Theory of chemical bonds in metalloenzymes IV: Hybrid‐DFT study of Rieske‐type [2Fe?2S] clusters

The Rieske‐type [2Fe? 2S] cores of electron‐transfer (ET) proteins in the mitochondrial respiratory chain have unusual properties, such as redox potentials and spectroscopy. In this study, part IV of a series, the inherent molecular structures and characteristic electronic structures of the Rieske‐type [2Fe? 2S] clusters are investigated using broken‐symmetry hybrid density functional theory (BS‐HDFT). Geometry optimizations for the oxidized and reduced states were performed and their characteristic vibrational modes are assigned. Magnetic properties are investigated using model Hamiltonians to describe the electron delocalization and the unsymmetric property. The parameters of the model Hamiltonian, such as exchange coupling J, valence delocalization B, and potential energy difference Δ, are evaluated from the BS‐HDFT calculations. The valence localization and excitation energy (ΔE) of the Rieske‐type [2Fe? 2S] cluster are discussed. The chemical bond nature is characterized by chemical indices from natural orbital analysis. Our theoretical results are reasonably consistent with experimental results. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Metabolic‐intermediate complex formation with cytochrome P450: Theoretical studies in elucidating the reaction pathway for the generation of reactive nitroso intermediate

Mechanism‐based inhibition (MBI) of cytochrome P450 (CYP) can lead to drug–drug interactions and often to toxicity. Some aliphatic and aromatic amines can undergo biotransformation reactions to form reactive metabolites such as nitrosoalkanes, leading to MBI of CYPs. It has been proposed that the nitrosoalkanes coordinate with the heme iron, forming metabolic‐intermediate complex (MIC), resulting in the quasi‐irreversible inhibition of CYPs. Limited mechanistic details regarding the formation of reactive nitroso intermediate and its coordination with heme‐iron have been reported. A quantum chemical analysis was performed to elucidate potential reaction pathways for the generation of nitroso intermediate and the formation of MIC. Elucidation of the energy profile along the reaction path, identification of three‐dimensional structures of reactive intermediates and transition states, as well as charge and spin density analyses, were performed using the density functional B3LYP method. The study was performed using Cpd I [iron (IV‐oxo] heme porphine with SH^? as the axial ligand) to represent the catalytic domain of CYP, simulating the biotransformation process. Three pathways: (i) N‐oxidation followed by proton shuttle, (ii) N‐oxidation followed by 1,2‐H shift, and (iii) H‐abstraction followed by rebound mechanism, were studied. It was observed that the proton shuttle pathway was more favorable over the whole reaction leading to reactive nitroso intermediate. This study revealed that the MIC formation from a primary amine is a favorable exothermic process, involving eight different steps and preferably takes place on the doublet spin surface of Cpd I . The rate‐determining step was identified to be the first N‐oxidation of primary amine. © 2012 Wiley Periodicals, Inc.     

The exact Fermi potential yielding the Hartree–Fock electron density from orbital‐free density functional theory

The exact expression for the Fermi potential yielding the Hartree–Fock electron density within an orbital‐free density functional formalism is derived. The Fermi potential, which is defined as that part of the potential that depends on the particles’ nature, is in this context given as the sum of the Pauli potential and the exchange potential. The exact exchange potential for an orbital‐free density functional formalism is shown to be the Slater potential.     

Theory of chemical bonds in metalloenzymes III: Full geometry optimization and vibration analysis of ferredoxin‐type [2Fe–2S] cluster

The nature of chemical bonds in a ferredoxin‐type [2Fe–2S] cluster has been investigated on the basis of natural orbitals and several bond indices developed in Parts I and II of this study. The broken‐symmetry hybrid density functional theory (BS‐HDFT) with spin projection approach has been applied to elucidate the natural orbitals and occupation numbers for a model compound [Fe₂S₂(SCH₃)₄] (1), which is used to calculate the indices. The molecular structure, vibration frequencies, electronic structures, and magnetic properties in both oxidized and reduced forms of 1 have been calculated and compared with the experimental values. The optimized molecular structures after approximate spin projection have been in good agreement with experimental data. The structure changes upon one‐electron reduction have been slight (<0.1 Å) and only limited around one side of the Fe atom. Raman and infrared (IR) spectra have been calculated, and their vibration modes have been assigned using the bridging ³⁴S isotope substitution. Their magnetic properties have been examined in terms of spin Hamiltonians that contain exchange interactions and double exchange interactions. The BS‐HDFT methods have provided the magnetic parameters; i.e., effective exchange integral (J) values and valence delocalization (B) values, which agree with the experimental results. It is found that large charge transfer (CT) from the bridging sulfur to the iron atoms has led to the strong antiferromagnetic interactions between iron atoms. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

An open‐source framework for analyzing N‐electron dynamics. II. Hybrid density functional theory/configuration interaction methodology

In this contribution, we extend our framework for analyzing and visualizing correlated many‐electron dynamics to non‐variational, highly scalable electronic structure method. Specifically, an explicitly time‐dependent electronic wave packet is written as a linear combination of N‐electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time‐dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open‐source Python program det CI@ORBKIT, which extends the capabilities of our recently published post‐processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom‐centered Gaussian‐type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one‐electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser‐driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher‐level method provided a judicious choice of functional is made. Broadband excitation of a medium‐sized organic chromophore further demonstrates the scalability of the method. In addition, the time‐dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance. © 2017 Wiley Periodicals, Inc.     

A density functional theory study on lewis acid‐catalyzed transesterification of β‐oxodithioesters

The detailed mechanisms of the Lewis acid‐catalyzed transesterification of β‐oxodithioesters at a solvent‐free condition were studied using density functional theory. Five possible reaction pathways, including one noncatalyzed (channel 1) and four Lewis acid‐catalyzed channels (SnCl₂‐catalyzed channels 2 and 3 and SnCl₂·2H₂O‐catalyzed channels 4 and 5), were investigated. Our calculated results indicate that the energy barriers of the catalyzed channels are significantly lower than that of channel 1. Channel 5, which has an energy barrier of 33.70 kcal/mol as calculated at the B3LYP/[6‐31G(d, p)+LANL2DZ] level, is the most energy‐favorable channel. Moreover, one water molecule of SnCl₂·2H₂O participated in the transesterification in channel 5. Thus, we report a novel function of the SnCl₂·2H₂O catalyst, which is quite different from the function of the conventional nonhydrated Lewis acid SnCl₂. To understand the function of these two Lewis acid catalysts better, the global reactivity indexes and natural bond orbital charge were analyzed. This work helps in understanding the function of the Lewis acid in transesterification, and it can provide valuable insight for the rational design of new Lewis acid catalysts. © 2014 Wiley Periodicals, Inc.     

About the compatibility between ansatzes and constraints for a local formulation of orbital‐free density functional theory

Functional properties that are exact for the Hohenberg–Kohn functional may turn into mutually exclusive constraints at a given level of ansatz. This is exemplarily shown for the local density approximation. Nevertheless, it is possible to reach exactly the Kohn–Sham data from an orbital‐free density functional framework based on simple one‐point functionals by starting from the Levy–Perdew–Sahni formulation. The energy value is obtained from the density‐potential pair, and therefore does not refer to the functional dependence of the potential expression. Consequently, the potential expression can be obtained from any suitable model and is not required to follow proper scaling behavior.     

Electronic structure and spectroscopic properties of 6‐aminophenanthridine and its derivatives: Insights from density functional theory

6‐Aminophenanthridine (6AP) and its derivatives show important biological activities as antiprion compounds and inhibitors of the protein folding activity of the ribosome. Both of these activities depend on the RNA binding property of these compounds, which has been recently characterized by fluorescence spectroscopy. Hence, fundamental insights into the photophysical properties of 6AP compounds are highly important to understand their biological activities. In this work, we have calculated electronic structures and optical properties of 6AP and its three derivatives 6AP8CF₃, 6AP8Cl, and 6APi by density functional theory (DFT) and time‐dependent density functional theory (TDDFT). Our calculated spectra show a good agreement with the experimental absorption and fluorescence spectra, and thus, provide deep insights into the optical properties of the compounds. Furthermore, comparing the results obtained with four different hybrid functionals, we demonstrate that the accuracy of the functionals varies in the order B3LYP > PBE0 > M062X > M06HF. © 2015 Wiley Periodicals, Inc.     

Cytochrome P450 compound I in the plane wave pseudopotential framework: GGA electronic and geometric structure of thiolate‐ligated iron(IV)–oxo porphyrin

The cytochromes P450 constitute a ubiquitous family of metalloenzymes, catalyzing manifold reactions of biological and synthetic importance via a thiolate‐ligated iron‐oxo (IV) porphyrin radical species denoted compound I (Cpd I). Experimental investigations have implicated this intermediate in a broad spectrum of biophysically interesting phenomena, further augmenting the importance of a Cpd I model system. Ab initio molecular dynamics, including Car–Parrinello and path integral methods, conjoin electronic structure theory with finite temperature simulation, affording tools most valuable to approach such enzymes. These methods are typically driven by density functional theory (DFT) in a plane‐wave pseudopotential framework; however, existing studies of Cpd I have been restricted to localized Gaussian basis sets. The appropriate choice of density functional and pseudopotential for such simulations is accordingly not obvious. To remedy this situation, a systematic benchmarking of thiolate‐ligated Cpd I is performed using several generalized‐gradient approximation (GGA) functionals in the Martins–Troullier and Vanderbilt ultrasoft pseudopotential schemes. The resultant electronic and structural parameters are compared to localized–basis DFT calculations using GGA and hybrid density functionals. The merits and demerits of each scheme are presented in the context of reproducing existing experimental and theoretical results for Cpd I. © 2013 Wiley Periodicals, Inc.     

Kinetic energy density for orbital‐free density functional calculations by axiomatic approach

An axiomatic approach is herein used to determine the physically acceptable forms for general D‐dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one‐point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large‐scale orbital free density functional theory calculations.     

Theory of variational calculation with a scaling correct moment functional to solve the electronic schrödinger equation directly for ground state one‐electron density and electronic energy

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a nonlinear, approximate density functional of a three spatial dimension one‐electron density for an N electron system which is tractable in practice, is a long‐desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital‐free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree–Fock (HF) and Kohn–Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫g_i( r ₁)g_k( r ₂)rd r ₁d r ₂, etc.) to estimate electron‐electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation. © 2012 Wiley Periodicals, Inc.     

Density functional studies on hydrogen‐bonded clusters of hydrogen halides and the interaction on halide anions

Density functional theory (DFT) calculations have been performed to study the structures and stability of X^?·(HX)_n=2–5 clusters where X = F, Cl, Br at B3LYP/6‐311++G** level of theory. The presence of halide ions in these clusters disintegrates the hydrogen halide clusters. All the hydrogen halides are then hydrogen bonded to the centrally placed halide ions, thereby forming multiple hydrogen bonds. The interaction energies have been corrected for the basis set superposition error (BSSE) using Boy's counterpoise correction method. Evidence for the destruction of hydrogen bonds in hydrogen halide clusters due to the presence of halide ions is further obtained from topological analysis and natural bond orbital analysis. The chemical hardness and chemical potential have been calculated for all the anion clusters. The above analysis reveals that hydrogen bonding in these systems is not an essentially electrostatic interaction. The nature of the stabilization interactions operative in these multiple hydrogen‐bonded clusters has been explained in terms of many‐body contribution to interaction energies. From these studies, an attempt has been made to understand the nature of the molecular properties resulting from different electronegativities of the halogens. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Differentiability of Lieb functional in electronic density functional theory

A solid understanding of the Lieb functional F_L is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of F_L at an ensemble‐V‐representable density are given by (minus) the potential. A widely accepted purported proof that F_L is Gâteaux differentiable at EV‐representable densities would say, “yes.” But that proof is fallacious, as shown here. F_L is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of F_L at an EV‐representable density ρ₀ in the direction of ρ₁ is given by the potential if ρ₀ and ρ₁ are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Regional self-interaction correction of density functional theory

We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizs?cker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional "pure" functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals.     

One‐particle density matrix functional for correlation in molecular systems

Based on the analysis of the general properties for the one‐ and two‐particle reduced density matrices, a new natural orbital functional is obtained. It is shown that by partitioning the two‐particle reduced density matrix in an antisymmeterized product of one‐particle reduced density matrices and a correction Γ^c we can derive a corrected Hartree–Fock theory. The spin structure of the correction term from the improved Bardeen–Cooper–Schrieffer theory is considered to take into account the correlation between pairs of electrons with antiparallel spins. The analysis affords a nonidempotent condition for the one‐particle reduced density matrix. Test calculations of the correlation energy and the dipole moment of several molecules in the ground state demonstrate the reliability of the formalism. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 317–323, 2003     

密度泛函理论模拟外电场对铁氧体电子结构的影响

通过密度泛函理论(DFT)模拟了3种典型的铁氧体(Fe₂O₃、Fe₃O₄和α-FeOOH)受外电场作用下的电子结构,研究了外电场对不同铁氧体电子结构的影响。DFT模拟结果显示：外电场的存在能够有效提高Fe₂O₃、Fe₃O₄和α-FeOOH晶体结构的价带位置,从而导致3种铁氧体的带隙出现明显的降低;当外电场强度为0.01 V·nm^-1时,Fe₂O₃、Fe₃O₄和α-FeOOH的带隙分别降低了0.36、0.12和0.34 eV;当电场增大至0.1 V·nm^-1时,Fe₂O₃晶体出现击穿现象,Fe—O化学键断裂导致Fe原子的电子沿外电场方向高度离域至相邻Fe原子,而Fe₃O₄和α-FeOOH则仅出现不同价带能级电子局域性增强且能量同质化,因而显示出相对稳定的物理化学结构。此外,外电场的存在可导致3种铁氧体价带电子均出现简并现象,且随电场强度增大而增强。3种铁氧体中,外电场的存在导致Fe₂O₃晶体中Fe原子的电荷密度增大而降低O原子的电荷密度; Fe₃O₄晶体结构中不同配位结构的Fe原子以及配位O原子的Hirshfeld电荷几乎不受外电场的影响; α-FeOOH晶体中共边FeO₆配位结构的Hirshfeld电荷受外电场影响较小,而共角FeO₆配位结构的Hirshfeld电荷受外电场影响较大,且H原子的电荷在强外电场作用下发生歧化响应。随着外电场强度逐渐增大,Fe₃O₄晶体的电子自旋态密度逐渐增大,而α-FeOOH晶体的电子自旋态密度则显示出降低的规律。     

密度泛函理论模拟外电场对铁氧体电子结构的影响

通过密度泛函理论(DFT)模拟了3种典型的铁氧体(Fe₂O₃、Fe₃O₄和α-FeOOH)受外电场作用下的电子结构,研究了外电场对不同铁氧体电子结构的影响。DFT模拟结果显示:外电场的存在能够有效提高Fe₂O₃、Fe₃O₄和α-FeOOH晶体结构的价带位置,从而导致3种铁氧体的带隙出现明显的降低;当外电场强度为0.01 V·nm^-1时,Fe₂O₃、Fe₃O₄和α-FeOOH的带隙分别降低了0.36、0.12和0.34 eV;当电场增大至0.1 V·nm^-1时,Fe₂O₃晶体出现击穿现象,Fe—O化学键断裂导致Fe原子的电子沿外电场方向高度离域至相邻Fe原子,而Fe₃O₄和α-FeOOH则仅出现不同...     

First‐order correlation‐kinetic contribution to Kohn–Sham exchange charge density function in atoms,using quantal density functional theory approach

Using the static exchange‐correlation charge density concept, the total integrated exchange‐charge density function is calculated within the nonrelativistic spin‐restricted exchange‐only (i) optimized effective potential model, and (ii) nonvariational local potential derived from the exchange‐only work potential within the quantal density functional theory, for the ground‐state isoelectronic series: Ga⁺, Zn, Cu^?; In⁺, Cd, Ag^?; and Tl⁺, Hg, Au^?. The difference between the exchange charge density function derived from these potentials is employed to evaluate the first‐order correlation‐kinetic contribution to the integrated exchange charge density. This contribution is found to be important for both the intra‐ and inter‐shell regions. Screening effects on the contribution due to the nd¹⁰ (n = 3–5) subshells are discussed through comparisons with similar calculations on Ca, Sr, and Ba, wherein nd¹⁰ electrons are absent. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005