DFT and MO calculations of atomic and molecular chemisorption energies on surface cluster models

Summary Density functional theory (DFT) (including gradient corrections) and MCPF calculations have been performed for atomic (H, C, N, O) and molecular CH _x (x = 1–3) chemisorption on cluster models of different sites of the Cu(100) surface. The DFT and MCPF results are in good agreement once the important effects of core-valence correlation have been accounted for in the MCPF calculations by including contributions from a core polarization potential (CPP); in the DFT approach the core-valence correlation is obtained directly from the total density using the functional. Very large effects on the four-fold hollow site binding energy from core-valence correlation are found for C, N and CH. Several different DFT functionals were employed and compared in the calculations.     

On the enthalpy of formation of thiophene

Thiophene is an important contaminant of petroleum-derived fuels, and it also plays an important role in molecular electronics. We have calculated the enthalpy of formation of thiophene employing the CCSD(T) methodology and the cc-pV(X + d)Z X = T,Q,5 basis sets. At the CCSD(T)/CBS limit and including corrections for scalar relativistic effects, anharmonic effects, spin–orbit and core-valence correlation effects, the estimated enthalpy of formation is 25.15 _-1 ^+0.5  kcal/mol. Our estimation is 2.3 kcal/mol lower than the experimental value. The discrepancies between experiment and theory are expected to be increased if higher-order correlation effects are taken into account. Thus, a new determination of the experimental value is highly recommended. Finally, we discuss the problems faced to make this estimation, in particular the determination of accurate Zero-point energy corrections and the evaluation of core-valence correlation effects.     

High‐Performance K–CO2 Batteries Based on Metal‐Free Carbon Electrocatalysts

Metal–CO₂ batteries have attracted much attention owing to their high energy density and use of greenhouse CO₂ waste as the energy source. However, the increasing cost of lithium and the low discharge potential of Na–CO₂ batteries create obstacles for practical applications of Li/Na–CO₂ batteries. Recently, earth‐abundant potassium ions have attracted considerable interest as fast ionic charge carriers for electrochemical energy storage. Herein, we report the first K–CO₂ battery with a carbon‐based metal‐free electrocatalyst. The battery shows a higher theoretical discharge potential (E^?=2.48 V) than that of Na–CO₂ batteries (E^?=2.35 V) and can operate for more than 250 cycles (1500 h) with a cutoff capacity of 300 mA h g^?1. Combined DFT calculations and experimental observations revealed a reaction mechanism involving the reversible formation and decomposition of P12₁/c1‐type K₂CO₃ at the efficient carbon‐based catalyst.     

Conformational properties of 1-methyl-1-germacyclohexane: low-temperature NMR and quantum chemical calculations

The conformational preference of the methyl group of 1-methyl-1-germacyclohexane was studied experimentally in solution (low-temperature ¹³C NMR) and by quantum chemical calculations (CCSD(T), MP2 and DFT methods). The NMR experiment resulted in an axial/equatorial ratio of 44/56 mol% at 114 K corresponding to an A value (A = G _ax ? G _eq) of 0.06 kcal mol^?1. An average value for ΔG _e→a ^#  = 5.0 ± 0.1 kcal mol^?1 was obtained for the temperature range 106–134 K. The experimental results are very well reproduced by the calculations. CCSD(T)/CBS calculations + thermal corrections resulted in an A value of 0.02 kcal mol^?1, whereas a ΔE value of ?0.01 kcal mol^?1 at 0 K was obtained.     

Core-valence correlation effects for molecules containing first-row atoms. Accurate results using effective core polarization potentials

The accuracy of employing effective core polarization potentials (CPPs) to account for the effects of core-valence correlation on the spectroscopic constants and dissociation energies of the molecules B₂, C₂, N₂, O₂, F₂, CO, CN, CH, HF, and C₂H₂ has been investigated by comparison to accurate all-electron benchmark calculations. The results obtained from the calculations employing CPPs were surprisingly accurate in every case studied, reducing the errors in the calculated valence D _e values from a maximum of nearly 2.5 kcal/mol to just 0.3 kcal/mol. The effects of enlarging the basis set and using higher-order valence electron correlation treatments were found to have only a small influence on the core-valence correlation effect predicted by the CPPs. Thus, to accurately recover the effects of intershell correlation, effective core polarization potentials such as the ones used in the present work provide an attractive alternative to carrying out computationally demanding calculations where the core electrons are explicitly included in the correlation treatment. Received: 11 May 1998 / Accepted: 27 July 1998 / Published online: 28 October 1998     

Formation of Superoxo Species by Interaction of O2 with Na Atoms Deposited on MgO Powders: A Combined Continuous‐Wave EPR (CW‐EPR), Hyperfine Sublevel Correlation (HYSCORE) and DFT Study

The formation of O₂^? radical anions by contact of O₂ molecules with a Na pre‐covered MgO surface is studied by a combined EPR and quantum chemical approach. Na atoms deposited on polycrystalline MgO samples are brought into contact with O₂. The typical EPR signal of isolated Na atoms disappears when the reaction with O₂ takes place and new paramagnetic species are observed, which are attributed to different surface‐stabilised O₂^? radicals. Hyperfine sublevel correlation (HYSCORE) spectroscopy allows the superhyperfine interaction tensor of O₂^?Na⁺ species to be determined, demonstrating the direct coordination of the O₂^? adsorbate to surface Na⁺ cations. DFT calculations enable the structural details of the formed species to be determined. Matrix‐isolated alkali superoxides are used as a standard to enable comparison of the formed species, revealing important and unexpected contributions of the MgO matrix in determining the electronic structure of the surface‐stabilised Na⁺? O₂^? complexes.     

A relativistic C.I. study on theJ=1/2 even spectrum of Sr II

We present a method for performing relativistic CI calculations in ground and excited atomic and ionic levels. An electron occupying a relativistic shellnκ in a given electronic configuration is described by a single numerical four-component Dirac-Fock orbital having the samen and κ quantum numbers to those of the shellnκ. Application of this method yields estimates for the I.P. (88 741 cm^?1) and the core correlation energy (?30916 cm^?1) for Sr II and for the total correlation energy in Sr III (?30916 cm^?1). Core-valence correlation energies for the |core 5s〉 (?4379 cm^?1), |core 6s〉 (?1191 cm^?1) and |core 13s〉 (?32 cm^?1) levels have been calculated for Sr II. Estimates for the total relativistic, Breit, vacuum polarization and self energy corrections for these levels are also reported. Configurations in which the core is not fully occupied have been found to yield significant contributions to the correlation energies of both ground and excited levels. Our results show that full scale relativistic CI calculations using numerical four-component Dirac-Fock orbitals are feasible and provide a useful ab-initio tool for the investigation of atomic properties within the framework of fully relativistic theories.     

Structure of a potassium-ion-exchanged nepheline hydrate I crystal

A nepheline hydrate I crystal, ion-exchanged using KCl(aq) at 80°C, was found to be orthorhombic, space group Pnm2₁, a = 8.113(3), b = 15.223(2), c = 5.1817(7)Å and showed no superlattice X-ray reflections. Structure analysis by means of Fourier and least-squares methods led to the composition K_1.1Na_1.9Al₃Si₃O₁₂ · H₂O (Z = 2, D_c = 2.40 g cm^?3) and the agreement factors: R = 0.032 and R_w = 0.040. Species assigned to the observed extra framework sites were K(1), K(2), and W(1) in the 8-ring tunnels along c plus Na(1) and Na(2) in the smaller 6-ring voids forming connections in the b direction. The atoms Na(1) and Na(2) coordinated framework oxygens exclusively and were but little affected by the ion-exchange process; K(1) was found near the center of an 8-ring and had five O atoms and two water molecules as closest neighbors, while the weakly occupied K(2) site was near a 6-ring and was found to have a coordination consisting of at least five oxygens and one water. The 10% vacancy of Na(2) is compensated for by an equal amount of K(2), which does not enter the Na(2) site for sterical reasons.     

Wechselwirkungen in Kristallen. 106. Mitteilung. Die Klaviatur der Na⊕-Koordinationszahlen in ihren Carbazolanion-Salzen

Interaction in Crystals: The Keyboard of Na⊕ Coordination Numbers in Its Carbazole Anion Salts Some local minima in the shallow potential of the system carbazole anion, sodium cation, and the ethers tetrahydrofuran, 1,2-dimethoxyethane, diglyme, triglyme, tetraglyme, 15-crown-5 as well as 2.2.1-cryptand are explored experimentally and by quantum-chemical calculations. Three prototype contact-ion multiples of Na⊕-solvated carbazole anion M? salts have been crystallized and structurally characterized: polyether-solvated monomers [M?Na⊕_solv]₁, solvent-shared dimers [M?Na⊕_solv]₂, and solvent-separated polyions [(M?)nNa?_solv](^n?1)? [Na⊕_solv](n_?1). The Na⊕ coordination numbers stretch from 3 to 7 as illustrated by the compounds [(M?)₃Na+]??[Na+(2.2.1-crytand)]₂ for 3 and 7, [(M?)₂Na+(THF)₂]? [Na⊕(2.2.1-cryptand)] for 4 and 7, [M? Na+(diglyme)]₂ for 5, or [M? Na+(l 5-crown-5)] for 6. Structural comparison is based on literature analogies as well as on results of MNDO calculations concerning charge distribution and enthalpies of formation. Taken together, the results demonstrate the delicate energy balance, by which cation solvation can influence the formation of organic salts.     

Hydroxoverbindungen. 12. Kristallstruktur und Konstitution von Natrium-trihydroxozinkat Na[Zn(OH)3] bei 190 K

Hydroxo Compounds. 12. Crystal Structure and Constitution of Sodium Trihydroxozincate Na[Zn(OH)₃] 1 The crystal structure of the very sensitive sodium trihydroxozincate Na[Zn(OH)₃] 1 has been determined at 190 K. Contrary to the observations of trigonal planar [Zn(OH)₃]^? anions at 298 K, the structure of 1 at lower temperatures is characterized by 1-dimensional chains [Zn(OH)₂(OH)_2/2]^? with the much more plausible (distorted) tetrahedral coordination of the Zn atoms (P4₂bc? C_4v ⁶; Nr. 106; a = 1083.9 pm; c = 530.8 pm; Z = 8; Zn? O = 194.3–200.5 pm). The H positions were determined unambigeously from the X-ray data in complete agreement with calculations of potential profiles. There are pronounced hydrogen bond distances present. The Na atoms are coordinated by (5+1) oxygen atoms (Na? O = 234.8–248.8 pm and 282.7 pm). The noncentric coordination of the atoms as well as the strong anisotropic and anharmonic temperature tensors indicate a second order phase transition between 190 K and 298 K.     

Spectroscopic Parameters of X3∑-, a1△, and A'3△ Electronic States of SO Radical

The potential energy curves (PECs) of three low-lying electronic states (X³∑^-, a¹△, and A^'3△) of SO radical have been studied by ab initio quantum chemical method. The calcula-tions were carried out with the full valence complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration in-teraction (MRCI) approach in combination with correlation-consistent basis sets. Effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. The core-valence correlation correction is carried out with the cc-pCVDZ basis set. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation, and the correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit by the two-point energy extrapolation scheme. With these PECs, the spectroscopic parameters are determined.     

A study of spiro[indoline-pyridobenzopyrans] by differential pulse voltammetry on a dropping mercury electrode and quantum chemistry

Spiropyrans of the indoline series were studied by differential pulse voltammetry in DMSO solutions. The experimental data obtained were supported by quantum-chemical calculations performed to examine the structural features and thermodynamic stability of a series of spiro-pyrans. The calculations revealed a correlation between the peak potential (E _p) of spiropyrans and the energy of the lowest unoccupied π orbital. Procedures were developed for identification and quantitative determination of all the spiropyrans in DMSO on a mercury dropping electrode in the concentration range from 1 × 10^?7 to 1 × 10^?6 M.     

Theoretical determination of lowest structures of all‐metal aromatic clusters M4L2 (M = Al,Ga, In,Tl; L = Li,Na, K,Rb, Cs)

The researches of all‐metal aromatic clusters have been a thermic theme in inorganic aromaticity domain both experimentally and theoretically since the Al₄L^? (L = Li, Na, Cu) clusters were created by laser vaporization. In systemic determination of the lowest structures of 20 gaseous all‐metal aromatic clusters M₄L₂ (M = Al, Ga, In, Tl; L = Li, Na, K, Rb, Cs), the isomer energy differences of four low‐lying structures of each cluster were evaluated at high‐quality quantum chemistry levels. Single point calculations at the coupled cluster level were performed at geometries optimized at the MP2, B3LYP, and B3PW91 levels, and harmonic frequency calculations and zero point energy corrections were implemented following optimizations at the B3LYP and B3PW91 levels. In addition to Li‐ and Na‐containing species, theoretical investigations came down to those new clusters including K, Rb, and Cs. For many clusters, the most convincing theoretical evidences indicate that the lowest structures are a square bipyramidal isomer rather than an edge‐caped square pyramidal species. A few discrepancies were addressed at the MP2, B3LYP, and B3PW91 levels in comparison with the coupled cluster results. These findings are significant because some clusters were generated by laser vaporization and served as theoretical prototypes to test the new means for assessing aromaticity. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Depolarization and fine structure effects in half collisions of sodium-noble gas systems

Population ratios and polarization of the Na3P _J fine structure states following far wing photon excitation of Na-noble gas collision pairs are studied with respect to the underlying interaction potentials and molecular coupling schemes. For this purpose spectral profiles of these quantities, i.e. its dependencies on excitation frequency, have been measured up to ±200 cm^?1 detuning from the NaD lines for NaAr and NaHe under nearly single collision conditions. Comparing the measured population ratios with quantummechanical coupled channels calculations the Σ potential well depths differ considerably from results of model potential calculations. Large residualJ=3/2 alignment observed in the far wings disagrees with simple models assuming incoherent excitation and/or full adiabatic reorientation of the radiating dipole along straight trajectories. By comparison with Lewis model calculations, using realistic trajectories and decoupling radius, it is found instead, that realistic trajectories are constitutive for alignment after Σ-excitation (blue wing), whereas coherence between the²Π_1/2 and²Π_3/2 states determine primarily alignment after Π-excitation (red wing).     

A Monte Carlo computer simulation of the thermodynamic properties of solid N2

Selected thermodynamic properties of solid N₂ are investigated by carrying out classical Monte Carlo calculations for a system of 108 rigid linear molecules initially disposed in the cubic Pa3 structure and interacting via Mie—Lennard-Jones pair potentials between their ends. One run was carried out at (T = 96.4 K, V = 23.6 cm³ mole^?I) using a (12-6) potential, the other at T = 192.8 K and the same volume using a (9-6) potential. Only the latter potential appears to correlate well with recent experimental pVT data. In both runs the molecules were found to be orientationally disordered.     

Ab initio study of the molecular structures, force fields, and vibrational spectra of alkaline metal fluoride dimers MM′F2 (M, M′=Li, Na, K)

Ab initio calculations of the equilibrium geometrical parameters, force constants, and IR vibration frequencies and intensities of Li₂F₂, Na₂F₂, K₂F₂, LiNaF₂, LiKF₂, and NaKF₂ are reported. The calculations use the Hartree-Fock-Roothaan method and second-order Möller-Plesset perturbation theory along with configuration interaction theory including singly and doubly excited configurations and corrections for quartic excitations with basis sets of grouped Gaussian functions: Li — (9s3p1d/4s3p1d), Na — (12s8p1d/6s4p1d), K — (14s11p3d/9s8p3d), F — (9s5p1d/4s2p1d). According to the results of calculations, the equilibrium structures of the molecules are planar cyclic structures of D_2h (for M₂F₂) and C_2v (for MM′F₂) symmetries. The linear configurations M-F-M′-F (of C_∞v symmetry) are 70–190 kJ/mole less stable than the cyclic ones; for all molecules except M-F-K-F, these configurations correspond to local minima on the potential energy surface. The role of correlation effects in ab initio calculations of the geometry, force fields, and IR characteristics of molecules with highly polar chemical bonds is discussed. The theoretical force fields of the molecules are represented in canonical form in a system of redundant natural vibrational coordinates. The force fields of MM′F₂ molecules are studied. The results of the ab initio calculations are compared with the experimental structural data and vibrational spectra available in the literature.     

Catalytic currents in fused salts: Discharge mechanism of nitrite in molten alkali nitrates(II)

The electrooxidation of NO₂^? ion in the (Na,K)NO₃ eutectic mixture containing water in the concentration range 10^?6–10^?2 mol kg^?1 has been studied on a platinum RDE. More work was done to confirm the preliminary mechanism reported by the authors:

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In the course of the present study step (a) was found to be potential determining under all experimental conditions while step (b) behaves as a “true” equilibrium reaction. By an approximate method based on the reaction layer concept the equilibrium constant for reaction (b) K=K′/[NO₃^?]=[H⁺]²[NO₂^?]/[NO₂]²[H₂O] was calculated. In the given nitrate solvent it was found to be K=(2.90±0.56)×10^?1 at 520 K. A value of ΔH equal to ?125.2 kJ mol^?1 was obtained on the basis of the temperature dependence of the equilibrium constant in the range 505–566 K.