Towards understanding performance differences between approximate density functionals for spin states of iron complexes

A divergent mode of activation of a nitrosyl iron complex with unusual antiangiogenic activity

Nitric oxide (NO) and nitroxyl (HNO) have gained broad attention due to their roles in several physiological and pathophysiological processes. Remarkably, these sibling species can exhibit opposing effects including the promotion of angiogenic activity by NO compared to HNO, which blocks neovascularization. While many NO donors have been developed over the years, interest in HNO has led to the recent emergence of new donors. However, in both cases there is an expressive lack of iron-based compounds. Herein, we explored the novel chemical reactivity and stability of the trans-[Fe(cyclam)(NO)Cl]Cl₂ (cyclam = 1,4,8,11-tetraazacyclotetradecane) complex. Interestingly, the half-life (t_1/2) for NO release was 1.8 min upon light irradiation, vs 5.4 h upon thermal activation at 37 °C. Importantly, spectroscopic evidence supported the generation of HNO rather than NO induced by glutathione. Moreover, we observed significant inhibition of NO donor- or hypoxia-induced HIF-1α (hypoxia-inducible factor 1α) accumulation in breast cancer cells, as well as reduced vascular tube formation by endothelial cells pretreated with the trans-[Fe(cyclam)(NO)Cl]Cl₂ complex. Together, these studies provide the first example of an iron-nitrosyl complex with anti-angiogenic activity as well as the potential dual activity of this compound as a NO/HNO releasing agent, which warrants further pharmacological investigation.

Exploring the Limit of Accuracy of the Global Hybrid Meta Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions

The hybrid meta density functionals M05-2X and M06-2X have been shown to provide broad accuracy for main group chemistry. In the present article we make the functional form more flexible and improve the self-interaction term in the correlation functional to improve its self-consistent-field convergence. We also explore the constraint of enforcing the exact forms of the exchange and correlation functionals through second order (SO) in the reduced density gradient. This yields two new functionals called M08-HX and M08-SO, with different exact constraints. The new functionals are optimized against 267 diverse main-group energetic data consisting of atomization energies, ionization potentials, electron affinities, proton affinities, dissociation energies, isomerization energies, barrier heights, noncovalent complexation energies, and atomic energies. Then the M08-HX, M08-SO, M05-2X, and M06-2X functionals and the popular B3LYP functional are tested against 250 data that were not part of the original training data for any of the functionals, in particular 164 main-group energetic data in 7 databases, 39 bond lengths, 38 vibrational frequencies, and 9 multiplicity-changing electronic transition energies. These tests include a variety of new challenges for complex systems, including large-molecule atomization energies, organic isomerization energies, interaction energies in uracil trimers, and bond distances in crowded molecules (in particular, cyclophanes). The M08-HX functional performs slightly better than M08-SO and M06-2X on average, significantly better than M05-2X, and much better than B3LYP for a combination of main-group thermochemistry, kinetics, noncovalent interactions, and electronic spectroscopy. More important than the slight improvement in accuracy afforded by M08-HX is the conformation that the optimization procedure works well for data outside the training set. Problems for which the accuracy is especially improved by the new M08-HX functional include large-molecule atomization energies, noncovalent interaction energies, conformational energies in aromatic peptides, barrier heights, multiplicity-changing excitation energies, and bond lengths in crowded molecules.

Cholesky Decomposition-Based Multiconfiguration Second-Order Perturbation Theory (CD-CASPT2): Application to the Spin-State Energetics of Co(III)(diiminato)(NPh)

The electronic structure and low-lying electronic states of a Co(III)(diiminato)(NPh) complex have been studied using multiconfigurational wave function theory (CASSCF/CASPT2). The results have been compared to those obtained with density functional theory. The best agreement with ab initio results is obtained with a modified B3LYP functional containing a reduced amount (15%) of Hartree-Fock exchange. A relativistic basis set with 869 functions has been employed in the most extensive ab initio calculations, where a Cholesky decomposition technique was used to overcome problems arising from the large size of the two-electron integral matrix. It is shown that this approximation reproduces results obtained with the full integral set to a high accuracy, thus opening the possibility to use this approach to perform multiconfigurational wave-function-based quantum chemistry on much larger systems relative to what has been possible until now.

Synthesis and electronic structure determination of N-alkyl-substituted bis(imino)pyridine iron imides exhibiting spin crossover behavior

Three new N-alkyl substituted bis(imino)pyridine iron imide complexes, ((iPr)PDI)FeNR ((iPr)PDI = 2,6-(2,6-(i)Pr(2)-C(6)H(3)-N═CMe)(2)C(5)H(3)N; R = 1-adamantyl ((1)Ad), cyclooctyl ((Cy)Oct), and 2-adamantyl ((2)Ad)) were synthesized by addition of the appropriate alkyl azide to the iron bis(dinitrogen) complex, ((iPr)PDI)Fe(N(2))(2). SQUID magnetic measurements on the isomeric iron imides, ((iPr)PDI)FeN(1)Ad and ((iPr)PDI)FeN(2)Ad, established spin crossover behavior with the latter example having a more complete spin transition in the experimentally accessible temperature range. X-ray diffraction on all three alkyl-substituted bis(imino)pyridine iron imides established essentially planar compounds with relatively short Fe-N(imide) bond lengths and two-electron reduction of the redox-active bis(imino)pyridine chelate. Zero- and applied-field Mössbauer spectroscopic measurements indicate diamagnetic ground states at cryogenic temperatures and established low isomer shifts consistent with highly covalent molecules. For ((iPr)PDI)FeN(2)Ad, Mössbauer spectroscopy also supports spin crossover behavior and allowed extraction of thermodynamic parameters for the S = 0 to S = 1 transition. X-ray absorption spectroscopy and computational studies were also performed to explore the electronic structure of the bis(imino)pyridine alkyl-substituted imides. An electronic structure description with a low spin ferric center (S = 1/2) antiferromagnetically coupled to an imidyl radical (S(imide) = 1/2) and a closed-shell, dianionic bis(imino)pyridine chelate (S(PDI) = 0) is favored for the S = 0 state. An iron-centered spin transition to an intermediate spin ferric ion (S(Fe) = 3/2) accounts for the S = 1 state observed at higher temperatures. Other possibilities based on the computational and experimental data are also evaluated and compared to the electronic structure of the bis(imino)pyridine iron N-aryl imide counterparts.

Steric, quantum, and electrostatic effects on S(N)2 reaction barriers in gas phase

Biomolecular nucleophilic substitution reactions, S(N)2, are fundamental and commonplace in chemistry. It is the well-documented experimental finding in the literature that vicinal substitution with bulkier groups near the reaction center significantly slows the reaction due to steric hindrance, but theoretical understanding in the quantitative manner about factors dictating the S(N)2 reaction barrier height is still controversial. In this work, employing the new quantification approach that we recently proposed for the steric effect from the density functional theory framework, we investigate the relative contribution of three independent effects-steric, electrostatic, and quantum-to the S(N)2 barrier heights in gas phase for substituted methyl halide systems, R(1)R(2)R(3)CX, reacting with the fluorine anion, where R(1), R(2), and R(3) denote substituting groups and X = F or Cl. We found that in accordance with the experimental finding, for these systems, the steric effect dominates the transition state barrier, contributing positively to barrier heights, but this contribution is largely compensated by the negative, stabilizing contribution from the quantum effect due to the exchange-correlation interactions. Moreover, we find that it is the component from the electrostatic effect that is linearly correlated with the S(N)2 barrier height for the systems investigated in the present study. In addition, we compared our approach with the conventional method of energy decomposition in density functional theory as well as examined the steric effect from the wave function theory for these systems via natural bond orbital analysis.

Molecular acidity: A quantitative conceptual density functional theory description

Accurate predictions of molecular acidity using ab initio and density functional approaches are still a daunting task. Using electronic and reactivity properties, one can quantitatively estimate pKa values of acids. In a recent paper [S. B. Liu and L. G. Pedersen, J. Phys. Chem. A 113, 3648 (2009)], we employed the molecular electrostatic potential (MEP) on the nucleus and the sum of valence natural atomic orbital (NAO) energies for the purpose. In this work, we reformulate these relationships on the basis of conceptual density functional theory and compare the results with those from the thermodynamic cycle method. We show that MEP and NAO properties of the dissociating proton of an acid should satisfy the same relationships with experimental pKa data. We employ 27 main groups and first to third row transition metal-water complexes as illustrative examples to numerically verify the validity of these strong linear correlations. Results also show that the accuracy of our approach and that of the conventional method through the thermodynamic cycle are statistically similar.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Chemical bonding and aromaticity in metalloporphyrins,

We report here the chemical bonding and aromaticity patterns in metalloporphyrins, which were obtained with density functional theory (DFT) calculations at the OPBE/TZP level. This level of theory was previously shown to be very accurate for determining spin-state splittings [J. Chem. Theory Comput. 2008, 4, 2057] of transition-metal complexes. We considered metalloporphyrins along the first-row transition metals (Sc–Zn) extended with alkaline-earth metals (Mg, Ca) and several second-row transition metals (Ru, Pd, Ag, Cd). An energy decomposition analysis was performed to study the metal–ligand interactions, which showed that almost all complexes are significantly stabilized through (covalent) orbital interactions. The only exception is with calcium as the central metal, which interacts with the porphyrin mainly through electrostatic interactions. Furthermore, we studied aromaticity patterns for these complexes by looking at a number of (structural and electronic) aromaticity descriptors, for both the inner-ring and outer-ring of the porphyrin and of the pyrroles. The inner-ring (N16) aromaticity is shown to be unaffected by metal complexation, while the outer-ring (N20) and the pyrrole (N5) aromaticities are found to increase significantly in the metal coordinated porphyrins.

Exploring the origin of the internal rotational barrier for molecules with one rotatable dihedral angle

Continuing our recent endeavor, we systematically investigate in this work the origin of internal rotational barriers for small molecules using the new energy partition scheme proposed recently by one of the authors [S. B. Liu, J. Chem. Phys. 126, 244103 (2007)], where the total electronic energy is decomposed into three independent components, steric, electrostatic, and fermionic quantum. Specifically, we focus in this work on six carbon, nitrogen, and oxygen containing hydrides, CH(3)CH(3), CH(3)NH(2), CH(3)OH, NH(2)NH(2), NH(2)OH, and H(2)O(2), with only one rotatable dihedral angle [angle]H-X-Y-H (X,Y=C,N,O). The relative contributions of the different energy components to the total energy difference as a function of the internal dihedral rotation will be considered. Both optimized-geometry (adiabatic) and fixed-geometry (vertical) differences are examined, as are the results from the conventional energy partition and natural bond orbital analysis. A wealth of strong linear relationships among the total energy difference and energy component differences for different systems have been observed but no universal relationship applicable to all systems for both cases has been discovered, indicating that even for simple systems such as these, there exists no omnipresent, unique interpretation on the nature and origin of the internal rotation barrier. Different energy components can be employed for different systems in the rationalization of the barrier height. Confirming that the two differences, adiabatic and vertical, are disparate in nature, we find that for the vertical case there is a unique linear relationship applicable to all the six molecules between the total energy difference and the sum of the kinetic and electrostatic energy differences. For the adiabatic case, it is the total potential energy difference that has been found to correlate well with the total energy difference except for ethane whose rotation barrier is dominated by the quantum effect.

Toward understanding the nature of internal rotation barriers with a new energy partition scheme: ethane and n-butane

On the basis of an alternative energy partition scheme where density-based quantification of the steric effect was proposed [Liu, S. B. J. Chem. Phys. 2007, 126, 244103], the origin of the internal rotation barrier between the eclipsed and staggered conformers of ethane and n-butane is systematically investigated in this work. Within the new scheme, the total electronic energy is decomposed into three independent components, steric, electrostatic, and fermionic quantum. The steric energy defined in this way is repulsive, exclusive, and extensive and intrinsically linked to Bader's atoms in molecules approach. Two kinds of differences, adiabatic (with optimal structure) and vertical (with fixed geometry), are considered for the molecules in this work. We find that in the adiabatic case the eclipsed conformer possesses a larger steric repulsion than the staggered conformer for both molecules, but in the vertical cases the staggered conformer retains a larger steric repulsion. For ethane, a linear relationship between the total energy difference and the fermionic quantum energy difference is discovered. This linear relationship, however, does not hold for n-butane, whose behaviors in energy component differences are found to be more complicated. The impact of basis set and density functional choices on energy components from the new energy partition scheme has been investigated, as has its comparison with another definition of the steric effect in the literature in terms of the natural bond orbital analysis through the Pauli Exclusion Principle. In addition, profiles of conceptual density functional theory reactivity indices as a function of dihedral angle changes have been examined. Put together, these results suggest that the new energy partition scheme provides insights from a different perspective of internal rotation barriers.

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations.Strongly-correlated phenomena emerging from symmetry breaking include the following.Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solid-state quantum-computing devices.Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit ro-vibrational excitation spectra, in analogy with natural molecules.At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit).Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the Gross-Pitaevskii solutions describing vortex formation.We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.

Protein Environment Facilitates O2 Binding in Non-Heme Iron Enzyme. An Insight from ONIOM Calculations on Isopenicillin N Synthase (IPNS)

Binding of dioxygen to a non-heme enzyme has been modeled using the ONIOM combined quantum mechanical/molecular mechanical (QM/MM) method. For the present system, isopenicillin N synthase (IPNS), binding of dioxygen is stabilized by 8-10 kcal/mol for a QM:MM (B3LYP:Amber) protein model compared to a quantum mechanical model of the active site only. In the protein system, the free energy change of O2 binding is close to zero. Two major factors consistently stabilize O2 binding. The first effect, evaluated at the QM level, originates from a change in coordination geometry of the iron center. The active-site model artificially favors the deoxy state (O2 not bound) because it allows too-large rearrangements of the five-coordinate iron site. This error is corrected when the protein is included. The corresponding effect on binding energies is 3-6 kcal/mol, depending on the coordination mode of O2 (side-on or end-on). The second major factor that stabilizes O2 binding is van der Waals interactions between dioxygen and the surrounding enzyme. These interactions, 3-4 kcal/mol at the MM level, are neglected in models that include only the active site. Polarization of the active site by surrounding amino acids does not have a significant effect on the binding energy in the present system.

Structural and Dynamic Properties of (SiO2)6 Silica Nanostructures: A Quantum Molecular Dynamics Study

Structural and dynamic properties of the building block of silica nanowires, (SiO2)6, are investigated by Born-Oppenheimer quantum molecular dynamics simulations. Thirteen conformers have been identified, seven of which have not been reported before. The energy component analysis shows that the lower electrostatic interaction differentiates the global minimum from the other structures. We also observe that the maximum hardness principle can be employed to justify the molecular stability for this system. Time profiles of a few density functional reactivity indices exhibit correlations of dynamic fluctuations between HOMO and LUMO and between chemical potential and hardness. Electrophilicity, nucleaofugality, and electrofugality indices are found to change concurrently and significantly, indicating that the nanostructures sampled during the dynamic process are exceedingly reactive and rich in chemistry.