Local potentials in independent‐electron models

Density functional theory, exact for ground states, is commonly assumed to imply an independent‐electron model in which only local potential functions appear. It has recently been shown that several paradoxes in different aspects of the theory can be resolved if this locality hypothesis is abandoned. However, the locality hypothesis itself appears to be implied by rigorous variational theory. This conflict is discussed and resolved here. The resolution involves embedding the density functional theory in an orbital functional theory whose functional derivatives are not confined to normalized ground states. The orbital Euler–Lagrange equations of this extended theory in general contain effective potentials that are linear operators acting on orbital wave functions. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 384–388, 2001     

Link between the kinetic‐ and exchange‐energy functionals in the generalized gradient approximation

An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Comment on “density and physical current density functional theory” by Xiao‐Yin Pan and Viraht Sahni

A recent paper by Xiao‐Yin Pan and Viraht Sahni [Int. J. Quant. Chem. 110, 2833 (2010)] claims that current density functional theory should be based on the physical current density rather than the paramagnetic current density, as in the standard Vignale‐Rasolt formulation. In this comment we show that the claims in the paper by Pan and Sahni are erroneous. © 2012 Wiley Periodicals, Inc.     

The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

An approximate expression for the Pauli kinetic energy functional T_p is advanced in terms of the Liu‐Parr expansion [S. Liu, R.G. Parr, Phys. Rev. A 1997 , 55, 1792] which involves a power series of the one‐electron density. We use this explicit functional for T_p to compute the value of the noninteracting kinetic energy functional T_s of 34 atoms, from Li to Kr (and their positive and negative monoions). In particular, we examine the effect that a shell‐by‐shell mean‐square optimization of the expansion coefficients has on the kinetic energy values and explore the effect that the size of the expansion, given by the parameter n, has on the accuracy of the approximation. The results yield a mean absolute percent error for 34 neutral atoms of 0.15, 0.08, 0.04, 0.03, and 0.01 for expansions with n = 3, 4, 5, 6, and 7, respectively (where ). We show that these results, which are the most accurate ones obtained to date for the representation of the noninteracting kinetic energy functional, stem from the imposition of shell‐inducing traits. We also compare these Liu‐Parr functionals with the exact but nonexplicit functional generated in the local‐scaling transformation version of DFT.     

Toward the complete range separation of non‐hybrid exchange–correlation functional

In this study, we use a very simple scheme to achieve range separation of a total exchange–correlation functional. We have utilized this methodology to combine a short‐range pure density functional theory (DFT) functional with a corresponding long‐range pure DFT, leading to a “Range‐separated eXchange–Correlation” (RXC) scheme. By examining the performance of a range of standard exchange–correlation functionals for prototypical short‐ and long‐range properties, we have chosen B‐LYP as the short‐range functional and PBE‐B95 as the long‐range counterpart. The results of our testing using a more diverse range of data sets show that, for properties that we deem to be short‐range in nature, the performance of this prescribed RXC‐DFT protocol does resemble that of B‐LYP in most cases, and vice versa. Thus, this RXC‐DFT protocol already provides meaningful numerical results. Furthermore, we envisage that the general RXC scheme can be easily implemented in computational chemistry software packages. This study paves a way for further refinement of such a range‐separation technique for the development of better performing DFT procedures. © 2015 Wiley Periodicals, Inc.     

New theoretically predicted RDX‐ and β‐HMX‐based high‐energy‐density molecules

Theoretically new high‐energy‐density materials (HEDM) in which the hydrogens on RDX and β‐HMX (hexahydro‐1,3,5‐trinitro‐1,3,5‐triazine and octahydro‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocine, respectively) were sequentially replaced by (N NO₂)x functional groups were designed and evaluated using density functional theory calculations in combination with the Kamlet–Jacobs equations and an atoms‐in‐molecules (AIM) analysis. Improved detonation properties and reduced sensitivity compared to RDX and β‐HMX were predicted. Interestingly, the RDX and β‐HMX derivatives having one attached N NO₂ group [RDX‐(NNO₂)1 and HMX‐(NNO₂)1] showed excellent detonation properties (detonation velocities: 9.529 and 9.575 km·s⁻¹, and detonation pressures: 40.818 and 41.570 GPa, respectively), which were superior to the parent compounds. Sensitivity estimations obtained by calculating impact sensitivities and HOMO‐LUMO gaps indicated that RDX‐(NNO₂)1 and HMX‐(NNO₂)1 were less stable than RDX and HMX but more stable than any of the other derivatives. This method of sequential NNO₂ group attachment on conventional HEDMs offers a firm basis for further studies on the design of new explosives. Furthermore, the newly found structures may be promising candidates for better HEDMs.     

Pd‐Catalyzed Cycloisomerization of 4‐Aza‐1,6‐enynes to 3‐Aza‐bicyclo[4.1.0]hept‐2‐enes

A method for the synthesis of bicyclo[4.1.0]heptenes from 1,6‐enynes through Pd‐catalyzed cycloisomerization has been developed. N‐ and O‐tethered 1,6‐enynes were successfully transformed to their corresponding 3‐aza‐ and 3‐oxabicyclo[4.1.0]heptenes in reasonable‐to‐high yields using the catalysts [PdCl₂(CH₃CN)₂]/P(OPh)₃ or [Pd(maleimidate)₂(PPh₃)₂] in toluene. The computational calculations using density functional theory indicate that [PdCl₂{P(OPh)₃}] in the oxidation state Pd^II acts as the active catalyst species for the formation of 3‐azabicyclo[4.1.0]heptenes through 6‐endo‐dig cyclization.     

The Triboracyclopropenyl Dianion: The Lightest Possible Main‐Group‐Element Hückel π Aromatic

Hückel π aromaticity is typically a domain of carbon‐rich compounds. Only very few analogues with non‐carbon frameworks are currently known, all involving the heavier elements. The isolation of the triboracyclopropenyl dianion is presented, a boron‐based analogue of the cyclopropenyl cation, which belongs to the prototypical class of Hückel π aromatics. Reduction of Cl₂BNCy₂ by sodium metal produced [B₃(NCy₂)₃]^2?, which was isolated as its dimeric Na⁺ salt (Na₄[B₃(NCy₂)₃]₂?2 DME; 1 ) in 45 % yield and characterized by single‐crystal X‐ray diffraction. Cyclic voltammetry measurements established an extremely high oxidation potential for 1 (E_pc=?2.42 V), which was further confirmed by reactivity studies. The Hückel‐type π aromatic character of the [B₃(NCy₂)₃]^2? dianion was verified by various theoretical methods, which clearly indicated π aromaticity for the B₃ core of a similar magnitude to that in [C₃H₃]⁺ and benzene.     

DFT Calculations Suggest a New Type of Self‐Protection and Self‐Inhibition Mechanism in the Mammalian Heme Enzyme Myeloperoxidase: Nucleophilic Addition of a Functional Water rather than One‐Electron Reduction

The mammalian heme enzyme myeloperoxidase (MPO) catalyzes the reaction of Cl^? to the antimicrobial‐effective molecule HOCl. During the catalytic cycle, a reactive intermediate “Compound I” (Cpd I) is generated. Cpd I has the ability to destroy the enzyme. Indeed, in the absence of any substrate, Cpd I decays with a half‐life of 100 ms to an intermediate called Compound II (Cpd II), which is typically the one‐electron reduced Cpd I. However, the nature of Cpd II, its spectroscopic properties, and the source of the additional electron are only poorly understood. On the basis of DFT and time‐dependent (TD)‐DFT quantum chemical calculations at the PBE0/6‐31G* level, we propose an extended mechanism involving a new intermediate, which allows MPO to protect itself from self‐oxidation or self‐destruction during the catalytic cycle. Because of its similarity in electronic structure to Cpd II, we named this intermediate Cpd II′. However, the suggested mechanism and our proposed functional structure of Cpd II′ are based on the hypothesis that the heme is reduced by charge separation caused by reaction with a water molecule, and not, as is normally assumed, by the transfer of an electron. In the course of this investigation, we found a second intermediate, the reduced enzyme, towards which the new mechanism is equally transferable. In analogy to Cpd II′, we named it Fe^II′. The proposed new intermediates Cpd II′ and Fe^II′ allow the experimental findings, which have been well documented in the literature for decades but not so far understood, to be explained for the first time. These encompass a) the spontaneous decay of Cpd I, b) the unusual (chlorin‐like) UV/Vis, circular dichroism (CD), and resonance Raman spectra, c) the inability of reduced MPO to bind CO, d) the fact that MPO‐Cpd II reduces SCN^? but not Cl^?, and e) the experimentally observed auto‐oxidation/auto‐reduction features of the enzyme. Our new mechanism is also transferable to cytochromes, and could well be viable for heme enzymes in general.     

Electron correlations in Kohn–Sham exchange‐only theory

We provide an interpretation for the “exchange” energy and potential of Kohn–Sham exchange‐only theory, or equivalently that of the optimized potential method (OPM), which shows that in addition to contribution due to the Pauli exclusion principle, there is a kinetic component to these properties. The interpretation is in terms of a conservative field R ^OPM( r ), which is a sum of two fields, one representative of Pauli electron correlations and the other of kinetic effects. The OPM exchange potential is derived via the differential virial theorem to be the work done to move an electron in the field R ^OPM( r ). The OPM exchange energy is then expressed via the integral virial theorem in terms of this field. A similar interpretation for the energy and potential may also be derived directly from the OPM integral equation. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71:473–480, 1999     

Configuration of MFI-type zeolite interacting with the probe molecule P(CH<Subscript>3</Subscript>)<Subscript>3</Subscript> – a theoretical study

With P(CH₃)₃ as the probe molecule adsorbed on titanium silicalite (TS-1) zeolite, the special and important role of T12 site in MFI-type zeolite was clearly elucidated. There are altogether three active sites present in TS-1 zeolite with Ti at the T12 site. Owing to the preferential adsorption of probe molecules on the first Brönsted acidic site, the Ti12 center will probably fail to show Lewis acidity. The ionic [HP(CH₃)₃]⁺ species can be stabilized by the first or second Brönsted acidic site, with the former energetically favored. The latter was formed through the transfer of the ionic [HP(CH₃)₃]⁺ species from the first to the second Brönsted acidic site.     

Solid‐State 73Ge NMR Spectroscopy of Simple Organogermanes

Germanium‐73 is an extremely challenging nucleus to examine by NMR spectroscopy due to its unfavorable NMR properties. Through the use of an ultrahigh (21.1 T) magnetic field, a systematic study of a series of simple organogermanes was carried out. In those cases for which X‐ray structural data were available, correlations were drawn between the NMR parameters and structural metrics. These data were combined with DFT calculations to obtain insight into the structures of several compounds with unknown crystal structures.     

The Physical and Electronic Structure of M<Subscript>2</Subscript> Quadruply Bonded Complexes: A Density Functional Theory Study

The electronic structures and the physical properties (vertical excitation energies, vibrational stretching frequencies, and bond lengths) of a variety of M–M quadruply bonded (M = Mo, W) complexes are investigated using density functional theory (DFT). By utilizing a variety of pure and hybrid exchange-correlation (XC) functionals and a number basis sets, we are able to recommend a theoretical methodology for most efficiently probing the electronic structures of homoleptic M₂(O₂CR)₄ and bridged M₂(O₂C-X-CO₂)M₂ (R = organic group, typically H; X = conjugated organic group) complexes.

Metal‐Catalyzed Cyclization Reactions of 2,3,4‐Trien‐1‐ols: A Joint Experimental–Computational Study

Controlled preparation of tri‐ and tetrasubstituted furans, as well as carbazoles has been achieved through chemo‐ and regioselective metal‐catalyzed cyclization reactions of cumulenic alcohols. The gold‐ and palladium‐catalyzed cycloisomerization reactions of cumulenols, including indole‐tethered 2,3,4‐trien‐1‐ols, to trisubstituted furans was effective, due to a 5‐endo‐dig oxycyclization by attack of the hydroxy group onto the central cumulene double bond. In contrast, palladium‐catalyzed heterocyclization/coupling reactions with 3‐bromoprop‐1‐enes furnished tetrasubstituted furans. Also studied was the palladium‐catalyzed cyclization/coupling sequence involving protected indole‐tethered 2,3,4‐trien‐1‐ols and 3‐bromoprop‐1‐enes that exclusively generated trisubstituted carbazole derivatives. These results could be explained through a selective 6‐endo‐dig cumulenic hydroarylation, followed by aromatization. DFT calculations were carried out to understand this difference in reactivity.     

Magnetic‐Structure‐Stabilized Polarization in an Above‐Room‐Temperature Ferrimagnet

Above‐room‐temperature polar magnets are of interest due to their practical applications in spintronics. Here we present a strategy to design high‐temperature polar magnetic oxides in the corundum‐derived A₂BB′O₆ family, exemplified by the non‐centrosymmetric (R3) Ni₃TeO₆‐type Mn²⁺₂Fe³⁺Mo⁵⁺O₆, which shows strong ferrimagnetic ordering with T_C=337 K and demonstrates structural polarization without any ions with (n?1)d¹⁰ns⁰, d⁰, or stereoactive lone‐pair electrons. Density functional theory calculations confirm the experimental results and suggest that the energy of the magnetically ordered structure, based on the Ni₃TeO₆ prototype, is significantly lower than that of any related structure, and accounts for the spontaneous polarization (68 μC cm^?2) and non‐centrosymmetry confirmed directly by second harmonic generation. These results motivate new directions in the search for practical magnetoelectric/multiferroic materials.     

Ligand‐Controlled Synthesis of [3]‐ and [4]Cyclo‐9,9‐dimethyl‐2,7‐fluorenes through Triangle‐ and Square‐Shaped Platinum Intermediates

The syntheses of [3]‐ and [4]cyclo‐9,9‐dimethyl‐2,7‐fluorenes ([3] and [4]CFRs), cyclic trimer, and tetramers of 9,9‐dimethyl‐2,7‐fluorene (FR), respectively, were achieved by the platinum‐mediated assembly of FR units and subsequent reductive elimination of platinum. A triangle‐shaped tris‐platinum complex and a square‐shaped tetra‐platinum complex were obtained by changing the platinum ligand. The structure of the triangle complex was unambiguously determined by X‐ray crystallographic analysis. Reductive elimination of each complex gave [3] and [4]CFRs. Two rotamers of [3]CFR were sufficiently stable at room temperature and were separated by chromatography. The physical properties of the CFRs were also investigated theoretically and experimentally.