Generalized Spin in the Variance-Based Wave Function Optimization Method within the Doubly Occupied Configuration Interaction Framework.

In this work, we implement a generalized spin formulation of the doubly occupied configuration interaction methodology using the energy variance of the N-electron Hamiltonian. We perform the optimization of the N-electron wave functions and calculate their corresponding energies, using a unified variational treatment for ground and excited states based on the energy variance, which allows us to describe the entire energy spectra on an equal footing. We analyze the effects produced by the breakdown of the S2 and Sz symmetries in the spectra of model hydrogenic clusters in terms of energies and spin-related quantities, arising from the restricted, unrestricted, and generalized spin methods. The results are compared with other related methods as well as full configuration interaction.

DOCSIC: A Mean-Field Method for Orbital-by-Orbital Self-Interaction Correction.

We introduce a new method to remove the one-electron self-interaction error in approximate density functional calculations on an orbital-by-orbital basis, as originally proposed by Perdew and Zunger [Phys. Rev. B 1981, 23, 5048]. This method is motivated by a recent proposal by Pederson et al. [J. Chem. Phys. 2014, 140, 121103] to remove self-interaction that employs orbitals derived from the real-space density matrix, known as FLOSIC (Fermi Löwdin orbitals self-interaction correction). However, instead of Fermi Löwdin orbitals, our scheme utilizes columns of the density matrix to determine localized orbitals, like the localization procedure proposed by Fuemmeler et al. [J. Chem. Theory Comput. 2023, 19, 8572]. The new method, dubbed DOCSIC for density matrix as orbital coefficients self-interaction correction, contrasts with traditional Perdew-Zunger or FLOSIC in that it does not incorporate additional optimization parameters, and, unlike the average density self-interaction correction of Ciofini et al. [Chem. Phys. Lett. 2003, 380, 12], it makes use of localized orbitals. Another advantage of DOCSIC is that it can be implemented as a mean-field formalism. We show details of the self-consistent generalized Kohn-Sham implementation, some illustrative results, and we finally highlight its advantages and limitations.

Bond length alternation of π-conjugated polymers predicted by the Fermi-Löwdin orbital self-interaction correction method.

π-conjugated polymers have been used in a wide range of practical applications, partly due to their unique properties that originate in the delocalization of electrons through the polymer backbone. The level of delocalization can be characterized by the induced bond length alternation (BLA), with shorter BLA connected with strong delocalization and vice versa. The accurate description of this structural parameter can be considered a benchmark for testing the capability of different electronic structure methods for self-interaction error (SIE) removal and electron correlation inclusion. Density functional theory (DFT), in its local or semi-local flavors, suffers from SIE and, thus, underestimates the BLA compared to self-interaction-free methods. In this work, we utilize the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method for one-electron self-interaction removal to characterize the BLA of five oligomers with increasing length extrapolated to the polymeric limit. We compare the self-interaction-free BLA to several DFT approximations, Møller-Plesset second-order perturbation theory (MP2), and the BLA obtained with the domain based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] approximation. Our findings show that FLOSIC corrects for the small BLA given by (semi-)local DFT approximations, but it tends to overcorrect with respect to CAM-B3LYP, MP2, and DLPNO-CCSD(T).

The rise and fall of stretched bond errors: Extending the analysis of Perdew-Zunger self-interaction corrections of reaction barrier heights beyond the LSDA.

Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of Jacob's ladder of approximations. The analysis is based on Fermi-Löwdin Orbital Self-Interaction Correction (FLOSIC) calculations performed at several steps along the reaction pathway from the reactants (R) to the transition state (TS) to the products (P) for four representative reactions selected from the BH76 benchmark set. For all three functionals, the major contribution to self-interaction corrections of the barrier heights can be traced to stretched bond orbitals that develop near the TS configuration. The magnitude of the ratio of the self-exchange-correlation energy to the self-Hartree energy (XC/H) for a given orbital is introduced as an indicator of one-electron self-interaction error. XC/H = 1.0 implies that an orbital's self-exchange-correlation energy exactly cancels its self-Hartree energy and that the orbital, therefore, makes no contribution to the SIC in the FLOSIC scheme. For the practical DFAs studied here, XC/H spans a range of values. The largest values are obtained for stretched or strongly lobed orbitals. We show that significant differences in XC/H for corresponding orbitals in the R, TS, and P configurations can be used to identify the major contributors to the SIC of barrier heights and reaction energies. Based on such comparisons, we suggest that barrier height predictions made using the strongly constrained and appropriately normed meta-generalized gradient approximation may have attained the best accuracy possible for a semi-local functional using the Perdew-Zunger SIC approach.

Density Matrix Implementation of the Fermi-Löwdin Orbital Self-Interaction Correction Method.

The Fermi-Löwdin orbital self-interaction correction (FLOSIC) method effectively provides a transformation from canonical orbitals to localized Fermi-Löwdin orbitals which are used to remove the self-interaction error in the Perdew-Zunger (PZ) framework. This transformation is solely determined by a set of points in space, called Fermi-Löwdin descriptors (FODs), and the occupied canonical orbitals or the density matrix. In this work, we provide a detailed workflow for the implementation of the FLOSIC method for removal of self-interaction error in DFT calculations in an orbital-by-orbital basis that takes advantage of the unitary invariant nature of the FLOSIC method. In this way, it is possible to cast the self-consistent energy minimization at fixed FODs in the same manner than standard Kohn-Sham with one additional term in the Kohn-Sham Hamiltonian that introduces the PZ self-interaction correction. Each energy minimization iteration is divided in two substeps, one for the density matrix and one for the FODs. Expressions for the effective Kohn-Sham matrix and FOD gradients are provided such that its implementation is suitable for most electronic structure codes. We analyze the convergence characteristics of the algorithm and present applications for the evaluation of NMR shielding constants and real-time time-dependent DFT simulations based on the Liouville-von Neumann equation to calculate excitation energies.

Generalized spin σ-SCF method.

We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3-7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states.

Use of FLOSIC for understanding anion-solvent interactions.

An Achille's heel of lower-rung density-functional approximations is that the highest-occupied-molecular-orbital energy levels of anions, known to be stable or metastable in nature, are often found to be positive in the worst case or above the lowest-unoccupied-molecular-orbital levels on neighboring complexes that are not expected to accept charge. A trianionic example, [Cr(C2O4)3]3-, is of interest for constraining models linking Cr isotope ratios in rock samples to oxygen levels in Earth's atmosphere over geological timescales. Here we describe how crowd sourcing can be used to carry out self-consistent Fermi-Löwdin-Orbital-Self-Interaction corrected calculations (FLOSIC) on this trianion in solution. The calculations give a physically correct description of the electronic structure of the trianion and water. In contrast, uncorrected local density approximation (LDA) calculations result in approximately half of the anion charge being transferred to the water bath due to the effects of self-interaction error. Use of group-theory and the intrinsic sparsity of the theory enables calculations roughly 125 times faster than our initial implementation in the large N limit reached here. By integrating charge density densities and Coulomb potentials over regions of space and analyzing core-level shifts of the Cr and O atoms as a function of position and functional, we unambiguously show that FLOSIC, relative to LDA, reverses incorrect solute-solvent charge transfer in the trianion-water complex. In comparison to other functionals investigated herein, including Hartree-Fock and the local density approximation, the FLOSIC Cr 1s eigenvalues provide the best agreement with experimental core ionization energies.

Self-interaction error overbinds water clusters but cancels in structural energy differences.

We gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi-Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction-corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/[Formula: see text] from about 42 meV/[Formula: see text] for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction-corrected SCAN. These results indicate that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

Magnetic Properties of High-Nuclearity Fex-oxo (x = 7, 22, 24) Clusters Analyzed by a Multipronged Experimental, Computational, and Magnetostructural Correlation Approach.

The synthesis, structure, and magnetic properties of three related iron(III)-oxo clusters are reported, [Fe7O3(O2CPh)9(mda)3(H2O)] (1), [Fe22O14(OH)3(O2CMe)21(mda)6](ClO4)2 (2), and [Fe24O15(OH)4(OEt)(O2CMe)21(mda)7](ClO4)2 (3), where mdaH2 is N-methyldiethanolamine. 1 was prepared from the reaction of [Fe3O(O2CPh)6(H2O)3](NO3) with mdaH2 in a 1:2 ratio in MeCN, whereas 2 and 3 were prepared from the reaction of FeCl3/NaO2CMe/mdaH2 in a 2:∼13:2 ratio and FeCl3/NaO2CMe/mdaH2/pyridine in a 2:∼13:2:25 ratio, respectively, both in EtOH. The core of 1 consists of a central octahedral FeIII ion held within a nonplanar Fe6 loop by three µ3-O2- and three µ2-RO- arms from the three mda2- chelates. The cores of the cations of 2 and 3 consist of an A:B:A three-layer topology, in which a central Fe6 (2) or Fe8 (3) layer B is sandwiched between two Fe8 layers A. The A layers structurally resemble 1 with the additional Fe added at the center to retain virtual C3 symmetry. The central Fe6 layer B of 2 consists of a {Fe4(µ4-O)2(µ3-OH)2}6+ cubane with an Fe on either side attached to cubane O2- ions, whereas that of 3 has the same cubane but with an {Fe3(µ3-O)(µ-OH)} unit attached on one side and a single Fe on the other. Variable-temperature dc and ac magnetic susceptibility studies revealed dominant antiferromagnetic coupling in all complexes leading to ground-state spins of S = 5/2 for 1 and S = 0 for 2 and 3. All Fe2 pairwise exchange parameters (Jij) for 1-3 were estimated by two independent methods: density functional theory (DFT) calculations using broken symmetry methods and a magnetostructural correlation previously developed for high-nuclearity FeIII/O complexes. The two approaches gave satisfyingly similar Jij values, and the latter allowed rationalization of the experimental ground states by identification of the spin frustration effects operative and the resultant relative spin vector alignments at each FeIII ion.

Synthesis, Structure, and Magnetic Properties of an Fe36 Dimethylarsinate Cluster: The Largest "Ferric Wheel".

The synthesis and characterization of a high-nuclearity FeIII/O/arsinate cluster is reported within the salt [Fe36O12(OH)6(O2AsMe2)63(O2CH)3(H2O)6](NO3)12 (1). The compound was prepared from the reaction of Fe(NO3)3·9H2O, dimethylarsinic acid (Me2AsO2H), and triethylamine in a 1:2:4 molar ratio in acetonitrile. The Fe36 cation of 1 is an unprecedented structural type consisting of nine Fe4 butterfly units of two types, three {FeIII4(µ3-O)2} units A, and six {FeIII4(µ3-O)(µ3-OH)} units B, linked by multiple bridging Me2AsO2- groups into an Fe36 triangular wheel/loop with C3 crystallographic and D3 virtual symmetry that looks like a guitar plectrum. The unusual structure has been rationalized on the basis of the different curvatures of units A and B, the presence of intra-Fe36 hydrogen bonding, and the tendency of Me2AsO2- groups to favor µ3-bridging modes. The cations stack into supramolecular nanotubes parallel to the crystallographic c axis and contain badly disordered solvent and NO3- anions. The cation of 1 is the highest-nuclearity "ferric wheel" to date and also the highest-nuclearity Fe/O cluster of any structural type with a single contiguous Fe/O core. Variable-temperature direct-current magnetic susceptibility data and alternating-current in-phase magnetic susceptibility data indicate that the cation of 1 possesses an S = 0 ground state and dominant antiferromagnetic interactions. The Fe2 pairwise Ji,j couplings were estimated by the combined use of a magnetostructural correlation for high-nuclearity FeIII/oxo clusters and density functional theory calculations using broken-symmetry methods and the Green's function approach. The three methods gave satisfyingly similar Ji,j values and allowed the identification of spin-frustration effects and the resulting relative spin-vector alignments and thus rationalization of the S = 0 ground state of the cation.

Validation of the Green's Function Approximation for the Calculation of Magnetic Exchange Couplings.

In this work, we assess the potential of the Green's function approximation to predict isotropic magnetic exchange couplings and to reproduce the standard broken-symmetry energy difference approach for transition metal complexes. To this end, we have selected a variety of heterodinuclear, homodinuclear, and polynuclear systems containing 3d transition metal centers and computed the couplings using both the Green's function and energy difference methods. The Green's function approach is shown to have mixed results for the cases tested. For dinuclear complexes with large strength couplings (≳50 cm-1), the Green's function method is unable to reliably reproduce the energy difference values. However, for weaker dinuclear couplings, the Green's function approach acceptably reproduces broken-symmetry energy difference couplings. In polynuclear cases, the Green's function approximation worked remarkably well, especially for FeIII complexes. On the other hand, for a NiII polynuclear complex, qualitatively wrong couplings are predicted. Overall, the evaluation of exchange couplings from local rigid magnetization rotations offers a powerful alternative to time-consuming energy differences methods for large polynuclear transition metal complexes, but to achieve a quantitative agreement, some improvements to the method are needed.

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods.

We examine the role of self-interaction error (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular, we analyze the effect of scaling down the self-interaction correction (SIC) for three nonempirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and the recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger SIC [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048.], the orbitalwise scaled SIC method [Vydrov, O. A. et al. J. Chem. Phys. 2006, 124, 094108.], and the recent local scaling method [Zope, R. R. et al. J. Chem. Phys. 2019, 151, 214108.]. We compute the magnetic exchange coupling constants using the spin projection and nonprojection approaches for sets of molecules composed of dinuclear and polynuclear H···He models, organic radical molecules, and chlorocuprate and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single-electron regions, PZSIC performs well, but for more complex organic systems and the chlorocuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases, LSIC with kinetic energy density ratio performs better than PZSIC. Analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.

Fermi-Löwdin orbital self-interaction correction of adsorption energies on transition metal ions.

Density functional theory (DFT)-based descriptions of the adsorption of small molecules on transition metal ions are prone to self-interaction errors. Here, we show that such errors lead to a large over-estimation of adsorption energies of small molecules on Cu+, Zn+, Zn2+, and Mn+ in local spin density approximation (LSDA) and Perdew, Burke, Ernzerhof (PBE) generalized gradient approximation calculations compared to reference values computed using the coupled-cluster with single, doubles, and perturbative triple excitations method. These errors are significantly reduced by removing self-interaction using the Perdew-Zunger self-interaction correction (PZ-SIC) in the Fermi-Löwdin Orbital (FLO) SIC framework. In the case of FLO-PBE, typical errors are reduced to less than 0.1 eV. Analysis of the results using DFT energies evaluated on self-interaction-corrected densities [DFT(@FLO)] indicates that the density-driven contributions to the FLO-DFT adsorption energy corrections are roughly the same size in DFT = LSDA and PBE, but the total corrections due to removing self-interaction are larger in LSDA.

How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations?

We examine the effect of removing self-interaction error (SIE) on the calculation of molecular polarizabilities in the local spin density (LSDA) and generalized gradient approximations (GGA). To this end, we utilize a database of 132 molecules taken from a recent benchmark study [Hait and Head-Gordon, Phys. Chem. Chem. Phys., 2018, 20, 19800] to assess the influence of SIE on polarizabilities by comparing results with accurate reference data. Our results confirm that the general overestimation of molecular polarizabilities by these density functional approximations can be attributed to SIE. However, removing SIE using the Perdew-Zunger self-interaction-correction (PZ-SIC) method, implemented using the Fermi-Löwdin Orbital SIC approach, leads to an underestimation of molecular polarizabilities, showing that PZ-SIC overcorrects when combined with LSDA or GGA. Application of a recently proposed locally scaled SIC [Zope, et al., J. Chem. Phys., 2019, 151, 214108] is found to provide more accurate polarizabilities. We attribute this to the ability of the local scaling scheme to selectively correct for SIE in the regions of space where the correction is needed most.

Density-related properties from self-interaction corrected density functional theory calculations.

The Perdew-Zunger self-interaction correction (PZ-SIC) removes unphysical electron self-interaction from calculations employing standard density functional approximations. Doing so improves many computed properties, bringing them into better agreement with experimental observations or with results from high-level quantum chemistry calculations. However, while PZ-SIC generally corrects in the right direction relative to the corresponding reference values, in many cases, it over-corrects. For this reason, scaled-down versions of PZ-SIC have been proposed and investigated. These approaches have mostly employed exterior scaling in which SIC correction terms are scaled in the same way at every point in space. Recently, a new local, or interior, scaling SIC method was proposed on non-empirical grounds to restore a property of the exact, but unknown, density functional that is broken in PZ-SIC. In this approach, the scaling at each point depends on the character of the charge density at that point. However, the local scaling can be done in various ways while still restoring the behavior of the exact functional. In this work, we compare and contrast the performance of various interior scaling approaches for addressing over-corrections of calculated molecular dipole moments and atomic polarizabilities and properties that reflect the nature of the electronic charge density.

Iron(III)-Oxo Cluster Chemistry with Dimethylarsinate Ligands: Structures, Magnetic Properties, and Computational Studies.

A program has been initiated to develop FeIII/oxo cluster chemistry with the "pseudocarboxylate" ligand dimethylarsinate (Me2AsO2-) for comparison with the well investigated FeIII/oxo/carboxylate cluster area. The synthesis and characterization of three polynuclear FeIII complexes are reported, [Fe12O4(O2CtBu)8(O2AsMe2)17(H2O)3]Cl3 (1), Na2[Fe12Na2O4(O2AsMe2)20(NO3)6(Me2AsO2H)2(H2O)4](NO3)6 (2), and [Fe3(O2AsMe2)6(Me2AsO2H)2(hqn)2](NO3) (3), where hqnH is 8-hydroxyquinoline. The Fe12 core of 1 is a type never previously encountered in FeIII carboxylate chemistry, consisting of two Fe6 units each of which comprises two {Fe3(µ3-O2-)} units bridged by three Me2AsO2- groups and linked into an Fe12 loop structure by two anti-anti η1:η1:µ Me2AsO2- groups, a bridging mode extremely rare with carboxylates. 2 also consists of two Fe6 units, differing in their ligation from those in 1, and this time linked together into a linear structure by a central {Na2(NO3)2} bridging unit. 3 is a linear Fe3 complex with no monatomic bridges between FeIII ions, a very rare situation in FeIII chemistry with any ligands and unprecedented in Fe carboxylate chemistry. The distinct differences observed in arsinate vs carboxylate ligation modes are rationalized largely based on the greater basicity of the former vs the latter. Variable-temperature dc and ac magnetic susceptibility data reveal all Fe2 pairwise interactions to be antiferromagnetic. For 1 and 2, the different Jij couplings were estimated by use of a magnetostructural correlation for high nuclearity FeIII-oxo clusters and by density functional theory calculations using broken symmetry methods, allowing identification of their relative spin vector alignments and thus rationalization of their S = 0 ground states. The Jij values were then used as input values to give excellent fits of the experimental χMT vs T data. For 3, the fits of the experimental χMT vs T data to the Van Vleck equation or with PHI gave a very weak J12 = -0.8(1) cm-1 (H = -2JSi·Sj convention) between adjacent FeIII ions and an S = 5/2 ground state. These initial FeIII arsinate complexes also provide structural parameters that help validate literature assignments of arsinate binding modes to iron oxide/hydroxide minerals as part of environmental concerns of using arsenic-containing herbicides in agriculture.

A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction. II. Gauge consistency of the energy density at three levels of approximation.

The Perdew-Zunger (PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional. Unfortunately, it spoils the slowly varying (in space) limits of the uncorrected approximate functionals, where those functionals are right by construction. The right limits can be restored by locally scaling down the energy density of the PZ SIC in many-electron regions, but then a spurious correction to the exact functional would be found unless the self-Hartree and exact self-xc terms of the PZ SIC energy density were expressed in the same gauge. Only the local density approximation satisfies the same-gauge condition for the energy density, which explains why the recent local-scaling SIC is found here to work excellently for atoms and molecules only with this basic approximation and not with the more advanced generalized gradient approximations (GGAs) and meta-GGAs, which lose the Hartree gauge via simplifying integrations by parts. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can also be applied to approximate functionals. Doing so leads to a simple scaled-down self-interaction correction that is typically much more accurate than PZ SIC in tests for many molecular properties (including equilibrium bond lengths). The present work unambiguously shows that the largest errors of PZ SIC applied to standard functionals at three levels of approximation can be removed by restoring their correct slowly varying density limits. It also confirms the relevance of these limits to atoms and molecules.

Interpretation and Automatic Generation of Fermi-Orbital Descriptors.

We present an interpretation of Fermi-orbital descriptors (FODs) and argue that these descriptors carry chemical bonding information. We show that a bond order derived from these FODs agrees well with reference values, and highlight that optimized FOD positions used within the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) method correspond to expectations from Linnett's double-quartet theory, which is an extension of Lewis theory. This observation is independent of the underlying exchange-correlation functional, which is shown using the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA), and the strongly constrained and appropriately normed meta-GGA. To make FOD positions generally accessible, we propose and discuss four independent methods for the generation of Fermi-orbital descriptors, their implementation as well as their advantages and drawbacks. In particular, we introduce a re-implementation of the electron force field, an approach based on the centers of mass of orbital densities, a Monte Carlo-based algorithm, and a method based on Lewis-like bonding information. All results are summarized with respect to future developments of FLO-SIC and related methods. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Analytic atomic gradients in the fermi-löwdin orbital self-interaction correction.

We derived, implemented, and thoroughly tested the complete analytic expression for atomic forces, consisting of the Hellmann-Feynman term and the Pulay correction, for the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) method. Analytic forces are shown to be numerically accurate through an extensive comparison to forces obtained from finite differences. Using the analytic forces, equilibrium structures for a small set of molecules were obtained. This work opens the possibility of routine self-interaction free geometrical relaxations of molecules using the FLO-SIC method. © 2018 Wiley Periodicals, Inc.

Magnetic Properties of Co(II) Complexes with Polyhedral Carborane Ligands.

In this work we present a computational analysis of a new family of magnetic Co(II) single-ion complexes with large magnetic anisotropy based on icosahedral and octahedral carborane ligands. In particular, we extend our previous computational work on mononuclear Co(II) complexes with 1,2-(HS)2-1,2-C2B10H10 and 9,12-(HS)2-1,2-C2B10H10 icosahedral o-carborane ligands to a larger set of complexes where the Co(II) ion is doubly chelated by those ligands and by other two positional isomers belonging to the 1,2-dicarba- closo-dodecaborane family. We also describe Co(II) complexes with octahedral ligands derived from 1,2-dicarba- closo-hexaborane and study the effects of replacing a thiol group by a hydroxy group in both polyhedral geometries, as well as the influence of the position of the carbon atoms. On analysis of the results for a total of 20 complexes, our results show that carborane-based Co(II) single-ion compounds present a distorted-tetrahedral geometry, high-spin ground states, and high values for the magnetic anisotropy parameters. We point out which of these would be suitable candidates to be synthesized and used as molecular magnets.