Quantum Chemical Modeling of Pressure-Induced Spin Crossover in Octahedral Metal-Ligand Complexes

Achieving Pressure Consistency in Mechanochemical Simulations of Chemical Reactions Under Pressure

The eXtended Hydrostatic Compression Force Field (X-HCFF) is a mechanochemical approach in which a cavity is used to exert hydrostatic pressure on a target system. The cavity used in this method is set up to represent the van der Waals (VDW) surface of the system by joining spheres sized according to the respective atomic VDW radii. The size of this surface can be varied via a scaling factor, and it can be shown that the compression forces exerted in X-HCFF in its current implementation depend on this factor. To address this dependency, we have developed a rescaling formalism for the applied forces, allowing us to drastically reduce the dependency of the compression forces on the chosen scaling factor. Independency from the scaling factor is important, as the scaling of the VDW spheres is often used to ensure an overlap of cavities in supramolecular complexes, which is necessary for the simulation of chemical reactions. Our rescaling formalism reduces the empiricism of the X-HCFF approach and boosts its applicability in the field of computational high-pressure chemistry.

Putting the squeeze on valence tautomerism in cobalt-dioxolene complexes

Molecules that can reversibly switch between electronic states under an external stimulus are of interest to numerous applications. Complexes of open shell metal ions with redox active ligands undergo valence tautomerism, resulting in magnetic, colour and structural switching, relevant to data storage and actuators. However, the precise structural changes occurring during valence tautomerism in the solid state are unclear due to the lack of atomic-resolution characterization. Here, variable temperature and high-pressure single crystal X-ray diffraction is used to characterize valence tautomerism in two isostructural cobalt complexes, [Co(bis(6-methyl-2-pyridylmethyl) amine)(3,5-di-tert-butyl-1,2-dioxolene)]+ and [Co(tris(6-methyl-2-pyridylmethyl)amine)(3,5-di-tert-butyl-1,2-dioxolene)]+ to atomic resolution. The less sterically hindered dimethylated complex exhibits two-step thermally-induced interconversion between the high-spin CoII-seminquinonate and low-spin CoIII-catecholate forms (valence tautomerism) at 155 and 95 K due to the presence of two symmetry-independent complexes. In contrast, the more sterically hindered trimethylated complex does not display thermal valence tautomerism. Both complexes exhibit unique behaviour under high pressure. The dimethylated species undergoes gradual, one-step valence tautomerism in both symmetry-independent complexes concurrently between 0.43 GPa and 1.30 GPa. In the trimethylated species, pressure is sufficient to overcome steric hindrance, leading to one-step valence tautomerism between 2.60 GPa and 3.10 GPa, demonstrating pressure-triggered valence tautomerism in a thermally inactive complex. This study is among the few investigations using in situ high-pressure single crystal X-ray diffraction to achieve atomic-level structural characterization of valence tautomerism, aiding the development of robust structure-property relationships in these types of complexes.

Bond Lengths and Dipole Moments of Diatomic Molecules under Isotropic Pressure with the XP-PCM and GOSTSHYP Models

While high-pressure chemistry has a well-established history, methods to simulate pressure at the single-molecule level have been somewhat lacking. The current work aims at comparing two static models (XP-PCM and GOSTSHYP) to apply isotropic pressure to single molecules, focusing on the equilibrium bond length and electric dipole moment of diatomic molecules. Numerical challenges arising in the potential energy surface using the XP-PCM method were examined, and a pragmatic approach was followed to mitigate these. The definition of the cavity was scrutinized, and two approaches to retrieve the isotropic character that could potentially be lost when using the standard methodology were suggested. Subsequently, equilibrium bond lengths under pressure were evaluated, showing reasonable agreement between GOSTSHYP and XP-PCM, but some discrepancies persist. A Taylor series analysis introduced elsewhere was then applied to rationalize the observed trends in terms of the bond surface. Finally, the dipole moment was shown to be highly sensitive to the cavity definition, and qualitative agreement necessitates the use of our adapted procedure.

Calculating high-pressure vibrational frequencies analytically with the extended hydrostatic compression force field approach

We report the implementation of the analytical Hessian for the mechanochemical extended hydrostatic compression force field method in the Q-Chem program package. To verify the implementation, the analytical Hessian was compared with finite difference calculations. In addition, we calculated the pressure dependency of the Raman active vibrational modes of methane, ethane, and hydrogen, as well as all IR and Raman active modes of Buckminsterfullerene, and compared the results with experimental and theoretical data. Our implementation paves the way for the analysis of geometric points on a pressure-deformed potential energy surface and provides a straightforward model to calculate the vibrational properties of molecules under high pressure.

Understanding Antiferromagnetic and Ligand Field Effects on Spin Crossover in a Triple-Decker Dimeric Cr(II) Complex

Two possible explanations for the temperature dependence of spin-crossover (SCO) behavior in the dimeric triple-decker Cr(II) complex ([(η5-C5Me5)Cr(μ2:η5-P5)Cr(η5-C5Me5)]+) have been offered. One invokes variations in antiferromagnetic interactions between the two Cr(II) ions, whereas the other posits the development of a strong ligand-field effect favoring the low-spin ground state. We perform multireference electronic structure calculations based on the multiconfiguration pair-density functional theory to resolve these effects. We find quintet, triplet, and singlet electronic ground states, respectively, for the experimental geometries at high, intermediate, and low temperatures. The ground-state transition from quintet to triplet at an intermediate temperature derives from increased antiferromagnetic interactions between the two Cr(II) ions. By contrast, the ground-state transition from triplet to singlet at low temperature can be attributed to increased ligand-field effects, which dominate with continued variations in antiferromagnetic coupling. This study provides quantitative detail for the degree to which these two effects can act in concert for the observed SCO behavior in this complex and others subject to temperature-dependent variations in geometry.

Trapping the Transition State in a [2,3]-Sigmatropic Rearrangement by Applying Pressure

Transition states are of central importance in chemistry. While they are, by definition, transient species, it has been shown before that it is possible to "trap" transition states by applying stretching forces. We here demonstrate that the task of transforming the transition state of a chemical reaction into a minimum on the potential energy surface can be achieved using hydrostatic pressure. We apply the computational extended hydrostatic compression force field (X-HCFF) approach to the educt of a [2,3]-sigmatropic rearrangement in both static and dynamic calculations and find that the five-membered cyclic transition state of this reaction becomes a minimum at pressures in the range between 100 and 150 GPa. Born-Oppenheimer molecular dynamics (BOMD) simulations suggest that slow decompression leads to a 70:30 mix of the product and the educt of the sigmatropic rearrangement. Our findings are discussed in terms of geometric parameters and electronic rearrangements throughout the reaction. To provide reference data for experimental investigations, we simulated the IR, Raman, and time-resolved UV/vis absorption spectra for the educt, transition state, and product. We speculate that the trapping of transition states by using pressure is generally possible if the transition state of a chemical reaction has a more condensed geometry than both the educt and the product, which paves the way for new ways of initiating chemical reactions.

Can a Finite Chain of Hydrogen Cyanide Molecules Model a Crystal?

When calculating structural or spectroscopic properties of molecular crystals, the question arises whether it is sufficient to simulate only a single molecule or a small molecular cluster or whether the simulation of the entire crystal is indispensable. In this work we juxtapose calculations on the high-pressure structural properties of the (periodic) HCN crystal and chains of HCN molecules of finite length. We find that, in most cases, the behavior of the crystal can be reproduced by computational methods simulating only around 15 molecules. The pressure-induced lengthening of the C-H bond in HCN found in calculations on both the periodic and finite material are explained in terms of orbital interaction. Our results pave the way for a more thorough understanding of high-pressure structural properties of materials and give incentives for the design of materials that expand under pressure. In addition, they shed light on the complementarity between calculations on periodic materials and systems of finite size.

Conceptual density functional theory under pressure: Part I. XP-PCM method applied to atoms

High pressure chemistry offers the chemical community a range of possibilities to control chemical reactivity, develop new materials and fine-tune chemical properties. Despite the large changes that extreme pressure brings to the table, the field has mainly been restricted to the effects of volume changes and thermodynamics with less attention devoted to electronic effects at the molecular scale. This paper combines the conceptual DFT framework for analyzing chemical reactivity with the XP-PCM method for simulating pressures in the GPa range. Starting from the new derivatives of the energy with respect to external pressure, an electronic atomic volume and an atomic compressibility are found, comparable to their enthalpy analogues, respectively. The corresponding radii correlate well with major known sets of this quantity. The ionization potential and electron affinity are both found to decrease with pressure using two different methods. For the electronegativity and chemical hardness, a decreasing and increasing trend is obtained, respectively, and an electronic volume-based argument is proposed to rationalize the observed periodic trends. The cube of the softness is found to correlate well with the polarizability, both decreasing under pressure, while the interpretation of the electrophilicity becomes ambiguous at extreme pressures. Regarding the electron density, the radial distribution function shows a clear concentration of the electron density towards the inner region of the atom and periodic trends can be found in the density using the Carbó quantum similarity index and the Kullback-Leibler information deficiency. Overall, the extension of the CDFT framework with pressure yields clear periodic patterns.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Modeling Molecules under Pressure with Gaussian Potentials

The computational modeling of molecules under high pressure is a growing research area that augments experimental high-pressure chemistry. Here, a new electronic structure method for modeling atoms and molecules under pressure, Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) approach, is introduced. In this method, a set of Gaussian potentials is distributed evenly on the van der Waals surface of the investigated chemical system, leading to a compression of the electron density and the atomic scaffold. Since no parameters other than pressure need to be specified, GOSTSHYP allows straightforward geometry optimizations and ab initio molecular dynamics simulations of chemical systems under pressure for nonexpert users. Calculated energies, bond lengths, and dipole moments under pressure fall within the range of established computational methods for high-pressure chemistry. A Diels-Alder reaction and the cyclotrimerization of acetylene showcase the ability of GOSTSHYP to model pressure-induced chemical reactions. The connection to mechanochemistry is pointed out.

The Mechanism of Flex-Activation in Mechanophores Revealed By Quantum Chemistry

Flex-activated mechanophores can be used for small-molecule release in polymers under tension by rupture of covalent bonds that are orthogonal to the polymer main chain. Using static and dynamic quantum chemical methods, we here juxtapose three different mechanical deformation modes in flex-activated mechanophores (end-to-end stretching, direct pulling of the scissile bonds, bond angle bendings) with the aim of proposing ways to optimize the efficiency of flex-activation in experiments. It is found that end-to-end stretching, which is a traditional approach to activate mechanophores in polymers, does not trigger flex-activation, whereas direct pulling of the scissile bonds or displacement of adjacent bond angles are efficient methods to achieve this goal. Based on the structural, energetic and electronic effects responsible for these observations, we propose ways of weakening the scissile bonds experimentally to increase the efficiency of flex-activation.

Quantitative and Chemically Intuitive Evaluation of the Nature of M-L Bonds in Paramagnetic Compounds: Application of EDA-NOCV Theory to Spin Crossover Complexes

To improve understanding of M-L bonds in 3d transition metal complexes, analysis by energy decomposition analysis and natural orbital for chemical valence model (EDA-NOCV) is desirable as it provides a full, quantitative and chemically intuitive ab initio description of the M-L interactions. In this study, a generally applicable fragmentation and computational protocol was established and validated by using octahedral spin crossover (SCO) complexes, as the transition temperature (T1/2 ) is sensitive to subtle changes in M-L bonding. Specifically, EDA-NOCV analysis of Fe-N bonds in five [FeII (Lazine )2 (NCBH3 )2 ], in both low-spin (LS) and paramagnetic high-spin (HS) states led to: 1) development of a general, widely applicable, corrected M+L6 fragmentation, tested against a family of five LS [FeII (Lazine )3 ](BF4 )2 complexes; this confirmed that three Lazine are stronger ligands (ΔEorb,σ+π =-370 kcal mol-1 ) than 2 Lazine +2 NCBH3 (=-335 kcal mol-1 ), as observed. 2) Analysis of Fe-L bonding on LS→HS, reveals more ionic (ΔEelstat ) and less covalent (ΔEorb ) character (ΔEelstat :ΔEorb 55:45 LS→64:36 HS), mostly due to a big drop in σ (ΔEorb,σ ↓50 %; -310→-145 kcal mol-1 ), and a drop in π contributions (ΔEorb,π ↓90 %; -30→-3 kcal mol-1 ). 3) Strong correlation of observed T1/2 and ΔEorb,σ+π , for both LS and HS families (R2 =0.99 LS, R2 =0.95 HS), but no correlation of T1/2 and ΔΔEorb,σ+π (LS-HS) (R2 =0.11). Overall, this study has established and validated an EDA-NOCV protocol for M-L bonding analysis of any diamagnetic or paramagnetic, homoleptic or heteroleptic, octahedral transition metal complex. This new and widely applicable EDA-NOCV protocol holds great promise as a predictive tool.

A mechanochemical model for the simulation of molecules and molecular crystals under hydrostatic pressure

A novel mechanochemical method for the simulation of molecules and molecular crystals under hydrostatic pressure, the eXtended Hydrostatic Compression Force Field (X-HCFF) approach, is introduced. In contrast to comparable methods, the desired pressure can be adjusted non-iteratively and molecules of general shape retain chemically reasonable geometries even at high pressure. The implementation of the X-HCFF approach is straightforward, and the computational cost is practically the same as for regular geometry optimization. Pressure can be applied by using any desired electronic structure method for which a nuclear gradient is available. The results of the X-HCFF for pressure-dependent intramolecular structural changes in the investigated molecules and molecular crystals as well as a simple pressure-induced dimerization reaction are chemically intuitive and fall within the range of other established computational methods. Experimental spectroscopic data of a molecular crystal under pressure are reproduced accurately.

Quantum Chemical Modeling of Pressure-Induced Spin Crossover in Octahedral Metal-Ligand Complexes

Spin state switching on external stimuli is a phenomenon with wide applicability, ranging from molecular electronics to gas activation in nanoporous frameworks. Here, we model the spin crossover as a function of the hydrostatic pressure in octahedrally coordinated transition metal centers by applying a field of effective nuclear forces that compress the molecule towards its centroid. For spin crossover in first-row transition metals coordinated by hydrogen, nitrogen, and carbon monoxide, we find the pressure required for spin transition to be a function of the ligand position in the spectrochemical sequence. While pressures on the order of 1 GPa are required to flip spins in homogeneously ligated octahedral sites, we demonstrate a fivefold decrease in spin transition pressure for the archetypal strong field ligand carbon monoxide in octahedrally coordinated Fe²⁺ in [Fe(II)(NH₃ )₅ CO]²⁺ .