Publications (302)725.33 Total impact
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ABSTRACT: The equationofmotion coupled cluster (EOMCC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a MøllerPlesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOMCC ansatz.The Journal of Chemical Physics 05/2014; 140(17):174114. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Using the coupled cluster Lagrangian technique, we have determined perturbative corrections to the coupled cluster singles and doubles (CCSD) energy that converge towards the coupled cluster singles, doubles, and triples (CCSDT) and coupled cluster singles, doubles, triples, and quadruples (CCSDTQ) energies, considering the CCSD state as the unperturbed reference state and the fluctuation potential as the perturbation. Since the Lagrangian technique is utilized, the energy corrections satisfy Wigner's 2n + 1 rule for the cluster amplitudes and the 2n + 2 rule for the Lagrange multipliers. The energy corrections define the CCSD perturbation series, CCSD(Tn) and CCSD(TQn), which are termwise size extensive to any order in the perturbation. A detailed comparison of the CCSD(TQn) series and the CC(2)PT(n) series of Hirata et al. [J. Chem. Phys. 114, 3919 (2001)] has been performed, revealing some deficiencies of the latter related to the target energy of the series and its lack of size extensivity.The Journal of Chemical Physics 02/2014; 140(6):064108. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A common perception about molecular systems with a nonlocal electronic structure (as manifested by a nonlocal Hartree–Fock (HF) density matrix), such as conjugated πsystems, is that they can only be described in terms of nonlocal molecular orbitals. This view is mostly founded on chemical intuition, and further, this view is strengthened by traditional approaches for obtaining local occupied and virtual orbital spaces, such as the occupied Pipek–Mezey orbitals, and projected atomic orbitals. In this article, we discuss the limitations for localizability of HF orbitals in terms of restrictions posed by the delocalized character of the underlying density matrix for the molecular system and by the orthogonality constraint on the molecular orbitals. We show that the locality of the orbitals, in terms of nonvanishing charge distributions of orbitals centered far apart, is much more strongly affected by the orthogonality constraint than by the physical requirement that the occupied orbitals must represent the electron density. Thus, the freedom of carrying out unitary transformations among the orbitals provides the flexibility to obtain highly local occupied and virtual molecular orbitals, even for molecular systems with a nonlocal density matrix, provided that a proper localization function is used. As an additional consideration, we clear up the common misconception that projected atomic orbitals in general are more local than localized orthogonal virtual orbitals.Theoretical Chemistry Accounts 01/2014; 133(1). · 2.14 Impact Factor  10/2013: pages 5199; , ISBN: 1402048491
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ABSTRACT: The shielding and indirect spinspin coupling tensors are calculated for HCN, HNC, CH3CN, and CH3NC, using large atomic basis sets and multiconfiguration wavefunctions that contain the most important correlation effects. The isotropic and anisotropic components of the tensors are compared with experimental data. Deviations between the calculated and experimental results appear to be largely due to vibrational and solvent effects.Journal of Magnetic Resonance, Series A. 06/2013;  [Show abstract] [Hide abstract]
ABSTRACT: For large molecular systems conventional implementations of second order Møller–Plesset (MP2) theory encounter a scaling wall, both memory and timewise. We describe how this scaling wall can be removed. We present a massively parallel algorithm for calculating MP2 energies and densities using the divide–expand–consolidate scheme where a calculation on a large system is divided into many small fragment calculations employing local orbital spaces. The resulting algorithm is linearscaling with system size, exhibits near perfect parallel scalability, removes memory bottlenecks and does not involve any I/O. The algorithm employs three levels of parallelisation combined via a dynamic job distribution scheme. Results on two molecular systems containing 528 and 1056 atoms (4278 and 8556 basis functions) using 47,120 and 94,240 cores are presented. The results demonstrate the scalability of the algorithm both with respect to the number of cores and with respect to system size. The presented algorithm is thus highly suited for large super computer architectures and allows MP2 calculations on large molecular systems to be carried out within a few hours – for example, the correlated calculation on the molecular system containing 1056 atoms took 2.37 hours using 94240 cores.Molecular Physics 04/2013; · 1.67 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Recent advances in orbital localization algorithms are used to minimize the PipekMezey localization function for both occupied and virtual HartreeFock orbitals. Virtual PipekMezey orbitals for large molecular systems have previously not been considered in the literature. For this work, the PipekMezey (PM) localization function is implemented for both the Mulliken and a Löwdin population analysis. The results show that the standard PM localization function (using either Mulliken or Löwdin population analyses) may yield local occupied orbitals, although for some systems the occupied orbitals are only semilocal as compared to stateoftheart localized occupied orbitals. For the virtual orbitals, a Löwdin population analysis shows improvement in locality compared to a Mulliken population analysis, but for both Mulliken and Löwdin population analyses, the virtual orbitals are seen to be considerably less local compared to stateoftheart localized orbitals. © 2013 Wiley Periodicals, Inc.Journal of Computational Chemistry 04/2013; · 3.84 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Using the threelevel energy optimization procedure combined with a refined version of the leastchange strategy for the orbitalswhere an explicit localization is performed at the valence basis levelit is shown how to more efficiently determine a set of local HartreeFock orbitals. Further, a corevalence separation of the leastchange occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied HartreeFock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality. © 2013 Wiley Periodicals, Inc.Journal of Computational Chemistry 03/2013; · 3.84 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: DivideExpandConsolidate (DEC) is a local correlation method where the inherent locality of the electron correlation problem is used to express the correlated calculation on a large molecular system in terms of small independent fragment calculations employing small subsets of local HF orbitals. A crucial feature of the DEC scheme is that the sizes of the local orbital spaces are determined in a black box manner during the calculation. In this way it is ensured that the correlation energy has been determined to a predefined precision compared to a conventional calculation. In the present work we apply the DEC scheme to calculate the correlation energy as well as the electron density matrix for the insulin molecule using second order MøllerPlesset (MP2) theory. This is the first DEC calculation on a molecular system which is too large to be treated using a conventional MP2 implementation. The fragmentation errors for the insulin DEC calculation are carefully analyzed using internal consistency checks. It is demonstrated that sizeintensive properties are determined to the same precision for small and large molecules. For example, the percentage of correlation energy recovered and the error per electron in the correlated density matrix depend only on the predefined precision and not on the molecular size.Physical Chemistry Chemical Physics 10/2012; · 3.83 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We demonstrate that the divideexpandconsolidate (DEC) scheme – which has previously been used to determine the secondorder Møller–Plesset (MP2) correlation energy – can be applied to evaluate the MP2 molecular gradient in a linearscaling and embarrassingly parallel manner using a set of local Hartree–Fock orbitals. All manipulations of fourindex quantities (describing electron correlation effects) are carried out using small local orbital fragment spaces, whereas twoindex quantities are treated for the full molecular system. The sizes of the orbital fragment spaces are determined in a blackbox manner to ensure that the error in the DECMP2 correlation energy compared to a standard MP2 calculation is proportional to a single input threshold denoted the fragment optimization threshold (FOT). The FOT also implicitly controls the error in the DECMP2 molecular gradient as substantiated by a theoretical analysis and numerical results. The development of the DECMP2 molecular gradient is the initial step towards calculating higher order energy derivatives for large molecular systems using the DEC framework, both at the MP2 level of theory and for more accurate coupledcluster methods.The Journal of Chemical Physics 09/2012; 137(11). · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The trust region method has been applied to the minimization of localization functions, and it is shown that both local occupied and local virtual Hartree–Fock (HF) orbitals can be obtained. Because step sizes are size extensive in the trust region method, large steps may be required when the method is applied to large molecular systems. For an exponential parametrization of the localization function only small steps are allowed, and the standard trust radius update therefore has been replaced by a scheme where the direction of the step is determined using a conservative estimate of the trust radius and the length of the step is determined from a line search along the obtained direction. Numerical results for large molecular systems have shown that large steps can then safely be taken, and a robust and nearly monotonic convergence is obtained.Journal of Chemical Theory and Computation 08/2012; 8(9):3137–3146. · 5.39 Impact Factor  Chemical Reviews 01/2012; 112(1):543631. · 41.30 Impact Factor
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ABSTRACT: Previously, we have introduced the linear scaling coupled cluster (CC) divideexpandconsolidate (DEC) method, using an occupied space partitioning of the standard correlation energy. In this article, we show that the correlation energy may alternatively be expressed using a virtual space partitioning, and that the Lagrangian correlation energy may be partitioned using elements from both the occupied and virtual partitioning schemes. The partitionings of the correlation energy leads to atomic site and pair interaction energies which are termwise invariant with respect to an orthogonal transformation among the occupied or the virtual orbitals. Evaluating the atomic site and pair interaction energies using local orbitals leads to a linear scaling algorithm and a distinction between Coulomb hole and dispersion energy contributions to the correlation energy. Further, a detailed error analysis is performed illustrating the error control imposed on all components of the energy by the chosen energy threshold. This error control is ultimately used to show how to reduce the computational cost for evaluating dispersion energy contributions in DEC.The Journal of Chemical Physics 01/2012; 136(1):014105. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We apply damped response theory to the phenomenon of magnetic circular dichroism (MCD), and we investigate how the numerical instability associated with the simulation of the MCD spectrum from individually calculated A and B terms for close lying states can be remedied by the use of damped response theory. We also present a method for calculating the Faraday A term, formulated as a double residue of the quadratic response function.The Journal of Chemical Physics 07/2011; 135(2):024112. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Damped response theory is applied to the calculation of twophoton absorption (TPA) spectra, which are determined directly, at each frequency, from a modified damped cubic response function. The TPA spectrum may therefore be evaluated for selected frequency ranges, making the damped TPA approach attractive for calculations on large molecules with a high density of states, where the calculation of TPA using standard theory is more problematic. Damped response theory can also be applied to the case of intermediate state resonances, where the standard TPA expression is divergent. Both exact damped response theory and its application within density functional theory are discussed. The latter is implemented using an atomicorbital based density matrix formulation, which makes the approach especially suitable for studies on large systems. A test preliminary study is presented for the TPA spectrum of R(+)1,1'bi(2naphtol).The Journal of Chemical Physics 06/2011; 134(21):214104. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: It is demonstrated that a set of local orthonormal HartreeFock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trustregion algorithm. For a power exponent equal to one, the Boys localization function is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and smaller maximum orbital spreads are encountered. Calculations on superbenzene, C(60), and a fragment of the titin protein show that for a power exponent equal to one, delocalized outlier orbitals may be encountered. These disappear when the exponent is larger than one. For a small penalty, the occupied orbitals are more local than the virtual ones. When the penalty is increased, the locality of the occupied and virtual orbitals becomes similar. In fact, when increasing the cardinal number for Dunning's correlation consistent basis sets, it is seen that for larger penalties, the virtual orbitals become more local than the occupied ones. We also show that the local virtual HF orbitals are significantly more local than the redundant projected atomic orbitals, which often have been used to span the virtual orbital space in local correlated wave function calculations. Our local molecular orbitals thus appear to be a good candidate for local correlation methods.The Journal of Chemical Physics 05/2011; 134(19):194104. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The response equations as occurring in the Hartree–Fock, multiconfigurational selfconsistent field, and Kohn–Sham density functional theory have identical matrix structures. The algorithms that are used for solving these equations are discussed, and new algorithms are proposed where trial vectors are split into symmetric and antisymmetric components. Numerical examples are given to compare the performance of the algorithms. The calculations show that the standard response equation for frequencies smaller than the highest occupied molecular orbital–lowest unoccupied molecular orbital gap is best solved using the preconditioned conjugate gradient or conjugate residual algorithms where trial vectors are split into symmetric and antisymmetric components. For larger frequencies in the standard response equation as well as in the damped response equation in general, the preconditioned iterative subspace approach with symmetrized trial vectors should be used. For the response eigenvalue equation, the Davidson algorithm with either paired or symmetrized trial vectors constitutes equally good options.Journal of Chemical Theory and Computation. 04/2011; 7(6).  [Show abstract] [Hide abstract]
ABSTRACT: The atomic axial tensor (AAT) of vibrational circular dichroism is expressed as the frequency derivative at zero frequency of a linear response function for operators referencing a nuclear displacement and a magnetic field. This is used in the density matrixbased quasienergy derivative Lagrangian approach of Thorvaldsen et al. [J. Chem. Phys., 2008, 129, 214108] to express the AAT in a form where the need to solve response equations for the nuclear displacements is removed, significantly reducing the computation cost compared to existing formulations. The density matrixbased quasienergy derivative Lagrangian approach also allows us straightforwardly to use London atomic orbitals to remove the gaugeorigin dependence and to account for the atomic orbitals' dependence on the nuclear coordinates. The formalism is entirely based on atomicorbital density and integral matrices and therefore amenable to linear scaling for sufficiently sparse matrices and given a linearly scaling response solver.Physical Chemistry Chemical Physics 03/2011; 13(10):42249. · 3.83 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a thorough locality analysis of the divide–expand–consolidate amplitude equations for secondorder Møller–Plesset perturbation theory and the coupled cluster singles doubles (CCSD) model, which demonstrates that the amplitude equations are local when expressed in terms of a set of local occupied and local unoccupied Hartree–Fock orbitals, such as the leastchange molecular basis. The locality analysis thus shows that a CC calculation on a large molecular system may be carried out in terms of CC calculations on small orbital fragments of the total molecular system, where the sizes of the orbital fragment spaces are determined in a black box manner to ensure that the CC correlation energy is calculated to a preset energy threshold. A practical implementation of the locality analysis is described, and numerical results are presented, which demonstrate that both the orbital fragment sizes and the relative energy error compared to a full CC calculation are independent of the molecular system size.J.Chem.Theo.Comp. 01/2011; 7:1677.  [Show abstract] [Hide abstract]
ABSTRACT: Coupled cluster calculations can be carried out for large molecular systems via a set of calculations that use small orbital fragments of the full molecular orbital space. The error in the correlation energy of the full molecular system is controlled by the precision in the small fragment calculations. The determination of the orbital spaces for the small orbital fragments is black box in the sense that it does not depend on any userprovided molecular fragmentation, rather orbital spaces are carefully selected and extended during the calculation to give fragment energies of a specified precision. The computational method scales linearly with the size of the molecular system and is massively parallel.The Journal of Chemical Physics 07/2010; 133(1):014107. · 3.12 Impact Factor
Publication Stats
7k  Citations  
725.33  Total Impact Points  
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Institutions

1974–2014

Aarhus University
 Department of Chemistry
Aarhus, Central Jutland, Denmark


1984–2012

University of Oslo
 Department of Chemistry
Oslo, Oslo, Norway


2004–2011

Università degli Studi di Trieste
 Department of Chemical and Pharmaceutical Sciences
Trieste, Friuli Venezia Giulia, Italy


2009

Universitetet i Tromsø
 Department of Chemistry
Tromsø, Troms Fylke, Norway


2007

University of Texas at Austin
 Department of Chemistry and Biochemistry
Austin, Texas, United States 
KTH Royal Institute of Technology
 Division of Theoretical Chemistry and Biology
Stockholm, Stockholm, Sweden


2006

University of Warsaw
Warszawa, Masovian Voivodeship, Poland


2000

University of Cambridge
 Department of Chemistry
Cambridge, ENG, United Kingdom


1989–1995

Lund University
 Department of Theoretical Chemistry
Lund, Skane, Sweden


1992–1993

Odense University Hospital
Odense, South Denmark, Denmark


1987

University of Minnesota Duluth
 Department of Chemistry and Biochemistry
Duluth, Minnesota, United States


1979–1980

Texas A&M University
 Department of Chemistry
College Station, TX, United States


1975

CUNY Graduate Center
New York City, New York, United States
