Publications (340)951.57 Total impact

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ABSTRACT: Molecular response properties for ground and excited states and for transitions between these states are defined by solving the timedependent Schrödinger equation for a molecular system in a field of a timeperiodic perturbation. In equation of motion coupled cluster (EOMCC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOMCC eigenvalue equation. We show here that EOMCC molecular response properties are identical to the molecular response properties that are obtained in the coupled clusterconfiguration interaction (CCCI) model, where the timedependent Schrödinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOMCC and CCCI molecular response properties only holds when the CI molecular response property expressionsfrom which the EOMCC expressions are derivedare determined using projection and not using the variational principle. In a previous article [F. Pawłowski, J. Olsen, and P. Jørgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOMCC and CCCI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOMCC and CCCI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, timedependent, perspective for understanding the basic assumptions on which the EOMCC molecular response property expressions are founded. Further, the equivalence between EOMCC and CCCI molecular response properties highlights how static molecular response properties can be obtained from finitefield EOMCC energy calculations.  [Show abstract] [Hide abstract]
ABSTRACT: We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the M{\o}llerPlesset fluctuation potential. We initially introduce the ECCSD(T$n$) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T$n$) series [J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. Both series are termwise size extensive and formally converge towards the CCSDT target energy. However, the two series are different, and the CCSD(T$n$) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the ECCSD(T$n$) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higherlevel target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a faster convergent perturbation series than the simpler energy expansion.  [Show abstract] [Hide abstract]
ABSTRACT: The accuracy with which total energies of openshell species may be calculated using coupled cluster perturbative triples expansions is investigated. In particular, the acclaimed CCSD(T) model, in which a noniterative correction for the effect of triple excitations is added to the coupled cluster singles and doubles (CCSD) energy, is compared to the second through sixthorder models of the recently proposed CCSD(Tn) triples series for both unrestricted as well as restricted openshell HartreeFock (UHF/ROHF) reference determinants. By comparing UHF and ROHFbased statistical results for a test set of 18 atoms and small radicals with comparable RHFbased results, it is found that not only the numerical consistency of the CCSD(T) model, but also its fortuitous cancellation of errors for closedshell systems break down in the transition from closed to openshell systems. For the higherorder models of the CCSD(Tn) series, however, no behavioral differences are found between the correlated descriptions of closed and openshell species, as the convergence rates throughout the series towards the coupled cluster singles, doubles, and triples (CCSDT) energy are identical for the two cases. The higherorder CCSD(Tn) models thus offerunlike the CCSD(T) modela balanced noniterative treatment of closed and openshell species, irrespective of the reference determinant used for the latter, albeit at an increased computational cost as compared to the CCSD(T) model.  [Show abstract] [Hide abstract]
ABSTRACT: We compare the numerical performance of various noniterative coupled cluster (CC) quadruples models. The results collectively show how approaches that attempt to correct the CC singles and doubles energy for the combined effect of triple and quadruple excitations all fail at recovering the correlation energy of the full CC singles, doubles, triples, and quadruples (CCSDTQ) model to within sufficient accuracy. Such a level of accuracy is only achieved by models that make corrections to the full CC singles, doubles, and triples (CCSDT) energy for the isolated effect of quadruple excitations of which the CCSDT(Q3) and CCSDT(Q4) models of the Lagrangianbased CCSDT(Qn) perturbation series are found to outperform alternative models that add either of the established [Q] and (Q) corrections to the CCSDT energy.  [Show abstract] [Hide abstract]
ABSTRACT: We propose a reformulation of the traditional (T) triples correction to the coupled cluster singles and doubles (CCSD) energy in terms of local HartreeFock (HF) orbitals such that its structural form aligns with our recently developed linearscaling divideexpandconsolidate (DEC) coupled cluster family of local correlation methods. In a DECCCSD(T) calculation, a basis of local occupied and virtual HF orbitals is used to partition the correlated calculation on the full system into a number of independent atomic fragment and pair fragment calculations, each performed within a truncated set of the complete orbital space. In return, this leads to a massively parallel algorithm for the evaluation of the DECCCSD(T) correlation energy, which formally scales linearly with the size of the full system and has a tunable precision with respect to a conventional CCSD(T) calculation via a single energybased input threshold. The theoretical developments are supported by proof of concept DECCCSD(T) calculations on a series of mediumsized molecular systems.  [Show abstract] [Hide abstract]
ABSTRACT: The DIIS (direct inversion of the iterative subspace) convergence acceleration algorithm is used in most electronic structure programs to solve the nonlinear coupled cluster amplitude equations. When DIIS is used the storage of previous trial vectors may become a bottleneck and discarding trial vectors may lead to a degradation of the convergence or even divergence. We discuss an alternative way of storing information from trial vectors where only the last 3 trial vectors are needed to maintain the convergence of the full set of previous trial vectors and which only requires minor modifications of an existing DIIS code. 
Article: Molecular response properties from a Hermitian eigenvalue equation for a timeperiodic Hamiltonian
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ABSTRACT: The timedependent Schrödinger equation for a timeperiodic perturbation is recasted into a Hermitian eigenvalue equation, where the quasienergy is an eigenvalue and the timeperiodic regular wave function an eigenstate. From this Hermitian eigenvalue equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasienergy with respect to perturbation strengths, (ii) the quasienergy can be determined from the timeperiodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and timeperiodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed state and its time evolution may differ also extends the range of the wave function models for which response functions can be determined. The simplicity and universality of the presented formulation is illustrated by applying it to the configuration interaction (CI) and the coupled cluster (CC) wave function models and by introducing a new modelthe coupled cluster configuration interaction (CCCI) modelwhere a coupled cluster exponential parametrization is used for the unperturbed state and a linear parametrization for its time evolution. For static perturbations, the CCCI response functions are shown to be the analytical analogues of the static molecular properties obtained from finite field equationofmotion coupled cluster (EOMCC) energy calculations. The structural similarities and differences between the CI, CC, and CCCI response functions are also discussed with emphasis on linear versus nonlinear parametrizations and the sizeextensivity of the obtained molecular properties. 
Article: The same number of optimized parameters scheme for determining intermolecular interaction energies
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ABSTRACT: We propose the Same Number Of Optimized Parameters (SNOOP) scheme as an alternative to the counterpoise method for treating basis set superposition errors in calculations of intermolecular interaction energies. The key point of the SNOOP scheme is to enforce that the number of optimized wave function parameters for the noninteracting system is the same as for the interacting system. This ensures a delicate balance between the quality of the monomer and dimer finite basis set calculations. We compare the SNOOP scheme to the uncorrected and counterpoise schemes theoretically as well as numerically. Numerical results for secondorder MøllerPlesset perturbation theory (MP2) and coupledcluster with single, double, and approximate triple excitations (CCSD(T)) show that the SNOOP scheme in general outperforms the uncorrected and counterpoise approaches. Furthermore, we show that SNOOP interaction energies calculated using a given basis set are of similar quality as those determined by basis set extrapolation of counterpoisecorrected results obtained at a similar computational cost.  [Show abstract] [Hide abstract]
ABSTRACT: Recently, we proposed a novel Lagrangianbased perturbation seriesthe CCSD(Tn) serieswhich systematically corrects the coupled cluster singles and doubles (CCSD) energy in orders of the MøllerPlesset fluctuation potential for effects due to triple excitations. In the present study, we report numerical results for the CCSD(Tn) series up through fourth order which show the predicted convergence trend throughout the series towards the energy of its target, the coupled cluster singles, doubles, and triples (CCSDT) model. Since effects due to the relaxation of the CCSD singles and doubles amplitudes enter the CCSD(Tn) series at fourth order (the CCSD(T4) model), we are able to separate these effects from the total energy correction and thereby emphasize their crucial importance. Furthermore, we illustrate how the ΛCCSD[T]/(T) and CCSD[T]/(T) models, which in slightly different manners augment the CCSD energy by the [T] and (T) corrections rationalized from manybody perturbation theory, may be viewed as approximations to the secondorder CCSD(T2) model. From numerical comparisons with the CCSD(Tn) models, we show that the extraordinary performance of the ΛCCSD[T]/(T) and CCSD[T]/(T) models relies on fortuitous, yet rather consistent, cancellations of errors. As a side product of our investigations, we are led to reconsider the asymmetric ΛCCSD[T] model due to both its rigorous theoretical foundation and its performance, which is shown to be similar to that of the CCSD(T) model for systems at equilibrium geometry and superior to it for distorted systems. In both the calculations at equilibrium and distorted geometries, however, the ΛCCSD[T] and CCSD(T) models are shown to be outperformed by the fourthorder CCSD(T4) model. 
Chapter: Spin in Second Quantization
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ABSTRACT: Second quantization formalism is introduced for an efficient description of molecular electronic systems in the nonrelativistic limit and an explicit description of electron spin. Spin orbitals are functions of three continuous spatial coordinates and one discrete spin coordinate. Quantummechanical operators may be classified according to how they affect the orbital and spin parts of wave functions. The operators are spinfree or spinless operator, pure spin operator and mixed operator. The author adopts the theory of spin tensor operators for angular momentum in quantum mechanics and develops a useful set of tools for the construction and classification of states and operators with definite spin symmetry properties. Singlet excitation operators play an important role in the secondquantization treatment of molecular electronic structure. This chapter shows how a basis of spin eigenfunctions can set up by taking linear combinations of Slater determinants.  [Show abstract] [Hide abstract]
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 MollerPlesset 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. (C) 2014 AIP Publishing LLC.  [Show abstract] [Hide abstract]
ABSTRACT: Dalton is a powerful generalpurpose program system for the study of molecular electronic structure at the HartreeFock, KohnSham, multiconfigurational selfconsistentfield, MøllerPlesset, configurationinteraction, and coupledcluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronicstructure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gaugeorigininvariant manner. Frequencydependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one, two, and threephoton processes. Environmental effects may be included using various dielectricmedium and quantummechanics/molecularmechanics models. Large molecules may be studied using linearscaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.  [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.  [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. 
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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.  [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.  [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.  [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.
Publication Stats
18k  Citations  
951.57  Total Impact Points  
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Institutions

14542015

Aarhus University
 • Department of Chemistry
 • Department of Medical Microbiology and Immunology
Aarhus, Central Jutland, Denmark


20042013

University of Oslo
 Department of Chemistry
Kristiania (historical), Oslo, Norway


2003

Università degli Studi di Trieste
Trst, Friuli Venezia Giulia, Italy


19831993

University of Utah
 Department of Chemistry
Salt Lake City, Utah, United States


1987

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


19791984

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