Associate Professor
Nicolaus Copernicus University in Torun, Institute of Physics, Poland.
I am a theoretical chemist interested in quantum chemical modeling of challenging electronic structures of heavy elements. Specifically, my research focuses on the ground and electronically excited states of actinide atoms and molecules, and their properties. My research expertise covers the DMRG (Density Matrix Renormalization Group) algorithm, Fock space coupled cluster, the Ap1roG (Antisymmetric Product of 1-reference orbital Geminal) model, and the WFT-in-DFT embedding techniques, as well as their performance in heavy-element chemistry. Moreover, I am developing intuitive tools to interpret electronic structures and chemical phenomena using concepts of quantum information theory.
I am currently looking for Ph. D. students to work with me on method development and their efficient implementations.
Nicolaus Copernicus University in Torun, Institute of Physics, Poland.
Nicolaus Copernicus University in Torun, Institute of Physics, Poland.
Nicolaus Copernicus University in Torun, Institute of Physics, Poland.
Nicolaus Copernicus University in Torun, Institute of Physics, Poland.
Nicolaus Copernicus University in Torun, Institute of Physics, Poland.
Nicolaus Copernicus University in Torun, Faculty of Chemistry, Poland.
McMaster University, Department of Chemistry and Chemical Biology, Canada
ETH Zurich, Laboratory of Physical Chemistry, Switzerland
Habilitation in Physics
Institute of Physics NCU Torun, Faculty of Physics, Astronomy and Informatics NCU Torun, Poland
Ph.D. in Chemistry
Division of Theoretical Chemistry, Department of Chemistry and Pharmaceutical Sciences, VU Amsterdam, The Netherlands
Thesis: Towards reliable modeling of excited states of uranium compounds
Master of Science in Chemistry
Bachelor of Science in Chemometrics
My research focuses on the modeling of electronic structures of heavy elements using quantum chemical methods varying from density functional theory, through coupled cluster-type methods, up to tensor network-based approaches. My primary interest is the reliable description of excited states of actinide species. I also use my experience in electronic structure theory to support experimental colleagues in determining and validating spectroscopic parameters of "cold molecules". Moreover, I am developing interpretative tools based on quantum entanglement to better understand orbital interactions and correlation effects in complex molecular systems.
A detailed description of my research interests can be found below.
My main research focus is aimed at reliable modeling of electronically excited states of actinide compounds. Specifically, I carefully assess the accuracy of time-dependent density functional theory by benchmarking it against more accurate wave function approaches for small model systems, like, the equation of motion coupled cluster and the Fock-space coupled cluster methods. Furthermore, I use this experience to model excited states of larger realistic actinide complexes with time-dependent density functional theory and hybrid approaches, like, wave function theory in density functional theory (WFT-in-DFT). Finally, I also evaluate the accuracy and reliability of relativistic models commonly used in quantum chemistry.
Selected key publications:
A reliable description of electron correlation effects in heavy-element chemistry often requires a multi-reference treatment of a large number of electrons and orbitals. In some cases, standard electron correlation approaches, like the complete active space self-consistent field theory, are not flexible enough to comprise all important orbitals for a given molecule in the active space. In such situations, the DMRG algorithm, which uses a compact and efficient parametrization of the wavefunction and can, therefore, handle much more orbitals in the active space, becomes advantageous.
Selected key publications:
I am working on an accurate description of the ground and electronically excite state potential energy surfaces of some weakly bonded diatomic molecules that are of importance in cold and ultra-cold experiments. This includes coupled cluster studies on the RbYb and Yb_{2} molecules, their optimal bond lengths and potential depths. Besides, I am involved in a number of small projects related to atomic and molecular spectroscopy that are of relevance for the "cold chemistry" community.
Selected key publications:
I am also involved in the development of new electron correlation models based on two-electron functions, called geminals. Specifically, we use the AP1roG (Antisymmetric Product of 1-reference orbital Geminal) ansatz to capture strong electron correlation effects. Its accuracy is assessed in various model systems and small heavy-element compounds.
Selected key publications:
My last research topic covers the development of new interpretative tools to analyze electronic structures. Specifically, together with Dr K. Boguslawski and Prof. Örs Legeza, we use concepts of quantum information theory to dissect electron correlation effects, determine bond orders, and monitor reaction pathways in various multi-reference systems.
Selected key publications:
In this paper, we scrutinize the ability of seniority-zero wave function-based methods to model different types of noncovalent interactions, such as hydrogen bonds, dispersion, and mixed noncovalent interactions as well as prototypical model systems with various contributions of dynamic and static electron correlation effects. Specifically, we focus on the pair Coupled Cluster Doubles (pCCD) ansatz combined with two different flavors of dynamic energy corrections, (i) based on a perturbation theory correction and (ii) on a linearized coupled cluster ansatz on top of pCCD. We benchmark these approaches against the A24 data set [Řezáč and Hobza J. Chem. Theory Comput. 2013, 9, 2151−2155.] extrapolated to the basis set limit and some model noncovalent complexes that feature covalent bond breaking. By dissecting different types of interactions in the A24 data set within the Symmetry-Adapted Perturbation Theory (SAPT) framework, we demonstrate that pCCD can be classified as a dispersion-free method. Furthermore, we found that both flavors of post-pCCD approaches represent encouraging and computationally more efficient alternatives to standard electronic structure methods to model weakly bound systems, resulting in small statistical errors. Finally, a linearized coupled cluster correction on top of pCCD proved to be most reliable for the majority of investigated systems, featuring smaller nonparallelity errors compared to perturbation-theory-based approaches.
Wave functions restricted to electron-pair states are promising models to describe static/nondynamic electron correlation effects encountered, for instance, in bond-dissociation processes and transition-metal and actinide chemistry. To reach spectroscopic accuracy, however, the missing dynamic electron correlation effects that cannot be described by electron-pair states need to be included a posteriori. In this Article, we extend the previously presented perturbation theory models with an Antisymmetric Product of 1-reference orbital Geminal (AP1roG) reference function that allows us to describe both static/ nondynamic and dynamic electron correlation effects. Specifically, our perturbation theory models combine a diagonal and off- diagonal zero-order Hamiltonian, a single-reference and multireference dual state, and different excitation operators used to construct the projection manifold. We benchmark all proposed models as well as an a posteriori Linearized Coupled Cluster correction on top of AP1roG against CR-CC(2,3) reference data for reaction energies of several closed-shell molecules that are extrapolated to the basis set limit. Moreover, we test the performance of our new methods for multiple bond breaking processes in the homonuclear N_{2}, C_{2}, and F_{2} dimers as well as the heteronuclear BN, CO, and CN+ dimers against MRCI-SD, MRCI-SD+Q, and CR-CC(2,3) reference data. Our numerical results indicate that the best performance is obtained from a Linearized Coupled Cluster correction as well as second-order perturbation theory corrections employing a diagonal and off- diagonal zero-order Hamiltonian and a single-determinant dual state. These dynamic corrections on top of AP1roG provide substantial improvements for binding energies and spectroscopic properties obtained with the AP1roG approach, while allowing us to approach chemical accuracy for reaction energies involving closed-shell species.
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.
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.
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 H_{2}, the automerization process of cyclobutadiene, the stability of the monocyclic form of pyridyne, and the aromatic stability of benzene.
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 C_{2} and LiF molecules, for the CH_{2} 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.
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 H_{50} hydrogen chain.
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.
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.
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.
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.
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)
Summer Student (TAPS program), Institute of Physics, NCU in Torun, Poland.
Project title: Quantum chemical description of spectroscopic parameters of actinide cation-cation interaction-driven complexes
Publication: in preparation
Summer Student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
Project title: Cation-cation interactions in actinides
Publication: Phys. Chem. Chem. Phys. 18, 18305-18311 (2016)
Summer Student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
Project title: Thermochemistry of actinide compounds
Publication: Phys. Chem. Chem. Phys. 18, 4317-4329 (2017)
Bachelor Student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
Project title: Dissecting the intermolecular interactions between uranyl cations
Co-op student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
Project title: Electronic structure of iridium complexes
Publication: RSC Adv. 5, 84311–84320 (2015)
Summer Student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
Project title: Metal–olefin bonding in Ni-ethylene complexes
Publication: Chem. Phys. Lett. 621, 160-164 (2015)
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: Phys. Chem. Chem. Phys. 16 (19), 8872-8880 (2014)
Master Student, Division of Theoretical Chemistry, Department of Chemistry and Pharmaceutical Sciences, VU Amsterdam, The Netherlands
Project title: Fock-space coupled cluster study of the halogen halides and halide dimers
Master Student, Division of Theoretical Chemistry, Department of Chemistry and Pharmaceutical Sciences, VU Amsterdam, The Netherlands
Project title: Electronic spectroscopy of the CUO molecule in noble gas matrices
Publication: J. Chem. Phys. 137 (8), 084308 (2012)
Tutor
Introduction to quantum chemistry.
Introduction to statistical thermodynamics.
Programming course for chemists.
Programming course for chemists.
Programming course for chemists.
Introduction to Quantum Chemistry.
• Prof. Piotr Żuchowski, Institute of Physics, Nicolaus Copernicus University in Torun, Toruń, Poland
• Dr. Dariusz Kędziera, Faculty of Chemistry, Nicolaus Copernicus University in Torun, Toruń, Poland
• Dr. Mateusz Borkowski, Institute of Physics, Nicolaus Copernicus University in Torun, Toruń, Poland
• Prof. Valerie Vallet, CNRS, Universite Lille, Lille, France
• Dr. Andre Severo Pereira Gomes, CNRS, Universite Lille, Lille, France
• Dr. Florent Real, CNRS, Universite Lille, Lille, France
• Prof. Örs Legeza, Wigner Research Center for Physics, Budapest, Hungary
• Dr. Gergely Barcza, Wigner Research Center for Physics, Budapest, Hungary
• Prof. Paul W. Ayers, Departement of CHemistry and Chemical Biology, McMaster University, Hamilton, Canada
• Prof. Dimitri Van Neck, Center for Molecular Modeling, Ghent University, Ghent, Belgium
• Dr. Stijn De Beardemacker, Center for Molecular Modeling, Ghent University, Ghent, Belgium
• Dr. Toon Verstraelen, Center for Molecular Modeling, Ghent University, Ghent, Belgium
Research funded from the POLONEZ fellowship program of the National Science Center (Poland), no. 2015/19/P/ST4/02480. This project had received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Składowska-Curie grant agreement No 665778.
• Int. J. Quantum Chem. e25983 (2019)
We present a comprehensive theoretical study of the electronic structures of the Yb atom and the Yb_{2}2 molecule, respectively, focusing on their ground and lowest-lying electronically excited states. Our study includes various state-of-the-art quantum chemistry methods such as CCSD, CCSD(T), CASPT2 (including spin-orbit coupling), and EOM-CCSD as well as some recently developed pCCD-based approaches and their extensions to target excited states. Specifically, we scan the lowest-lying poten- tial energy surfaces of the Yb_{2} dimer and provide a reliable benchmark set of spectro- scopic parameters including optimal bond lengths, vibrational frequencies, potential energy depths, and adiabatic excitation energies. Our in-depth analysis unravels the complex nature of the electronic spectrum of Yb_{2}, which is difficult to model accu- rately by any conventional quantum chemistry method. Finally, we scrutinize the bi-excited character of the first ^{1}Σ^{+}_{g} excited state and its evolution along the potential energy surface.
• J. Chem. Theory Comput. 15, 4021-4035 (2019)
In this paper, we scrutinize the ability of seniority-zero wave function-based methods to model different types of noncovalent interactions, such as hydrogen bonds, dispersion, and mixed noncovalent interactions as well as prototypical model systems with various contributions of dynamic and static electron correlation effects. Specifically, we focus on the pair Coupled Cluster Doubles (pCCD) ansatz combined with two different flavors of dynamic energy corrections, (i) based on a perturbation theory correction and (ii) on a linearized coupled cluster ansatz on top of pCCD. We benchmark these approaches against the A24 data set [Řezáč and Hobza J. Chem. Theory Comput. 2013, 9, 2151−2155.] extrapolated to the basis set limit and some model noncovalent complexes that feature covalent bond breaking. By dissecting different types of interactions in the A24 data set within the Symmetry-Adapted Perturbation Theory (SAPT) framework, we demonstrate that pCCD can be classified as a dispersion-free method. Furthermore, we found that both flavors of post-pCCD approaches represent encouraging and computationally more efficient alternatives to standard electronic structure methods to model weakly bound systems, resulting in small statistical errors. Finally, a linearized coupled cluster correction on top of pCCD proved to be most reliable for the majority of investigated systems, featuring smaller nonparallelity errors compared to perturbation-theory-based approaches.
• Phys. Chem. Chem. Phys. 21, 19039-19053 (2019)
We scrutinize the performance of different variants of equation of motion coupled cluster (EOM-CC) methods to predict electronic excitation energies and excited state potential energy surfaces in closed- shell actinide species. We focus our analysis on various recently presented pair coupled cluster doubles (pCCD) models [J. Chem. Phys., 2016, 23, 234105 and J. Chem. Theory Comput., 2019, 15, 18–24] and compare their performance to the conventional EOM-CCSD approach and to the completely renormalized EOM-CCSD with perturbative triples ansatz. Since the single-reference pCCD model allows us to efficiently describe static/nondynamic electron correlation, while dynamical electron correlation is accounted for a posteriori, the investigated pCCD-based methods represent a good compromise between accuracy and computational cost. Such a feature is particularly advantageous when modelling electronic structures of actinide-containing compounds with stretched bonds. Our work demonstrates that EOM-pCCD-based methods reliably predict electronic spectra of small actinide building blocks containing thorium, uranium, and protactinium atoms. Specifically, the standard errors in adiabatic and vertical excitation energies obtained by the conventional EOM-CCSD approach are reduced by a factor of 2 when employing the EOM-pCCD-LCCSD variant resulting in a mean error of 0.05 eV and a standard deviation of 0.25 eV.
• Phys. Chem. Chem. Phys. 21, 744-759 (2019)
Understanding the binding mechanism in neptunyl clusters formed due to cation–cation interactions is of crucial importance in nuclear waste reprocessing and related areas of research. Since experimental manipulations with such species are often rather limited, we have to rely on quantum-chemical predictions of their electronic structures and spectroscopic parameters. In this work, we present a state- of-the-art quantum chemical study of the T-shaped and diamond-shaped neptunyl(V) and neptunyl(VI) dimers. Specifically, we scrutinize their molecular structures, (implicit and explicit) solvation effects, the interplay of static and dynamical correlation, and the influence of spin–orbit coupling on the ground state and lowest-lying excited states for different total spin states and total charges of the neptunyl dications. Furthermore, we use the picture of interacting orbitals (quantum entanglement and correlation analysis) to identify strongly correlated orbitals in the cation–cation complexes that should be included in complete active space calculations. Most importantly, our study highlights the complex interplay of correlation effects and relativistic corrections in the description of the ground and lowest- lying excited states of neptunyl dications.
This chapter discusses contemporary quantum chemical methods and provides general insights into modern electronic structure theory with a focus on heavy-element-containing compounds. We first give a short overview of relativistic Hamiltonians that are frequently applied to account for relativistic effects. Then, we scrutinize various quantum chemistry methods that approximate the N-electron wave function. In this respect, we will review the most popular single- and multi-reference approaches that have been developed to model the multi-reference nature of heavy element compounds and their ground- and excited-state electronic structures. Specifically, we introduce various flavors of post-Hartree–Fock methods and optimization schemes like the complete active space self-consistent field method, the configuration interaction approach, the Fock-space coupled cluster model, the pair-coupled cluster doubles ansatz, also known as the antisymmetric product of 1 reference orbital geminal, and the density matrix renormalization group algorithm. Furthermore, we will illustrate how concepts of quantum information theory provide us with a qualitative understanding of complex electronic structures using the picture of interacting orbitals. While modern quantum chemistry facilitates a quantitative description of atoms and molecules as well as their properties, concepts of quantum information theory offer new strategies for a qualitative interpretation that can shed new light onto the chemistry of complex molecular compounds.
• Phys. Chem. Chem. Phys. 20, 23424-23432 (2018)
We present a comprehensive relativistic coupled cluster study of the electronic structures of the ThO and ThS molecules in the spinor basis. Specifically, we use the single-reference coupled cluster and the multi-reference Fock Space Coupled Cluster (FSCC) methods to model their ground and electronically- excited states. Two variants of the FSCC method have been investigated: (a) one where the electronic spectrum is obtained from sector (1,1) of the Fock space, and (b) another where the excited states come from the doubly attached electronic states to the doubly charged systems (ThO^{2+} and ThS^{2+}), that is, from sector (0,2) of the Fock space. Our study provides a reliable set of spectroscopic parameters such as bond lengths, excitation energies, and vibrational frequencies, as well as a detailed analysis of the electron correlation effects in the ThO and ThS molecules. Finally, we examine the first ionization potential and electron affinity of the above mentioned molecules.
If you have any questions, feel free to contact me.
Prof. Paweł Tecmer
Institute of Physics
Faculty of Physics, Astronomy and Informatics
ul. Grudziadzka 5/7
87-100 Torun
Poland
ptecmer"at"gmail.com
ptecmer"at"fizyka.umk.pl
You can find me at my office located at the Institute of Physics, Nicolaus Copernicus University in Torun, room 557B.
If I am not around, please, write me an email to fix an appointment.