Poul Jørgensen

Aarhus University, Aars, Region North Jutland, Denmark

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Publications (296)707.14 Total impact

  • [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(T-n) and CCSD(TQ-n), which are term-wise size extensive to any order in the perturbation. A detailed comparison of the CCSD(TQ-n) 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. · 3.16 Impact Factor
  • 10/2013: pages 51-99; , ISBN: 1-4020-4849-1
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    ABSTRACT: The shielding and indirect spin-spin 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;
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    ABSTRACT: For large molecular systems conventional implementations of second order Møller–Plesset (MP2) theory encounter a scaling wall, both memory- and time-wise. 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 linear-scaling 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
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    ABSTRACT: Recent advances in orbital localization algorithms are used to minimize the Pipek-Mezey localization function for both occupied and virtual Hartree-Fock orbitals. Virtual Pipek-Mezey orbitals for large molecular systems have previously not been considered in the literature. For this work, the Pipek-Mezey (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 state-of-the-art 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 state-of-the-art localized orbitals. © 2013 Wiley Periodicals, Inc.
    Journal of Computational Chemistry 04/2013; · 3.84 Impact Factor
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    ABSTRACT: Using the three-level energy optimization procedure combined with a refined version of the least-change strategy for the orbitals-where an explicit localization is performed at the valence basis level-it is shown how to more efficiently determine a set of local Hartree-Fock orbitals. Further, a core-valence separation of the least-change 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 Hartree-Fock 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
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    ABSTRACT: Divide-Expand-Consolidate (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 Møller-Plesset (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 size-intensive 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
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    ABSTRACT: We demonstrate that the divide-expand-consolidate (DEC) scheme – which has previously been used to determine the second-order Møller–Plesset (MP2) correlation energy – can be applied to evaluate the MP2 molecular gradient in a linear-scaling and embarrassingly parallel manner using a set of local Hartree–Fock orbitals. All manipulations of four-index quantities (describing electron correlation effects) are carried out using small local orbital fragment spaces, whereas two-index quantities are treated for the full molecular system. The sizes of the orbital fragment spaces are determined in a black-box manner to ensure that the error in the DEC-MP2 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 DEC-MP2 molecular gradient as substantiated by a theoretical analysis and numerical results. The development of the DEC-MP2 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 coupled-cluster methods.
    The Journal of Chemical Physics 09/2012; 137(11). · 3.16 Impact Factor
  • Chemical Reviews 01/2012; 112(1):543-631. · 41.30 Impact Factor
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    ABSTRACT: Previously, we have introduced the linear scaling coupled cluster (CC) divide-expand-consolidate (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 term-wise 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. · 3.16 Impact Factor
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    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. · 3.16 Impact Factor
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    ABSTRACT: Damped response theory is applied to the calculation of two-photon 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 atomic-orbital 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(2-naphtol).
    The Journal of Chemical Physics 06/2011; 134(21):214104. · 3.16 Impact Factor
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    ABSTRACT: It is demonstrated that a set of local orthonormal Hartree-Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trust-region 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. · 3.16 Impact Factor
  • Joanna Kauczor, Poul Jørgensen, Patrick Norman
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    ABSTRACT: The response equations as occurring in the Hartree–Fock, multiconfigurational self-consistent 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.
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    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 matrix-based 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 matrix-based quasienergy derivative Lagrangian approach also allows us straightforwardly to use London atomic orbitals to remove the gauge-origin dependence and to account for the atomic orbitals' dependence on the nuclear coordinates. The formalism is entirely based on atomic-orbital 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):4224-9. · 3.83 Impact Factor
  • J.Chem.Theo.Comp. 01/2011; 7:1677.
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    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 user-provided 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. · 3.16 Impact Factor
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    ABSTRACT: A new strategy is introduced for obtaining localized orthonormal Hartree-Fock (HF) orbitals where the underlying principle is to minimize the size of the transformation matrix from the atomic orbital basis to the HF optimized orbital basis. The new strategy gives both localized occupied and localized virtual orbital spaces. The locality of the occupied orbital space is similar to one obtained using standard localization schemes. For the virtual space, standard localization schemes fail to give local orbitals while the new strategy gives a virtual space which has a locality similar to the one of a Lowdin orthonormalization of the atomic orbital basis. Since Lowdin orthonormalization gives the most local orthonormal basis functions in the sense that they have the largest similarity with the local atomic basis functions, the new strategy thus allows the orthonormal basis to become optimized without introducing significant delocalization.
    The Journal of Chemical Physics 09/2009; 131(12):124112. · 3.16 Impact Factor
  • Thomas Kjærgaard, Poul Jørgensen
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    ABSTRACT: A Lagrangian approach has been used to derive gauge-origin independent expressions for two properties that rationalize magneto-optical activity, namely the Verdet constant V(ω) of the Faraday effect and the term of magnetic circular dichroism. The approach is expressed in terms of an atomic-orbital density-matrix based formulation of response theory and use London atomic orbitals to parametrize the magnetic field dependence. It yields a computational procedure which is both gauge-origin independent and suitable for linear-scaling at the level of time-dependent Hartree−Fock and density functional theory. The formulation includes a modified preconditioned conjugated gradient algorithm, which projects out the excited state component from the solution to the linear response equation. This is required when solving one of the response equations for the determination of the term and divergence is encountered if this component is not projected out. Illustrative results are reported for the Verdet constant of H2, HF, CO, N2O, and CH3CH2CH3 and for the term of pyrimidine, phosphabenzene, and pyridine. The results are benchmarked against gauge-origin independent CCSD values.
    Journal of Chemical Theory and Computation - J CHEM THEORY COMPUT. 08/2009; 5(8).
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    ABSTRACT: We present a quasienergy-based formulation of damped response theory where a common effective lifetime parameter has been introduced for all excited states in terms of complex excitation energies. The introduction of finite excited state lifetimes leads to a set of (complex) damped response equations, which have the same form to all orders in the perturbation. An algorithm is presented for solving the damped response equations in Hartree-Fock theory and Kohn-Sham density functional theory. The use of the quasienergy formulation allows us to obtain directly the computationally simplest expressions for damped response functions by applying a set of response parameter elimination rules, which minimize the total number of damped response equations to be solved. In standard response theory broadened absorption spectra are obtained by ad hoc superimposing lineshape functions onto the absorption stick spectra, whereas an empirical lineshape function common to all excitations is an integrated part of damped response theory. By superimposing the lineshape functions inherent in damped response theory onto the stick spectra of standard response theory, we show that the absorption spectra obtained in standard and damped response theory calculations are identical. We demonstrate that damped response theory may be applied to obtain absorption spectra in all frequency ranges, also those that are not readily addressed using standard response theory. This makes damped response theory an effective tool, e.g., for determining absorption spectra for large molecules, where the density of the excited states may be very high, and where standard response theory therefore is not applicable in practice. A thorough comparison is given between our formulation of damped response theory and the formulation by Norman et al. [J. Chem. Phys. 123, 194103 (2005)].
    The Journal of Chemical Physics 08/2009; 131(4):044112. · 3.16 Impact Factor

Publication Stats

2k Citations
707.14 Total Impact Points


  • 1974–2013
    • Aarhus University
      • Department of Chemistry
      Aars, Region North 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
  • 1979–1984
    • Texas A&M University
      • Department of Chemistry
      College Station, Texas, United States
  • 1975
    • CUNY Graduate Center
      New York City, New York, United States