arXiv subjects

Paweł Tecmer

Publications and source records attributed to Paweł Tecmer.

32 records · Page 2Linked to original sources

arXiv2020

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

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.

physics.chem-ph↗

arXiv2020

Benchmarking the accuracy of seniority-zero wavefunction methods for non-covalent interactions

In this paper, we scrutinize the ability of seniority-zero wavefunction-based methods to model different types of non-covalent interactions, such as hydrogen bonds, dispersion, and mixed non-covalent 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 flavours 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 [Řez{á}{č} and Hobza, J.~Chem.~Theory~Comput., 9, 2151-2155 (2013)] extrapolated to the basis set limit and some model non-covalent 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 flavours 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 non-parallelity errors compared to perturbation-theory-based approaches.

physics.chem-ph↗

arXiv2020

Electron correlation effects of the ThO and ThS molecules in the spinor basis. A relativistic coupled cluster study of ground and excited states properties

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.

physics.chem-ph↗

arXiv2020

Assessing the accuracy of simplified Coupled Cluster methods for electronic excited states in f0 actinide compounds

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., 23, 234105 (2016) and J.~Chem.~Theory~Comput. 15, 18--24 (2019)] 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 \textit{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.

physics.chem-ph↗

arXiv2017

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

Wavefunctions 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 \textit{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 allow 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 multi-reference dual state, and different excitation operators used to construct the projection manifold. We benchmark all proposed models as well as an \textit{a posteriori} linearized coupled cluster correction on top of AP1roG against CR-CCSD(T) 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 N$_2$, C$_2$, and BN dimers against MRCI-SD and MRCI-SD+Q 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 allow us to reliably model molecular systems dominated by static/nondynamic as well as dynamic electron correlation.

physics.chem-ph↗

arXiv2016

Orbital entanglement in quantum chemistry

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.

physics.chem-ph↗

arXiv2016

On the Multi-Reference Nature of Plutonium Oxides: PuO$_2^{2+}$, PuO$_2$, PuO$_3$ and PuO$_2$(OH)$_2$

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 (PuO$_3$ and PuO$_2$(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.

physics.chem-ph↗

arXiv2016

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

Wavefunctions 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 wavefunctions restricted to electron-pair states. We focus on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG) method combined with an orbital optimization protocol presented in [Phys. Rev. B, 89, 201106(R), 2014] whose performance is assessed against electronic structures obtained form DMRG reference data. Our numerical analysis covers model systems for strong correlation: the one-dimensional Hubbard model with periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of 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 AP1roG method. Furthermore, we examine the effect of orbital rotations within the AP1roG model on correlations between orbital pairs.

cond-mat.str-el↗

arXiv2015

Dissecting the Bond Formation Process of $d^{10}$-Metal-Ethene Complexes with Multireference Approaches

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.

cond-mat.str-el↗

arXiv2014

A quantum informational approach for dissecting chemical reactions

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.

physics.chem-ph↗

arXiv2014

Efficient description of strongly correlated electrons with mean-field cost

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. %which is based on orbital optimization of electron pairs. The performance of our approach is illustrated for the one-dimensional Hubbard model with periodic boundary conditions for different chain lengths, and for the non-relativistic quantum chemical Hamiltonian exploring the symmetric dissociation of the H$_{50}$ hydrogen chain.

cond-mat.str-el↗

arXiv2014

Projected seniority-two orbital optimization of the Antisymmetric Product of one-reference orbital Geminal

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 [J. Chem. Phys., 135, 044119 (2011)]. A numerical analysis is performed for the C$_2$, LiF and CH$_2$ molecules 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.

cond-mat.str-el↗

arXiv2013

Scattering lengths in isotopologues of the RbYb system

We model the binding energies of rovibrational levels of the RbYb molecule using experimental data from two-color photoassociation spectroscopy in mixtures of ultracold $^{87}$Rb with various Yb isotopes. The model uses a theoretical potential based on state-of-the-art \emph{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 $-\infty$ to $+\infty$. For example, the $^{87}$Rb$^{174}$Yb system is characterized by a large positive scattering length of $+880(120)$~a.u., while $^{87}$Rb$^{173}$Yb has $a=-626(88)$~a.u.. On the other hand $^{87}$Rb$^{170}$Yb has a very small scattering length of $-14.5(1.8)$~a.u. confirmed by the pair's extremely low thermalization rate. For isotopic combinations including $^{85}$Rb the variation of the interspecies scattering lengths is much smoother ranging from $+39.0(1.6)$ a.u. for $^{85}$Rb$^{176}$Yb to $+230(10)$ a.u. in the case of $^{85}$Rb$^{168}$Yb. 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 $C_6$=2837(13)~a.u. and is in agreement and more precise than the current state-of-the-art theoretical predictions (S. G. Porsev, M. S. Safronova, A. Derevianko, and C.W. Clark, arXiv:1307.2654 (2013)).

physics.atom-ph↗

arXiv2012

Entanglement Measures for Single- and Multi-Reference Correlation Effects

Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference 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 multi-reference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.

quant-ph↗