About Us

Our current research focuses on geminal-based wavefunction ansätze and alternative Coupled-Cluster models for strongly-correlated systems, the Density Matrix Renormalization Group (DMRG) algorithm, and the application of these methods to challenging problems in chemistry (e.g., chemical bond breaking/forming and actinide chemistry). We also apply intuitive tools to interpret electronic structures and chemical phenomena using concepts of quantum information theory.

Furthermore, together with the research groups of Dariusz Kędziera, Paweł Tecmer, and Piotr Żuchowski, we develop our own open-source quantum chemistry software package called Piernik, where all our proposed methods are implemented.

Scientific Experience

Education & Training

Honors, Awards, and Grants

  • 2016
    Scholarship for outstanding young scientists (12.2016-present)
    Scholarships for young, outstanding researchers under 35 of the Ministry of Science and Higher Education.
  • 2016
    Stipend Start 2016 (07.2016-present)
    Stipends for young, talented researchers under 30 of the Foundation for Polish Science. I am among the laureates of 2016.
  • 2016
    Marie-Skłodowska-Curie Individual Fellowship (European Fellowship) (07.2016-present)
    Hosted by Dariusz Kędziera.
  • 2016
    SONATA BIS 5 (04.2016-present)
    Research grant to establish a new research group (SONATA BIS - ST panel).
  • 2016
    Wroclaw Centre for Networking and Supercomputing
    Computing grant of the WCSS.
  • 2015
    France-Canada Research Fund (2015-2017)
    Together with the group of Prof. Valerie Vallet.
  • 2015
    Banting Postdoctoral Fellowship (04.2015-07.2015)
    I was awarded with the first Banting Postdoctoral Fellowship in the history of the Department of Chemistry and Chemical Biology at McMaster University.
  • 2013
    Early-Postdoc Mobility Fellowship of the Swiss National Science Foundation (07.2013-12.2014)
  • 2010
    Chemiefonds-scholarship of the Fond der Chemischen Industrie (07.2010-06.2012)
  • 09.2011
    Poster Prize
    Poster Prize of the Swiss Chemical Society Fall Meeting, Lausanne, Switzerland, for presenting the poster "Reconstruction of CI-type wavefunctions for very large active spaces"
  • 09.2009
    Willi–Studer–Award of the ETH Zurich
    Awarded to the best Master’s degree students
  • 2006
    Scholarship of the German National Academic Foundation (03.2006-08.2009)
  • 2006
    Scholarship of the Solidarity Fund for Foreign Students (ETHZ) (10.2006-08.2008)
  • 2005
    ETHZ scholarship (10.2005-10.2006)

Supervision of Graduate Students

  • present 10.2016

    Aleksandra Lachmanska

    Master student, Institute of Physics, Nicolaus Copernicus University, Poland.
    Project title: Dissecting cation-cation interactions using unconventional wavefunction approaches

    08.2015 08.2014

    Yilin Zhao

    PhD student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
    Project title: DMRG and Tensor Network states in heavy element chemistry
    Publication: Theoretical Chemistry Accounts, 134, 120 (2015)

Student Supervision

  • 08.2015 05.2015

    Corinne Duperrouzel

    Summer Student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
    Project title: Thermochemistry of actinide compounds
    Publication: to be submitted

  • 08.2015 09.2014

    Sung W Hong

    Bachelor Student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
    Project title: Cation-cation interactions in actinide oxides
    Publication: Physical Chemistry Chemical Physics, 18, 18305-18311 (2016)

  • 08.2015 08.2014

    Daniel Stuart

    Co-op student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
    Project title: Electronic structure of iridium complexes
    Publication: RSC Advances, 5, 84311–84320 (2015)

  • 08.2014 04.2014

    Corinne Duperrouzel

    Summer Student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
    Project title: Metal–olefin bonding in Ni-ethylene complexes
    Publication: Chemical Physics Letters 621, 160-164 (2015)

  • 12.2013 04.2013

    Matthieu Mottet

    Semester Student, Laboratory of Physical Chemistry, ETH Zurich, Switzerland.
    Project title: Bond breaking processes of Carbon/Carbon and Carbon/Homologues — A quantum entanglement study
    Publication: Physical Chemistry Chemical Physics 16 (19), 8872-8880 (2014)

  • 04.2012 02.2012

    Simon Pintarelli

    Semester Student, Laboratory of Physical Chemistry, ETH Zurich, Switzerland.
    Project title: Assessment of extrapolation schemes for the DMRG algorithm

Teaching (tutor and TA)

  • Fall 2017

    Electronic structure theory (tutor)

    Introduction to DFT, CC, and MCSCF and their applications.

  • Fall 2016

    Electronic structure theory (tutor)

    Introduction to DFT, CC, and MCSCF and their applications.

  • Spring 2013

    Physical Chemistry II for Biology and Pharmacy

    Kinetics, Surface- and Transport-phenomena.

  • Fall 2012

    Informatics I for Chemists

    Introduction to Computer Science.

  • Fall 2011

    General Chemistry I

    Physical Chemistry.

  • Spring 2011

    Quantum Chemistry

    Introduction to Quantum Chemistry.

  • Fall 2009

    Advanced Quantum Chemistry

    Relativistic Quantum Chemistry.

Current group members

Odile Franck

Postdoctoral fellow

Topic: Combining DFT with geminal-based approaches

Aleksandra (Ola) Łachmańska

PhD student

Topic: Development of new wavefunction approaches for actinide chemistry

Artur Nowak

PhD stduent

Topic: Development of new wavefunction approaches for actinide chemistry

Research Projects

  • image

    Geminal-based approaches

    Quantum mechanical models for strong and weak correlation.

    I am developing new methods for strong and weak electron correlation based on electron-pair states, called geminals. In geminal-based methods, the electronic wavefunction is constructed as an antisymmetric product of two-electron functions. By construction, this captures the essential part of strong correlation. I presented the first implementation of the Antisymmetric Product of 1-reference orbital Geminals (AP1roG) for molecules including a fully variational optimization scheme for the molecular orbitals using a Lagrangian function. I further developed different flavours of non-variational orbital optimization techniques based on the seniority concept. Although geminal-based methods are able to describe strong electron correlation, they miss a large fraction of the weak electron correlation energy. Recently, I presented a multi-reference linearized coupled-cluster correction based on an AP1roG reference function to include weak correlation on top of an AP1roG wavefunction. Specifically, the linearized coupled-cluster model outperformed various perturbation theory corrections previously developed for AP1roG.

    Selected key publications are:

  • image

    Tensor-Network-based Approaches in Quantum Chemistry

    The quantum chemical density matrix renormalization group algorithm.

    Tensor Network States approaches, like the DMRG algorithm, are a promising alternative to standard electron correlation methods. I am investigating the performance of DMRG to accurately predict electronic structures and molecular properties. Specifically, I developed a reconstruction algorithm to construct configuration-interaction-type wavefunctions from the matrix-product-state representation optimized by DMRG using a Monte-Carlo sampling algorithm. Furthermore, I implemented and studied the calculation of spin density and magnetization density distributions from DMRG wavefunctions.

    Selected key publications are:

  • image

    Interpretative Tools Based on Orbital Entanglement and Correlation

    Analysing chemical processes using the picture of interacting orbitals.

    The interaction of orbitals is a useful concept in chemistry. It is frequently used to understand chemical processes and reaction mechanisms. Unfortunately, the interaction of orbitals is commonly understood using qualitative arguments, like molecular-orbital diagrams, Frontier-orbital theory, and ligand field theory. I am developing quantitative means to measure the interaction of orbitals using concepts of quantum information theory. Specifically, I have shown that orbital entanglement and correlation are particularly useful and intuitive measures to quantify the interaction of orbitals and to elucidate electronic structures and changes in electronic structure that accompany chemical processes. Furthermore, I presented various applications where orbital entanglement was used to identify bond orders, transition states, and electron correlation effects.

    Selected key publications are:

  • image

    Modeling of Heavy-Element Chemistry

    Theoretical description of electronic structures and properties of heavy-element-containing materials.

    My research also focuses on theoretical modeling of heavy-element compounds and their properties using conventional and unconventional electron correlation methods. Specifically, I presented the first DMRG study on actinide chemistry. I investigated the anticipated singlet-triplet spin crossover of the CUO molecule diluted in a noble gas matrix (within a scalar relativistic treatment) and elucidated the mysterious interaction of the CUO unit with the noble gas environment. Most importantly, this was the first theoretical study confirming the experimentally anticipated singlet-triplet ground state change of the CUO molecule. Furthermore, I presented the first geminal study on actinide chemistry. Specifically, AP1roG was the first quantum chemistry method to completely dissociate the UO22+ molecule into its atomic fragments.

    Selected key publications are:

  • image

    Software Development

    Development of quantum chemical software: The Horton program package.

    I am actively involved in software development. I am one of the main authors of the Horton program package, an open-source quantum chemistry software package written in Python and C++. Specifically, I am the main developer of the post-Hartree-Fock modules. All geminal methods and optimization schemes I am developing are implemented in the Horton 2.0.0 program package. My contributions include

    • the geminal module (restricted AP1roG with and without orbital optimization)
    • the dynamical correlation module (Møller-Plesset Perturbation Theory of second order, Perturbation Theory corrections on top of AP1roG, Linearized Coupled Cluster correction based on a Hartree-Fock and AP1roG reference function)
    • the orbital entanglement module (single-orbital entropy and mutual information for seniority-zero wavefunctions)
    • the orbital localization module (Pipek-Mezey localization)

    You can find more information and download Horton here.

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On the Multi-Reference Nature of Plutonium Oxides: PuO22+, PuO2, PuO3 and PuO2(OH)2

K Boguslawski, Florent Réal, Paweł Tecmer, Corinne Duperrouzel, André Severo Pereira Gomes, Örs Legeza, Paul W Ayers, Valérie Vallet
Journal Paper Physical Chemistry Chemical Physics (in press) (2017)


Actinide-containing complexes present formidable challenges for electronic structure methods due to the large number of degenerate or quasi-degenerate electronic states arising from partially occupied 5f and 6d shells. Conventional multi-reference methods can treat active spaces that are often at the upper limit of what is required for a proper treatment of species with complex electronic structures, leaving no room for verifying their suitability. In this work we address the issue of properly defining the active spaces in such calculations, and introduce a protocol to determine optimal active spaces based on the use of the Density Matrix Renormalization Group algorithm and concepts of quantum information theory. We apply the protocol to elucidate the electronic structure and bonding mechanism of volatile plutonium oxides (PuO3 and PuO2(OH)2), species associated with nuclear safety issues for which little is known about the electronic structure and energetics. We show how, within a scalar relativistic framework, orbital-pair correlations can be used to guide the definition of optimal active spaces which provide an accurate description of static/non-dynamic electron correlation, as well as to analyse the chemical bonding beyond a simple orbital model. From this bonding analysis we are able to show that the addition of oxo- or hydroxo-groups to the plutonium dioxide species considerably changes the pi-bonding mechanism with respect to the bare triatomics, resulting in bent structures with considerable multi-reference character.

Targeting excited states in all-trans polyenes with electron-pair states

K Boguslawski
Journal Paper Journal of Chemical Physics, 145, 234105 (2016)


Wavefunctions restricted to electron pair states are promising models for strongly-correlated systems. Specifically, the pair Coupled Cluster Doubles (pCCD) ansatz allows us to accurately describe bond dissociation processes and heavy-element containing compounds with multiple quasi-degenerate single-particle states. Here, we extend the pCCD method to model excited states using the equation of motion (EOM) formalism. As the cluster operator of pCCD is restricted to electron-pair excitations, EOM-pCCD allows us to target excited electron-pair states only. To model singly excited states within EOM-pCCD, we modify the configuration interaction ansatz of EOM-pCCD to contain also single excitations. Our proposed model represents a simple and cost-effective alternative to conventional EOM-CC methods to study singly excited electronic states. The performance of the excited state models is assessed against the lowest-lying excited states of the uranyl cation and the two lowest-lying excited states of all-trans polyenes. Our numerical results suggest that EOM-pCCD including single excitations is a good starting point to target singly excited states.

Analysis of two-orbital correlations in wave functions restricted to electron-pair states

K Boguslawski, P Tecmer, O Legeza
Journal Paper Physical Review B, 94, 155126 (2016)


Wave functions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of electron correlation effects that can be captured by wave functions restricted to electron-pair states. We focus on the pair-coupled-cluster doubles (pCCD) ansatz also called the antisymmetric product of the 1-reference orbital geminal (AP1roG) method, combined with an orbital optimization protocol presented in Boguslawski et al. [Phys. Rev. B 89, 201106(R) (2014)], whose performance is assessed against electronic structures obtained form density-matrix renormalization-group reference data. Our numerical analysis covers model systems for strong correlation: the one-dimensional Hubbard model with a periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of pCCD/AP1roG is benchmarked using the single-orbital entropy, the orbital-pair mutual information, as well as the eigenvalue spectrum of the one-orbital and two-orbital reduced density matrices. Our study indicates that contributions from singly occupied states become important in the strong correlation regime which highlights the limitations of the pCCD/AP1roG method. Furthermore, we examine the effect of orbital rotations within the pCCD/AP1roG model on correlations between orbital pairs.

Dissecting the cation-cation interaction between two uranyl units

P Tecmer, S W Hong, K Boguslawski
Journal Paper Physical Chemistry Chemical Physics, 18, 18305-18311 (2016)


We present a state-of-the-art computational study of the uranyl(VI) and uranyl(V) cation-cation interactions (dications) in aqueous solution. Reliable electronic structures of two interacting uranyl(VI) and uranyl(V) subunits as well as of the uranyl(VI) and uranyl(V) cluster are presented for the first time. Our theoretical study elucidates the impact of cation-cation interactions on changes in molecular structure as well as changes in vibrational and UV-VIS spectra of the bare uranyl(VI) and uranyl(V) moieties for different total spin-states and total charges of the dications.

Relativistic Two-Component Methods in Computational Chemistry

P Tecmer, K Boguslawski, D Kędziera
Book Chapter in Handbook of Computational Chemistry, Springer Netherlands (2016)


In this chapter, we briefly discuss the theoretical foundations of relativistic two-component methods used in quantum chemistry calculations. Specifically, we focus on two groups of methods. These are (i) methods based on the elimination of the small component, such as the zeroth-order regular approximation (ZORA), the first-order regular approximation (FORA), and the normalized elimination of small component (NESC) formalisms, and (ii) approaches that use a unitary transformation to decouple the electronic and positronic states such as the Douglas–Kroll–Hess (DKH) and the infinite-order two-component (IOTC) Hamiltonians. Furthermore, we describe the algebraic approach to IOTC and scrutinize pure algebraic schemes that paved the way to the eXact 2-Component (X2C) Hamiltonians taking advantage of the nonsymmetric algebraic Riccati equation (nARE). Finally, we assess the accuracy of the aforementioned methods in calculating core and valence properties of heavy-element compounds and discuss some challenging examples of computational actinide chemistry.

Linearized Coupled Cluster Correction on the Antisymmetric Product of 1-reference orbital Geminals

K Boguslawski, PW Ayers
Journal PaperJournal of Chemical Theory and Computation, 11, 5252-5261 (2015)


We present a Linearized Coupled Cluster (LCC) correction based on an Antisymmetric Product of 1-reference orbital Geminals (AP1roG) reference state. In our LCC ansatz, the cluster operator is restricted to double or to single and double excitations, as in standard single-reference CC theory. The performance of the AP1roG-LCC models is tested for the dissociation of diatomic molecules in their lowest-lying singlet state (C2, F2, and BN), the symmetric dissociation of the H50 hydrogen chain, and spectroscopic constants of the uranyl cation (UO22+). Our study indicates that an LCC correction based on an AP1roG reference function is more robust and reliable than corrections based on perturbation theory, yielding spectroscopic constants that are in very good agreement with theoretical reference data.

The Effect of Nitrido, Azide, and Nitrosyl Ligands on Magnetization Densities and Magnetic Properties of Iridium PNP Pincer-Type Complexes

D Stuart, P Tecmer, PW Ayers, K Boguslawski
Journal PaperRSC Advances, 5, 84311–84320 (2015)


We present a systematic theoretical study of electronic structures, magnetization densities, and magnetic properties of iridium PNP pincer-type complexes containing non-innocent nitrido, azide, and nitrosyl ligands. Specifically, the quality and accuracy of density functional theory (DFT) in predicting magnetization densities obtained from various approximate exchange–correlation functionals is assessed by comparing them to complete active space self-consistent field (CASSCF) reference distributions. Our analysis points to qualitative differences in DFT magnetization densities at the iridium metal center and the pincer ligand backbone compared to CASSCF reference data when the non-innocent ligands are changed from nitrido, to azide, to nitrosyl. These observations are reflected in large differences in hyperfine couplings calculated for the iridium metal center.

Dissecting the Bond Formation Process of d10-Metal-Ethene Complexes with Multireference Approaches

Y Zhao, K Boguslawski, P Tecmer, C Duperrouzel, G Barcza, O Legeza, PW Ayers
Journal PaperTheoretical Chemistry Accounts, 134, 120 (2015)


The bonding mechanism of ethene to a nickel or palladium center is studied by the density matrix renormalization group algorithm, the complete active space self-consistent field method, coupled cluster theory, and density functional theory. Specifically, we focus on the interaction between the metal atom and bis-ethene ligands in perpendicular and parallel orientations. The bonding situation in these structural isomers is further scrutinized using energy decomposition analysis and quantum information theory. Our study highlights the fact that when two ethene ligands are oriented perpendicular to each other, the complex is stabilized by the metal-to-ligand double-back-bonding mechanism. Moreover, we demonstrate that nickel–ethene complexes feature a stronger and more covalent interaction between the ligands and the metal center than palladium–ethene compounds with similar coordination spheres.

Orbital Entanglement in Quantum Chemistry

K Boguslawski, P Tecmer
Journal PaperInternational Journal of Quantum Chemistry, 115, 1289–1295 (2015)


The basic concepts of orbital entanglement and its application to chemistry are briefly reviewed. The calculation of orbital entanglement measures from correlated wavefunctions is discussed in terms of reduced n-particle density matrices. Possible simplifications in their evaluation are highlighted in case of seniority-zero wavefunctions. Specifically, orbital entanglement allows us to dissect electron correlation effects in its strong and weak contributions, to determine bond orders, to assess the quality and stability of active space calculations, to monitor chemical reactions, and to identify points along the reaction coordinate where electronic wavefunctions change drastically. Thus, orbital entanglement represents a useful and intuitive tool to interpret complex electronic wavefunctions and to facilitate a qualitative understanding of electronic structure and how it changes in chemical processes.

Selection of Active Spaces for Multiconfigurational Wave Functions

S Keller, K Boguslawski, T Janowski, M Reiher, P Pulay
Journal PaperJournal of Chemical Physics 142, 244104 (2015)


The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximate the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F2, ozone, and NO2), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr2). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential solutions are discussed: finding the UHF solutions, discontinuities on potential energy surfaces, and inclusion of dynamical electron correlation and generalization to excited states.

Singlet Ground State Actinide Chemistry with Geminals

P Tecmer, K Boguslawski, PW Ayers
Journal PaperPhysical Chemistry Chemical Physics 17, 14427-14436 (2015)


We present the first application of the variationally orbital optimized antisymmetric product of 1-reference orbital geminals (vOO-AP1roG) method to singlet-state actinide chemistry. We assess the accuracy and reliability of the AP1roG ansatz in modelling the ground-state electronic structure of small actinide compounds by comparing it to standard quantum chemistry approaches. Our study of the ground state spectroscopic constants (bond lengths and vibrational frequencies) and potential energy curves of actinide oxides (UO22+ and ThO2) as well as the energetic stability of ThC2 isomers reveals that vOO-AP1roG describes the electronic structure of heavy-element compounds accurately, at mean-field computational cost.

A Quantum Informational Approach for Dissecting Chemical Reactions

C Duperrouzel, P Tecmer, K Boguslawski, G Barcza, O Legeza, PW Ayers
Journal PaperChemical Physics Letters 621, 160-164 (2015)


We present a conceptionally different approach to dissect bond-formation processes in metal-driven catalysis using concepts from quantum information theory. Our method uses the entanglement and correlation among molecular orbitals to analyze changes in electronic structure that accompany chemical processes. As a proof-of-principle example, the evolution of nickel–ethene bond-formation is dissected, which allows us to monitor the interplay of back-bonding and π-donation along the reaction coordinate. Furthermore, the reaction pathway of nickel–ethene complexation is analyzed using quantum chemistry methods, revealing the presence of a transition state. Our study supports the crucial role of metal-to-ligand back-donation in the bond-forming process of nickel–ethene.

Nonvariational Orbital Optimization Techniques for the AP1roG Wave Function

K Boguslawski, P Tecmer, P Bultinck, S De Baerdemacker, D Van Neck, PW Ayers
Journal PaperJournal of Chemical Theory and Computation 10 (11), 4873-4882 (2014)


We introduce new nonvariational orbital optimization schemes for the antisymmetric product of one-reference orbital geminal (AP1roG) wave function (also known as pair-coupled cluster doubles) that are extensions to our recently proposed projected seniority-two (PS2-AP1roG) orbital optimization method [J. Chem. Phys. 2014, 140, 214114)]. These approaches represent less stringent approximations to the PS2-AP1roG ansatz and prove to be more robust approximations to the variational orbital optimization scheme than PS2-AP1roG. The performance of the proposed orbital optimization techniques is illustrated for a number of well-known multireference problems: the insertion of Be into H2, the automerization process of cyclobutadiene, the stability of the monocyclic form of pyridyne, and the aromatic stability of benzene.

Projected Seniority-Two Orbital Optimization of the Antisymmetric Product of One-Reference Orbital Geminal

K Boguslawski, P Tecmer, PA Limacher, PA Johnson, PW Ayers, P Bultinck, S De Baerdemacker, D Van Neck
Journal PaperThe Journal of Chemical Physics 140 (21), 214114 (2014)


We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys.135, 044119 (2011)]. A numerical analysis is performed for the C2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.

Chemical Bonding in Open-Shell Transition Metal Complexes

K Boguslawski, M Reiher
Book ChapterThe Chemical Bond: Chemical Bonding Across the Periodic Table", vol. 2 (2014)


image This chapter discusses chemical bonding in open-shell molecules that can be attributed to its unpaired electrons. We first give a short overview of contemporary single- and multireference quantum chemical methods that can be employed for quantitative bond energy calculations. Quantum chemistry provides us with electronic wave function and (spin) density, which represent the central ingredients for a subsequent analysis of the chemical bond. In this respect, we review different strategies that have been developed for a qualitative interpretation of open-shell electronic structures. A key feature of such approaches is the introduction of local quantities such as local spins. Different decomposition schemes of the total spin expectation value for multireference wave functions are presented and compared. In particular, the localization of spins facilitates the description of magnetically coupled centers. Such coupling phenomena generally require a multideterminant treatment, yet a one-determinant picture can be enforced if the spin symmetry of the system is broken. Different approaches that optimize such broken-symmetry solutions are discussed. Furthermore, various definitions of the covalent bond order applicable to open-shell electronic structures are discussed, which are based either on the (spin) density matrix or on a simple electron-counting scheme. While the former suffers from its method and basis-set dependence, the latter represents a reliable estimate only if one considers all bonding and antibonding orbitals that are crucial for a correct description of the chemical bond.

Efficient Description of Strongly Correlated Electrons With Mean-Field Cost

K Boguslawski, P Tecmer, PW Ayers, P Bultinck, S De Baerdemacker, D Van Neck
Journal PaperPhysical Review B 89 (20), 201106(R) (2014)


We present an efficient approach to the electron correlation problem that is well suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. The performance of our approach is illustrated for one-dimensional Hubbard rings with different numbers of sites, and for the nonrelativistic quantum-chemical Hamiltonian exploring the symmetric dissociation of the H50 hydrogen chain.

Assessing The Accuracy Of New Geminal-Based Approaches

P Tecmer, K Boguslawski, PA Johnson, PA Limacher, M Chan, T Verstraelen, PW Ayers
Journal PaperThe Journal of Physical Chemistry A 118 (39), 9058–9068 (2014)


We present a systematic theoretical study on the dissociation of diatomic molecules and their spectroscopic constants using our recently presented geminal-based wave function ansätze. Specifically, the performance of the antisymmetric product of rank two geminals (APr2G), the antisymmetric product of 1-reference-orbital geminals (AP1roG) and its orbital-optimized variant (OO-AP1roG) are assessed against standard quantum chemistry methods. Our study indicates that these new geminal-based approaches provide a cheap, robust, and accurate alternative for the description of bond-breaking processes in closed-shell systems requiring only mean-field-like computational cost. In particular, the spectroscopic constants obtained from OO-AP1roG are in very good agreement with reference theoretical and experimental data.

Quantum Entanglement in Carbon–Carbon, Carbon–Phosphorus and Silicon–Silicon Bonds

M Mottet, P Tecmer, K Boguslawski, O Legeza, M Reiher
Journal PaperPhysical Chemistry Chemical Physics 16 (19), 8872-8880 (2014)


The chemical bond is an important local concept to understand chemical compounds and processes. Unfortunately, like most local concepts, the chemical bond and the bond order do not correspond to any physical observable and thus cannot be determined as an expectation value of a quantum chemical operator. We recently demonstrated [Boguslawski et al., J. Chem. Theory Comput., 2013, 9, 2959–2973] that one- and two-orbital-based entanglement measures can be applied to interpret electronic wave functions in terms of orbital correlation. Orbital entanglement emerged as a powerful tool to provide a qualitative understanding of bond-forming and bond-breaking processes, and allowed for an estimation of bond orders of simple diatomic molecules beyond the classical bonding models. In this article we demonstrate that the orbital entanglement analysis can be extended to polyatomic molecules to understand chemical bonding.

Unravelling the Quantum-Entanglement Effect of Noble Gas Coordination on the Spin Ground State of CUO

P Tecmer, K Boguslawski, O Legeza, M Reiher
Journal PaperPhysical Chemistry Chemical Physics 16 (2), 719-727 (2014)


The accurate description of the complexation of the CUO molecule by Ne and Ar noble gas matrices represents a challenging task for present-day quantum chemistry. Especially, the accurate prediction of the spin ground state of different CUO–noble-gas complexes remains elusive. In this work, the interaction of the CUO unit with the surrounding noble gas matrices is investigated in terms of complexation energies and dissected into its molecular orbital quantum entanglement patterns. Our analysis elucidates the anticipated singlet–triplet ground-state reversal of the CUO molecule diluted in different noble gas matrices and demonstrates that the strongest uranium–noble gas interaction is found for CUOAr4 in its triplet configuration.

Orbital Entanglement in Bond-Formation Processes

K Boguslawski, P Tecmer, G Barcza, O Legeza, M Reiher
Journal PaperJournal of Chemical Theory and Computation 9 (7), 2959-2973 (2013)


The accurate calculation of the (differential) correlation energy is central to the quantum chemical description of bond-formation and bond-dissociation processes. In order to estimate the quality of single- and multireference approaches for this purpose, various diagnostic tools have been developed. In this work, we elaborate on our previous observation [J. Phys. Chem. Lett.2012, 3, 3129] that one- and two-orbital-based entanglement measures provide quantitative means for the assessment and classification of electron correlation effects among molecular orbitals. The dissociation behavior of some prototypical diatomic molecules features all types of correlation effects relevant for chemical bonding. We demonstrate that our entanglement analysis is convenient to dissect these electron correlation effects and to provide a conceptual understanding of bond-forming and bond-breaking processes from the point of view of quantum information theory.

Optimized Unrestricted Kohn–Sham Potentials From Ab Initio Spin Densities

K Boguslawski, CR Jacob, M Reiher
Journal PaperThe Journal of Chemical Physics 138 (4), 044111 (2013)


The reconstruction of the exchange–correlation potential from accurate ab initio electron densities can provide insights into the limitations of the currently available approximate functionals and provide guidance for devising improved approximations for density-functional theory (DFT). For open-shell systems, the spin density is introduced as an additional fundamental variable in spin-DFT. Here, we consider the reconstruction of the corresponding unrestricted Kohn–Sham (KS) potentials from accurate ab initio spin densities. In particular, we investigate whether it is possible to reconstruct the spin exchange–correlation potential, which determines the spin density in unrestricted KS-DFT, despite the numerical difficulties inherent to the optimization of potentials with finite orbital basis sets. We find that the recently developed scheme for unambiguously singling out an optimal optimized potential [Ch. R. Jacob, J. Chem. Phys.135, 244102 (Year: 2011)10.1063/1.3670414] can provide such spin potentials accurately. This is demonstrated for two test cases, the lithium atom and the dioxygen molecule, and target (spin) densities from full configuration interaction and complete active space self-consistent field calculations, respectively.

Entanglement Measures for Single-and Multireference Correlation Effects

K Boguslawski, P Tecmer, O Legeza, M Reiher
Journal PaperThe Journal of Physical Chemistry Letters 3 (21), 3129-3135 (2012)


Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multireference nature of electronic structures as well as of the dominant contributions to the correlation energy can facilitate the decision regarding the optimum quantum chemical method of choice. We propose concepts from quantum information theory as orbital entanglement measures that allow us to evaluate the single- and multireference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.

Accurate Ab Initio Spin Densities

K Boguslawski, KH Marti, O Legeza, M Reiher
Journal PaperJournal of Chemical Theory and Computation 8 (6), 1970-1982 (2012)


We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys. 2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and β electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740].

Dissecting the Quantum Chemical Spin State Problem: Entropy Measures, Matrix Product States and Reconstruction Algorithms

K Boguslawski
Thesis PhD Thesis, (2012)

Can DFT Accurately Predict Spin Densities? Analysis of Discrepancies in Iron Nitrosyl Complexes

K Boguslawski, CR Jacob, M Reiher
Journal Paper Journal of Chemical Theory and Computation 7 (9), 2740-2752 (2011)


Iron nitrosyl complexes are a particularly challenging case for density functional theory. In particular, for the low-spin state, different exchange–correlation functionals yield very different spin densities [Conradie, J.; Ghosh, A. J. Phys. Chem. B 2007, 111, 12621−12624]. Here, we investigate the origin of these differences in detail by analyzing the Kohn–Sham molecular orbitals. Furthermore, to decide which exchange–correlation functionals yield the most accurate spin densities, we make comparisons to CASSCF calculations. To ensure that the spin densities are converged with respect to the size of the active space, this comparison is performed for [Fe(NO)]2+ as a model system. We find that none of the investigated exchange–correlation functionals are able to reproduce the CASSCF spin densities accurately.

Construction of CASCI-type Wave Functions for Very Large Active Spaces

K Boguslawski, KH Marti, M Reiher
Journal Paper Journal of Chemical Physics 134 (22), 224101 (2011).


We present a procedure to construct a configuration-interaction expansion containing arbitrary excitations from an underlying full-configuration-interaction-type wave function defined for a very large active space. Our procedure is based on the density-matrix renormalization group (DMRG) algorithm that provides the necessary information in terms of the eigenstates of the reduced density matrices to calculate the coefficient of any basis state in the many-particle Hilbert space. Since the dimension of the Hilbert space scales binomially with the size of the active space, a sophisticated Monte Carlo sampling routine is employed. This sampling algorithm can also construct such configuration-interaction-type wave functions from any other type of tensor network states. The configuration-interaction information obtained serves several purposes. It yields a qualitatively correct description of the molecule’s electronic structure, it allows us to analyze DMRG wave functions converged for the same molecular system but with different parameter sets (e.g., different numbers of active-system (block) states), and it can be considered a balanced reference for the application of a subsequent standard multi-reference configuration-interaction method.

A Refined, Efficient Mean Solvation Force Model that Includes the Interior Volume Contribution

JR Allison, K Boguslawski, F Fraternali, WF van Gunsteren
Journal Paper The Journal of Physical Chemistry B 115 (15), 4547-4557 (2011).


A refined implicit aqueous solvation model is proposed for the simulation of biomolecules without the explicit inclusion of the solvent degrees of freedom. The mean force due to solvation is approximated by the derivative of a simple analytic function of the solvent accessible surface area combined with two atomic solvation parameters, as described previously, with the addition of a novel term to account for the interaction of the interior atoms of the solute with the solvent. The extended model is parametrized by comparing the structural properties and energies computed from simulations of six test proteins of varying sizes and shapes using the new solvation energy term with the corresponding values obtained from simulations in vacuum, using the original implicit solvent model and in explicit water, and from the X-ray or NMR model structures. The mean solvation model proposed here improves the structural properties relative to vacuum simulations and relative to the simpler model that neglects the volume contribution, while remaining significantly more efficient than simulations in explicit water.

Kasia's Talks

  • 2017
    Thursday Seminar, Institute of Physics, Nicolaus Copernicus University, Poland
    Title: Computationally inexpensive electronic structure methods applicable to light and heavy elements (January 2017)
  • 2016
    EMN Meeting on Computation and Theory, Las Vegas, USA
    Title: Novel coupled cluster approaches for heavy element chemistry (October 2016)
  • 2016
    Seminar at the Quantum Chemistry Laboratory, Faculty of Chemistry, University of Warsaw, Poland
    Title: Novel electronic structure methods for light and heavy element chemistry (May 2016)
  • 2015
    Pacifichem 2015, International Chemical Congress of Pacific Basin Societies 2015, Honolulu, Hawaii, USA
    Title: Electronic structure of trans-polyenes from two electron functions (December 2015)
  • 2015
    Special Colloquium, Department of Quantum Physics, NCU, Torun, Poland
    Title: Unconventional Methods in Quantum Chemistry Based on Two-Electron Functions: Geminals and Beyond (September 2015)
  • 2015
    Theoretical Chemistry Seminar at the VU University Amsterdam, Amsterdam, The Netherlands
    Title: Alternative Wavefunction Models for Strong and Weak Electron Correlation (May 2015)
  • 2015
    Theoretical Chemistry Seminar at the PhLAM institute at the University of Lille, Lille, France
    Title: Modeling the Chemistry of d- and f -Block Elements (May 2015)
  • 2015
    Department of Chemistry Seminar at Syracuse University, Syracuse, USA
    Title: The Electron Correlation Problem across the Periodic Table (March 2015)
    More details.
  • 2014
    Meeting on New Approaches in Theoretical Chemistry, Santiago, Chile
    Title: Nonvariational Orbital Optimization Techniques (October 2014)
  • 2013
    Meeting on Methods for Modeling Molecules and Materials, Hamilton, Canada
    Title: A DMRG Walk Through the Periodic Table — An Entanglement Study of Electronic Structures (December 2013)
  • 2013
    Canada Days Workshop, Ghent, Belgium
    Title: Geminals — Past, Present and Future Perspectives (November 2013)
  • 2013
    8th Mathematical Methods for Ab Initio Quantum Chemistry, Nice, France
    Title: How Quantum Entanglement Can Promote the Understanding of Electronic Structures of Molecules (November 2013)
    More details.
  • 2012
    Entanglement Based Approaches in Quantum Chemistry, Dresden, Germany
    Title: Tensor Decompositions, Entanglement, and other Unconventional Approaches to Challenging Problems in Transition Metal Chemistry (September 2012)
    More details
  • 2012
    Ab initio Valence Bond Workshop, Paris, France
    Title: Modern Multi-Determinantial Total-State Wave Functions and their Relation to One-Electron Pictures like Valence Bond Theory (July 2012)
    More details
  • 2012
    Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zurich, Switzerland
    Title: Accurate Ab Initio Spin Density Distributions (April 2012)
  • 2012
    Amsterdam Center for Multiscale Modeling, VU Amsterdam, The Netherlands
    Title: Accurate Ab Initio Spin Density Distributions (January 2012)
  • 2011
    Theoretical Chemistry Seminar, VU Amsterdam, The Netherlands
    Title: The DMRG Algorithm in Quantum Chemistry (January 2011)
  • 2010
    Theoretical Chemistry Seminar, Karlsruhe Institute of Technology, Germany
    Title: The DMRG Algorithm in Quantum Chemistry (September 2010)

Talks by Group Members

  • 2017
    Odile Franck, International Meeting on Atomic and Molecular Physics and Chemistry 2017, Torun, Poland.
    Title: Range-separated hybrid scheme combining AP1roG with density functional theory

Poster Presentations by Group Members

  • 2017
    Odile Franck, WATOC 2017, Munich, Germany.
  • 2017
    Ola Łachmańska, European Summerschool of Quantum Chemistry 2017, Sicily, Italy.
  • 2017
    Artur Nowak, European Summerschool of Quantum Chemistry 2017, Sicily, Italy.
  • 2017
    Ola Łachmańska, International Meeting on Atomic and Molecular Physics and Chemistry 2017, Torun, Poland.
  • 2017
    Artur Nowak, International Meeting on Atomic and Molecular Physics and Chemistry 2017, Torun, Poland.

Actinide-related projects

DMRG-related projects

Geminals-related projects

Open Positions

PostDoctoral Fellows

Full-time employment

Currently, no funded positions are available.
If, however, you are still interested to join my group and

  • are interested in developing new electronic structure methods
  • possess programming skills using novel languages (Python, C++)
  • are interested in applying new theories to heavy-element compounds

send me a CV and a description of their own research interests.

We also welcome applications from postdoctoral candidates with a background in theoretical chemistry and computational science who are interested in many-body electronic structure theory and the application of computer science tools to challenging electronic structure problems.

PhD Students

Stipend position

If you are interested in

  • developing new electronic structure methods that provide new insights into the chemistry and physics of heavy-element compounds
  • applying conventional and unconventional theories to quantum many-body systems
  • building efficient codes that can be used in large-scale quantum modeling

then please email me. I will ensure that you will learn about

  • electronic structures of molecules
  • object-oriented programming
  • applying the quantum-mechanical models we develop to challenging problems in chemistry and physics

Bachelor/Master Students

Semester/Master thesis projects

Are you curious about many-body electronic structure theory?

Would you like to learn more about conventional and unconventional electronic structure methods?

Are you interested in applying existing quantum-chemistry programs to challening problems in heavy-element chemistry, including the description of relativistic effects and the correlated motion of electrons?

If so, you are welcome to join our group. Please, contact me if you consider working on a research project or your Master thesis.

At My Office

You can find me at my office located at the Department of Quantum Physics, Institute of Physics, Nicolaus Copernicus University, room 480.

If I am not around, please, write me an email to fix an appointment.


  • Katharina Boguslawski

    Department of Quantum Physics

    Institute of Physics

    Faculty of Physics, Astronomy and Informatics

    Nicolaus Copernicus University in Torun

    ul. Grudziadzka 5/7

    87-100 Torun