Influence of the protein and DFT method on the broken‐symmetry and spin states in nitrogenase

The enzyme nitrogenase contains a complicated MoFe₇CS₉ cofactor with 35 possible broken‐symmetry (BS) states. We have studied how the energies of these states depend on the geometry, the surrounding protein, the DFT functional and the basis set, studying the resting state, a one‐electron reduced state and a protonated state. We find that the effect of the basis set is small, up to 11 kJ/mol. Likewise, the effect of the surrounding protein is restricted, up to 10 and 7 kJ/mol for the electrostatic and van der Waals energy terms. Single‐point energies calculated on a single geometry give a good correlation (R² = 0.92‐0.98) to energies calculated after geometry optimization, but some BS states may be disfavored by up to 37 kJ/mol. A change from the pure TPSS functional to the hybrid B3LYP functional may change the relative energies by up to 58 kJ/mol and the correlation between the two results is only 0.57‐0.72. Both functionals agree that BS7 is the most stable BS state and that the ground spin state is the quartet for the resting state and the quintet for the reduced state. With the TPSS functional, the BS6 state is the second most stable state, always at least 21 kJ/mol less stable than the BS7 state. However, with the B3LYP functional, BS10 is the second most stable state and for the protonated state it comes close in energy. Based on these results, we suggest a procedure how to consider the 35 BS states in future investigations of the nitrogenase reaction mechanism.     

Theoretical study of aromaticity in small hydrogen and metal cation clusters X (X=H,Li, Na,K, and Cu)

Five cation clusters X (X=H, Li, Na, K, and Cu) with two possible isomers, i.e., regular trigonal structure (D_3h) and linear structure (D_∞h), have been investigated using four methods: B3LYP, B3PW91, MP2, CCSD(T) and basis set 6‐311+G(3df). The calculations show that only the regular trigonal structure (D_3h) is stable. The related neutral clusters X₃Cl (X=H, Li, Na, K, and Cu) are also investigated using two methods: B3LYP, MP2, and basis set 6‐311+G(3df). For H₃Cl species, there is no a stable structure to be found. For other four X₃Cl (X=Li, Na, K, and Cu) species, there are two stable isomers, for which the bidentate structures (C_2v‐1) [see Fig. 1 (d)] are global minima. According to the general criteria for aromaticity including resonance energy (RE) and nucleus‐independent chemical shift (NICS), the five trigonal isomers exhibit a higher degree of aromaticity. Molecular orbital analysis reveals that the five trigonal X(X=H, Li, Na, K, and Cu) isomers possess only σ‐aromaticity originating from s orbitals. For the Cu ring the d orbitals do not play a significant role in the electron delocalization effects. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Interaction of NO molecules with Pd clusters: Ab initio density–functional study

The adsorption of NO molecules on small Pd_n (n = 1?6) clusters has been studied using first‐principles density‐functional theory. Three adsorption sites were considered: vertex (on–top), bridge, and hollow. Adsorption is strong, ranging from 2 to 3 eV. In all cases NO adsorbs in a bent configuration. Calculated shifts in N–O bond vibration frequencies (with anharmonic corrections) agree very well with available experimental data. In contrast to metallic Pd surfaces, adsorption of NO on palladium clusters causes considerable changes in geometry around adsorption site because palladium d‐orbitals rehybridize to maximize the overlap with NO orbitals (mainly the antibonding π*). Thus, the overall energetic effect of NO adsorption is the result of two competing processes: lowering of the total energy through tighter bonding with NO and rising the energy due to cluster deformation. The Pd_n–NO bond creation is governed by electron transfer from Pd–d orbitals into the NO π*. As a result, the Pd cluster becomes locally demagnetized (with total magnetic moment of 1 μ_B located at Pd atoms not connected to NO) and the NO molecule is activated: the N–O bond length is increased and the vibration frequency is redshifted. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

The para‐didehydropyridine,para‐didehydropyridinium,and related biradicals—a contribution to the chemistry of enediyne antitumor drugs

Structure and stability of seven singlet (S) biradicals formed by Bergman cyclization from enediynes are investigated with unrestricted DFT using B3LYP/6‐31G(d,p) and B3LYP/6‐311+G(3df,3pd). The corresponding triplets (T) are also calculated and compared with their S states utilizing the on‐top pair density and the S‐T difference on‐top pair density. A relationship between the geometry of a S biradical, its stability, and its biradical character is established using the on‐top pair density and calculated S‐T splittings. Through‐bond coupling between the single electrons of the S biradical can be enhanced by the incorporation of a N atom into para‐didehydrobenzene 1 due to lowering of antibonding orbitals, shortening of ring bonds by anomeric effect, and increased overlap between the interacting orbitals. Strong through‐bond interactions lead to a stabilization of the S state and an increase of the S‐T splitting. Because through‐bond interactions also determine the degree of coupling between the single electrons, stabilization of the S biradical, and an increase of the S‐T splitting always means a lowering of the biradical character and the H abstraction ability, which is relevant for the use of N‐containing enediynes and their biradicals in connection with the design of new antitumor drugs. The S para‐didehydropyridine biradical 2 is strongly stabilized and, therefore, has only reduced biradical character. However, the latter can be enhanced by protonation, because this always leads to a lengthening of ring bonds and a reduction of the overlap between interacting orbitals. In the weakly acidic medium of a tumor cell, S biradicals containing an amidine group can be protonated to yield S biradicals with high biradical character (low S‐T splittings, small changes in bond alternation relative to the T state), which will abstract H atoms from the DNA of a tumor cell. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 216–229, 2001     

Ab initio molecular orbital theory study of GaAs clusters: The geometry

We have studied the structure and geometry of neutral and charged atomic clusters consisting of Ga and As atoms via ab initio Hartree–Fock (HF) and second‐order Møller–Plesset methods. The Ga_mAs_n cluster with m≠n composition prefers a nontetrahedral geometry in the charge neutral (q=0) state. These clusters tend to be stable in tetrahedral geometry when appropriately charged. The Ga_mAs_n cluster with m=n composition (1:1 ratio of Ga to As atoms) tends to be stable in a tetrahedral geometry in the charge neutral (q=0) state. With increasing size of the cluster, the geometry of Ga_nAs_n cluster approaches the zinc‐belende‐type crystalline structure. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 563–573, 2000     

Octacarbonyl Anion Complexes of Group Three Transition Metals [TM(CO)8]− (TM=Sc,Y, La) and the 18‐Electron Rule

We report the gas‐phase synthesis of stable 20‐electron carbonyl anion complexes of group 3 transition metals, TM(CO)₈⁻ (TM=Sc, Y, La), which are studied by mass‐selected infrared (IR) photodissociation spectroscopy. The experimentally observed species, which are the first octacarbonyl anionic complexes of a TM, are identified by comparison of the measured and calculated IR spectra. Quantum chemical calculations show that the molecules have a cubic (O_h) equilibrium geometry and a singlet (¹A_1g) electronic ground state. The 20‐electron systems TM(CO)₈⁻ are energetically stable toward loss of one CO ligand, yielding the 18‐electron complexes TM(CO)₇⁻ in the ¹A₁ electronic ground state; these exhibit a capped octahedral structure with C_3v symmetry. Analysis of the electronic structure of TM(CO)₈⁻ reveals that there is one occupied valence molecular orbital with a_2u symmetry, which is formed only by ligand orbitals without a contribution from the metal atomic orbitals. The adducts of TM(CO)₈⁻ fulfill the 18‐electron rule when only those valence electrons that occupy metal–ligand bonding orbitals are considered.     

Octacarbonyl Anion Complexes of Group Three Transition Metals [TM(CO)8]− (TM=Sc,Y, La) and the 18‐Electron Rule

We report the gas‐phase synthesis of stable 20‐electron carbonyl anion complexes of group 3 transition metals, TM(CO)₈^? (TM=Sc, Y, La), which are studied by mass‐selected infrared (IR) photodissociation spectroscopy. The experimentally observed species, which are the first octacarbonyl anionic complexes of a TM, are identified by comparison of the measured and calculated IR spectra. Quantum chemical calculations show that the molecules have a cubic (O_h) equilibrium geometry and a singlet (¹A_1g) electronic ground state. The 20‐electron systems TM(CO)₈^? are energetically stable toward loss of one CO ligand, yielding the 18‐electron complexes TM(CO)₇^? in the ¹A₁ electronic ground state; these exhibit a capped octahedral structure with C_3v symmetry. Analysis of the electronic structure of TM(CO)₈^? reveals that there is one occupied valence molecular orbital with a_2u symmetry, which is formed only by ligand orbitals without a contribution from the metal atomic orbitals. The adducts of TM(CO)₈^? fulfill the 18‐electron rule when only those valence electrons that occupy metal–ligand bonding orbitals are considered.     

On the triplet ground state of tetrahedral X4 clusters (X = Li, Na, K, Cu)

The lowest electronic state of distorted tetrahedral X(4) clusters (with X = Li, Na, K, Cu) is studied at coupled-cluster level using high-quality atomic basis sets. The ground state is found to have a triplet spin symmetry for this kind of geometry and for all the considered atomic species. The equilibrium geometries correspond to Jahn-Teller-distorted oblate tetrahedra having D(2d) symmetry, and tetrahedric structures are local minima on the potential-energy surfaces for the triplet states. Their energies lie between 0.2 eV (for the K(4) cluster) and 0.9 eV (for Cu(4)) above the absolute minimum of the corresponding systems, which is a spin singlet having a rhombus geometry.     

Size dependent structural and electronic properties of MgO nanotube clusters

MgO nanotube clusters which cross sections are composed of two‐, three‐, four‐, and five‐membered rings are constructed and studied by the density functional theory at B3LYP/6‐31G(d) level. The variations of bond length present anisotropic effect. Three‐membered ring nanotube cluster is the most stable tube among these MgO isomers. Mixed covalent and ionic bonding always exists in MgO nanotube clusters. With increasing length of MgO nanotube clusters, the averaged atomic charge increases, and converge to 1.227; the s‐p separation of O bands decreases; whereas energy gap nearby frontier orbitals present dramatic difference corresponding to various structure family. It is possible that MgO nanotube clusters show electronic properties of semiconductor. An interpretation for MgO nanotube clusters fabricated by simply thermal methods is proposed. The structural and electronic properties of MgO nanotube clusters are discussed systematically in details. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Adjusting magnetic moments of Sc13 and Y13 clusters by doping different X atom (X = Na,Mg, Al,Si, P)

We have investigated the structural and magnetic properties of the doped XM₁₂ and charged M₁₃ (X = Na, Mg, Al, Si, P; M = Sc, Y) clusters using the density‐functional theory with spin‐polarized generalized gradient approximation. It was found that doped atoms can induce significant change of the magnetic moments of Sc₁₃ and Y₁₃ clusters. The total magnetic moments of the NaM₁₂, MgM₁₂, AlM₁₂, SiM₁₂, and PM₁₂ clusters are regular 5, 6 (12), 7, 8, and 9 μ_b, respectively (but 19 μ_b for Sc₁₃ and Y₁₃, 12 μ_b for Y, 18 μ_b for Sc, Sc, and Y). The doped atom substituting the surface atom of the plausible icosahedral configuration is viewed as the ground‐state structure of the XM₁₂ (X = Na, P; M = Sc, Y) and MgSc₁₂ clusters. While for XM₁₂ (X = Al, Si; M = Sc, Y) and MgY₁₂ clusters, the doped atom occupying the central position of the icosahedral configuration is viewed as the ground‐state structure. The doping and the charging both enhance the stability of the Sc₁₃ and Y₁₃ clusters. These findings should have an important impact on the design of the adjustable magnetic moments systems. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Ab initio calculation of the NH(3sigma-)-NH(3sigma-) interaction potentials in the quintet, triplet, and singlet states

We present the ab initio potential-energy surfaces of the NH-NH complex that correlate with two NH molecules in their 3sigma- electronic ground state. Three distinct potential-energy surfaces, split by exchange interactions, correspond to the coupling of the S(A) = 1 and S(B) = 1 electronic spins of the monomers to dimer states with S = 0, 1, and 2. Exploratory calculations on the quintet (S = 2), triplet (S = 1), and singlet (S = 0) states and their exchange splittings were performed with the valence bond self-consistent-field method that explicitly accounts for the nonorthogonality of the orbitals on different monomers. The potential surface of the quintet state, which can be described by a single Slater determinant reference function, was calculated at the coupled cluster level with single and double excitations and noniterative treatment of the triples. The triplet and singlet states require multiconfiguration reference wave functions and the exchange splittings between the three potential surfaces were calculated with the complete active space self-consistent-field method supplemented with perturbative configuration interaction calculations of second and third orders. Full potential-energy surfaces were computed as a function of the four intermolecular Jacobi coordinates, with an aug-cc-pVTZ basis on the N and H atoms and bond functions at the midpoint of the intermolecular vector R. An analytical representation of these potentials was given by expanding their dependence on the molecular orientations in coupled spherical harmonics, and representing the dependence of the expansion coefficients on the intermolecular distance R by the reproducing kernel Hilbert space method. The quintet surface has a van der Waals minimum of depth D(e) = 675 cm(-1) at R(e) = 6.6a0 for a linear geometry with the two NH electric dipoles aligned. The singlet and triplet surfaces show similar, slightly deeper, van der Waals wells, but when R is decreased the weakly bound NH dimer with S = 0 and S = 1 converts into the chemically bound N2H2 diimide (also called diazene) molecule with only a small energy barrier to overcome.     

A hybrid ab initio/free electron computational model for conjugated dye molecules: Simple cyanines and oxonols

Justifications developed for the application the free electron model to the π‐orbitals of conjugated molecules suggest that the optical properties of these molecules would be well described by a one‐dimensional free electron model with a potential chosen to reproduce the energy level spacing of the ground state occupied π‐orbitals. Such a hybrid ab initio/free electron modeling approach, where the free electron potential parameters are optimized on a molecule‐by‐molecule basis, is developed, and applied to a series of simple cyanine and oxonol dyes. The ensuing predictions for λ_max, oscillator strengths, and redox properties compare well to available experimental information. Two important strengths of this approach are that no explicit calculations of the excited electronic state are required, and that the ab initio determination of the occupied π‐orbital level spacing considers all the electrons (π and σ) of the entire molecule in a specified geometry, environment, etc. This second characteristic gives the ability to efficiently model modifications of the optical properties of conjugated molecules resulting from chemical and/or physical modifications occuring within and remote to the conjugated region of the molecule. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 943–953, 2000     

Aromaticity of planar boron clusters confirmed

Low-energy boron clusters are characterized by two-dimensional geometry. Aromaticity of these planar boron clusters was established in terms of topological resonance energy (TRE). All planar boron clusters were found to be highly aromatic with large positive TREs even if they have 4n pi-electrons. Aromaticity must therefore be the origin of unusual planar or quasi-planar geometry. Thus, the aromaticity concept is as useful in boron chemistry as it is in general organic chemistry. It is evident that the Hückel 4n + 2 rule of aromaticity should not be applied to such polycyclic pi-systems. Some of the boron clusters are in the triplet electronic state to attain higher aromaticity. Multivalency and electron deficiency of boron atoms are responsible for lowering the energies of low-lying pi molecular orbitals and then for enhancing aromaticity. For polycyclic pi-systems, paratropicity does not always indicate antiaromaticity.     

Local density functional study of the structural and electronic properties of C60 and XC60 (X=K, Rb, Cs)

Results of first principles local density total energy and atomic force calculations carried out for free C₆₀ and XC₆₀ (X=K, Rb, Cs) molecular clusters are reported. The optimization of the geometry results in the bond lengths between adjacent carbon atoms being 1.387 and 1.445 Å, which are in very good agreement with the latest X-ray diffraction values. Energy levels, charge distributions, and wavefunction characteristics are obtained and discussed. The results for C₆₀ are in very good agreement with recently measured photoemission energy distribution curves (EDC) for the valence band states. The highest occupied molecular orbitals (HOMO) are found to be fully occupied H_u states and are 1.7 eV below the lowest unoccupied molecular orbitals (LUMO) which are of T_1u symmetry. Similar results obtained for the XC₆₀ clusters show that rigid-band-like behavior is found in the electronic structures after putting an alkali atom at the center of a C₆₀ ball. In each case, the alkali atom is almost fully ionized with the transferred electron distributed over the surface shell of C₆₀; the center region of the ball has very low charge density.     

Visible‐Light‐Activated C−C Bond Cleavage and Aerobic Oxidation of Benzyl Alcohols Employing BiMXO5 (M=Mg,Cd, Ni,Co, Pb,Ca and X=V,P)

The synthesis, structure, optical and photocatalytic studies of a family of compounds with the general formula, BiMXO₅; M=Mg, Cd, Ni, Co, Pb, Ca and X=V, P is presented. The compounds were prepared by regular solid‐state reaction of constituents in the temperature range of 720–810 °C for 24 h. The compounds were characterized by powder X‐ray diffraction (PXRD) methods. The Rietveld refinement of the PXRD patterns have been carried out to establish the structure. The optical absorption spectra along with the colors in daylight have been explained employing the allowed d‐d transition. In addition, the observed colors of some of the V⁵⁺ containing compounds were explained using metal‐to‐metal charge transfer (MMCT) from the partially filled transition‐metal 3d orbitals to the empty 3d orbitals of V⁵⁺ ions. The near IR (NIR) reflectivity studies indicate that many compounds exhibit good NIR reflectivity, suggesting that these compounds can be employed as ‘cool pigments’. The experimentally determined band gaps of the prepared compounds were found to be suitable to exploit them for visible light activated photocatalysis. Photocatalytic C?C bond cleavage of alkenes and aerobic oxidation of alcohols were investigated employing visible light, which gave good yields and selectivity. The present study clearly demonstrated the versatility of the Paganoite family of compounds (BiMXO₅) towards new colored inorganic materials, visible‐light photocatalysts and ‘cool pigments’.     

Topochemical Transformations of CaX2 (X=C,Si, Ge) to Form Free‐Standing Two‐Dimensional Materials

Topochemical transformations of layered materials CaX₂ (X=Si, Ge) are the method of choice for the high‐yield synthesis of pristine, defect‐free two‐dimensional systems silicane and germanane, which have advanced electronic properties. Based on solid‐state dispersion‐corrected calculations, mechanisms for such transformations are elucidated that provide an in‐depth understanding of phase transition in these layered materials. While formation of such layered materials is highly favorable for silicane and germanane, a barrier of 1.2 eV in the case of graphane precludes its synthesis from CaC₂ topochemically. The energy penalty required for distorting linear acetylene into a trans‐bent geometry accounts for this barrier. In contrast it is highly favorable in the heavier analogues, resulting in barrierless topochemical generation of silicane and germanane. Photochemical generation of the trans‐bent structure of acetylene in its first excited state (S₁) can directly generate graphane through a barrierless condensation. Unlike the buckled structure of silicene, the phase‐h of CaSi₂ with perfectly planar silicene layers exhibits the Dirac cones at the high symmetry points K and H. Interestingly, topochemical acidification of the cubic phase of calcium carbide is predicted to generate the previously elusive platonic hydrocarbon, tetrahedrane.     

Light Absorption Properties and Electronic Band Structures of Lead‐Vanadium Oxyhalide Apatites Pb5(VO4)3X (X=F,Cl, Br,I)

The Pb‐V oxyhalide apatite compounds Pb₅(VO₄)₃X (X=F, Cl, Br, I) were successfully synthesized using a facile solution method and studied with respect to their structural/optical characteristics and electronic band structures. UV‐visible diffuse reflectance spectroscopy, electrochemical analysis and first‐principles calculations showed that the synthesized apatites behaved as n‐type semiconductors, with absorption bands in the UV‐visible region that could be assigned to electron transitions from the valence band to a conduction band formed by hybridized V 3d and Pb 6p orbitals. Among the apatites examined, Pb₅(VO₄)₃I had the smallest band gap of 2.7 eV, due to an obvious contribution of I 5p orbitals to the valence band maximum. Based on its visible light absorption capability, Pb₅(VO₄)₃I generated a continuous anodic photocurrent under visible light (λ>420 nm) in a solution of 0.1 m NaI in acetonitrile.     

Magnetic Properties and Electronic Structure of Neptunyl(VI) Complexes: Wavefunctions,Orbitals, and Crystal‐Field Models

The electronic structure and magnetic properties of neptunyl(VI), NpO₂²⁺, and two neptunyl complexes, [NpO₂(NO₃)₃]^? and [NpO₂Cl₄]^2?, were studied with a combination of theoretical methods: ab initio relativistic wavefunction methods and density functional theory (DFT), as well as crystal‐field (CF) models with parameters extracted from the ab initio calculations. Natural orbitals for electron density and spin magnetization from wavefunctions including spin–orbit coupling were employed to analyze the connection between the electronic structure and magnetic properties, and to link the results from CF models to the ab initio data. Free complex ions and systems embedded in a crystal environment were studied. Of prime interest were the electron paramagnetic resonance g‐factors and their relation to the complex geometry, ligand coordination, and nature of the nonbonding 5f orbitals. The g‐factors were calculated for the ground and excited states. For [NpO₂Cl₄]^2?, a strong influence of the environment of the complex on its magnetic behavior was demonstrated. Kohn–Sham DFT with standard functionals can produce reasonable g‐factors as long as the calculation converges to a solution resembling the electronic state of interest. However, this is not always straightforward.     

Geometries,vibrational frequencies,and electron affinities of X2Cl (X=C,Si,Ge) clusters

Ab initio quantum chemical calculations have been performed on X₂Cl^? and X₂Cl (X = C, Si, Ge) clusters. The geometrical structures, vibrational frequencies, electronic properties and dissociation energies are investigated at the Hartree–Fock (HF), Møller–Plesset second‐ and fourth‐order (MP2, MP4), CCSD(T) level with the 6‐311+G(d) basis set. The X₂Cl (X = C, Si, Ge) and X₂Cl^? (X = Si, Ge) take a bent shape obtained at the ground state, while C₂Cl^? has a linear structure. The impact on internal electron transfer between the X₂Cl and the corresponding anional clusters is studied. The three different types of electron affinities (EAs) at the CCSD(T) are reported. The most reliable adiabatic electronic affinities, obtained at the CCSD(T)/cc‐pvqz level of theory, are predicted to be 3.30, 2.62, and 1.98 eV for C₂Cl, Si₂Cl, and Ge₂Cl, respectively. The calculated EAs of C₂Cl and Ge₂Cl are in good agreement with theoretical results reported. The correlation effects and basis sets effects on the geometrical structures and dissociation energies are discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007