Vibrational motion in connection with the fact that molecular properties are often highly non-linear functions of the internal displacements means that one must, as a minimum, average theseproperties over the vibrational ground state, giving rise to zero-point vibrational averages (ZPVA).This may be calculated using vibrational perturbation theory to second order1,2 or, alternatively,using vibrational structure. At higher temperatures the excited vibrational states become pop-ulated, and thus one should perform a Boltzmann average. For systems with more than a fewvibrational degrees of freedom (modes) this is a formidable task and the goal of this project is toderive an alternative formulation which allow for inclusion of anharmonic effects. Thus, we do notuse the closed harmonic oscillator forms which are found in many statistical mechanics textbooks,

    but still avoidthe exponential explosion of vibrational states.In this project we treat the vibrational degrees of freedom quantum mechanically within the

    vibrational self-consistent field (VSCF) framework. We implement and test a new method3 forobtaining thermally averaged properties and thermodynamic properties, i.e. partition function,internal energy, entropy, and free energy. The method is tested on systems of various size includingup to 264 coupled modes and even for this system the vibrational part of the calculation of thementioned properties takes just a few minutes while scaling at most quadratically with the numberof modes. Computing the partition function scales linearly with the number of modes.

    References:

    1 C. W. Kern and R. L. Matcha, J. Chem. Phys. 49, 2081 (1968).2 T. A. Ruden, O. B. Lutns, T. Helgaker, and K. Ruud, J. Chem. Phys. 118, 9572 (2003).3 M. B. Hansen, O. Christiansen, D. Toffoli, and J. Kongsted, J. Chem. Phys. 128,174106 (2008).

    1

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    On the Performance of Spin-Component Scaled CC2

    ApproachesChristof Httig

    Lehrstuhl fr Theoretische Chemie Ruhr-Universitt Bochum, Germany

    Universittsstrasse 150 D-44780 Bochum

    Abstract:-----------------------------------------------------------------------------Recently S. Grimme and M.G. Head-Gordon and co-workers proposedempirical spin component dependent scaling schemes for the doubles

    amplitudes in second-order Moller-Plesset perturbation theory, SCS-MP2 andSOS-MP2, which lead to subtantial improvements in reaction energies, bondlengths and vibrational frequencies in the electronic ground state. In this talka generalization of these spin-component scaled approaces to the approximate

    coupled-cluster singles-and-doubles model CC2 will be presented and firstresults will be shown for structures, vibrational frequencies and 0-0 excitationenergies of typical excited states in organic chromophores. It will bedemonstrated which improvements can be expected by these approaches and

    their furture perspectives will be discussed, in particular regarding that SOS-CC2 can be implemented with computational costs comparable to those ofTDDFT with hybrid functionals.The poster will show detailed numerical results of the benchmarks forvertical and 0-0 transition energies for different classes ofexcited states (n-pi*, pi-pi*, and Rydberg excitations).-------------------------------------------------------------------------

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    Damped response theory

    Kasper Kristensen, Joanna Kauczor, Thomas Kjrgaard, Poul Jrgensen

    Lundbeck Foundation Center for Theoretical Chemistry,

    Department of Chemistry, University of Aarhus

    In standard response theory absorption strengths are obtained from residues of response

    functions. To simulate an experimental spectrum a suitable lineshape function is subse-

    quently imposed onto the absorption strengths. In damped response theory, in contrast, the

    broadening of absorption peaks is inherent in the theory. The main advantage of damped re-

    sponse theory is that absorption spectra may be calculated in any frequency region, whereas

    in standard response theory only the few lowest lying excitation energies are usually deter-

    mined. In addition, dispersion effects are correctly described in damped response theory

    which avoids the divergence of standard response functions at resonance frequencies.

    1

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    The vibrational auto-adjusting perturbation theoryEduard MatitoPostdoctoral ResearcherLundbeck Foundation, Center for Theoretical Chemistry

    University of Aarhus, AarhusAbstract:A new method to calculate anharmonic vibrational ground and excited stateenergies is proposed. The method relies on the auto-adjusting perturbationtheory (APT) which has been successfully used to diagonalize square matrices.We use as zeroth order correction the self-consistent vibrational energies, andwith the APT approach we calculate the vibrational anharmonic correlation

    correction to any desired order. We present the methodology and apply it to amodel system and formaldehyde. Vibrational APT approach shows a robustconvergent behavior even for the states where the standard (Rayleigh-Schrdinger) vibrational Mller-Plesset perturbation theory is clearly divergent.

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    From Molecular Rotors to Molecular Bubbles

    Josef Michl, University of Colorado

    Abstract (optional)Self-assembly of molecular rotors yielded cage-like structuresfor mounting on surfaces. An examination of their properties revealedweird behavior that we were only able to rationalize by postulatingthat in solution these open-end cages are not filled with liquidsolvent, but with a bubble of solvent vapor. This was suggested bymolecular dynamics simulations. Ways of detecting the presence of

    bubbles directly will be discussed, and their possible relation tothe function of biological ion channels and anesthesia will beoutlined.

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    Theoretical Chemistry Meets Genomics: Predicting andUnderstanding Protein Function at the Molecular Level

    Mary Jo Ondrechen

    Abstract

    Prediction of functional information about proteins from their sequenceor 3D structure is an important problem in the post-genomic age. Thepresent paper will show how to take advantage of the intrinsic, special,chemical and electrostatic properties of the particular residues in aprotein structure that are involved in catalysis or recognition. Theseunusual properties can be identified with a simple calculation andtherefore active sites and binding sites for any protein may be predictedwith accuracy from the 3D structure alone. This method of functional site

    prediction for proteins, called THEMATICS (for Theoretical MicroscopicTitration Curves), is based on Poisson-Boltzmann calculations of theelectrical potential function for the protein structure, followed bycomputation of the theoretical microscopic titration curves for eachresidue that can exchange protons. A new machine learningmethodology called Partial Order Optimal Likelihood (POOL) has beendeveloped to maximize the performance of THEMATICS in functionalsite prediction. The success of the method is illustrated with the 170annotated enzymes in the Catalytic Site Atlas (CSA). It is shown that,

    compared with other structure-based site prediction methods, theprotonation properties show good sensitivity and superior precision forbetter overall performance. The ability to predict precise, well-localizedsites is necessary for applications, including functional annotation andligand design. Applications to difficult cases, such as systems with alarge apo-holo conformational change, are shown. Predictions for novelfolds from Structural Genomics, including examples with orphansequences, are presented. The physicochemical basis for the success

    of the method is discussed. Some interesting insights into the atomic-level basis for enzyme catalysis emerge from these studies. Inparticular, the ability of the ionizable residues in the active site to exist inboth protonation states over a wide pH range appears to be animportant property in enzymes. Evidence for the participation of remoteresidues in catalysis is also presented.

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    Basis-set limit of the aurophilic attraction using the MP2 method.

    The examples of [ClAuPH3]2 dimer and [P(AuPH3)4]+

    ion

    Pekka Pyykk and Patryk Zaleski-Ejgierd

    Department of Chemistry, University of HelsinkiP.O. Box 55, A. I. Virtasen aukio 1, 00014 Helsinki, Finland

    Both structural and temperature-dependent NMR evidence suggests that two Au(I)

    cations in compounds may experience an attraction of the order of 30 kJ mol1

    atequilibrium distances of the order of 300 pm. The interaction was ascribed to electron

    correlation effects[1] and narrowed down to a predominantly dispersion typeR6 leading

    term[2] with higher, virtual-electron transfer terms.

    Methodologically, basis set superposition error (BSSE) corrections were added

    since[5],ffunctions to the Au basis and at least dfunctions at the ligands such as P were

    also found to be important[3]. All methodological aspects were critically considered in1997 by Pyykk et al..

    The basis-set limit of the metallophilic interaction has not been earlier criticallyinvestigated. In this work[7], the basis-set limit of the aurophilic attraction is studied at

    the MP2 level for the free model dimer [ClAuPH3]2 and for a [P(AuPH3)4]+

    ion. The lattersystem is found to prefer a C4v symmetry, instead of Td, in agreement with Li and

    Pyykk[3] but in contradiction to recent results of Fang and Wang[6]. The Karlsruhe splitvalence and the Dunning correlation-consistent basis sets converge to the same limit.

    [1] P. Pyykk and Y.-F. Zhao, Angew. Chem., Int. Ed. Engl. 30, 604 (1991).[2] P. Pyykk, Angew. Chem., Int. Ed. 43, 4412 (2004).

    [3] J. Li and P. Pyykk, Inorg. Chem. 32, 2630 (1993).[4] P. Pyykk and F. Mendizabal, Chem.-Eur. J. 3, 1458 (1997).

    [5] J. Li and P. Pyykk, Chem. Phys. Lett. 197, 586 (1992).[6] H. Fang and S.-G. Wang, J. Phys. Chem. A 111, 1562 (2006).

    [7] P. Pyykk and P. Zaleski-Ejgierd, J. Chem. Phys., 128, 124309 (2008).

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    Linear response calculations of models of thechromophore of GFP: possible implications within the protein.

    J. Rajput, D. Rahbek, L. H Andersen, T. Rocha-Rinza, O. Christiansen,A. Bochenkova, K. M. Solntsev, L. M. Tolbert, M. Brndsted Nielsen

    Abstract

    Model chromophores of the green fluorescent protein are characterizedusing linear response RI-CC2 and TDDFT. Overall, there is a goodagreement between theory and experiment. Red shift effects ofhydrogen bonds and a positive chargein the proximities of the chromophore are evidenced.The consequences of such factors in the tuning of the chromophorewithin the protein are discussed.

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    Dynamics of the Collision of EndrohedralFullerenes with Graphene Sheets

    John R. Sabin,

    1,2

    Victor V. Albert,

    1

    and Frank E. Harris

    1,3

    1. Department of Physics, Quantum Theory Project, University of Florida.2. Institut for Fysik og Kemi, Syddansk Universitet.3. Department of Physics, University of Utah.

    (December 7, 2008)

    Collisions between Xe@C60 and a target wall comprised of 1-4 sheets of graphene ofvarious dimensions were simulated. A Tersoff many-body potential modeled theinteractions among carbon atoms and a Lennard-Jones potential simulated the xenon-carbon interactions. The number of carbon atoms comprising the graphene sheets, the

    number of layers of graphene making up the target, the offset among the targetgraphene sheets, and the velocity and orientation of the Xe@C60 projectile were allvaried. The simulations were compared to experiment and with simulations whichimplemented other potentials. Four qualitative scenarios were observed:PENETRATION of the entire system by at least one atom; REFLECTION of fullereneprojectile from the graphene barrier; CONNECTION between the projectile and thetarget the barrier; and FUSION of projectile into target.

    Penetration, as expected, occurs at the largest velocities for all barriers. The projectilepenetrates less as the wall size and wall thickness increase. Reflection of the projectileby the target occurs at lower projectile velocities and decreases significantly as the wall

    size and thickness increase. Connection occurs in the middle of the velocity spectrumand increases and surpasses reflection as the wall size and thickness increase. Thepoint where connection takes place in 50% of the simulations in a batch occurs at aslower velocity as the number of layers increases. Consequently, connectionovercomes reflection at lower velocities as the wall gains size. Fusion occurs generallyin the range of the spectrum between connection and penetration and also increases asthe wall gains size.

    Extrapolations to an infinite size for the 4-layer thick barrier can be taken with thefollowing results: reflection at 0.010-0.055 /fs, connection at 0.055-0.140 /fs, fusion at0.140-0.215 /fs, and penetration at 0.215-0.300 /fs. At a thickness of 3 and 4 layers,

    the 780-atom barrier is generally a good approximation for the larger 1128-atom barrier.The results of the one-layer graphene tests are not as well correlated with increasingwall size, implying that a wall larger than 1128 atoms might be needed to accuratelysimulate one-layer graphite.

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    A Comparison of 2nd Order Response Methods for the Calculation of Vertical Excita-

    tion Energies

    S.P.A. Sauer,1,2 H.H. Falden,1 M. Ramos da Silva,2 and W. Thiel2

    1Department of Chemistry, University of Copenhagen, Copenhagen, Denmark2

    Max-Planck-Institut fr Kohlenforschung, Mlheim, Germany

    Vertical excitation energies are most elegantly calculated with linear response or polarization prop-

    agator methods. Linear response functions have been derived for many different quantum chemical

    methods such as Hartree-Fock and multiconfigurational Hartree-Fock theory, Mller-Plesset pertur-

    bation theory, coupled cluster theory and recently density functional theory. Response functions to

    second order in Mller-Plesset perturbation theory, i.e. at a level corresponding to the very popular

    MP2 method for the calculation of ground state energies and geometries, can alternatively be de-

    rived as extension to second order of the Hartree-Fock response function, often called the random

    phase approximation (RPA), or as approximation to the coupled cluster singles and doubles (CCSD)

    response function. The former approach leads to the second order polarization propagator approxi-

    mation (SOPPA) [1,2,3] whereas the latter is the basis for the CC2 approximation [4]. Both methods

    and some of their variants, the doubles corrected random phase approximation - RPA(D) [5], the

    second order polarization propagator approximation with coupled cluster singles and doubles ampli-

    tudes - SOPPA(CCSD) [6] or the doubles corrected configuration singles method - CIS(D) [7], have

    been widely employed in the literature. However, no systematic comparison of all these methods

    has so far been published. In this contribution calculations of vertical excitation energies for systems

    with conjugated and isolated -systems with all these methods are compared with each other and

    with results from more accurate third order methods such as CC3 [8] or CCSDR(3) [9].

    [1] E.S. Nielsen, P. Jrgensen, and J. Oddershede, J. Chem. Phys. 73, 6238 (1980).

    [2] M.J. Packer, E.K. Dalskov, T. Enevoldsen, H.J.Aa. Jensen, and J. Oddershede, J. Chem. Phys.

    105, 5886 (1996).

    [3] K.L. Bak, H. Koch, J. Oddershede, O. Christiansen, and S.P.A. Sauer, J. Chem. Phys. 112,

    4173 (2000).

    [4] O. Christiansen, H. Koch, and P. Jrgensen, Chem. Phys. Lett. 243, 409 (1995).

    [5] O. Christiansen, K.L. Bak, H. Koch, and S.P.A. Sauer, Chem. Phys. Lett. 284, 47 (1998).

    [6] S.P.A. Sauer, J. Phys. B: At. Mol. Opt. Phys. 30, 3773 (1997).

    [7] M. Head-Gordon, R.J. Ricco, M. Oumi, T.J. Lee, Chem. Phys. Lett. 219, 21 (1994).

    [8] O. Christiansen, H. Koch, and P. Jrgensen, J. Chem. Phys. 103, 7429 (1995).

    [9] O. Christiansen, H. Koch, and P. Jrgensen, J. Chem. Phys. 105, 1451 (1996).

    1

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    Investigation of electron-atom/molecule scattering resonances using a complex

    multiconfigurational self-consistent field method (CMCSCF)

    Danny L. Yeager

    Department of Chemistry, MS-3255, Texas A&M University,

    College Station, TX 77843-3255

    USA

    Resonances are temporarily bound states which lie in the continuum part of the Hamiltonian. If the

    electronic coordinates of the Hamiltonian are scaled (dilated) by a complex parameter, = ei

    (,

    real), then, according to the complex scaling theorem, the dilated Hamiltonian becomes non-Hermitian

    and complex symmetric and its complex eigenvalues represent the scattering states (resonant and non-

    resonant) while the eigenvalues corresponding to the bound states and the ionization and the excitation

    thresholds remain real and unmodified. The invariance of the eigenvalue corresponding to a resonance

    with respect to changes in forgreater than some system-specific critical value causes the resonance

    to stand out among other continuum states and the corresponding eigenfunction is square integrable in

    this region. These make the study of these transient species amenable to the bound state methods. The

    real part of the comlex resonance energy is the resonance position and the imaginary part gives the

    width.

    In this work, we employ a quadratically convergent multiconfigurational self-consistent field method

    (MCSCF) using a dilated Hamiltonian to investigate the resonances. This is made possible by the

    adoption of a modified second quantization algebra suitable for a set of biorthogonal (a result of the

    complex scaling transformation) spin orbitals, and a modified step-length constraining algorithm to

    control the walk on the complex energy hypersurface while searching for the stationary point using a

    multidimensional Newton-Raphson scheme. We present our computational results for the2PBe

    shape

    resonances using two different methods that utilize complex MCSCF (CMCSCF). It was found that

    there are actually two2PBe

    shape resonances very close in energy.

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    Marcin Ziolkowski, Ville Weijo, Poul Jrgensen, Jeppe Olsen

    CROPNewAlgorithmforSolvingCoupledClusterEquations

    Abstract:

    Coupled-cluster (CC) theory became in last twenty years amethod-of-choice for many quantum chemists. However, CC givesresults with a chemical accuracy, number of available solvers for CCequations is limited.

    We present Conjugate Residual with Optimal trial vectors (CROP)algorithm for solving the equations of coupled-cluster using

    minimal number of trial vectors. Our approach leads to the solutionfaster and ensures stable convergence.

    Theory behind new algorithm and benchmarks are presented for atomicorbital based coupled-cluster methods.

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    - 1 -

    Andreas Andersen work aa@skanderborg-gym.dk

    Poul Rasmus Andersen home beritpoul@gmail.com

    Keld Lars Bak work klb@iha.dk

    Rodney J. Bartlett work bartlett@qtp.ufl.eduhome beverly@acesqc.com

    Nelson H. F. Beebe work beebe@math.utah.edu

    Flemming Besenbacher work fbe@phys.au.dk

    Lisegrete Blach home lisegreteblach@get2net.com

    Ove Christiansen work ove@chem.au.dk

    Sonia Coriani work coriani@units.itother coriani@univ.trieste.it

    Esper Dalgaard work ESDG@km.dkother TJD@km.dk

    Eduard Matito Gras work eduard@chem.au.dk

    Werner Gyrffy work werner@chem.au.dk

    Mikkel Bo Hansen work mbh@chem.au.dk

    Christof Httig work Christof.Haettig@theochem.rub.de

    Trygve Ulf Helgaker work t.u.helgaker@kjemi.uio.nowork2 trygve.helgaker@kjemi.uio.no

    Stinne Hst home stinne@chem.au.dk

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    - 2 -

    Branislav Jansik work jansik@chem.au.dk

    MichaJaszuski work michaljz@icho.edu.pl

    Frank Jensen work frj@chem.au.dk

    Hans Jrgen Aa. Jensen work hjj@chem.sdu.dk

    Mikael Johansson work mpjohans@chem.au.dk

    Poul Jrgensen work pou@chem.au.dk

    Per Kaijser home per@kaijser.de

    Joanna Kauczor work joanna@chem.au.dk

    Hanne M. Kirkegaard work bay@chem.au.dk

    Thomas Kjrgaard work tkjaergaard@chem.au.dk

    Henrik Koch work koch@phys.chem.ntnu.noother henrik.koch@chem.ntnu.no

    Kasper Kristensen work kasperk@chem.au.dk

    Lars Kristensen work Larskris@post8.tele.dk

    Ying-Chan Lin work yingchan@chem.helsinki.fi

    Jan Linderberg work jan@chem.au.dkhome boforsarn@mail.dk

    Josef Michl work michl@eefus.colorado.edu

    Kurt Valentin Mikkelsen work kmi@theory.ki.ku.dkother kmi@kemi.ku.dk

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    - 3 -

    Ole Nrager home Ole.NORAGER@ec.europa.eu

    Thomas Mostrup Nymand work thomas@signaturgruppen.dkhome thomas@nymand.net

    Jens Oddershede home bod@munkebo-borger.dkwork jod@sdu.dk

    N. Yngve hrn home annohrn@mac.comwork ohrn@qtp.ufl.edu

    Jeppe Olsen work jeppe@chem.au.dk

    home jettesvensson561@hotmail.com

    Mary Jo Ondrechen work m.ondrechen@neu.eduother mjo@neu.edu

    Sren Berg Padkjr home sbp@novonordisk.com

    Thomas Bondo Pedersen work Thomas.Pedersen@teokem.lu.sehome thomas.b.pedersen@gmail.com

    Pekka Pyykk work Pekka.Pyykko@helsinki.fi

    Mark A. Ratner work ratner@chem.northwestern.eduhome nratner@nancyratner.com

    Toms Rocha Rinza work tomas@chem.au.dk

    Antonio Rizzo work rizzo@ipcf.cnr.ithome rizzoant@tiscalinet.itother rizzorizzo@katamail.com

    Berta Fernandez Rodriguez work berta.fernandez@usc.es

    Inge Reggen work iroeggen@chem.au.dk

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    - 4 -

    John R. Sabin work sabin@qtp.ufl.edu

    Alfredo Manuel Sanchez de Mers work sanchez@uv.es

    Stephan Sauer work sauer@kiku.dk

    Peter Seidler work seidler@chem.au.dk

    Inger Brgger Sevre norge ingersev@online.nospanien ingersevre@hotmail.com

    Jack Simons work simons@chem.utah.edu

    central J.Simons@m.cc.utah.edu

    Kristian Sneskov work sneskov@chem.au.dk

    Jens Spanget-Larsen work spanget@ruc.dk

    Manuel Sparta work msparta@chem.au.dk

    Peter Swanstrm home peter.swanstroem@mail.dk

    Erik Waaben Thulstrup work ewt@ruc.dk

    Danny Yeager work Yeager@Mail.Chem.Tamu.edu

    Marcin Ziolkowski work marcin@chem.au.dk

    Alberto Zoccante work zoccante@chem.au.dk

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    Acknowledgements

    Carlsbergfondet

    Lundbeckfondet

    DetNaturvidenskabeligeFakultet

    KemiskInstitut