Synthesis, X-ray analysis and DFT study of 2-amino-3-(N-oxipiridin-4-ilsulfanil)-propionic acid dihydrate

The title compound, C(8)H(14)N(2)O(5)S 2(H(2)O), 2-amino-3-(N-oxipiridin-4-ilsulfanil)-propionic acid dihydrate, is obtained by the reaction of cysteine and 4-nitropyridine N-oxide in dimethylformamide, removing the NO(2) group from the benzene ring and releasing nitrous acid into the solution. The molecule exists as a Zwitterion. Hydrogen bond interactions involving the title molecule and water molecules allow the formation of R(5)(5)(23) edge fused rings parallel to (010). Water molecules are connected independently, forming infinite chains (wires), in square wave form, along the b-axis. The chirality of the cysteine molecule used in the synthesis is retained in the title molecule. A density functional theory (DFT) optimized structure at the B3LYP/6-311G(3df,2p) level allows comparison of calculated and experimental IR spectra.

Extraction and purification of the zwitterions cylindrospermopsin and deoxycylindrospermopsin from Cylindrospermopsis raciborskii

The hepatotoxin cylindrospermopsin (CYN) has been isolated from the cyanobacterium Cylindrospermopsis raciborskii (C. raci.). Efforts to study this toxin have been hampered by the time-consuming requirement to extract it from cultures of the organism. It is usually extracted from lyophilized cells collected from a laboratory culture. Our preliminary work suggested far more of the toxin is available in solution in the culture media than in the cells collected. We have therefore investigated the use of commercially available solid phase extraction sorbents to extract CYN from culture media in which C. raci. has been grown. A range of reverse phase and ion-exchange sorbents were tested across a range of pHs for their ability to retain CYN without success. Subsequently, graphitized carbon cartridges were found to retain CYN strongly. Elution with 5% formic acid in methanol allowed the CYN to be regained for final purification by HPLC. Deoxy-CYN, an analog of CYN can also be extracted using this procedure. (C) 2001 John Wiley & Sons, Inc.

2-pyrazinylnitrene and 4-pyrimidylnitrene. Ring expansion to 1,3,5-triazacyclohepta-1,2,4,6-tetraene and ring opening to (2-isocyanovinyl)carbodiimide

Tetrazolo[1,5-a]pyrazine/2-azidopyrazine 9T/9A undergo photolysis in Ar matrix at cryogenic temperatures to yield 1,3,5-triazacyclohepta-1,2,4,6-tetraene 21 as the first observable intermediate, and 1-cyanoimidazole 11 and (2-isocyanovinyl)carbodiimide 22 as the final products. The latter tautomerizes to 2-(isocyanovinyl)cyanamide 23 on warming to 40 K. The same intermediate 21 and the same final products are obtained on matrix photolysis of the isomeric tetrazolo[1,5-c]pyrimidine/4-azidopyrimidine 24T/24A. These photolysis results as well as those of the previously reported thermal ring contraction of N-15-labeled 2-pyrazinyl- and 4-pyrimidylnitrenes to 1-cyanoimidazoles can all be rationalized in terms of selective ring opening of 21 or nitrine 10 to a nitrile ylide zwitterion 28 prior to formation of the final products, 11 and 22. The results are supported by high-level ab initio and DFT calculations (CASPT2-CASSCF(6,6), G3(MP2), and B3LYP/6-31+G*) of the energies and IR spectra of the intermediates and products.

Quinolizine-2,4-diones by reversible dimerisation 2-pyridylketenes

Quinolizine-2,4-diones 11 are obtained by ash vacuum thermolysis (FVT) of 3-acyl-1,2,3-triazolo[1,5-a]pyridines 7. The reaction takes place via methyl- and phenyl(2-pyridyl)ketenes 10, which are directly observable by infrared spectroscopy in low temperature matrices. FVT of 11 regenerates the ketenes 10.

Chemistry of stable iminopropadienones, RN=C=C=C=O

The synthesis, spectroscopic properties, and chemical reactions of the stable (neopentylimino)-, (mesitylimino)-, and (o-tert-butylphenylimino)propadienones (6) are reported. Nucleophilic addition of amines affords the malonic amidoamidines 7 and 8. 3,5-Dimethylpyrazole reacts analogously to form 9b. Addition of 1,2-dimethylhydrazine produces pyrazolinones 10-12. Addition of N,Y'-dimethyldiaminoethane, -propane, and -butane gives diazepine, diazocine, and diazonine derivatives 13-15, respectively (X-ray structures of 13c, 14a, and 15a are available). The mesoionic pyridopyrimidinium olates IS are obtained by addition of 2-(methylamino)pyridine (X-ray structure of 18b available). Primary 2-aminopyridines afford the pyridopyrimidininones 20-29 and 31 (X-ray structure of 21a available), and 2-aminopyrimidines and 2-aminopyrazine afford pyrimidopyrimidinones and pyrazinopyrimidinones 33-35. Pyrimidoisoquinolinone 36 results from 1-aminoisoquinoline and pyridoquinolinone 40 from 8-aminoquinoline. 2-Aminothiazoline and 2-aminothiazole afford thiazolopyrimidinone derivatives 41-43 (X-ray structure of 43a available).

Influence of ionization state on the activation of temocapril by hCES1: a molecular-dynamics study.

Temocapril is a prodrug whose hydrolysis by carboxylesterase 1 (CES1) yields the active ACE inhibitor temocaprilat. This molecular-dynamics (MD) study uses a resolved structure of the human CES1 (hCES1) to investigate some mechanistic details of temocapril hydrolysis. The ionization constants of temocapril (pK1 and pK3) and temocaprilat (pK1, pK2, and pK3) were determined experimentally and computationally using commercial algorithms. The constants so obtained were in good agreement and revealed that temocapril exists mainly in three ionic forms (a cation, a zwitterion, and an anion), whereas temocaprilat exists in four major ionic forms (a cation, a zwitterion, an anion, and a dianion). All these ionic forms were used as ligands in 5-ns MS simulations. While the cationic and zwitterionic forms of temocapril were involved in an ion-pair bond with Glu255 suggestive of an inhibitor behavior, the anionic form remained in a productive interaction with the catalytic center. As for temocaprilat, its cation appeared trapped by Glu255, while its zwitterion and anion made a slow departure from the catalytic site and a partial egress from the protein. Only its dianion was effectively removed from the catalytic site and attracted to the protein surface by Lys residues. A detailed mechanism of product egress emerges from the simulations.

Distribution profile of zwitterions and hydrolysis of esters derived from N-benzylpiperazine

Résumé Les esters sont des agents thérapeutiques largement utilisés comme médicaments et prodrogues. Leurs dégradation est chimique et enzymatique. Le Chapitre IV de cette thèse a comme objet l'hydrolyse chimique de plusieurs dérivés esters du 2,3-dimethoxyphenol. Des composés modèles ont été synthétisés dans le but de déterminer leur mécanismes de dégradation. Les profils d'ionisation et d'hydrolyse de ces composés ont permis d'identifier la présence d'une catalyse intramoléculaire basique par un atome d'azote non-protoné. Les effets électroniques exercés par les groupes phenylethenyle et phenylcyclopropyle influencent également la vitesse d'hydrolyse des esters. La résolution des problèmes liés à l'adsorption et la perméation est devenue à nos jours l'étape limitante dans la conception de nouveaux médicaments car de trop nombreux candidats prometteurs ont échoué à cause d'une mauvaise biodisponibilité. La lipophilie décrit le partage d'un médicament entre une membrane lipidique et son environnement physiologique aqueux, et de ce fait elle influence sa pharmacocinétique. Des études récents ont mis en évidence l'importance de la détermination de la lipophilie des espèces ionisées vu leur considérable impact biologique. Le Chapitre V de cette thèse est centré sur une classe particulière de composés ionisables, les zwitterions. Plusieurs methoxybenzylpiperazines de nature zwitterionique ont été étudiées. Leurs profils d'ionisation ont montré que dans un large intervalle de pH, l'espèce prédominante est le zwitterion. Les profils de lipophilie ont montré que leur lipophilie est plus élevée que celles des zwitterions courants. Une interaction électrostatique entre l'oxygène du carboxylate et l'azote protoné est responsable de ce profil et rend la plupart des zwitterions non-donneurs de liaison hydrogène. Ces deux aspects peuvent favoriser le passage de la barrière hémato-éncephalique. Les données biologiques ont par la suite confirmé cette hypothèse pour un certain nombre de composés. Résumé large public Les esters sont des composés souvent rencontrés en chimie thérapeutique. Ils sont dégradés en milieu aqueux par une réaction d'hydrolyse, avec ou sans la participation d'enzymes. Dans ce travail de thèse, une série d'esters ont été étudiés dans le but d'établir une relation entre leur structure et les mécanismes responsables de leur dégradation chimique. Il a été prouvé que la dégradation est accélérée par un atome d'azote non-protoné. D'autres mécanismes peuvent intervenir en fonction du pH du milieu. La présence d'une liaison simple ou double ou d'un groupe phenylcyclopropyle peut également influencer la vitesse de dégradation. Il est essentiel, dans la conception de nouveaux médicaments, d'optimiser les étapes qui influencent leur distribution dans le corps. Ce dernier peut être visualisé comme une série infinie de compartiments aqueux séparés par des membranes lipidiques. La lipophilie est une propriété moléculaire importante qui décrit le passage des barrières rencontrées par les médicaments. Des études récentes ont mis en évidence l'importance de déterminer la lipophilie des espèces ionisées vu leur considérable impact biologique. Dans ce travail de thèse a été étudiée une série particulière de composés ionisables , les zwitterions. Une relation a été établie entre leur structure et leur proprietés physico-chimiques. Une lipophilie plus élevée par rapport à celle des zwitterions courants a été trouvée. Une interaction entre les groupes chargés des zwitterions étudiés est responsable de ce comportement inattendu et rend la plupart d'entre eux non-donneurs de liaison hydrogène. Ces deux facteurs peuvent favoriser la pénétration cérébrale. Les données biologiques ont confirmé cette hypothèse pour un certain nombre de composés. Summary Esters are often encountered in medicinal chemistry. Their hydrolysis may be chemical as well as enzymatic. Chapter IV of this manuscript provides a mechanistic insight into the chemical hydrolysis of a particular series of basic esters derived from 2,3-dimethoxyphenol. Their ionization and pH-rate profiles allowed to identify the presence of an intramolecular base catalysis by a non-protonated nitrogen atom. Electronic effects exerted by the phenylethenyl and phenylcyclopropyl groups that are present in the structure of the esters also influenced their rate of hydrolysis. Numerous works in the literature witness of the importance of lipophilicity in determining the fate of a drug. Most published partition coefficients are those of neutral species. In contrast, no exhaustive treatment of the lipophilicity of charged molecules is available at present, and a lack of information characterizes in particular zwitterions. Chapter V of this manuscript provides an insight into the physicochemical parameters of a series of zwitterionic methoxybenzylpiperazines. Their ionization profiles showed that they exist predominantly in the zwitterionic form in a broad pH-range. An electrostatic interaction between the oxygen of the carboxylate and the protonated nitrogen atom is increases the lipophilicity of the investigated zwitterions, and prevents the majority of them to express their hydrogen-bonding capacity. These two aspects may favor the crossing of the blood-brain barrier. The available ratios PSt/PSf measured in vitro have confirmed this point for a number of compounds.

Modulating the electronic structure of amino acids: interaction of model lewis acids with anthranilic acid

On the basis of theoretical B3LYP calculations, Yáñez and co-workers (J. Chem. Theory Comput. 2012, 8, 2293) illustrated that beryllium ions are capable of significantly modulating (changing) the electronic structures of imidazole. In this computational organic chemistry study, the interaction of this β-amino acid and five model Lewis acids (BeF1+, Be2+, AlF2(1+), AlF2+, and Al3+) were investigated. Several aspects were addressed: natural bond orbitals, including second order perturbation analysis of intra-molecular charge delocalization and the natural population analysis atomic charges; molecular geometries; selected infrared stretching frequencies (C-N, C-O, and N-H), and selected ¹H-NMR chemical shifts. The data illustrate that this interaction can weaken the H-O bond and goes beyond strengthening the intra-molecular hydrogen bond (N...H-O) to cause a spontaneous transfer of the proton to the nitrogen atom in five cases generating zwitterion structures. Many new features are observed. Most importantly, the zwitterion structures include a stabilizing hydrogen bond (N-H...O) that varies in relative strength according to the Lewis acid. These findings explain the experimental observations of α-amino acids (for example: J. Am. Chem. Soc. 2001, 123, 3577) and are the first reported fundamental electronic structure characterization of β-amino acids in zwitterion form.

Reactivity characteristics of cytochrome c, cytochrome oxidase and the electrostatic cytochrome c - cytochrome oxidase complex /

The mechanism whereby cytochrome £ oxidase catalyses elec-. tron transfer from cytochrome £ to oxygen remains an unsolved problem. Polarographic and spectrophotometric activity measurements of purified, particulate and soluble forms of beef heart mitochondrial cytochrome c oxidase presented in this thesis confirm the following characteristics of the steady-state kinetics with respect to cytochrome £: (1) oxidation of ferrocytochrome c is first order under all conditions. -(2) The relationship between sustrate concentration and velocity is of the Michaelis-Menten type over a limited range of substrate. concentrations at high ionic strength. (3) ~he reaction rate is independent from oxygen concentration until very low levels of oxygen. (4) "Biphasic" kinetic plots of enzyme activity as a function of substrate concentration are found when the range of cytochrome c concentrations is extended; the biphasicity ~ is more apparent in low ionic strength buffer. These results imply two binding sites for cytochrome £ on the oxidase; one of high affinity and one of low affinity with Km values of 1.0 pM and 3.0 pM, respectively, under low ionic strength conditions. (5) Inhibition of the enzymic rate by azide is non-c~mpetitive with respect to cytochrome £ under all conditions indicating an internal electron transfer step, and not binding or dissociation of £ from the enzyme is rate limiting. The "tight" binding of cytochrome '£ to cytochrome c oxidase is confirmed in column chromatographic experiments. The complex has a cytochrome £:oxidase ratio of 1.0 and is dissociated in media of high ionic strength. Stopped-flow spectrophotometric studies of the reduction of equimolar mixtures and complexes of cytochrome c and the oxidase were initiated in an attempt to assess the functional relevance of such a complex. Two alternative routes -for reduction of the oxidase, under conditions where the predominant species is the £ - aa3 complex, are postulated; (i) electron transfer via tightly bound cytochrome £, (ii) electron transfer via a small population of free cytochrome c interacting at the "loose" binding site implied from kinetic studies. It is impossible to conclude, based on the results obtained, which path is responsible for the reduction of cytochrome a. The rate of reduction by various reductants of free cytochrome £ in high and low ionic strength and of cytochrome £ electrostatically bound to cytochrome oxidase was investigated. Ascorbate, a negatively charged reagent, reduces free cytochrome £ with a rate constant dependent on ionic strength, whereas neutral reagents TMPD and DAD were relatively unaffected by ionic strength in their reduction of cytochrome c. The zwitterion cysteine behaved similarly to uncharged reductants DAD and TI~PD in exhibiting only a marginal response to ionic strength. Ascorbate reduces bound cytochrome £ only slowly, but DAD and TMPD reduce bound cytochrome £ rapidly. Reduction of cytochrome £ by DAD and TMPD in the £ - aa3 complex was enhanced lO-fold over DAD reduction of free £ and 4-fold over TMPD reduction of free c. Thus, the importance of ionic strength on the reactivity of cytochrome £ was observed with the general conclusion being that on the cytochrome £ molecule areas for anion (ie. phosphate) binding, ascorbate reduction and complexation to the oxidase overlap. The increased reducibility for bound cytochrome £ by reductants DAD and TMPD supports a suggested conformational change of electrostatically bound c compare.d to free .£. In addition, analysis of electron distribution between cytochromes £ and a in the complex suggest that the midpotential of cytochrome ~ changes with the redox state of the oxidase. Such evidence supports models of the oxidase which suggest interactions within the enzyme (or c - enzyme complex) result in altered midpoint potentials of the redox centers.

Experimental and theoretical evidence for homogeneous catalysis in the gas-phase reaction of SiH2 with H2O (and D2O): a combined kinetic and quantum chemical study

Time-resolved kinetic studies of the reaction of silylene, SiH2, with H2O and with D2O have been carried out in the gas phase at 297 K and at 345 K, using laser flash photolysis to generate and monitor SiH2. The reaction was studied independently as a function of H2O (or D2O) and SF6 (bath gas) pressures. At a fixed pressure of SF6 (5 Torr), [SiH2] decay constants, k(obs), showed a quadratic dependence on [H2O] or [D2O]. At a fixed pressure of H2O or D2O, k(obs) Values were strongly dependent on [SF6]. The combined rate expression is consistent with a mechanism involving the reversible formation of a vibrationally excited zwitterionic donor-acceptor complex, H2Si...OH2 (or H2Si...OD2). This complex can then either be stabilized by SF6 or it reacts with a further molecule of H2O (or D2O) in the rate-determining step. Isotope effects are in the range 1.0-1.5 and are broadly consistent with this mechanism. The mechanism is further supported by RRKM theory, which shows the association reaction to be close to its third-order region of pressure (SF6) dependence. Ab initio quantum calculations, carried out at the G3 level, support the existence of a hydrated zwitterion H2Si...(OH2)(2), which can rearrange to hydrated silanol, with an energy barrier below the reaction energy threshold. This is the first example of a gas-phase-catalyzed silylene reaction.

Heterosite effects in novel heteronuclear clusters [OS2Ru(CO)(11)(PPh3)] and Os2Ru(CO)(10)(2-acetylpyridine-N-isopropylimine)]

A new synthetic route towards the mixed-metal cluster [OS2Ru(CO)(12)] is described together with the syntheses of its PPh3 and iPr-AcPy (iPr-AcPy = 2-acetylpyridine-N-isopropylimine) derivatives. The molecular structures of the novel clusters [Os2Ru(CO)(11)(PPh3)] and [Os2Ru(CO)(10)(iPr-AcPy)] were determined on the basis of crystalline solid solutions of the Os2Ru and corresponding Os-3 species. The structures reveal that coordination of the Lewis bases occurs exclusively at the ruthenium site of [Os2Ru(CO)(12)], which is in agreement with density functional theory (DFT) calculations on several structural isomers of these compounds. According to the time-dependent DFT results, the lowest optically accessible excited state of [Os2Ru(CO)(10)(iPr-AcPy)] has a prevailing sigma(Ru-Os-2)pi*(iPr-AcPy) character, with a partial sigma sigma*(Ru-Os-2) contribution. In weakly coordinating 2-chlorobutane, the excited state has a lifetime tau = 10.4 +/- 1.2 ps and produces biradicals considerably faster than observed for [Os-3(CO)10(iPr-AcPy) (tau = 25.3 +/- 0.7ps)]. In coordinating acetonitrile, the excited state of [Os2Ru(CO)(10)(iPr-AcPy)] decays mono-exponentially with a lifetime tau = 2.1 +/- 0.2 ps. In contrast to [Os-3(CO)(10)(iPr-AcPy)] that forms biradicals as the main primary photoproduct even in strongly coordinating solvents, zwitterion formation from the solvated lowest excited state is observed for the heterometallic cluster. This is concluded from time-resolved absorption studies in the microsecond time domain. Due to the lower tendency of the coordinatively unsaturated Ru+(CO)(2)(iPr-AcPy-/0) moiety to bind a Lewis base, the heteronuclear biradical and zwitterionic photoproducts live significantly shorter than their triosmium counterparts. The influence of the weaker Os-2-Ru(iPr-AcPy) bond on the redox reactivity is clearly reflected in very reactive radical anions formed upon electrochemical reduction of [Os2Ru(CO)(10)(iPr-AcPy)]. The dimer [-OS(CO)(4)-Os(CO)(4)-Ru(CO)(2)(iPr-AcPy)](2)(2-) is the only IR-detectable intermediate reduction product. The dinuclear complex [Os-2(CO)(8)](2-) and insoluble [Ru(CO)(2)(iPr-AcPy)](n), are the ultimate reduction products, proving fragmentation of the OS2Ru core.

Redox control of light-induced charge separation in a transition metal cluster: photochemistry of a methyl viologen-substituted [Os-3(CO)10(a-diimine)] cluster

Sub)picosecond transient absorption (TA) and time-resolved infrared (TRIR) spectra of the cluster [OS3(CO)(10-) (AcPy-MV)](2+) (the clication AcPy-MV = Acpy-MV2+ = [2-pyridylacetimine-N-(2-(1'-methyl-4,4'-bipyridine-1,1'-diium-1-yl) ethyl)] (PF6)(2)) (1(2+)) reveal that photoinduced electron transfer to the electron-accepting 4,4'-bipyridine-1,1'diium (MV2+) moiety competes with the fast relaxation of the initially populated sigmapi* excited state of the cluster to the ground state and/or cleavage of an Os-Os bond. The TA spectra of cluster 12 in acetone, obtained by irradiation into its lowest-energy absorption band, show the characteristic absorptions of the one-electron-reduced MV*(+) unit at 400 and 615 nm, in accordance with population of a charge-separated (CS) state in which a cluster-core electron has been transferred to the lowest pi* orbital of the remote MV2+ unit. This assignment is confirmed by picosecond TRIR spectra that show a large shift of the pilot highest-frequency nu(CO) band of 1(2+) by ca. +40 cm(-1), reflecting the photooxidation of the cluster core. The CS state is populated via fast (4.2 x 10(11) s(-1)) and efficient (88%) oxidative quenching of the optically populated sigmapi* excited state and decays biexponentially with lifetimes of 38 and 166 ps (1:2:1 ratio) with a complete regeneration of the parent cluster. About 12% of the cluster molecules in the sigmapi* excited state form long-lived open-core biradicals. In strongly coordinating acetonitrile, however, the cluster core-to-MV2+ electron transfer in cluster 12+ results in the irreversible formation of secondary photoproducts with a photooxidized cluster core. The photochemical behavior of the [Os-3(CO)(10)(alpha-diimine-MV)](2+) (donor-acceptor) dyad can be controlled by an externally applied electronic bias. Electrochemical one-electron reduction of the MV2+ moiety prior to the irradiation reduces its electron-accepting character to such an extent that the photoinduced electron transfer to MV*+ is no longer feasible. Instead, the irradiation of reduced cluster 1(.)+ results in the reversible formation of an open-core zwitterion, the ultimate photoproduct also observed upon irradiation of related nonsubstituted clusters [Os-3(CO)(10)(alpha-diimine)] in strongly coordinating solvents such as acetonitrile.

Intracellular or intercellular localization of the polar pathway of penetration across stratum corneum

A pharmacokinetic hypothesis of stratum corneum with two parallel pathways, lipophilic and porous hydrophilic, is not well documented yet. Still questionable is the localization of the pores, and the present experiments were designed to elucidate the contribution of extracellular lipids and intracellular keratin to the structure of this pathway. Percutaneous penetration of baclofen, a model zwitterion, was studied in vitro using human cadaver skin. Aqueous or ethanolic saturated solutions of the drug (Cs = 4.6 and 0.4 mg/ mL, respectively) were applied on the skin that was pretreated with: methanol/chloroform (Me/Ch) or acetone-chloroform (Ac/Ch) (1:1) mixtures, or with these solvents followed by 0.2% solution of sodium lauryl sulfate (SLS). As controls, baclofen penetration through the intact full-thickness skin was determined, and the fluxes were 0.18 ±0.08 and 0.14 ±0.07 µg/cm2/h for aqueous and ethanolic solutions, respectively. When Me/Ch was used for 1 h, an expected increase of the penetration was observed, but the lag time, Tlag, was still nearly 20 h. When the less polar mixture, Ac/Ch, was used, no flux enhancement was observed, and with ethanol as the vehicle, decreased penetration was even noted. No effect on baclofen penetration was observed when SLS was used for 1 h after delipidization of the skin was done with either the Me/Ch or Ac/Ch mixture. The results suggest that the polar pathway may be located intercellularly and comprises aqueous regions surrounded by polar lipids, which create the walls of such microchannels.

Cyclocreatine, an anticancer and neuroprotective agent. Spectroscopic, structural and theoretical study

The structural, spectroscopic and theoretical study of cyclocreatine (1-carboxymethyl-2-iminoimidazolidine, CyCre) has been performed prompted by the biological relevance of the molecule and its potential role as a ligand in biometalic compounds. The crystal structure of CyCre has been determined by X-ray diffraction methods. The compound crystallizes as a zwitterion in the monoclinic system, space group P2(1)/c. The crystal is further stabilized by a network of N-H center dot center dot center dot O bonds. Infrared and Raman spectra of the solid, electronic spectra of aqueous solutions at different pH values and (1)H and (13)C NMR spectra have been recorded and analyzed. Band assignments were accomplished with the help of theoretical calculations. Optimized molecular geometries, harmonic vibrational frequencies and molecular electrostatic potentials were calculated using methods based on the density functional theory. (C) 2010 Elsevier B.V. All rights reserved.