Relative energy of the high-(T2g5) and low-(A1g1) spin states of the ferrous complexes [Fe(L)(NHS4)]: CASPT2 versus density functional theory

Performance of quantum chemistry methods for a benchmark set of spin-state energetics derived from experimental data of 17 transition metal complexes (SSE17)

Accurate prediction of spin-state energetics for transition metal (TM) complexes is a compelling problem in applied quantum chemistry, with enormous implications for modeling catalytic reaction mechanisms and computational discovery of materials. Computed spin-state energetics are strongly method-dependent and credible reference data are scarce, making it difficult to conduct conclusive computational studies of open-shell TM systems. Here, we present a novel benchmark set of first-row TM spin-state energetics, which is derived from experimental data of 17 complexes containing FeII, FeIII, CoII, CoIII, MnII, and NiII with chemically diverse ligands. The estimates of adiabatic or vertical spin-state splittings, which are obtained from spin crossover enthalpies or energies of spin-forbidden absorption bands, suitably back-corrected for the vibrational and environmental effects, are employed as reference values for benchmarking density functional theory (DFT) and wave function methods. The results demonstrate a high accuracy of the coupled-cluster CCSD(T) method, which features the mean absolute error (MAE) of 1.5 kcal mol-1 and maximum error of -3.5 kcal mol-1, and outperforms all the tested multireference methods: CASPT2, MRCI+Q, CASPT2/CC and CASPT2+δMRCI. Switching from Hartree-Fock to Kohn-Sham orbitals is not found to consistently improve the CCSD(T) accuracy. The best performing DFT methods are double-hybrids (PWPB95-D3(BJ), B2PLYP-D3(BJ)) with the MAEs below 3 kcal mol-1 and maximum errors within 6 kcal mol-1, whereas the DFT methods so far recommended for spin states (e.g., B3LYP*-D3(BJ) and TPSSh-D3(BJ)) are found to perform much worse with the MAEs of 5-7 kcal mol-1 and maximum errors beyond 10 kcal mol-1. This work is the first such extensive benchmark study of quantum chemistry methods for TM spin-state energetics making use of experimental reference data. The results are relevant for the proper choice of methods to characterize TM systems in computational catalysis and (bio)inorganic chemistry, and may also stimulate new developments in quantum-chemical or machine learning approaches.

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

How important is the amount of exact exchange for spin-state energy ordering in DFT? Case study of molybdenum carbide cluster, Mo4C2

Since the form of the exact functional in density functional theory is unknown, we must rely on density functional approximations (DFAs). In the past, very promising results have been reported by combining semi-local DFAs with exact, i.e. Hartree-Fock, exchange. However, the spin-state energy ordering and the predictions of global minima structures are particularly sensitive to the choice of the hybrid functional and to the amount of exact exchange. This has been already qualitatively described for single conformations, reactions, and a limited number of conformations. Here, we have analyzed the mixing of exact exchange in exchange functionals for a set of several hundred isomers of the transition metal carbide, Mo4C2. The analysis of the calculated energies and charges using PBE0-type functional with varying amounts of exact exchange yields the following insights: (1) The sensitivity of spin-energy splitting is strongly correlated with the amount of exact exchange mixing. (2) Spin contamination is exacerbated when correlation is omitted from the exchange-correlation functional. (3) There is not one ideal value for the exact exchange mixing which can be used to parametrize or choose among the functionals. Calculated energies and electronic structures are influenced by exact exchange at a different magnitude within a given distribution; therefore, to extend the application range of hybrid functionals to the full periodic table the spin-energy splitting energies should be investigated.

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew-Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. The quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

Environmental Control of the Magnetic Behavior of Transition Metal Complexes: Density Functional Theory Study of Zeolite Y Embedded Complexes [M(bpy)3]2+@Y (M = Fe2+, Co2+)

Using the supramolecular approach developed for the study of the guest-host interactions in the zeolite Y encapsulated [Fe(bpy)₃]²⁺ compound: [Fe(bpy)₃]²⁺@Y (bpy = 2,2'-bipyridine) [Vargas et al., J. Chem. Theory Comput. 2009, 5, 97-115], we apply density functional theory (DFT) to the study of the influence of zeolite Y encapsulation on the structural and energetic properties of [Co(bpy)₃]²⁺ in the low-spin (LS) and high-spin (HS) states, while revisiting [Fe(bpy)₃]²⁺@Y. Although the accurate prediction of the HS-LS energy difference ΔE_HL^el remains challenging for current DFT methods, they give accurate estimates of its variation Δ(ΔE_HL^el) in a series of complexes of a given transition metal ion. Therefore, denoting [M(bpy)₃]²⁺@Y_SM as the supramolecular model of the inclusion compounds, the values of ΔE_HL^el for the bpy complexes in the gas phase and in the supercage of zeolite Y were determined by combining the DFT estimates of Δ(ΔE_HL^el) in the series {[M(NCH)₆]²⁺, [M(bpy)₃]²⁺, and [M(bpy)₃]²⁺@Y_SM}, with accurate CCSD(T) estimates of ΔE_HL^el in the benchmark complexes [M(NCH)₆]²⁺ (M = Fe, Co) [Lawson Daku et al., J. Chem. Theory Comput., 2012, 8, 4216-4231]. Generalized gradient approximations as well as global and range-separated hybrids were employed. In order to better account for the key role of dispersion, they were also augmented with the semiempirical D2, D3BJ, and D3BJM dispersion corrections when available. The use of the D3BJ and D3BJM corrections led to similar results, and this is only with the use of the D2 scheme that (i) the free and encapsulated [Fe(bpy)₃]²⁺ are correctly predicted as LS species and that (ii) the encapsulation of both complexes translates into a destabilization of their HS state with respect to their LS state. The increase of the HS-LS energy difference is smaller for [Co(bpy)₃]²⁺ than [Fe(bpy)₃]²⁺ because the HS-LS molecular volume difference ΔV_HL in [Co(bpy)₃]²⁺ is ∼50% smaller than in [Fe(bpy)₃]²⁺. Periodic DFT calculations performed on crystalline [M(bpy)₃]²⁺@Y show that the employed [M(bpy)₃]²⁺@Y_SM supramolecular model allows the influence of encapsulation on the geometry and the spin-state energetics of [M(bpy)₃]²⁺ (M = Fe, Co) to be quantitatively captured.

Benchmarking CASPT3 Vertical Excitation Energies

Based on 280 reference vertical transition energies of various natures (singlet, triplet, valence, Rydberg, n → π∗, π → π∗, and double excitations) extracted from the QUEST database, we assess the accuracy of third-order multireference perturbation theory, CASPT3, in the context of molecular excited states. When one applies the disputable ionization- potential-electron-affinity (IPEA) shift, we show that CASPT3 provides a similar accuracy as its second-order counterpart, CASPT2, with the same mean absolute error of 0.11 eV. However, as already reported, we also observe that the accuracy of CASPT3 is almost insensitive to the IPEA shift, irrespective of the transition type and system size, with a small reduction of the mean absolute error to 0.09 eV when the IPEA shift is switched off.

Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies

Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events but also to provide reference values for vertical transition energies, hence allowing benchmarking of lower-order models. In this category, both the complete-active-space second-order perturbation theory (CASPT2) and the N-electron valence state second-order perturbation theory (NEVPT2) are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches, the present work relies on highly accurate (±0.03 eV) aug-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 n → π*, 119 π → π*, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially contracted (PC) and strongly contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of 0.11 and 0.13 eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focused on single-reference wave function methods ( J. Chem. Theory Comput. 2018, 14, 4360; J. Chem. Theory Comput. 2020, 16, 1711), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.

The many-body electronic interactions of Fe(II)–porphyrin

Fe(II)–porphyrin complexes exhibit a diverse range of electronic interactions between the metal and macrocycle. Herein, the incremental full configuration interaction method is applied to the entire space of valence orbitals of a Fe(II)–porphyrin model using a modest basis set. A novel visualization framework is proposed to analyze individual many-body contributions to the correlation energy, providing detailed maps of this complex’s highly correlated electronic structure. This technique is used to parse the numerous interactions of two low-lying triplet states (3A2g and 3Eg) and to show that strong metal d–d and macrocycle π–π orbital interactions preferentially stabilize the 3A2g state. d–π interactions, on the other hand, preferentially stabilize the 3Eg state and primarily appear when correlating six electrons at a time. Ultimately, the Fe(II)–porphyrin model’s full set of 88 valence electrons are correlated in 275 orbitals, showing the interactions up to the 4-body level, which covers the great majority of correlations in this system.

CASPT2 molecular geometries of Fe(II) spin-crossover complexes

Using fully internally contracted (FIC)-CASPT2 analytical gradients, geometry optimizations of spin-crossover complexes are reported. This approach is tested on a series of Fe(II) complexes with different sizes, ranging from 13 to 61 atoms. A combination of active space and basis set choices are employed to investigate their role in determining reliable molecular geometries. The reported strategy demonstrates that a wave function-based level of theory can be used to optimize the geometries of metal complexes in reasonable times and enables one to treat the molecular geometry and electronic structure of the complexes using the same level of theory. For a series of smaller Fe(II) SCO complexes, strong field ligands in the LS state result in geometries with the largest differences between DFT and CASPT2; however, good agreement overall is observed between DFT and CASPT2. For the larger complexes, moderate sized basis sets yield geometries that compare well with DFT and available experimental data. We recommend using the (10e,12o) active space since convergence to a minimum structure was more efficient than with truncated active spaces despite having similar Fe-ligand bond distances.

Improved Spin-State Energy Differences of Fe(II) Molecular and Crystalline Complexes via the Hubbard U-Corrected Density

We recently showed that the DFT+U approach with a linear-response U yields adiabatic energy differences biased toward high spin [Mariano et al. J. Chem. Theory Comput. 2020, 16, 6755-6762]. Such bias is removed here by employing a density-corrected DFT approach where the PBE functional is evaluated on the Hubbard U-corrected density. The adiabatic energy differences of six Fe(II) molecular complexes computed using this approach, named PBE[U] here, are in excellent agreement with coupled cluster-corrected CASPT2 values for both weak- and strong-field ligands resulting in a mean absolute error (MAE) of 0.44 eV, smaller than that of the recently proposed Hartree-Fock density-corrected DFT (1.22 eV) and any other tested functional, including the best performer TPSSh (0.49 eV). We take advantage of the computational efficiency of this approach and compute the adiabatic energy differences of five molecular crystals using PBE[U] with periodic boundary conditions. The results show, again, an excellent agreement (MAE = 0.07 eV) with experimentally extracted values and a superior performance compared with the best performers M06-L (MAE = 0.08 eV) and TPSSh (MAE = 0.31 eV) computed on molecular fragments.

First principle simulation of coated hydroxychloroquine on Ag, Au and Pt nanoparticles

From the first month of the COVID-19 pandemic, the potential antiviral properties of hydroxychloroquine (HCQ) and chloroquine (CQ) against SARS-CoV-2 suggested that these drugs could be the appropriate therapeutic candidates. However, their side effects directed clinical tests towards optimizing safe utilization strategies. The noble metal nanoparticles (NP) are promising materials with antiviral and antibacterial properties that can deliver the drug to the target agent, thereby reducing the side effects. In this work, we applied both the quantum mechanical and classical atomistic molecular dynamics approaches to demonstrate the adsorption properties of HCQ/CQ on Ag, Au, AgAu, and Pt nanoparticles. We found the adsorption energies of HCQ/CQ towards nanoparticles have the following trend: PtNP > AuNP > AuAgNP > AgNP. This shows that PtNP has the highest affinity in comparison to the other types of nanoparticles. The (non)perturbative effects of this drug on the plasmonic absorption spectra of AgNP and AuNP with the time-dependent density functional theory. The effect of size and composition of NPs on the coating with HCQ and CQ were obtained to propose the appropriate candidate for drug delivery. This kind of modeling could help experimental groups to find efficient and safe therapies.

Theoretical inspection of the spin-crossover [Fe(tzpy)2(NCS)2] complex on Au(100) surface

We explore the deposition of the spin-crossover [Fe(tzpy)₂(NCS)₂] complex on the Au(100) surface by means of density functional theory (DFT) based calculations. Two different routes have been employed: low-cost finite cluster-based calculations, where both the Fe complex and the surface are maintained fixed while the molecule approaches the surface; and periodic DFT plane-wave calculations, where the surface is represented by a four-layer slab and both the molecule and surface are relaxed. Our results show that the bridge adsorption site is preferred over the on-top and fourfold hollow ones for both spin states, although they are energetically close. The LS molecule is stabilized by the surface, and the HS-LS energy difference is enhanced by about 15%-25% once deposited. The different Fe ligand field for LS and HS molecules manifests on the composition and energy of the low-lying bands. Our simulated STM images indicate that it is possible to distinguish the spin state of the deposited molecules by tuning the bias voltage of the STM tip. Finally, it should be noted that the use of a reduced size cluster to simulate the Au(100) surface proves to be a low-cost and reliable strategy, providing results in good agreement with those resulting from state-of-the-art periodic calculations for this system.

Controlling the Lifetime of the Triplet MLCT State in Fe(II) Polypyridyl Complexes through Ligand Modification

A computational study is presented in which two strategies of ligand modifications have been explored to invert the relative energy of the metal-to-ligand charge transfer (MLCT) and metal-centered (MC) state in Fe(II)-polypyridyl complexes. Replacing the bipyridines by stronger σ donors increases the ligand-field strength and pushes the MC state to higher energy, while the use of ligands with a larger π conjugation leads to lower MLCT energies.

Transition Metal Spin-State Energetics by MC-PDFT with High Local Exchange

The energetics of the spin states of transition metal complexes have been explored with a variety of electronic structure methods, but the calculations require a compromise between accuracy and affordability. In this work, the spin splittings of several iron complexes are studied with multiconfiguration pair-density functional theory (MC-PDFT). The results are compared to previously published results obtained by complete active space second-order perturbation theory (CASPT2) and CASPT2 with coupled-cluster semicore correlation (CASPT2/CC). In contrast to CASPT2's systematic overstabilization of high-spin states with respect to the CASPT2/CC reference, MC-PDFT with the tPBE on-top functional understabilizes high-spin states. This systematic understabilization is largely corrected by revising the exchange and correlation contributions to the on-top functional using the high local-exchange approximation (tPBE-HLE). Moreover, tPBE-HLE correctly predicts the spin of the ground state in most cases, while CASPT2 incorrectly predicts high-spin ground states in all cases. This is encouraging for practical work because tPBE and tPBE-HLE are faster than CASPT2 by a factor of 50 even in a moderately sized example.

Light-Induced Spin Crossover in an Intermediate-Spin Penta-Coordinated Iron(III) Complex

(PMe₃)₂FeCl₃ is an Fe(III) complex that exists in the intermediate-spin ground state in a distorted trigonal bipyramidal geometry. An electronic state with high-spin configuration lies in close vicinity to the ground state, making it a potential spin crossover candidate. A mechanistic account of the spin crossover from the lowest quartet state (Q₀) to the lowest sextet state (S₁) of this complex is provided by exploring both thermal and light-induced pathways. The presence of a large barrier between the two spin states suggests a possible thermal spin crossover at a rather high temperature. The light-induced spin crossover is investigated by employing complete active space self-consistent field calculations together with dynamic correlation and spin-orbit coupling for the lowest seven quartet and lowest five sextet states. The system in the Q₀ state upon light absorption is excited to the optically bright Q₄ LMCT state. By following minimum energy pathways along the electronic states, two light-induced pathways for spin crossover are identified. From the Q₄ state, the system can photo-regenerate the ground intermediate-spin state (Q₀) through an internal conversion of Q₄/Q₃ followed by Q₃/S₁ and S₁/Q₀ intersystem crossings. In an alternate route, through Q₄/S₂ intersystem crossing followed by S₂/S₁ internal conversion, the system can complete the spin crossover from the Q₀ to S₁ state.

Calculating spin crossover temperatures by a first-principles LDA+U scheme with parameter U evaluated from GW

The prediction of spin crossover (SCO) temperatures (T_1/2) depends sensitively on the description of local Coulomb correlation. Due to its balance between accuracy and computational cost, local density approximation combined with Hubbard U model (LDA+U) is an appealing tool for this purpose. Despite its accurate performance on energetic properties, such as spin adiabatic energy difference, it is well-known that the LDA+U approach would lose its predictive power if U is tuned to achieve close agreement with experiment for a certain property. On the other hand, a static U value cannot account for changes in the electronic structure. Here, we propose a framework to derive dynamical U (U_dyn) values for iron(ii) complexes from the many-body GW calculations. By performing model calculations on a series of compounds with varying ligand fields, we show that the U values determined in this way are local environment dependent, and the resulting LDA+U_dyn method could reproduce their experimental ground spin states. We present applications to selected SCO complexes illustrating that U_dyn considerably overcomes some of the drawbacks of employing a constant U in the calculation of thermochemical quantities. Using the described calculation procedure, the T_1/2 values are predicted with a small mean absolute error of 176 K with respect to experiment.

The Role of Vibrational Anharmonicity in the Computational Study of Thermal Spin Crossover

Spin crossover in transition metal complexes can be studied in great detail with computational chemistry. Over the years, the understanding has grown that the relative stability of high-spin (HS) versus low-spin (LS) states is a subtle balance of many factors that all need to be taken into account for a reliable description. Among the different contributions, the zero-point energy (ZPE) and the entropy play key roles. These quantities are usually calculated assuming a harmonic oscillator model for the molecular vibrations. We investigated the impact of including anharmonic corrections on the ZPE and the entropy and indirectly on the critical temperature of spin crossover. As test systems, we used a set of ten Fe(II) complexes and one Fe(III) complex, covering different coordination modes (mono-, bi-, and tri-dentate ligands), decreasing coordination number upon spin crossover, coordination by second- and third-row atoms, and changes in the oxidation state. The results show that the anharmonicity has a measurable effect, but it is in general rather small, and tendencies are not easily recognized. As a conclusion, we put forward that for high precision results, one should be aware of the anharmonic effects, but as long as computational chemistry is still struggling with other larger factors like the influence of the environment and the accurate determination of the electronic energy difference between HS and LS, the anharmonicity of the vibrational modes is a minor concern.

Benchmarking quantum chemistry methods for spin-state energetics of iron complexes against quantitative experimental data

The accuracy of relative spin-state energetics predicted by selected quantum chemistry methods: coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation theory (CASPT2, NEVPT2), multireference configuration interaction at the MRCISD+Q level, and a number of DFT methods, is quantitatively evaluated by comparison with the experimental data of four octahedral iron complexes. The available experimental data, either spin-forbidden transition energies or spin crossover enthalpies, are corrected for relevant environmental effects in order to derive the quantitative benchmark set of iron spin-state energetics. Comparison of theory predictions with the resulting reference data: (1) validates the high accuracy of the CCSD(T) method, particularly when based on Kohn-Sham orbitals, giving the maximum error below 2 kcal mol-1 and the mean absolute error (MAE) below 1 kcal mol-1; (2) corroborates the tendency of CASPT2 to systematically overstabilize higher-spin states by up to 5.5 kcal mol-1; (3) confirms that the latter problem is partly remedied by the recently proposed CASPT2/CC approach [Phung et al., J. Chem. Theory Comput., 2018, 14, 2446-2455]; (4) demonstrates that NEVPT2 performs worse than CASPT2, by giving errors up to 7 kcal mol-1; (5) shows that the accuracy of MRCISD+Q spin-state energetics strongly depends on the size-consistency correction: the Davidson-Silver and Pople corrections perform best (MAE < 3 kcal mol-1), whereas the standard Davidson correction is not recommended (MAE of 7 kcal mol-1). Only a few DFT methods (including the best performing ones identified in this study: B2PLYP-D3 and OPBE) are able to provide a balanced description of the spin-state energetics for all four studied iron complexes simultaneously, corroborating the non-universality problem of approximate density functionals.

Unveiling the role of intra and interatomic interactions in the energetics of reaction schemes: a quantum chemical topology analysis

In this work we present a detailed analysis of selected reaction schemes in terms of the atomic components of the electronic energy defined by the quantum theory of atoms in molecules and the interacting quantum atoms method. The aim is to provide an interpretation tool for the energy change involved in a chemical reaction by means of the atomic and interaction contributions to the energies of the molecules involved. Ring strain in cyclic alkanes, the resonance energy of aromatic and antiaromatic molecules, local aromaticity in polycyclic aromatic hydrocarbons, intermolecular bonding in hydrogen fluoride clusters, and hydration of d-block metal dications were selected for the study. It was found that in addition to the changes in the strong C-C interactions in the carbon skeleton of the organic molecular rings, other contributions not usually considered to be important such as those between C and H atoms (either bonded or not) need to be considered in order to account for the net energy changes. The analysis unveils the role of the ionic and covalent contributions to the hydrogen bonding in HF clusters and the energetic origin and extent of cooperative effects involved. Moreover, the "double-hump" behavior observed for the hydration energy trend of [M(H2O)6]2+ complexes is explained in terms of the deformation energy of the metal cation and the increasingly covalent metal-water interactions. In addition, proper comparisons with the description provided by other methodologies are briefly discussed. The topological approach proposed in this contribution proves to be useful for the description of energy changes of apposite reaction schemes in chemically meaningful terms.

Molecular Modeling Study toward Development of H2S-Free Removal of Iron Sulfide Scale from Oil and Gas Wells

A common problem that faces the oil and gas industry is the formation of iron sulfide scale in various stages of production. Recently an effective chemical formulation was proposed to remove all types of iron sulfide scales (including pyrite), consisting of a chelating agent diethylenetriaminepentaacetic acid (DTPA) at high pH using potassium carbonate (K₂CO₃). The aim of this molecular modeling study is to develop insight into the thermodynamics and kinetics of the chemical reactions during scale removal. A cluster approach was chosen to mimic the overall system. Standard density functional theory (B3LYP/6-31G*) was used for all calculations. Low spin K₄Fe(II)₄(S₂H)₁₂ and K₃Fe(II)(S₂H)₅ clusters were derived from the crystal structure of pyrite and used as mimics for surface scale FeS₂. In addition, K₅DTPA was used as a starting material too. High spin K₃Fe(II)DTPA, and K₂S₂ were considered as products. A series of K _m Fe(II)(S₂H) _n complexes (m = n-2, n = 5-0) with various carboxylate and glycinate ligands was used to establish the most plausible reaction pathway. Some ligand exchange reactions were investigated on even simpler Fe(II) complexes in various spin states. It was found that the dissolution of iron sulfide scale with DTPA under basic conditions is thermodynamically favored and not limited by ligand exchange kinetics as the activation barriers for these reactions are very low. Singlet-quintet spin crossover and aqueous solvation of the products almost equally contribute to the overall reaction energy. Furthermore, seven-coordination to Fe(II) was observed in both high spin K₃Fe(II)DTPA and K₂Fe(II)(EDTA)(H₂O) albeit in a slightly different manner.

In Search of the Reason for the Breathing Effect of MIL53 Metal-Organic Framework: An ab Initio Multiconfigurational Study

Multiconfigurational methods are applied to study electronic properties and structural changes in the highly flexible metal-organic framework MIL53(Cr). Via calculated bending potentials of angles, that change the most during phase transition, it is verified that the high flexibility of this material is not a question about special electronic properties in the coordination chemistry, but about overall linking of the framework. The complex posseses a demanding electronic structure with delocalized spin density, antifferomagnetic coupling and high multi-state character requiring multiconfigurational methods. Calculated properties are in good agreement with known experimental values confirming our chosen methods.

Nonclassical Single-State Reactivity of an Oxo-Iron(IV) Complex Confined to Triplet Pathways

C-H bond activation mediated by oxo-iron (IV) species represents the key step of many heme and nonheme O₂-activating enzymes. Of crucial interest is the effect of spin state of the Fe^IV(O) unit. Here we report the C-H activation kinetics and corresponding theoretical investigations of an exclusive tetracarbene ligated oxo-iron(IV) complex, [L^NHCFe^IV(O)(MeCN)]²⁺ (1). Kinetic traces using substrates with bond dissociation energies (BDEs) up to 80 kcal mol^-1 show pseudo-first-order behavior and large but temperature-dependent kinetic isotope effects (KIE 32 at -40 °C). When compared with a topologically related oxo-iron(IV) complex bearing an equatorial N-donor ligand, [L^TMCFe^IV(O) (MeCN)]²⁺ (A), the tetracarbene complex 1 is significantly more reactive with second order rate constants k'₂ that are 2-3 orders of magnitude higher. UV-vis experiments in tandem with cryospray mass spectrometry evidence that the reaction occurs via formation of a hydroxo-iron(III) complex (4) after the initial H atom transfer (HAT). An extensive computational study using a wave function based multireference approach, viz. complete active space self-consistent field (CASSCF) followed by N-electron valence perturbation theory up to second order (NEVPT2), provided insight into the HAT trajectories of 1 and A. Calculated free energy barriers for 1 reasonably agree with experimental values. Because the strongly donating equatorial tetracarbene pushes the Fe-d_x²-y² orbital above d_z², 1 features a dramatically large quintet-triplet gap of ∼18 kcal/mol compared to ∼2-3 kcal/mol computed for A. Consequently, the HAT process performed by 1 occurs on the triplet surface only, in contrast to complex A reported to feature two-state-reactivity with contributions from both triplet and quintet states. Despite this, the reactive Fe^IV(O) units in 1 and A undergo the same electronic-structure changes during HAT. Thus, the unique complex 1 represents a pure "triplet-only" ferryl model.

Multiconfiguration Pair-Density Functional Theory Predicts Spin-State Ordering in Iron Complexes with the Same Accuracy as Complete Active Space Second-Order Perturbation Theory at a Significantly Reduced Computational Cost

The spin-state orderings in nine Fe(II) and Fe(III) complexes with ligands of diverse ligand-field strength were investigated with multiconfiguration pair-density functional theory (MC-PDFT). The performance of this method was compared to that of complete active space second-order perturbation theory (CASPT2) and Kohn-Sham density functional theory. We also investigated the dependence of CASPT2 and MC-PDFT results on the size of the active-space. MC-PDFT reproduces the CASPT2 spin-state ordering, the dependence on the ligand field strength, and the dependence on active space at a computational cost that is significantly reduced as compared to CASPT2.

The IPEA dilemma in CASPT2

Multi-configurational second order perturbation theory (CASPT2) has become a very popular method for describing excited-state properties since its development in 1990. To account for systematic errors found in the calculation of dissociation energies, an empirical correction applied to the zeroth-order Hamiltonian, called the IPEA shift, was introduced in 2004. The errors were attributed to an unbalanced description of open-shell versus closed-shell electronic states and is believed to also lead to an underestimation of excitation energies. Here we show that the use of the IPEA shift is not justified and the IPEA should not be used to calculate excited states, at least for organic chromophores. This conclusion is the result of three extensive analyses. Firstly, we survey the literature for excitation energies of organic molecules that have been calculated with the unmodified CASPT2 method. We find that the excitation energies of 356 reference values are negligibly underestimated by 0.02 eV. This value is an order of magnitude smaller than the expected error based on the calculation of dissociation energies. Secondly, we perform benchmark full configuration interaction calculations on 137 states of 13 di- and triatomic molecules and compare the results with CASPT2. Also in this case, the excited states are underestimated by only 0.05 eV. Finally, we perform CASPT2 calculations with different IPEA shift values on 309 excited states of 28 organic small and medium-sized organic chromophores. We demonstrate that the size of the IPEA correction scales with the amount of dynamical correlation energy (and thus with the size of the system), and gets immoderate already for the molecules considered here, leading to an overestimation of the excitation energies. It is also found that the IPEA correction strongly depends on the size of the basis set. The dependency on both the size of the system and of the basis set, contradicts the idea of a universal IPEA shift which is able to compensate for systematic CASPT2 errors in the calculation of excited states.

Assessment of electronic structure methods for the determination of the ground spin states of Fe(ii), Fe(iii) and Fe(iv) complexes

We studied spin states of Fe²⁺ ion, gaseous FeO, and 14 Fe(ii), Fe(iii) and Fe(iv) complexes using density functional theory.

Diffusion Monte Carlo Perspective on the Spin-State Energetics of [Fe(NCH)6](2.)

The energy difference between the high spin and the low spin state of the model compound [Fe(NCH)6](2+) is investigated by means of Diffusion Monte Carlo (DMC), where special attention is dedicated to analyzing the effect of the fix node approximation on the accuracy of the results. For this purpose, we compare several Slater-Jastrow and multireference Slater-Jastrow trial wave functions. We found that a Slater-Jastrow trial wave function constructed with the generalized Kohn-Sham orbitals from hybrid DFT represents the optimal choice. This is understood by observing that hybrid functionals account for the subtle balance between exchange and correlation effects and the respective orbitals accurately describe the ligand-metal hybridization as well as the charge reorganization accompanying the spin transition. Finally the DMC results are compared with those obtained by Hartree-Fock, DFT, CASSCF, and CASPT2. While there is no clear reference value for the high spin-low spin energy difference, DMC and high level CCSD(T) calculations agree within around 0.3 eV.

Water Dissociation upon Adsorption onto Free Iron Clusters Is Size Dependent

Cationic iron clusters, produced through laser ablation and subsequently complexed with a water molecule Fen(+)-H2O (n = 6-15) are mass-selectively investigated via infrared multiple photon dissociation (IR-MPD) spectroscopy in the 300-1700 cm(-1) spectral range. The experimental data are complemented by density functional theory calculations at the OPBE/TZP level for the Fe13(+)-H2O system. The observed spectra can be explained by a mixture of clusters where for a majority water is adsorbed molecularly but for a small but significant fraction also dissociation of water molecules occurs. The bands observed at frequencies 300-700 cm(-1) exhibit regular, size-dependent frequency shifts, showing that (a) dissociation takes places on all cluster sizes and (b) the interaction of water with the cluster surface is not influenced much by the particular cluster structure. The intensity evolution of the absorption bands suggests that dissociation is increasingly probable for larger cluster sizes.

Molecular and Interfacial Calculations of Iron(II) Light Harvesters

Iron-carbene complexes show considerable promise as earth-abundant light-harvesters, and adsorption onto nanostructured TiO2 is a crucial step for developing solar energy applications. Intrinsic electron injection capabilities of such promising Fe(II) N-heterocyclic complexes (Fe-NHC) to TiO2 are calculated here, and found to correlate well with recent experimental findings of highly efficient interfacial injection. First, we examine the special bonding characteristics of Fe-NHC light harvesters. The excited-state surfaces are examined using density functional theory (DFT) and time-dependent DFT (TD-DFT) to explore relaxed excited-state properties. Finally, by relaxing an Fe-NHC adsorbed on a TiO2 nanocluster, we show favorable injection properties in terms of interfacial energy level alignment and electronic coupling suitable for efficient electron injection of excited electrons from the Fe complex into the TiO2 conduction band on ∼100 fs time scales.

Theoretical Study of Spin Crossover in 30 Iron Complexes

Iron complexes are important spin crossover (SCO) systems with vital roles in oxidative metabolism and promising technological potential. The SCO tendency depends on the free energy balance of high- and low-spin states, which again depends on physical effects such as dispersion, relativistic effects, and vibrational entropy. This work studied 30 different iron SCO systems with experimentally known thermochemical data, using 12 different density functionals. Remarkably general entropy-enthalpy compensation across SCO systems was identified (R = 0.82, p = 0.002) that should be considered in rational SCO design. Iron(II) complexes displayed higher ΔH and ΔS values than iron(III) complexes and also less steep compensation effects. First-coordination sphere ΔS values computed from numerical frequencies reproduce most of the experimental entropy and should thus be included when modeling spin-state changes in inorganic chemistry (R = 0.52, p = 3.4 × 10(-3); standard error in TΔS ≈ 4.4 kJ/mol at 298 K vs 16 kJ/mol of total TΔS on average). Zero-point energies favored high-spin states by 9 kJ/mol on average. Interestingly, dispersion effects are surprisingly large for the SCO process (average: 9 kJ/mol, but up to 33 kJ/mol) and favor the more compact low-spin state. Relativistic effects favor low-spin by ∼9 kJ/mol on average, but up to 24 kJ/mol. B3LYP*, TPSSh, B2PLYP, and PW6B95 performed best for the typical calculation scheme that includes ZPE. However, if relativistic and dispersion effects are included, only B3LYP* remained accurate. On average, high-spin was favored by LYP by 11-15 kJ/mol relative to other correlation functionals, and by 4.2 kJ/mol per 1% HF exchange in hybrids. 13% HF exchange was optimal without dispersion, and 15% was optimal with all effects included for these systems.

Theoretical Study of the Dissociation Energy of First-Row Metallocenium Ions

The bond dissociation energy of a series of metallocenium ions, i.e., the energy difference of the reaction MCp2(+) → MCp(+) + Cp· (with M = Ti, V, Cr, Mn, Fe, Co, and Ni), was studied by means of multiconfigurational perturbation theory (CASPT2, RASPT2, NEVPT2) and restricted coupled cluster theory (CCSD(T)). From a comparison between the results obtained from these different methods, and a detailed analysis of their treatment of electron correlation effects, a set of MCp(+)-Cp binding energies are proposed with an accuracy of 5 kcal/mol. The computed results are in good agreement with the experimental data measured by threshold photoelectron photoion coincidence (TPEPICO) spectroscopy but disagree with the more recent threshold collision-induced dissociation (TCID) experiments.

Conformational Stability and Spin States of Cobalt(II) Acetylacetonate: CASPT2 and DFT Study

Electronic structure and conformation of bis(acetylacetonate) cobalt(II), Co(acac)2, a prototypical mediator in controlled radical polymerization of olefins, is reinvestigated. The ab initio multiconfigurational CASSCF/CASPT2 method is used to resolve the doubts stemming from density functional theory results. We assign the quartet ground state for a single molecule and point at tetrahedral conformation as the preferred one. Several density functionals are tested against the ab initio calculations, and their performance is assessed. The strength of intermolecular interactions in the crystal structure composed of square-planar Co(acac)2 molecules ( Burgess , J. ; et al. Acta Crystallogr. 2000 , C56 , 649 - 650 ) is estimated to be sufficient for their planarization (suggested by Matyjaszewski , K. ; et al. Chem.-Eur. J. 2007 , 13 , 2480 - 2492 ).