trends in quantum chemistry

8/3/2019 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 [email protected] poster session is being held and additional contributors are encouraged to reserve their slotas soon as possible by e-mail [email protected].

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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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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Aarhus 2008-12-11

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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: [email protected] 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).



[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).

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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.

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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 [email protected]

Poul Rasmus Andersen home [email protected]

Keld Lars Bak work [email protected]

Rodney J. Bartlett work [email protected] [email protected]

Nelson H. F. Beebe work [email protected]

Flemming Besenbacher work [email protected]

Lisegrete Blach home [email protected]

Ove Christiansen work [email protected]

Sonia Coriani work [email protected] [email protected]

Esper Dalgaard work [email protected] [email protected]

Eduard Matito Gras work [email protected]

Werner Gyrffy work [email protected]

Mikkel Bo Hansen work [email protected]

Christof Httig work [email protected]

Trygve Ulf Helgaker work [email protected] [email protected]

Stinne Hst home [email protected]


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- 2 -

Branislav Jansik work [email protected]

MichaJaszuski work [email protected]

Frank Jensen work [email protected]

Hans Jrgen Aa. Jensen work [email protected]

Mikael Johansson work [email protected]

Poul Jrgensen work [email protected]

Per Kaijser home [email protected]

Joanna Kauczor work [email protected]

Hanne M. Kirkegaard work [email protected]

Thomas Kjrgaard work [email protected]

Henrik Koch work [email protected] [email protected]

Kasper Kristensen work [email protected]

Lars Kristensen work [email protected]

Ying-Chan Lin work [email protected]

Jan Linderberg work [email protected] [email protected]

Josef Michl work [email protected]

Kurt Valentin Mikkelsen work [email protected] [email protected]


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- 3 -

Ole Nrager home [email protected]

Thomas Mostrup Nymand work [email protected] [email protected]

Jens Oddershede home [email protected] [email protected]

N. Yngve hrn home [email protected] [email protected]

Jeppe Olsen work [email protected]

home [email protected]

Mary Jo Ondrechen work [email protected] [email protected]

Sren Berg Padkjr home [email protected]

Thomas Bondo Pedersen work [email protected] [email protected]

Pekka Pyykk work [email protected]

Mark A. Ratner work [email protected] [email protected]

Toms Rocha Rinza work [email protected]

Antonio Rizzo work [email protected] [email protected] [email protected]

Berta Fernandez Rodriguez work [email protected]

Inge Reggen work [email protected]


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- 4 -

John R. Sabin work [email protected]

Alfredo Manuel Sanchez de Mers work [email protected]

Stephan Sauer work [email protected]

Peter Seidler work [email protected]

Inger Brgger Sevre norge [email protected] [email protected]

Jack Simons work [email protected]

central [email protected]

Kristian Sneskov work [email protected]

Jens Spanget-Larsen work [email protected]

Manuel Sparta work [email protected]

Peter Swanstrm home [email protected]

Erik Waaben Thulstrup work [email protected]

Danny Yeager work [email protected]

Marcin Ziolkowski work [email protected]

Alberto Zoccante work [email protected]


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Acknowledgements

Carlsbergfondet

Lundbeckfondet

DetNaturvidenskabeligeFakultet

KemiskInstitut

trends in quantum chemistry

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