Working Experience

Honors, Awards, and Grants

  • 2020
    Research grant OPUS (2020-2023)
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    Title: Towards a reliable and efficient description of electron correlation effects in large molecules: embedding pCCD-type methods
    OPUS funding scheme
  • 2016
    Research grant SONATA 11 (2017-2020)
  • 2016
    Research grant POLONEZ 1 (2017-2019)
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    Title: Elucidating electronic structures and atomic and molecular properties across the actinide series, POLONEZ funding scheme
  • 2016
    Computing Grant from the Wroclaw Centre for Networking and Supercomputing (2016-present)
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    WCSS grant No. 411 (01.2016-present).
  • 2015
    France-Canada Research Fund (2015-2017)
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    Travel grant for "Novel theoretical approaches to the electronic structure of actinid compounds" together with the group of Prof. Valerie Vallet.
  • 2013
    OPUS (07.2013-06.2017)
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    Research grant for "Precise quantum chemistry calculations and dynamics of ultracold molecules" together with Dr. Dariusz Kędziera and Dr. hab. Piotr Żuchowski.
  • 2011
    The Pacific Northwest National Laboratory Alternate Sponsored Fellowship (ASF) (05.2011)
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Research Projects

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Mixed uranyl and neptunyl cation–cation interaction-driven clusters: structures, energetic stability, and nuclear quadrupole interactions

P Tecmer, F Schindler, A Leszczyk, K Boguslawski
Journal Paper Phys. Chem. Chem. Phys. 22, 10845-10852 (2020)

Abstract

We present a state-of-the-art quantum chemical study of mixed cation–cation interaction (CCI) driven complexes composed of uranyl and neptunyl units. Specifically, we consider the stability of the D-shaped and T-shaped structural rearrangements in CCIs, various oxidation states of the uranium and neptunium atom (V and VI), as well as a different number of unpaired electrons. Furthermore, we scrutinize the nuclear quadrupole interactions of the bare actinyl subunits and the most stable mixed CCI clusters. The electric field gradients (and nuclear quadrupole coupling constants) of neptunyls are reported for the first time. The characteristic features of the nuclear quadrupole interactions for the bare neptunyl ions are very similar to those predicted for uranyls. When the CCI clusters are formed, a considerable asymmetry is introduced compared to the bare actinyl cations. Most importantly, we are able to distinguish different types of CCIs with respect to their structural arrangement and their total charge by analyzing the electric field gradients at the uranium and neptunium nuclei.

Modeling the Electronic Structures of the Ground and Excited States of the Ytterbium atom and the Ytterbium dimer: A Modern Quantum Chemistry Perspective

P Tecmer, K Boguslawski, M Borkowski, PS Żuchowski, and D Kędziera
Journal Paper Int. J. Quantum Chem. e25983 (2019)

Abstract

We present a comprehensive theoretical study of the electronic structures of the Yb atom and the Yb22 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 Yb2 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 Yb2, which is difficult to model accu- rately by any conventional quantum chemistry method. Finally, we scrutinize the bi-excited character of the first 1Σ+g excited state and its evolution along the potential energy surface.

Benchmarking the Accuracy of Seniority-Zero Wave Function Methods for Noncovalent Interactions

F Brzęk, K Boguslawski, P Tecmer, and PS Żuchowski
Journal Paper J. Chem. Theory Comput. 15, 4021-4035 (2019)

Abstract

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.

Assessing the Accuracy of Simplified Coupled Cluster Methods for Electronic Excited States in f0 Sctinide Compounds

A Nowak P Tecmer, and K Boguslawski
Journal Paper Phys. Chem. Chem. Phys. 21, 19039-19053 (2019)

Abstract

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.

Elucidating Cation-Cation Interactions in Neptunyl Dications using Multi-Reference Ab Initio Theory

A Łachmańska P Tecmer, Ö Legeza, and K Boguslawski
Journal Paper Phys. Chem. Chem. Phys. 21, 744-759 (2019)

Abstract

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.

New Strategies in Modeling Electronic Structures and Properties with Applications to Actinide

A. Leszczyk, P Tecmer, and K Boguslawski
Book Chapters Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 29), title: Transition Metals in Coordination Chemistry pp. 121-160 (2019)

Abstract

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.

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Electron Correlation Effects of the ThO and ThS Molecules in the Spinor Basis. A relativistic Coupled Cluster Study of Ground and Excited States Properties

P Tecmer and CE Gonzalez-Espinoza
Journal Paper Phys. Chem. Chem. Phys. 20, 23424-23432 (2018)

Abstract

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 (ThO2+ and ThS2+), 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.

Benchmark of dynamic electron correlation models for seniority-zero wavefunctions and their application to thermochemistry

K Boguslawski, and P Tecmer
Journal Paper J. Chem. Theory Comput. 13, 5966-5983 (2017)

Abstract

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 N2, C2, and F2 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.

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

K Boguslawski, F Réal, P Tecmer, C Duperrouzel, ASP Gomes, Ö egeza, PW Ayers, V Vallet
Journal Paper Phys. Chem. Chem. Phys. 19, 4317-4329 (2017)

Abstract

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.

Analysis of Two-Orbital Correlations in Wave Functions Restricted to Electron-Pair States

Katharina Boguslawski, P Tecmer, O Legeza
Journal PaperPhys. Rev. B, 94, 155126 (2016)

Abstract

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, Sung W. Hong, and K Boguslawski
Journal PaperPhys. Chem. Chem. Phys., 18, 18305-18311 (2016)

Abstract

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 those of the uranyl(VI) and uranyl(V) clusters are presented for the first time. Our theoretical study elucidates the impact of cation–cation interactions on changes in the 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 Methods in Computational Quantum Chemistry

P Tecmer, K Boguslawski, and D Kędziera
Book Chapter Handbook of Computational Chemistry, pp. 885-926, Springer (2017)

Abstract

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 non-symmetric 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.

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)

Abstract

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)

Abstract

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)

Abstract

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.

Singlet Ground State Actinide Chemistry with Geminals

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

Abstract

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)

Abstract

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)

Abstract

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.

Communication: Relativistic Fock-Space Coupled Cluster Study of Small Building Blocks of Larger Uranium Complexes

P Tecmer, ASP Gomes, S Knecht, L Visscher
Journal PaperThe Journal of Chemical Physics 141 (4), 041107 (2014)

Abstract

We present a study of the electronic structure of the [UO2]+, [UO2]2+, [UO2]3+, NUO, [NUO]+, [NUO]2+, [NUN]-, NUN, and [NUN]+ molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin–orbit coupling and Gaunt interactions are compared to results obtained with the Dirac–Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity).

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)

Abstract

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.

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)

Abstract

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)

Abstract

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)

Abstract

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)

Abstract

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.

Scattering Lengths in Isotopologues of the RbYb System

M Borkowski, PS Żuchowski, R Ciuryło, PS Julienne, D Kędziera, Ł Mentel, P Tecmer, F Münchow, C Bruni, A Görlitz
Journal PaperPhysical Review A 88 (5), 052708 (2013)

Abstract

We model the binding energies of rovibrational levels of the RbYb molecule using experimental data from two-color photoassociation spectroscopy in mixtures of ultracold 87Rb with various Yb isotopes. The model uses a theoretical potential based on state-of-the-art ab initio potentials, further improved by least-squares fitting to the experimental data. We have fixed the number of bound states supported by the potential curve, so that the model is mass scaled, that is, it accurately describes the bound-state energies for all measured isotopic combinations. Such a model enables an accurate prediction of the s-wave scattering lengths of all isotopic combinations of the RbYb system. The reduced mass range is broad enough to cover the full scattering lengths range from −∞ to +∞. For example, the 87Rb147Yb system is characterized by a large positive scattering length of +880(120) a.u., while 87Rb173Yb has a=−626(88) a.u. On the other hand 87Rb170Yb has a very small scattering length of −11.5(2.5) a.u. confirmed by the pair's extremely low thermalization rate. For isotopic combinations including 85Rb the variation of the interspecies scattering lengths is much smoother ranging from +39.0(1.6) a.u. for 85Rb176Yb to +230(12) a.u. in the case of 85Rb168Yb. Hyperfine corrections to these scattering lengths are also given. We further complement the fitted potential with interaction parameters calculated from alternative methods. The recommended value of the van der Waals coefficient is C6=2837(13) a.u. agrees with but is more precise than the current state-of-the-art theoretical predictions [M. S. Safronova, S. G. Porsev, and C. W. Clark, Phys. Rev. Lett. 109, 230802 (2012)].

Reliable Modeling of the Electronic Spectra of Realistic Uranium Complexes

P Tecmer, N Govind, K Kowalski, WA De Jong, L Visscher
Journal PaperThe Journal of Chemical Physics 139 (3), 034301 (2013)

Abstract

We present an EOMCCSD (equation of motion coupled cluster with singles and doubles) study of excited states of the small [UO2]2+ and [UO2]+ model systems as well as the larger UVIO2(saldien) complex. In addition, the triples contribution within the EOMCCSDT and CR-EOMCCSD(T) (completely renormalized EOMCCSD with non-iterative triples) approaches for the [UO2]2+ and [UO2]+ systems as well as the active-space variant of the CR-EOMCCSD(T) method—CR-EOMCCSd(t)—for the UVIO2(saldien) molecule are investigated. The coupled cluster data were employed as benchmark to choose the "best" appropriate exchange–correlation functional for subsequent time-dependent density functional (TD-DFT) studies on the transition energies for closed-shell species. Furthermore, the influence of the saldien ligands on the electronic structure and excitation energies of the [UO2]+ molecule is discussed. The electronic excitations as well as their oscillator dipole strengths modeled with TD-DFT approach using the CAM-B3LYP exchange–correlation functional for the [UVO2(saldien)]− with explicit inclusion of two dimethyl sulfoxide molecules are in good agreement with the experimental data of Takao et al. [Inorg. Chem. 49, 2349 (Year: 2010) 10.1021/ic902225f].

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)

Abstract

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.

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)

Abstract

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.

Towards Reliable Modeling of Excited States of Uranium Compounds

P Tecmer
Thesis PhD Thesis, (2012)

The Electronic Spectrum of CUONg4 (Ng= Ne, Ar, Kr, Xe): New Insights in the Interaction of the CUO Molecule with Noble Gas Matrices

P Tecmer, H Van Lingen, ASP Gomes, L Visscher
Journal PaperThe Journal of Chemical Physics 137 (8), 084308 (2012)

Abstract

The electronic spectrum of the CUO molecule was investigated with the IHFSCC-SD (intermediate Hamiltonian Fock-space coupled cluster with singles and doubles) method and with TD-DFT (time-dependent density functional theory) employing the PBE and PBE0 exchange–correlation functionals. The importance of both spin–orbit coupling and correlation effects on the low-lying excited-states of this molecule are analyzed and discussed. Noble gas matrix effects on the energy ordering and vibrational frequencies of the lowest electronic states of the CUO molecule were investigated with density functional theory(DFT) and TD-DFT in a supermolecular as well as a frozen density embedding (FDE) subsystem approach. This data is used to test the suitability of the FDE approach to model the influence of different matrices on the vertical electronic transitions of this molecule. The most suitable potential was chosen to perform relativistic wave functiontheory in density functional theory calculations to study the vertical electronic spectra of the CUO and CUONg4 with the IHFSCC-SD method.

Charge-Transfer Excitations in Uranyl Tetrachloride ([UO2Cl4]2-): How Reliable are Electronic Spectra from Relativistic Time-Dependent Density Functional Theory?

P Tecmer, R Bast, K Ruud, L Visscher
Journal PaperThe Journal of Physical Chemistry A 116 (27), 7397-7404 (2012)

Abstract

Four-component relativistic time-dependent density functional theory (TD-DFT) is used to study charge-transfer (CT) excitation energies of the uranyl molecule as well as the uranyl tetrachloride complex. Adiabatic excitation energies and vibrational frequencies of the excited states are calculated for the lower energy range of the spectrum. The results for TD-DFT with the CAM-B3LYP exchange–correlation functional for the [UO2Cl4]2- system are in good agreement with the experimentally observed spectrum of this species and agree also rather well with other theoretical data. Use of the global hybrid B3LYP gives qualitatively correct results, while use of the BLYP functional yields results that are qualitatively wrong due to the too low CT states calculated with this functional. The applicability of the overlap diagnostic of Peach et al. (J. Chem. Phys. 2008, 128, 044118) to identify such CT excitations is investigated for a wide range of vertical transitions using results obtained with three different approximate exchange–correlation functionals: BLYP, B3LYP, and CAM-B3LYP.

Electronic Spectroscopy of UO22+, NUO+ and NUN: an Evaluation of Time-Dependent Density Functional Theory for Actinides

P Tecmer, AS Pereira Gomes, U Ekström, L Visscher
Journal PaperPhysical Chemistry Chemical Physics, 13, 6249-6259 (2011)

Abstract

The performance of the time-dependent density functional theory (TDDFT) approach has been evaluated for the electronic spectrum of the UO22+, NUO+ and NUN molecules. Different exchange–correlation functionals (LDA, PBE, BLYP, B3LYP, PBE0, M06, M06-L, M06-2X, CAM-B3LYP) and the SAOP model potential have been investigated, as has the relative importance of the adiabatic local density approximation (ALDA) to the exchange-correlation kernel. The vertical excitation energies have been compared with reference data obtained using accurate wave-function theory (WFT) methods.

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Supervision of Graduate Students (co-supervision)

  • 12.2015 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

  • 08.2019

    Frank Schindler

    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

  • 08.2015 05.2015

    Sung W Hong

    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)

  • 08.2015 05.2015

    Corinne Duperrouzel

    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)

  • 03.2015 09.2014

    Sung W Hong

    Bachelor Student, Department of Chemistry and Chemical Biology, McMaster University, Canada.
    Project title: Dissecting the intermolecular interactions between uranyl cations

  • 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 Adv. 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: Chem. Phys. Lett. 621, 160-164 (2015)

  • 04.2013 12.2013

    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: Phys. Chem. Chem. Phys. 16 (19), 8872-8880 (2014)

  • 09.2011 01.2012

    Anna Hehn

    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

  • 07.2011 10.2011

    Henk van Lingen

    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)

Teaching History

  • Fall 2018

    Theory for Many-Electron Systems, NCU Torun

    Tutor

  • Spring 2013

    Basic Quantum Chemistry, ETH Zurich

    Introduction to quantum chemistry.

  • Fall 2012

    Advanced Physical Chemistry, ETH Zurich

    Introduction to statistical thermodynamics.

  • Winter 2012

    C++ Programming, VU Amsterdam

    Programming course for chemists.

  • Winter 2011

    C++ Programming, VU Amsterdam

    Programming course for chemists.

  • Winter 2010

    C++ Programming, VU Amsterdam

    Programming course for chemists.

  • Winter 2009

    Quantum Chemistry, VU Amsterdam

    Introduction to Quantum Chemistry.

  • 2020
    103rd Canadian Chemistry Conference and Exhibition
    Title: TBA (May 24-28, 2020)
  • 2019
    Seminar at the Institute of Physics, Univeristy of Szczecin, Szczecin, Poland
    Title: Towards reliable modeling of electronic structures and spectroscopic parameters of actinide species (May 29, 2019)
  • 2018
    2018 ENM Meting on Computation and Theory, San Sebastian, Spain
    Title: Relativistic coupled cluster study of small actinide species. Ground and excited states properties (September 3-7, 2018)
  • 2018
    Departamental Seminar at the Wigner Research Centre for Physics, Budapest, Hungary
    Title: Unconventional electronic structure methods for actinides (June 5, 2018)
  • 2017
    2017 ENM Meting on Computation and Theory, Dubai, United Arab Emirates
    Title: New Insights into Molecular Interactions Using Concepts of Quantum Information Theory (November 6-11, 2017)
  • 2016
    2016 EMN Meeting on Computation and Theory, Las Vegas, USA
    Title: Towards reliable modeling of electronic structures and spectroscopic parameters of uranium oxides (October 10-14, 2016)
  • 2016
    Seminar "Coherence-Correlations-Complexity", Institute of Physics, Wroclaw University of Technology , Wroclaw, Poland
    Title: Two-electron functions as alternative models for strongly correlated systems (June 8, 2016)
  • 2015
    Pacifichem 2015, Honolulu, USA
    Title: Large scale modelling of strong electron correlation effects in extended systems from geminals (December 18, 2015)
  • 2015
    Pacifichem 2015, Honolulu, USA
    Title: Efficient description of electron correlation effects in actinide compounds, (December 16, 2015)
  • 2015
    Special Colloquium, Department of Quantum Mechanics, NCU, Toruń, Poland
    Title: Alternative approaches to model strongly correlated systems (September 9, 2015)
  • 2015
    Theoretical Chemistry Seminar at the VU University Amsterdam, Amsterdam, The Netherlands
    Title: Alternative approaches to model and interpret strongly correlated systems (May 27, 2015)
  • 2015
    Theoretical Chemistry Seminar at the PhLAM institute at the University of Lille, Lille, France
    Title: Breaking the course of dimension using two-electron functions (May 26, 2015)
  • 2014
    WATOC 2014 Satellite Meeting on Large Condensed and Biological Systems, Conceptión, Chile
    Title: Dissecting the mysterious interaction of uranium with noble gases (October 13, 2014)
  • 2014
    Meeting on New Approaches in Theoretical Chemistry, Santiago, Chile
    Title: Efficient description of strongly correlated electrons (October 3, 2014)
  • 2013
    Meeting on Methods for Modeling Molecules and Materials, Hamilton, Canada
    Title: Towards efficient description of strongly correlated electrons (December 17, 2013)
  • 2013
    Canada Days Workshop, Ghent, Belgium
    Title: Geminals — Past, Present and Future Perspectives (November 7, 2013)
  • 2012
    Theoretical Chemistry Seminar, ETH Zürich, Zürich, Switzerland
    Title: Electronic spectroscopy of uranium-containing complexes (March 27, 2012)

Cold and ultarcold molecules

Actinide-related projects

DMRG-related projects

Geminals-related projects (past)

Results of the project are listed below

  • Int. J. Quantum Chem. e25983 (2019)

    We present a comprehensive theoretical study of the electronic structures of the Yb atom and the Yb22 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 Yb2 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 Yb2, which is difficult to model accu- rately by any conventional quantum chemistry method. Finally, we scrutinize the bi-excited character of the first 1Σ+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.

  • Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 29), title: Transition Metals in Coordination Chemistry pp. 121-160 (2019)

    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 (ThO2+ and ThS2+), 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.

Correspondence

  • Prof. Paweł Tecmer

    Institute of Physics

    Faculty of Physics, Astronomy and Informatics

    Mountain View

    ul. Grudziadzka 5/7

    87-100 Torun

    Poland

  •    ptecmer"at"gmail.com

  •    ptecmer"at"fizyka.umk.pl

At My Office

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.