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Mihail Atanasov - One of the best experts on this subject based on the ideXlab platform.
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Improvement of Ab Initio Ligand Field Theory by Means of Multistate Perturbation Theory
The journal of physical chemistry. A, 2020Co-Authors: Lucas Lang, Mihail Atanasov, Frank NeeseAbstract:Over the last few years, ab initio Ligand Field Theory (AILFT) has evolved into an important tool for the extraction of Ligand Field models from ab initio calculations. The inclusion of dynamic correlation on top of complete active space self-consistent Field (CASSCF) reference functions, which is important for accurate results, was so far realized at the level of second-order N-electron valence state perturbation Theory (NEVPT2). In this work, we introduce two alternative methods for the inclusion of dynamic correlation into AILFT calculations, the second-order dynamic correlation dressed complete active space method (DCD-CAS(2)) and the Hermitian quasi-degenerate NEVPT2 (HQD-NEVPT2). These methods belong to the class of multistate perturbation Theory approaches, which allow for the mixing of CASSCF states under the effect of dynamic correlation (state-mixing). The two new versions of AILFT were tested for a diverse set of transition-metal complexes. It was found that the multistate methods have, compared to NEVPT2, an AILFT fit with smaller root mean square deviations (rmsds) between ab initio and AILFT energies. A comparison of AILFT excitation energies with the experiment shows that for some systems, the agreement gets better at the multistate level because of the smaller rmsds. However, for some systems, the agreement gets worse, which could be attributed to a cancellation of errors at the NEVPT2 level that is partly removed at the multistate level. An investigation of trends in the extracted Ligand Field parameters shows that at the multistate level, the Ligand Field splitting Δ gets larger, whereas the Racah parameters B and C get smaller and larger, respectively. An investigation of the reasons for the observed improvement for octahedral CrIII halide complexes shows that the possibility of state-mixing relaxes constraints that are present at the NEVPT2 level and that keep Δ and B from following their individual preferences.
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Ab Initio Ligand-Field Theory Analysis and Covalency Trends in Actinide and Lanthanide Free Ions and Octahedral Complexes.
Inorganic chemistry, 2017Co-Authors: Julie Jung, Mihail Atanasov, Frank NeeseAbstract:Actinide chemistry is gaining increased focus in modern research, particularly in the Fields of energy research and molecular magnetism. However, the structure–function and structure–property relationships of actinides have still not been studied as intensely as those for transition metals. In this work, we report a detailed ab initio study of the spectroscopic, magnetic, and bonding properties of the trivalent actinide free ions and their associated hexachloride complexes in octahedral symmetry. The electronic structures of these systems are examined using complete active-space self-consistent-Field calculations followed by second-order N-electron valence perturbation Theory, including both scalar relativistic and spin–orbit-coupling effects. The computed energies and wave functions are further analyzed by means of ab initio Ligand-Field Theory (AILFT) and finally chemically interpreted by means of the angular overlap model (AOM). The derived Slater–Condon and spin–orbit parameters have allowed us to sys...
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A Modern First-Principles View on Ligand Field Theory Through the Eyes of Correlated Multireference Wavefunctions
Structure and Bonding, 2011Co-Authors: Mihail Atanasov, Dmitry Ganyushin, Kantharuban Sivalingam, Frank NeeseAbstract:Recent developments in AI methods for strongly correlated electronic systems and their implementations in highly efficient quantum chemistry programs allow one to calculate – from first principles – the spectroscopic and magnetic properties of transition metal complexes with open d- and f-shells. For a long time, this Field was the domain of Ligand Field Theory (LFT), subject to various assumptions and approximations which are solely justified by the success of using this Theory for the interpretation of experimental data. Yet the chemical significance of the Ligand Field parameters, while being under intense debate, remains unclear as far as the roots of LFT in its relation to rigorous quantum chemistry are concerned. In the present review, we attempt to answer the question how well Ligand Field Theory performs from the point of view of state-of-art first principle calculations and how to connect the two areas. To achieve this goal, energies of electronic states originating from d n configurations of spectroscopically and structurally well-documented complexes of 3d metals from complete active space self-consistent Field (CASSCF) wavefunctions and their improved energy eigenvalues from N-electron valence perturbation Theory (NEVPT2) have been analyzed employing various Ligand Field parameterization schemes. Case studies include classical coordination compounds such as octahedral CrX 6 3− and tetrahedral CrX4 complexes (X = F, Cl, Br, I), distorted tetrahedral to square planar CuCl 4 2− complexes and the distorted pseudotetrahedral NiCl 4 2− . In addition, bis and tris-chelate complexes of NiII, and MIII = Cr, Mn, respectively [Ni(L-L)2, L-L = ethyldithiocarbamate (Et2dtc−), 2,2,6,6-tetramethylheptane-3,5-dionato (DPM−), pentane-2,4 dionato (acac−), and M(acac)3 (MIII = Cr, Mn), all complex Ligands possessing π-conjugate electronic systems] have been included in the analysis. Values of 10Dq, the energy difference between the e- and t 2-type orbitals in octahedral or tetrahedral complexes, identified as the energy of the first spin-allowed transition, in for example, octahedral CrIII and NiII complexes, and the angular overlap parameters for σ and π metal 3d–Ligand interactions (e σ and e π ) for CrX 6 3− and CrX4 (X− = F, Cl, Br, I) compare nicely with their counterparts deduced from a fit to experimental d–d spectra. The expected variations of these parameters embodied in the well-known orderings of Ligands, according to the spectrochemical series and two-dimensional maps accounting for the Ligand σ- and π-functions toward the metal 3d orbitals (quantified by the parameters e σ and e π ) are reasonably well reproduced and hence also justified by AI Theory. In addition, the parameters of the covalently reduced d–d interelectronic repulsion B and C (the nephelauxetic series) are also well reproduced from a fit of these parameters to AI data, more specifically to NEVPT2 results. Being able to reproduce the AI data for all multiplets of a given d n -complex using only three to four parameters, we conclude from these studies that the CASSCF and NEVPT2 AI methods and classical LFT are remarkably well compatible. A procedure of obtaining Ligand Field parameters from AI data described in this work opens the unique possibility to analyze numerical data from AI calculations. In turn, comparison between Ligand Field parameters, deduced from AI data and, independently, from available high-resolution electronic d–d absorption spectra can stimulate the validation and further development of multireference AI Theory. Using this approach, the effects of π-bonding (in Ni(L-L)2, L = Et2dtc, acac, DPM and Cr(acac)3) and the interplay between π-bonding and Jahn–Teller coupling in the case of Mn(acac)3 on their optical spectra and the magnetic anisotropy (the zero-Field splitting tensor) as studied by EPR spectroscopy are discussed. Finally optically detected transitions between the Zeeman levels of Cr(acac)3 and Mn(acac)3 have been analyzed in detail.
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Theoretical studies on the electronic properties and the chemical bonding of transition metal complexes using dft and Ligand Field Theory
CHIMIA International Journal for Chemistry, 2005Co-Authors: Mihail Atanasov, Claude A. DaulAbstract:The research activity within our laboratory of computational chemistry at the University of Fribourg is presented. In this review, a brief outline of a recently proposed Ligand Field Density Functional Theory (LFDFT) model for single nuclear and its extension to dimer transition metal complexes is given. Applications of the model to dinuclear complexes are illustrated for the interpretation of exchange coupling in the bis-μ-hydroxo-bridged dimer of Cu(II) and to the description of the quadruple metal-metal bond in Re 2 Cl 8 2 - . The analysis of the chemical bonding is compared with results obtained using other approaches, i.e. the Extended Transition State model and the Electron Localization Function. It is shown that the DFT supported Ligand Field Theory provides consistent description of the ground and excited state properties of transition metal complexes.
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A DFT Based Ligand Field Theory
Structure and Bonding, 2004Co-Authors: Mihail Atanasov, Claude Daul, Cédrick RauzyAbstract:A general and user-oriented Ligand Field (LF) Theory – LFDFT with parameters adjusted to DFT energies of separate Slater Determinants (SD) of the partly filled dn shell [n=2(8), 3(7), 4(6) and 5] of transition metals (TM) complexes – is developed and tested using 22 well documented examples from the literature. These include CrIII, d3 and CoII d7 in octahedral and CrIV, MnV, FeVI d2, CoII d7, MnII d5, NiII d8 in tetrahedral complexes for which reliable values of d-d transition energies available from high-resolute Ligand Field spectra of complexes with halogenide (F, Cl, Br and I), oxide and cyanide Ligands have been reported. The formalism has been implemented and consists of three steps allowing provision of geometries, Ligand Field Kohn-Sham orbitals and SD-energies in a way consistent with the LF phenomenology. In a fourth step LF parameters are utilized to yield multiplet energies using a full CI LF program. Comparing SD energies from DFT with those calculated using the LF parameter values, we can state for all considered cases, that the LF parameterization scheme is remarkably compatible with SD energies from DFT; standard deviations between DFT SD-energies and their LFDFT values being calculated between 0.016 and 0.124 eV. We find that, when based on the average of configuration with n/5 occupancy of each MO dominated by TM d-orbitals and on geometries with metal-Ligand bond lengths from experiment, the 10Dq parameter values (cubic symmetry) are very close to the ones obtained from a fit to reported Ligand Field transitions. In contrast, when using common functionals such as LDA or gradient corrected ones (GGA) we find that the parameters B and C deduced from a fit to the SD energies are systematically lower than experimental. Thus spin-forbidden transitions which are particularly sensitive to B and C are calculated to be by 2000 to 3000 cm–1 at lower energies compared to experiment. Based on DFT and experimental B and C values we propose scaling factors, which allow one to improve the agreement between DFT and experimental transition energies, or alternatively to develop a DFT Theory based on effective LF functionals and/or basis sets. Using a thorough analysis of the dependence of the Kohn-Sham orbital energy on the orbital occupation numbers, following Slater Theory, we propose a general LFDFT scheme allowing one to treat, within the same formalism low symmetric Ligand Fields as well. Test examples, which illustrate the efficiency of this approach, include Cs distorted CrO44– and D2d distorted MnO43– chromophores. Finally, for cubic LF we propose a hybrid LFDFT model (HLFDFT) which leads to an improvement of the existing DFT-multiplet theories. We show, taking low-spin Co(CN)63– as an example, that the new model yields better results as compared to time-depending DFT (TDDFT). A discussion of the LFDFT method in the context of other CI-DFT approaches is given.
Frank Neese - One of the best experts on this subject based on the ideXlab platform.
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Improvement of Ab Initio Ligand Field Theory by Means of Multistate Perturbation Theory
The journal of physical chemistry. A, 2020Co-Authors: Lucas Lang, Mihail Atanasov, Frank NeeseAbstract:Over the last few years, ab initio Ligand Field Theory (AILFT) has evolved into an important tool for the extraction of Ligand Field models from ab initio calculations. The inclusion of dynamic correlation on top of complete active space self-consistent Field (CASSCF) reference functions, which is important for accurate results, was so far realized at the level of second-order N-electron valence state perturbation Theory (NEVPT2). In this work, we introduce two alternative methods for the inclusion of dynamic correlation into AILFT calculations, the second-order dynamic correlation dressed complete active space method (DCD-CAS(2)) and the Hermitian quasi-degenerate NEVPT2 (HQD-NEVPT2). These methods belong to the class of multistate perturbation Theory approaches, which allow for the mixing of CASSCF states under the effect of dynamic correlation (state-mixing). The two new versions of AILFT were tested for a diverse set of transition-metal complexes. It was found that the multistate methods have, compared to NEVPT2, an AILFT fit with smaller root mean square deviations (rmsds) between ab initio and AILFT energies. A comparison of AILFT excitation energies with the experiment shows that for some systems, the agreement gets better at the multistate level because of the smaller rmsds. However, for some systems, the agreement gets worse, which could be attributed to a cancellation of errors at the NEVPT2 level that is partly removed at the multistate level. An investigation of trends in the extracted Ligand Field parameters shows that at the multistate level, the Ligand Field splitting Δ gets larger, whereas the Racah parameters B and C get smaller and larger, respectively. An investigation of the reasons for the observed improvement for octahedral CrIII halide complexes shows that the possibility of state-mixing relaxes constraints that are present at the NEVPT2 level and that keep Δ and B from following their individual preferences.
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Ab Initio Ligand-Field Theory Analysis and Covalency Trends in Actinide and Lanthanide Free Ions and Octahedral Complexes.
Inorganic chemistry, 2017Co-Authors: Julie Jung, Mihail Atanasov, Frank NeeseAbstract:Actinide chemistry is gaining increased focus in modern research, particularly in the Fields of energy research and molecular magnetism. However, the structure–function and structure–property relationships of actinides have still not been studied as intensely as those for transition metals. In this work, we report a detailed ab initio study of the spectroscopic, magnetic, and bonding properties of the trivalent actinide free ions and their associated hexachloride complexes in octahedral symmetry. The electronic structures of these systems are examined using complete active-space self-consistent-Field calculations followed by second-order N-electron valence perturbation Theory, including both scalar relativistic and spin–orbit-coupling effects. The computed energies and wave functions are further analyzed by means of ab initio Ligand-Field Theory (AILFT) and finally chemically interpreted by means of the angular overlap model (AOM). The derived Slater–Condon and spin–orbit parameters have allowed us to sys...
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Introduction to Ligand Field Theory
Practical Approaches to Biological Inorganic Chemistry, 2013Co-Authors: Frank NeeseAbstract:Ligand Field Theory is a conerstone of modern coordination chemistry. Ligand Field Theory creates a simple, yet effctive and pictorial language in which a multitude of properties of coordination complexes can be succesfully accounted for. In this chapter an elementary and non-mathematical introduction to Ligand Field Theory is provided which is aimed at a non-expert audience with mainly experimental background. The chapter stresses important fundamental concepts and proceeds to the stage where comparison between Theory and experiment is possible.
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A Modern First-Principles View on Ligand Field Theory Through the Eyes of Correlated Multireference Wavefunctions
Structure and Bonding, 2011Co-Authors: Mihail Atanasov, Dmitry Ganyushin, Kantharuban Sivalingam, Frank NeeseAbstract:Recent developments in AI methods for strongly correlated electronic systems and their implementations in highly efficient quantum chemistry programs allow one to calculate – from first principles – the spectroscopic and magnetic properties of transition metal complexes with open d- and f-shells. For a long time, this Field was the domain of Ligand Field Theory (LFT), subject to various assumptions and approximations which are solely justified by the success of using this Theory for the interpretation of experimental data. Yet the chemical significance of the Ligand Field parameters, while being under intense debate, remains unclear as far as the roots of LFT in its relation to rigorous quantum chemistry are concerned. In the present review, we attempt to answer the question how well Ligand Field Theory performs from the point of view of state-of-art first principle calculations and how to connect the two areas. To achieve this goal, energies of electronic states originating from d n configurations of spectroscopically and structurally well-documented complexes of 3d metals from complete active space self-consistent Field (CASSCF) wavefunctions and their improved energy eigenvalues from N-electron valence perturbation Theory (NEVPT2) have been analyzed employing various Ligand Field parameterization schemes. Case studies include classical coordination compounds such as octahedral CrX 6 3− and tetrahedral CrX4 complexes (X = F, Cl, Br, I), distorted tetrahedral to square planar CuCl 4 2− complexes and the distorted pseudotetrahedral NiCl 4 2− . In addition, bis and tris-chelate complexes of NiII, and MIII = Cr, Mn, respectively [Ni(L-L)2, L-L = ethyldithiocarbamate (Et2dtc−), 2,2,6,6-tetramethylheptane-3,5-dionato (DPM−), pentane-2,4 dionato (acac−), and M(acac)3 (MIII = Cr, Mn), all complex Ligands possessing π-conjugate electronic systems] have been included in the analysis. Values of 10Dq, the energy difference between the e- and t 2-type orbitals in octahedral or tetrahedral complexes, identified as the energy of the first spin-allowed transition, in for example, octahedral CrIII and NiII complexes, and the angular overlap parameters for σ and π metal 3d–Ligand interactions (e σ and e π ) for CrX 6 3− and CrX4 (X− = F, Cl, Br, I) compare nicely with their counterparts deduced from a fit to experimental d–d spectra. The expected variations of these parameters embodied in the well-known orderings of Ligands, according to the spectrochemical series and two-dimensional maps accounting for the Ligand σ- and π-functions toward the metal 3d orbitals (quantified by the parameters e σ and e π ) are reasonably well reproduced and hence also justified by AI Theory. In addition, the parameters of the covalently reduced d–d interelectronic repulsion B and C (the nephelauxetic series) are also well reproduced from a fit of these parameters to AI data, more specifically to NEVPT2 results. Being able to reproduce the AI data for all multiplets of a given d n -complex using only three to four parameters, we conclude from these studies that the CASSCF and NEVPT2 AI methods and classical LFT are remarkably well compatible. A procedure of obtaining Ligand Field parameters from AI data described in this work opens the unique possibility to analyze numerical data from AI calculations. In turn, comparison between Ligand Field parameters, deduced from AI data and, independently, from available high-resolution electronic d–d absorption spectra can stimulate the validation and further development of multireference AI Theory. Using this approach, the effects of π-bonding (in Ni(L-L)2, L = Et2dtc, acac, DPM and Cr(acac)3) and the interplay between π-bonding and Jahn–Teller coupling in the case of Mn(acac)3 on their optical spectra and the magnetic anisotropy (the zero-Field splitting tensor) as studied by EPR spectroscopy are discussed. Finally optically detected transitions between the Zeeman levels of Cr(acac)3 and Mn(acac)3 have been analyzed in detail.
Claude Daul - One of the best experts on this subject based on the ideXlab platform.
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A Ligand Field Theory-based methodology for the characterization of the Eu2+ [Xe]4f65d1 excited states in solid state compounds
Chemical Physics Letters, 2015Co-Authors: Amador García-fuente, Fanica Cimpoesu, Harry Ramanantoanina, Benjamin Herden, Claude Daul, Markus Suta, Claudia Wickleder, Werner UrlandAbstract:Abstract The theoretical rationalization of the open-shell 4f and 5d configuration of Eu 2+ is by far not trivial because it involves a non-standard version of Ligand Field Theory, based on a two-shell Hamiltonian. Here we present our methodology based on Ligand Field Theory, taking the system CsCaBr 3 :Eu 2+ as a case study with an octahedral coordination sphere of Eu 2+ . The Ligand Field, interelectronic and spin-orbit coupling parameters are deduced from experimental data. The assignment of the transitions to the corresponding irreducible representations of the double group was performed together with the intensity modelling resulting in an excellent match to the experimental spectra.
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Non-empirical Prediction of the Photophysical and Magnetic Properties of Systems with Open d- and f-Shells Based on Combined Ligand Field and Density Functional Theory (LFDFT).
Chimia, 2014Co-Authors: Claude DaulAbstract:Despite the important growth of ab initio and computational techniques, Ligand Field Theory in molecular science or crystal Field Theory in condensed matter offers the most intuitive way to calculate multiplet energy levels arising from systems with open shells d and/or f electrons. Over the past decade we have developed a Ligand Field treatment of inorganic molecular modelling taking advantage of the dominant localization of the frontier orbitals within the metal-sphere. This feature, which is observed in any inorganic coordination compound, especially if treated by Density Functional Theory calculation, allows the determination of the electronic structure and properties with a surprising good accuracy. In Ligand Field Theory, the theoretical concepts consider only a single atom center; and treat its interaction with the chemical environment essentially as a perturbation. Therefore success in the simple Ligand Field Theory is no longer questionable, while the more accurate molecular orbital Theory does in general over-estimate the metal-Ligand covalence, thus yields wave functions that are too delocalized. Although LF Theory has always been popular as a semi-empirical method when dealing with molecules of high symmetry e.g. cubic symmetry where the number of parameters needed is reasonably small (3 or 5), this is no more the case for molecules without symmetry and involving both an open d- and f-shell (# parameters ∼90). However, the combination of LF Theory and Density Functional (DF) Theory that we introduced twenty years ago can easily deal with complex molecules of any symmetry with two and more open shells. The accuracy of these predictions from 1(st) principles achieves quite a high accuracy (
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non empirical prediction of the photophysical and magnetic properties of systems with open d and f shells based on combined Ligand Field and density functional Theory lfdft
Chimia, 2014Co-Authors: Claude DaulAbstract:Despite the important growth of ab initio and computational techniques, Ligand Field Theory in molecular science or crystal Field Theory in condensed matter offers the most intuitive way to calculate multiplet energy levels arising from systems with open shells d and/or f electrons. Over the past decade we have developed a Ligand Field treatment of inorganic molecular modelling taking advantage of the dominant localization of the frontier orbitals within the metal-sphere. This feature, which is observed in any inorganic coordination compound, especially if treated by Density Functional Theory calculation, allows the determination of the electronic structure and properties with a surprising good accuracy. In Ligand Field Theory, the theoretical concepts consider only a single atom center; and treat its interaction with the chemical environment essentially as a perturbation. Therefore success in the simple Ligand Field Theory is no longer questionable, while the more accurate molecular orbital Theory does in general over-estimate the metal-Ligand covalence, thus yields wave functions that are too delocalized. Although LF Theory has always been popular as a semi-empirical method when dealing with molecules of high symmetry e.g. cubic symmetry where the number of parameters needed is reasonably small (3 or 5), this is no more the case for molecules without symmetry and involving both an open d- and f-shell (# parameters ∼90). However, the combination of LF Theory and Density Functional (DF) Theory that we introduced twenty years ago can easily deal with complex molecules of any symmetry with two and more open shells. The accuracy of these predictions from 1(st) principles achieves quite a high accuracy (<5%) in terms of states energies. Hence, this approach is well suited to predict the magnetic and photo-physical properties arbitrary molecules and materials prior to their synthesis, which is the ultimate goal of each computational chemist. We will illustrate the performance of LFDFT for the design of phosphors that produces light similar to our sun and predict the magnetic anisotropy energy of single ion magnets.
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A DFT Based Ligand Field Theory
Structure and Bonding, 2004Co-Authors: Mihail Atanasov, Claude Daul, Cédrick RauzyAbstract:A general and user-oriented Ligand Field (LF) Theory – LFDFT with parameters adjusted to DFT energies of separate Slater Determinants (SD) of the partly filled dn shell [n=2(8), 3(7), 4(6) and 5] of transition metals (TM) complexes – is developed and tested using 22 well documented examples from the literature. These include CrIII, d3 and CoII d7 in octahedral and CrIV, MnV, FeVI d2, CoII d7, MnII d5, NiII d8 in tetrahedral complexes for which reliable values of d-d transition energies available from high-resolute Ligand Field spectra of complexes with halogenide (F, Cl, Br and I), oxide and cyanide Ligands have been reported. The formalism has been implemented and consists of three steps allowing provision of geometries, Ligand Field Kohn-Sham orbitals and SD-energies in a way consistent with the LF phenomenology. In a fourth step LF parameters are utilized to yield multiplet energies using a full CI LF program. Comparing SD energies from DFT with those calculated using the LF parameter values, we can state for all considered cases, that the LF parameterization scheme is remarkably compatible with SD energies from DFT; standard deviations between DFT SD-energies and their LFDFT values being calculated between 0.016 and 0.124 eV. We find that, when based on the average of configuration with n/5 occupancy of each MO dominated by TM d-orbitals and on geometries with metal-Ligand bond lengths from experiment, the 10Dq parameter values (cubic symmetry) are very close to the ones obtained from a fit to reported Ligand Field transitions. In contrast, when using common functionals such as LDA or gradient corrected ones (GGA) we find that the parameters B and C deduced from a fit to the SD energies are systematically lower than experimental. Thus spin-forbidden transitions which are particularly sensitive to B and C are calculated to be by 2000 to 3000 cm–1 at lower energies compared to experiment. Based on DFT and experimental B and C values we propose scaling factors, which allow one to improve the agreement between DFT and experimental transition energies, or alternatively to develop a DFT Theory based on effective LF functionals and/or basis sets. Using a thorough analysis of the dependence of the Kohn-Sham orbital energy on the orbital occupation numbers, following Slater Theory, we propose a general LFDFT scheme allowing one to treat, within the same formalism low symmetric Ligand Fields as well. Test examples, which illustrate the efficiency of this approach, include Cs distorted CrO44– and D2d distorted MnO43– chromophores. Finally, for cubic LF we propose a hybrid LFDFT model (HLFDFT) which leads to an improvement of the existing DFT-multiplet theories. We show, taking low-spin Co(CN)63– as an example, that the new model yields better results as compared to time-depending DFT (TDDFT). A discussion of the LFDFT method in the context of other CI-DFT approaches is given.
Claus Erik Schäffer - One of the best experts on this subject based on the ideXlab platform.
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Kohn-Sham DFT and Ligand-Field Theory: Is there a synergy?
Canadian Journal of Chemistry, 2009Co-Authors: Claus Erik Schäffer, Jesper BendixAbstract:In forming electronic states of the partially filled shell of transition-metal atomic and molecular systems, real, symmetry-based, fixed, Kohn–Sham eigenorbitals can be used to bridge KS-states wit...
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Elucidation of Ligand-Field Theory. Reformulation and Revival by Density Functional Theory
Structure and Bonding, 2004Co-Authors: Christian Anthon, Jesper Bendix, Claus Erik SchäfferAbstract:Constrained by the use of an “average-of-configuration” computation, Kohn-Sham-DFT allows identification of the complete set of dq states of the Ligand Field plus repulsion model, LFR. A one-to-one correspondence is assumed between states defined by integer occupation numbers of real KS spin orbitals and single-determinant Ligand-Field states of a hierarchic cubic-tetragonal-orthorhombic strong-Field approximation. The energies of these LFR states are parameterized by using mutually orthogonal parametrical operators. This orthogonality secures optimal meaningfulness of the parameters. The DFT state energies are taken as computed “data”. For d2, each parameter is defined by a 45-dimensional coefficient vector, which is orthogonal to that of all the other parameters. By forming the scalar products of the coefficient vectors and the “data” vector, the values of the parameters are determined. Identically the same parameter values may be obtained by performing the “data” reduction using a linear least squares procedure. The Amsterdam Density Functional program package (ADF) is constrained and then its shortcomings in reproducing the LFR models is quantified. Small “random errors” and “spatial errors” are identified and eliminated. Thereafter, the KS-DFT model for atomic ions is equivalent to the five-parameter Parametrical Multiplet Term model, PMT. This model is finally contracted to the three-parameter Slater-Condon-Shortley model, SCS. This “data” reduction has substantial errors. The computed sum square splitting, SSSADF, which for systems with two electrons in the partially filled shell is the sum of the squares of the 45 barycentered ADF energies, was taken as a measure of the integrated information contents of the 44 independent computed energy differences. Then, for atomic ions, by discarding 0.05% of unsystematic information a 1:1 relationship between the constrained ADF model and the PMT model was obtained. By discarding another 2% of systematic information, a 1:1 relationship with the SCS model resulted. The SCS model is parameterized in terms of Jorgensen’s spin-pairing energy parameter D and the Racah parameter B. Even though KS-DFT does not lend itself to the direct determination of non-diagonal elements, the present parameterization procedure allows the full dq spaces to be explored.
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An average-of-configuration method for using Kohn-Sham density functional Theory in modeling Ligand-Field Theory.
Inorganic chemistry, 2003Co-Authors: Christian Anthon, Jesper Bendix, Claus Erik SchäfferAbstract:The Amsterdam Density Functional (ADF) package has been used to constrain Kohn-Sham DFT in such a fashion that a transition from KS-DFT to Ligand-Field Theory in the form of the parametrical d(q)() model is completely well-defined. A relationship is established between the strong-Field approximation of the parametrical d(2) model for the tetrahedral complexes VCl(4)(-) and VBr(4)(-) and certain fixed-orbital ADF-computed energies. In this way values for all the parameters of the d(2)() model may be computed, thus allowing the ADF results to be expressed in terms of a KS-DFT energy matrix that can be diagonalized. This means that the KS-DFT deficiency with regard to computation of nondiagonal elements has been overcome and the KS-DFT eigenenergies have become available through the KS-DFT mimicking of the Ligand-Field plus repulsion model. By using mutually orthogonal strong-Field energy matrices, the mimicking has been further elucidated. The computed values for the empirical parameters of VCl(4)(-) and VBr(4)(-) are in good agreement with experimental data. The spectrochemical and the nephelauxetic series have been computed by including the remaining halide complexes and the quantitatively special position of F(-)() among the halides corroborated for both series.
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Extension of Ligand-Field Theory to encompass bridged structures. Emphasis on the angular overlap model
Inorganica Chimica Acta, 2000Co-Authors: Claus Erik SchäfferAbstract:Abstract The concepts of weak and strong exchange Fields are defined as a way of introducing Ligand-Field Theory into problems associated with bridging. Then the molecular orbital angular overlap model (MO-AOM) is used to illuminate the concept of nephelauxetism and contribute to the understanding of the complementarity between charge transfer and electron transfer in bonding and spectroscopy. Charge transfer is associated with orthogonalization, electronic density and diffraction experiments; electron transfer with covalency, transfer of unpaired electron spins and population numbers of predominantly central-ion-localized orbitals. This discussion lends further support to the idea that the chemical concept of oxidation states in Ligand-Field complexes has an important physical meaning independent from the degree of charge transfer. This is illustrated by a number of chemical examples. It emerges that the MO-AOM has a mutual character in that not only can Ligand orbitals be conceived as perturbers of central ion orbitals, but also vice versa. The perturbations are in pairs and have the same values angularly. The importance of the orthogonality of the AOM operators in this context is illustrated. This is also used to extend the MO-AOM to cover nonlinear ligation and bridging. The concept of angular overlap (AO) is given wider scope. The usual chemical distinction between the two limiting cases of bonding, the covalent bond and the heteropolar bond, is exhibited in the model description. The d-electron Ligand-Field-Theory contribution to the problem of bridging emphasizes the usefulness of the concept of the parametrical d q model for this Theory. For a bicentric system, for example, the electronic d q ⊗d q Hamiltonian of this model can be partitioned into AA and BB parts associated with the individual centers and a part, (AB+BA), associated with the (weak) coupling between the centers and its various symmetry/geometry-determined one-electron pathways, and this partition can be made at the orbital as well as at the d q -state level. The AA and BB parts can then be diagonalized and the (AB+BA) part rediagonalized, so as to follow the associated basis change. One is left with an almost diagonal description in cases of weak exchange coupling.
Robert J. Deeth - One of the best experts on this subject based on the ideXlab platform.
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d-orbital energy levels in planar [MIIF4]2-, [MII(NH3)4]2+ and [MII(CN)4]2- complexes: the nature of M-L π bonding and the implications for Ligand Field Theory.
Dalton transactions (Cambridge England : 2003), 2020Co-Authors: Robert J. DeethAbstract:Qualitative MO Theory predicts degenerate dπ orbitals for planar coordination complexes with formally σ-only Ligands and the splitting energy, ΔEπ = E(dxy) - E(dxz,dyz), should be zero. For π-donor Ligands, ΔEπ should be positive (dxy > dxz,yz) while for π-acceptors, ΔEπ should be negative (dxy < dxz,yz). However, experimental d-d spectra, ab initio Ligand Field Theory (AI LFT) and crystal Field Theory for σ-only [M(NH3)4]2+ complexes give pronounced dπ splittings with ΔEπ around +2500 cm-1 for first-row, divalent metal ions. AI LFT further suggests ΔEπ values around +4500 cm-1 for [MF4]2- and +1000 cm-1 for [M(CN)4]2- species. The origins of these dπ orbital splittings can be traced to the effects of the Ligand Field potential surrounding the metal centre which includes not only the intrinsic metal-Ligand π bonding but also substantial contributions from the 'void' regions above and below the molecular plane. The π component of the 'void cell' potentials increases ΔEπ which, if not explicitly taken into account, artificially enhances the apparent π-donor strength of the Ligands. With the inclusion of void cell π interactions, even though the AI LFT d orbital sequence always places dxz,yz below dxy, the Ligand Field analysis provides a chemically-reasonable description of the M-L π interactions with cyanide being a weak π acceptor, ammonia being π-neutral and fluoride being a strong π donor. In the case of [Ni(CN)4]2-, Ligand Field calculations further show that, contrary to the recent claims of Oppenheim et al. (Inorg. Chem., 2019, 58, 15202) the sequence of the many-electron excited states is not a definitive guide to the underlying order of one-electron d orbital energies and that the observed sequence of nA2g > nEg > nB1g, n = 1 or 3, does not guarantee a d-orbital sequence of dxy < dxz,yz < dz2.
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Ligand Field Theory for Planar Complexes: First Principles Validation of the Critical Effects of Coordination Voids
European Journal of Inorganic Chemistry, 2020Co-Authors: Robert J. DeethAbstract:Multi reference CASSCF/NEVPT2 wavefunction calculations on planar cis‐[MA2B2] complexes show that large dxz/dyz splittings are a feature of the symmetry of the Ligand Field and are not due to the Orgel effect or phase coupled ligation as previously proposed based on the MO version of the angular overlap model. Instead, the splitting can be attributed to the π components of the local Ligand Fields in the “void” regions above and below the molecular plane. The potential in these regions is lower than the d orbital barycentre leading to negative parameter values which is fully consistent with the cellular Ligand Field interpretation of Ligand Field Theory. The wider implications of Ligand Field effects from coordination voids are considered.
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Impact on Ligand-Field Theory of the real ground state for CuCl2
Journal of the Chemical Society Dalton Transactions, 1993Co-Authors: Robert J. DeethAbstract:The recent prediction by coupled pair functional Hartree–Fock calculations of a degenerate 2Πg ground term for linear CuCl2 has been confirmed by local density funtional (LDF) Slater-type orbital calculations. This has prompted a new cellular Ligand Field (CLF) analysis. Contrary to previous results on higher-co-ordinate chlorocuprates(II) and other complexes, the relative σ to π Cu–Cl bonding ratios for CuCl2, as predicted by the CLF eλ parameters on the one hand and by the LDF overlap populations on the other, do not agree. However, the CLF data do correlate with the computed LDF bonding energies but only when the whole d manifold (i.e. the 2Πg, 2Σg+ and 2Δg states) is taken into account. The interpretation and implications of these results within the Ligand-Field formalism are discussed.