Stanislav Komorovsky - Academia.edu (original) (raw)

Papers by Stanislav Komorovsky

Research paper thumbnail of The four-component DFT method for the calculation of the EPR g-tensor using a restricted magnetically balanced basis and London atomic orbitals

The Journal of Chemical Physics

Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so fa... more Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so far been based on a common gauge origin and a restricted kinetically balanced basis. The results of such calculations are prone to exhibit a dependence on the choice of the gauge origin for the vector potential associated with uniform magnetic field and a related dependence on the basis set quality. In this work, this gauge problem is addressed by a distributed-origin scheme based on the London atomic orbitals, also called gauge-including atomic orbitals (GIAOs), which have proven to be a practical approach for calculations of other magnetic properties. Furthermore, in the four-component relativistic domain, it has previously been shown that a restricted magnetically balanced (RMB) basis for the small component of the four-component wavefunctions is necessary for achieving robust convergence with regard to the basis set size. We present the implementation of a four-component density functi...

Research paper thumbnail of Relativistic Spin–Orbit Electronegativity and the Chemical Bond Between a Heavy Atom and a Light Atom

Chemistry – A European Journal, 2022

Relativistic effects are known to alter the chemical bonds and spectroscopic properties of heavy-... more Relativistic effects are known to alter the chemical bonds and spectroscopic properties of heavy-element compounds. In this work, we introduce the concept of spin-orbit (SO) electronegativity of a heavy atom as reflected by an SO-induced change in the interatomic distance between the heavy atom (HA) and a neighboring light atom (LA). We provide a transparent interpretation of these SO effects by using the concept of spin-orbit electron deformation density (SO-EDD). Spin-orbit coupling at the HA induces rearrangement of the electron density for the scalar-relativistically optimized geometry that in turn exerts a new force on the LA. The resulting expansion or contraction of the HA-LA bond depends on the nature and electron configuration of the HA. In addition, we quantify the change in atomic electronegativity induced by SO coupling for a series of hydrides, complementing the SO-EDD picture. The trends in the SO-induced electronegativity and the HA-LA bond distance across the Periodic Table of Elements are demonstrated and interpreted, and also linked, intuitively, with the SO-induced NMR shielding at the LA.

Research paper thumbnail of CCDC 1465352: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1465350: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1465349: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1465348: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1465347: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1544885: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory

Inorganic Chemistry, 2021

The simulation of X-ray absorption spectra requires both scalar and spin−orbit (SO) relativistic ... more The simulation of X-ray absorption spectra requires both scalar and spin−orbit (SO) relativistic effects to be taken into account, particularly near Land M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac−Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L 2,3and M 4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange−correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee−Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L 2,3-edge X-ray absorption spectra of [RuCl 2 (DMSO) 2 (Im) 2 ] and [WCl 4 (PMePh 2) 2 ], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.

Research paper thumbnail of Determination of the orbital and paramagnetic contributions to the 1H and 13C NMR chemical shifts of ruthenium(III) complexes

The paramagnetic NMR (pNMR) spectroscopy is becoming crucially important in many areas of researc... more The paramagnetic NMR (pNMR) spectroscopy is becoming crucially important in many areas of research despite the fact that unpaired electrons affect the NMR chemical-shift tensors, the isotropic NMR chemical shifts, and indirect nuclear spin-spin coupling constants [1]. Therefore the resonance frequencies for paramagnetic species lie typically out of the standard chemical-shift ranges for their diamagnetic analogs and the NMR signals are significantly broadened. The observed total NMR chemical shift can be decomposed into temperature-independent orbital term and temperature-dependent paramagnetic term [2]. In this study, the orbital and paramagnetic contributions to the NMR chemical shifts were determined experimentally from the 1H and 13C NMR measurements at various temperatures for a series of ruthenium(III) complexes - Ru(X-acac)3 and Ru(dbm)3 (X = H, Br, Me, NO2; acac = acetylacetonate; dbmH = dibenzoylmethane). The relativistic DFT calculations (two-component SO-ZORA and four-com...

Research paper thumbnail of Hyperfine effects on the 13C NMR chemical shifts in Ru(III) compounds

A series of Ru(III) complexes with 2-substituted beta-diketones was synthesized and analyzed usin... more A series of Ru(III) complexes with 2-substituted beta-diketones was synthesized and analyzed using 1H and 13C NMR spectroscopy. The NMR spectra recorded at several temperatures were used to construct Curie plots and estimate the temperature-independent (orbital) and temperature-dependent (hyperfine) contributions to the NMR shift. Relativistic DFT calculations of electron paramagnetic resonance and NMR parameters were performed to interpret the experimental observations. The effects of individual factors such as basis set, density functional, exact-exchange admixture, and relativity were analyzed and discussed.

Research paper thumbnail of Crystal and Substituent Effects on Paramagnetic NMR Shifts in Transition-Metal Complexes

Inorganic Chemistry, 2021

Nuclear magnetic resonance (NMR) spectroscopy of paramagnetic molecules provides detailed informa... more Nuclear magnetic resonance (NMR) spectroscopy of paramagnetic molecules provides detailed information about their molecular and electron-spin structure. The paramagnetic NMR spectrum is a very rich source of information about the hyperfine interaction between the atomic nuclei and the unpaired electron density. The Fermi-contact contribution to ligand hyperfine NMR shifts is particularly informative about the nature of the metal-ligand bonding and the structural arrangements of the ligands coordinated to the metal center. In this account, we provide a detailed experimental and theoretical NMR study of compounds of Cr(III) and Cu(II) coordinated with substituted acetylacetonate (acac) ligands in the solid state. For the first time, we report the experimental observation of extremely paramagnetically deshielded 13C NMR resonances for these compounds in the range of 900-1200 ppm. We demonstrate an excellent agreement between the experimental NMR shifts and those calculated using relativistic density-functional theory. Crystal packing is shown to significantly influence the NMR shifts in the solid state, as demonstrated by theoretical calculations of various supramolecular clusters. The resonances are assigned to individual atoms in octahedral Cr(acac)3 and square-planar Cu(acac)2 compounds and interpreted by different electron configurations and magnetizations at the central metal atoms resulting in different spin delocalizations and polarizations of the ligand atoms. Further, effects of substituents on the 13C NMR resonance of the ipso carbon atom reaching almost 700 ppm for Cr(acac)3 compounds are interpreted based on the analysis of Fermi-contact hyperfine contributions.

Research paper thumbnail of ReSpect: Relativistic spectroscopy DFT program package

The Journal of Chemical Physics, 2020

Note: This article is part of the JCP Special Topic on Electronic Structure Software.

Research paper thumbnail of Linking the Character of Metal-Ligand Bond to the Ligand NMR Shielding in Transition-Metal Complexes: NMR Contributions from Spin-Orbit Coupling

Journal of chemical theory and computation, Jan 6, 2017

Relativistic effects significantly affect various spectroscopic properties of compounds containin... more Relativistic effects significantly affect various spectroscopic properties of compounds containing heavy elements. Particularly in Nuclear Magnetic Resonance (NMR) spectroscopy, the heavy atoms strongly influence the NMR shielding constants of neighboring light atoms. In this account we analyze paramagnetic contributions to NMR shielding constants and their modulation by relativistic spin-orbit effects in a series of transition-metal complexes of Pt(II), Au(I), Au(III), and Hg(II). We show how the paramagnetic NMR shielding and spin-orbit effects relate to the character of metal-ligand (M‒L) bond. A correlation between the (back)-donation character of the M‒L bond in d10 Au(I) complexes and the propagation of the spin-orbit (SO) effects from M to L through the M‒L bond influencing the ligand NMR shielding via Fermi-contact mechanism is found and rationalized by using third-order perturbation theory. The SO effects on the ligand NMR shielding are demonstrated to be driven by both the...

Research paper thumbnail of New quantum number for the many-electron Dirac-Coulomb Hamiltonian

Physical Review A, 2016

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences wa... more By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator K+, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator K, the K 2 + has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that K+ is connected to K through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call K+ the generator of the many-electron TR symmetry. By diagonalizing the operator K 2 + in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with K 2 + has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree-Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

Research paper thumbnail of Acceleration of Relativistic Electron Dynamics by Means of X2C Transformation: Application to the Calculation of Nonlinear Optical Properties

Journal of Chemical Theory and Computation, 2016

The Liouville-von Neumann equation based on the four-component matrix Dirac-Kohn-Sham Hamiltonian... more The Liouville-von Neumann equation based on the four-component matrix Dirac-Kohn-Sham Hamiltonian is transformed to a quasirelativistic exact two-component (X2C) form, and then used to solve the time evolution of the electronic states only. By this means, a significant acceleration by a factor of seven or more has been achieved. The transformation of the original four-component equation of motion is formulated entirely in matrix algebra, following closely the X2C decoupling procedure of Ilias and Saue [J. Chem. Phys. 126, 064102 (2007)]

Research paper thumbnail of Interpreting the Paramagnetic NMR Spectra of Potential Ru(III) Metallodrugs: Synergy between Experiment and Relativistic DFT Calculations

Journal of the American Chemical Society, Jul 5, 2016

Ruthenium-based compounds are potential candidates for use as anticancer metallodrugs. The centra... more Ruthenium-based compounds are potential candidates for use as anticancer metallodrugs. The central ruthenium atom can be in the oxidation state +2 (e.g., RAPTA, RAED) or +3 (e.g., NAMI, KP). In this study we focus on paramagnetic NAMI analogs of a general structure [4-R-pyH](+)trans-[Ru(III)Cl4(DMSO)(4-R-py)](-), where 4-R-py stands for a 4-substituted pyridine. As paramagnetic systems are generally considered difficult to characterize in detail by NMR spectroscopy, we performed a systematic structural and methodological NMR study of complexes containing variously substituted pyridines. The effect of the paramagnetic nature of these complexes on the (1)H and (13)C NMR chemical shifts was systematically investigated by temperature-dependent NMR experiments and density-functional theory (DFT) calculations. To understand the electronic factors influencing the orbital (δ(orb), temperature-independent) and paramagnetic (δ(para), temperature-dependent) contributions to the total NMR chemi...

Research paper thumbnail of Structure, solvent, and relativistic effects on the NMR chemical shifts in square-planar transition-metal complexes: assessment of DFT approaches

Physical Chemistry Chemical Physics, 2015

The role of various factors (geometry, solvent, relativistic treatment, functional) influencing t... more The role of various factors (geometry, solvent, relativistic treatment, functional) influencing the relativistic NMR chemical shift calculations for square-planar transition-metal complexes.

Research paper thumbnail of Exact two-component TDDFT with simple two-electron picture-change corrections: X-ray absorption spectra near L- and M-edges of four-component quality at two-component cost

Cornell University - arXiv, Nov 29, 2022

X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter wit... more X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivity. However, the theoretical modelling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped-response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchangecorrelation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on Land M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimatation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modelling XAS. 1 Introduction X-ray absorption spectroscopy (XAS) provides local information about molecular geometry and electronic structure with high elemental specificity due to the energy separation of core levels in different elements. 1 XAS spectra are conventionally divided into X-ray absorption fine structure (NEXAFS), also known as X-ray absorption near-edge structure

Research paper thumbnail of Relativistic Heavy-Neighbor-Atom Effects on NMR Shifts: Concepts and Trends Across the Periodic Table

Chemical Reviews

Chemical shifts present crucial information about an NMR spectrum. They show the influence of the... more Chemical shifts present crucial information about an NMR spectrum. They show the influence of the chemical environment on the nuclei being probed. Relativistic effects caused by the presence of an atom of a heavy element in a compound can appreciably, even drastically, alter the NMR shifts of the nearby nuclei. A fundamental understanding of such relativistic effects on NMR shifts is important in many branches of chemical and physical science. This review provides a comprehensive overview of the tools, concepts, and periodic trends pertaining to the shielding effects by a neighboring heavy atom in diamagnetic systems, with particular emphasis on the "spin-orbit heavy-atom effect on the light-atom" NMR shift (SO-HALA effect). The analyses and tools described in this review provide guidelines to help NMR spectroscopists and computational chemists estimate the ranges of the NMR shifts for an unknown compound, identify intermediates in catalytic and other processes, analyze conformational aspects and intermolecular interactions, and predict trends in series of compounds throughout the Periodic Table. The present review provides a current snapshot of this important subfield of NMR spectroscopy and a basis and framework for including future findings in the field.

Research paper thumbnail of The four-component DFT method for the calculation of the EPR g-tensor using a restricted magnetically balanced basis and London atomic orbitals

The Journal of Chemical Physics

Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so fa... more Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so far been based on a common gauge origin and a restricted kinetically balanced basis. The results of such calculations are prone to exhibit a dependence on the choice of the gauge origin for the vector potential associated with uniform magnetic field and a related dependence on the basis set quality. In this work, this gauge problem is addressed by a distributed-origin scheme based on the London atomic orbitals, also called gauge-including atomic orbitals (GIAOs), which have proven to be a practical approach for calculations of other magnetic properties. Furthermore, in the four-component relativistic domain, it has previously been shown that a restricted magnetically balanced (RMB) basis for the small component of the four-component wavefunctions is necessary for achieving robust convergence with regard to the basis set size. We present the implementation of a four-component density functi...

Research paper thumbnail of Relativistic Spin–Orbit Electronegativity and the Chemical Bond Between a Heavy Atom and a Light Atom

Chemistry – A European Journal, 2022

Relativistic effects are known to alter the chemical bonds and spectroscopic properties of heavy-... more Relativistic effects are known to alter the chemical bonds and spectroscopic properties of heavy-element compounds. In this work, we introduce the concept of spin-orbit (SO) electronegativity of a heavy atom as reflected by an SO-induced change in the interatomic distance between the heavy atom (HA) and a neighboring light atom (LA). We provide a transparent interpretation of these SO effects by using the concept of spin-orbit electron deformation density (SO-EDD). Spin-orbit coupling at the HA induces rearrangement of the electron density for the scalar-relativistically optimized geometry that in turn exerts a new force on the LA. The resulting expansion or contraction of the HA-LA bond depends on the nature and electron configuration of the HA. In addition, we quantify the change in atomic electronegativity induced by SO coupling for a series of hydrides, complementing the SO-EDD picture. The trends in the SO-induced electronegativity and the HA-LA bond distance across the Periodic Table of Elements are demonstrated and interpreted, and also linked, intuitively, with the SO-induced NMR shielding at the LA.

Research paper thumbnail of CCDC 1465352: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1465350: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1465349: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1465348: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1465347: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of CCDC 1544885: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Research paper thumbnail of Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory

Inorganic Chemistry, 2021

The simulation of X-ray absorption spectra requires both scalar and spin−orbit (SO) relativistic ... more The simulation of X-ray absorption spectra requires both scalar and spin−orbit (SO) relativistic effects to be taken into account, particularly near Land M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac−Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L 2,3and M 4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange−correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee−Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L 2,3-edge X-ray absorption spectra of [RuCl 2 (DMSO) 2 (Im) 2 ] and [WCl 4 (PMePh 2) 2 ], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.

Research paper thumbnail of Determination of the orbital and paramagnetic contributions to the 1H and 13C NMR chemical shifts of ruthenium(III) complexes

The paramagnetic NMR (pNMR) spectroscopy is becoming crucially important in many areas of researc... more The paramagnetic NMR (pNMR) spectroscopy is becoming crucially important in many areas of research despite the fact that unpaired electrons affect the NMR chemical-shift tensors, the isotropic NMR chemical shifts, and indirect nuclear spin-spin coupling constants [1]. Therefore the resonance frequencies for paramagnetic species lie typically out of the standard chemical-shift ranges for their diamagnetic analogs and the NMR signals are significantly broadened. The observed total NMR chemical shift can be decomposed into temperature-independent orbital term and temperature-dependent paramagnetic term [2]. In this study, the orbital and paramagnetic contributions to the NMR chemical shifts were determined experimentally from the 1H and 13C NMR measurements at various temperatures for a series of ruthenium(III) complexes - Ru(X-acac)3 and Ru(dbm)3 (X = H, Br, Me, NO2; acac = acetylacetonate; dbmH = dibenzoylmethane). The relativistic DFT calculations (two-component SO-ZORA and four-com...

Research paper thumbnail of Hyperfine effects on the 13C NMR chemical shifts in Ru(III) compounds

A series of Ru(III) complexes with 2-substituted beta-diketones was synthesized and analyzed usin... more A series of Ru(III) complexes with 2-substituted beta-diketones was synthesized and analyzed using 1H and 13C NMR spectroscopy. The NMR spectra recorded at several temperatures were used to construct Curie plots and estimate the temperature-independent (orbital) and temperature-dependent (hyperfine) contributions to the NMR shift. Relativistic DFT calculations of electron paramagnetic resonance and NMR parameters were performed to interpret the experimental observations. The effects of individual factors such as basis set, density functional, exact-exchange admixture, and relativity were analyzed and discussed.

Research paper thumbnail of Crystal and Substituent Effects on Paramagnetic NMR Shifts in Transition-Metal Complexes

Inorganic Chemistry, 2021

Nuclear magnetic resonance (NMR) spectroscopy of paramagnetic molecules provides detailed informa... more Nuclear magnetic resonance (NMR) spectroscopy of paramagnetic molecules provides detailed information about their molecular and electron-spin structure. The paramagnetic NMR spectrum is a very rich source of information about the hyperfine interaction between the atomic nuclei and the unpaired electron density. The Fermi-contact contribution to ligand hyperfine NMR shifts is particularly informative about the nature of the metal-ligand bonding and the structural arrangements of the ligands coordinated to the metal center. In this account, we provide a detailed experimental and theoretical NMR study of compounds of Cr(III) and Cu(II) coordinated with substituted acetylacetonate (acac) ligands in the solid state. For the first time, we report the experimental observation of extremely paramagnetically deshielded 13C NMR resonances for these compounds in the range of 900-1200 ppm. We demonstrate an excellent agreement between the experimental NMR shifts and those calculated using relativistic density-functional theory. Crystal packing is shown to significantly influence the NMR shifts in the solid state, as demonstrated by theoretical calculations of various supramolecular clusters. The resonances are assigned to individual atoms in octahedral Cr(acac)3 and square-planar Cu(acac)2 compounds and interpreted by different electron configurations and magnetizations at the central metal atoms resulting in different spin delocalizations and polarizations of the ligand atoms. Further, effects of substituents on the 13C NMR resonance of the ipso carbon atom reaching almost 700 ppm for Cr(acac)3 compounds are interpreted based on the analysis of Fermi-contact hyperfine contributions.

Research paper thumbnail of ReSpect: Relativistic spectroscopy DFT program package

The Journal of Chemical Physics, 2020

Note: This article is part of the JCP Special Topic on Electronic Structure Software.

Research paper thumbnail of Linking the Character of Metal-Ligand Bond to the Ligand NMR Shielding in Transition-Metal Complexes: NMR Contributions from Spin-Orbit Coupling

Journal of chemical theory and computation, Jan 6, 2017

Relativistic effects significantly affect various spectroscopic properties of compounds containin... more Relativistic effects significantly affect various spectroscopic properties of compounds containing heavy elements. Particularly in Nuclear Magnetic Resonance (NMR) spectroscopy, the heavy atoms strongly influence the NMR shielding constants of neighboring light atoms. In this account we analyze paramagnetic contributions to NMR shielding constants and their modulation by relativistic spin-orbit effects in a series of transition-metal complexes of Pt(II), Au(I), Au(III), and Hg(II). We show how the paramagnetic NMR shielding and spin-orbit effects relate to the character of metal-ligand (M‒L) bond. A correlation between the (back)-donation character of the M‒L bond in d10 Au(I) complexes and the propagation of the spin-orbit (SO) effects from M to L through the M‒L bond influencing the ligand NMR shielding via Fermi-contact mechanism is found and rationalized by using third-order perturbation theory. The SO effects on the ligand NMR shielding are demonstrated to be driven by both the...

Research paper thumbnail of New quantum number for the many-electron Dirac-Coulomb Hamiltonian

Physical Review A, 2016

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences wa... more By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator K+, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator K, the K 2 + has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that K+ is connected to K through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call K+ the generator of the many-electron TR symmetry. By diagonalizing the operator K 2 + in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with K 2 + has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree-Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

Research paper thumbnail of Acceleration of Relativistic Electron Dynamics by Means of X2C Transformation: Application to the Calculation of Nonlinear Optical Properties

Journal of Chemical Theory and Computation, 2016

The Liouville-von Neumann equation based on the four-component matrix Dirac-Kohn-Sham Hamiltonian... more The Liouville-von Neumann equation based on the four-component matrix Dirac-Kohn-Sham Hamiltonian is transformed to a quasirelativistic exact two-component (X2C) form, and then used to solve the time evolution of the electronic states only. By this means, a significant acceleration by a factor of seven or more has been achieved. The transformation of the original four-component equation of motion is formulated entirely in matrix algebra, following closely the X2C decoupling procedure of Ilias and Saue [J. Chem. Phys. 126, 064102 (2007)]

Research paper thumbnail of Interpreting the Paramagnetic NMR Spectra of Potential Ru(III) Metallodrugs: Synergy between Experiment and Relativistic DFT Calculations

Journal of the American Chemical Society, Jul 5, 2016

Ruthenium-based compounds are potential candidates for use as anticancer metallodrugs. The centra... more Ruthenium-based compounds are potential candidates for use as anticancer metallodrugs. The central ruthenium atom can be in the oxidation state +2 (e.g., RAPTA, RAED) or +3 (e.g., NAMI, KP). In this study we focus on paramagnetic NAMI analogs of a general structure [4-R-pyH](+)trans-[Ru(III)Cl4(DMSO)(4-R-py)](-), where 4-R-py stands for a 4-substituted pyridine. As paramagnetic systems are generally considered difficult to characterize in detail by NMR spectroscopy, we performed a systematic structural and methodological NMR study of complexes containing variously substituted pyridines. The effect of the paramagnetic nature of these complexes on the (1)H and (13)C NMR chemical shifts was systematically investigated by temperature-dependent NMR experiments and density-functional theory (DFT) calculations. To understand the electronic factors influencing the orbital (δ(orb), temperature-independent) and paramagnetic (δ(para), temperature-dependent) contributions to the total NMR chemi...

Research paper thumbnail of Structure, solvent, and relativistic effects on the NMR chemical shifts in square-planar transition-metal complexes: assessment of DFT approaches

Physical Chemistry Chemical Physics, 2015

The role of various factors (geometry, solvent, relativistic treatment, functional) influencing t... more The role of various factors (geometry, solvent, relativistic treatment, functional) influencing the relativistic NMR chemical shift calculations for square-planar transition-metal complexes.

Research paper thumbnail of Exact two-component TDDFT with simple two-electron picture-change corrections: X-ray absorption spectra near L- and M-edges of four-component quality at two-component cost

Cornell University - arXiv, Nov 29, 2022

X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter wit... more X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivity. However, the theoretical modelling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped-response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchangecorrelation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on Land M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimatation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modelling XAS. 1 Introduction X-ray absorption spectroscopy (XAS) provides local information about molecular geometry and electronic structure with high elemental specificity due to the energy separation of core levels in different elements. 1 XAS spectra are conventionally divided into X-ray absorption fine structure (NEXAFS), also known as X-ray absorption near-edge structure

Research paper thumbnail of Relativistic Heavy-Neighbor-Atom Effects on NMR Shifts: Concepts and Trends Across the Periodic Table

Chemical Reviews

Chemical shifts present crucial information about an NMR spectrum. They show the influence of the... more Chemical shifts present crucial information about an NMR spectrum. They show the influence of the chemical environment on the nuclei being probed. Relativistic effects caused by the presence of an atom of a heavy element in a compound can appreciably, even drastically, alter the NMR shifts of the nearby nuclei. A fundamental understanding of such relativistic effects on NMR shifts is important in many branches of chemical and physical science. This review provides a comprehensive overview of the tools, concepts, and periodic trends pertaining to the shielding effects by a neighboring heavy atom in diamagnetic systems, with particular emphasis on the "spin-orbit heavy-atom effect on the light-atom" NMR shift (SO-HALA effect). The analyses and tools described in this review provide guidelines to help NMR spectroscopists and computational chemists estimate the ranges of the NMR shifts for an unknown compound, identify intermediates in catalytic and other processes, analyze conformational aspects and intermolecular interactions, and predict trends in series of compounds throughout the Periodic Table. The present review provides a current snapshot of this important subfield of NMR spectroscopy and a basis and framework for including future findings in the field.