Fast and Reasonable Geometry Optimization of Lanthanoid Complexes with an Extended Tight Binding Quantum Chemical Method

Abstract

The recently developed tight binding electronic structure approach GFN-xTB is tested in a comprehensive and diverse lanthanoid geometry optimization benchmark containing 80 lanthanoid complexes. The results are evaluated with reference to high-quality X-ray molecular structures obtained from the Cambridge Structural Database and theoretical DFT-D3(BJ) optimized structures for a few Pm (Z = 61) containing systems. The average structural heavy-atom root-mean-square deviation of GFN-xTB (0.65 Å) is smaller compared to its competitors, the Sparkle/PM6 (0.86 Å) and HF-3c (0.68 Å) quantum chemical methods. It is shown that GFN-xTB yields chemically reasonable structures, less outliers, and performs well in terms of overall computational speed compared to other low-cost methods. The good reproduction of large lanthanoid complex structures corroborates the wide applicability of the GFN-xTB approach and its value as an efficient low-cost quantum chemical method. Its main purpose is the search for energetically low-lying complex conformations in the elucidation of reaction mechanisms.

Structure Optimisation of Large Transition‐Metal Complexes with Extended Tight‐Binding Methods

“…Ac hemical-intuition-based structural correctness (SC) criterion by visual inspection of each structure is used to identify structures that are chemically transformed, dissociated, or critically deformed during optimisation (see Ref. [22]). Statistical standard deviations correlate well with mean absolute deviations (MADs), and hence only the latter are discussed in addition to the mean deviation (MD), which usually indicates systematic errors.…”

“…In particular,t he treatment of transition metals is limited or even impossible in many SQM methods.T his is contradicting the importance of transition metals in numerous and diverse areas of chemistry,partly involving very large or extended molecular or periodic systems.E xamples are supramolecular organometallic aggregates such as metalorganic polyhedra (MOPs) or macrocycles (MOMs), metalorganic frameworks (MOFs), and metal-containing biomolecules,s uch as metalloproteins or ac ombination to metal-biomolecule frameworks (MBioFs). [16,17] Thep otential field of application for efficient SQM methods is correspondingly large.However,universally applicable methods that are fully parameterised for transition metals are mostly limited to two method families,namely the already frequently used neglect of diatomic differential overlap (NDDO) based PMx (parametric method x)m ethods [4][5][6] and the recently introduced extended tight-binding methods GFNn-xTB, [1,2] (geometries,vibrational frequencies, and noncovalent interactions extended tight binding) from our laboratory.The robustness and quality of the GFNn-xTB methods has already been demonstrated in numerous applications with apredominant focus on organic chemistry.These applications include simulations of electron ionisation mass spectra, [18] fully automated computation of spin-spin-coupled nuclear resonance spectra, [19] including conformer-rotamer ensemble generation, atomic charge generation for the new D4 dispersion correction, [20,21] geometry optimisation of lanthanoid complexes, [22] automated determination of protonation sites, [23] pK a calculation in the SAMPL6 blind challenge, [24] metadynamics-based exploration of chemical compound conformation and reaction space, [25] and few studies on organometallic systems. [16,17] Thep otential field of application for efficient SQM methods is correspondingly large.However,universally applicable methods that are fully parameterised for transition metals are mostly limited to two method families,namely the already frequently used neglect of diatomic differential overlap (NDDO) based PMx (parametric method x)m ethods [4][5][6] and the recently introduced extended tight-binding methods GFNn-xTB, [1,2] (geometries,vibrational frequencies, and noncovalent interactions extended tight binding) from our laboratory.The robustness and quality of the GFNn-xTB methods has already been demonstrated in numerous applications with apredominant focus on organic chemistry.These applications include simulations of elect...…”

“…[8] Such compounds are not only highly interesting from af undamental chemistry point of view,b ut their unique properties also make them valuable for industrial technologies.T hey are used, for example,incatalysis, [9] for fuel storage, [10,11] as semi-conductor materials, [12] in ferroelectrics, [13] as filtration or selection materials,i nb iomedical applications such as bioimaging and sensing, [14] biomimetic mineralisation, [15] or as drug delivery systems. [16,17] Thep otential field of application for efficient SQM methods is correspondingly large.However,universally applicable methods that are fully parameterised for transition metals are mostly limited to two method families,namely the already frequently used neglect of diatomic differential overlap (NDDO) based PMx (parametric method x)m ethods [4][5][6] and the recently introduced extended tight-binding methods GFNn-xTB, [1,2] (geometries,vibrational frequencies, and noncovalent interactions extended tight binding) from our laboratory.The robustness and quality of the GFNn-xTB methods has already been demonstrated in numerous applications with apredominant focus on organic chemistry.These applications include simulations of electron ionisation mass spectra, [18] fully automated computation of spin-spin-coupled nuclear resonance spectra, [19] including conformer-rotamer ensemble generation, atomic charge generation for the new D4 dispersion correction, [20,21] geometry optimisation of lanthanoid complexes, [22] automated determination of protonation sites, [23] pK a calculation in the SAMPL6 blind challenge, [24] metadynamics-based exploration of chemical compound conformation and reaction space, [25] and few studies on organometallic systems. [26] Thefocus here is on demonstrating the quality of GFN2-xTB and its precursor GFN1-xTB for the structure optimisation of transition-metal complexes and in particular of very large organometallic systems,w hich are to date not possible otherwise.T he recently published GFN2-xTB approach features less empiricism, improved electrostatic interactions (multipole terms up to atomic dipolequadrupole interactions), as well as adensity (atomic charge)dependent London dispersion energy correction [27,28] at even slightly ...…”

Structure Optimisation of Large Transition‐Metal Complexes with Extended Tight‐Binding Methods

“…A chemical‐intuition‐based structural correctness (SC) criterion by visual inspection of each structure is used to identify structures that are chemically transformed, dissociated, or critically deformed during optimisation (see Ref. ). Statistical standard deviations correlate well with mean absolute deviations (MADs), and hence only the latter are discussed in addition to the mean deviation (MD), which usually indicates systematic errors.…”

“…The robustness and quality of the GFNn‐xTB methods has already been demonstrated in numerous applications with a predominant focus on organic chemistry. These applications include simulations of electron ionisation mass spectra, fully automated computation of spin–spin‐coupled nuclear resonance spectra, including conformer–rotamer ensemble generation, atomic charge generation for the new D4 dispersion correction, geometry optimisation of lanthanoid complexes, automated determination of protonation sites, p K a calculation in the SAMPL6 blind challenge, metadynamics‐based exploration of chemical compound conformation and reaction space, and few studies on organometallic systems . The focus here is on demonstrating the quality of GFN2‐xTB and its precursor GFN1‐xTB for the structure optimisation of transition‐metal complexes and in particular of very large organometallic systems, which are to date not possible otherwise.…”