Canonical partition function for the hydrogen atom in curved space

The electronic partition function for the hydrogen atom was recently derived by integration over the Coulomb propagator. A much simpler derivation is given here, based on Schrödinger's exact solution for a hydrogenic atom in a Riemannian space of positive curvature. The energy spectrum is entirely discrete, including states which correspond to the ionized atom. The curvature in Riemannian space is shown to be equivalent to a finite volume in Euclidean space.     

The molecular Zeeman effect in HCP,HCN, and HCCBr and a comparison with similar molecules

The molecular Zeeman effect has been observed in the J = 0 → 1 ΔM = 0, and ± 1 transitions in H¹²CP, D¹²CP, H¹²C¹⁵N, H¹²C¹²C⁷⁹Br, and H¹²C¹²C⁸¹ Br giving the molecular g-values, magnetic susceptibility anisotropies, and corresponding molecular quadrupole moments. The results are g_⊥(HCP) = ?0.0430 ± 0.0010, g_⊥(DCP) = ?0.0353 ± 0.0010, x_⊥ - x_| = (8.4 ± 0.9) × 10^?6 erg/G² mole and Q_|(HCP) = (4.4 ± 1.2) × 10^?26 esu; g_⊥(HC¹⁵N) = ?0.0904 ± 0.0003, x_⊥ - x_| = (7.2 ± 0.4) × 10^?6 erg/G² mole, and Q_|(HC¹⁵N) = (3.1 ± 0.6) × 10^?26 esu; g_⊥(HCC⁷⁹Br) = ?0.00395 ± 0.00032, g_⊥(HCC⁸¹Br) = ?0.00388 ± 0.00014, x_⊥ - x_| = (9.5 ± 0.9) × 10^?6 erg/G² mole, and Q_| = (8.5 ± 1.1) × 10^?26 esu. The results in HCN agree very well with an earlier prediction of the magnetic properties. The new results presented here are compared to other members in the acetylene and cyanide series of molecules and we conclude that the sign of the g-value in acetylene should be positive.The deuterium nuclear quadrupole coupling constant was also determined in DCP to be x_D = 233 ± 40 kHz.     

Relativistic free complement method for correctly solving the Dirac equation with the applications to hydrogen isoelectronic atoms

The accuracy of the relativistic free complement (FC) method, which was previously reported for solving the Dirac?CCoulomb equations of atoms and molecules, has been strictly examined with the applications to hydrogen isoelectronic atoms. The FC wave function grown up by the Hamiltonian automatically takes care of the correct relationship between large and small components, i.e., FC or ICI balance. Combining the FC method with the inverse Hamiltonian method can help to obtain correct solutions safely against to several obstacles characteristic to the Dirac?CCoulomb equation. To ensure the exactness of the obtained wave function, we examined the total square deviation from the exact wave function, local energy constancy, H-square error, and energy upper and lower bounds for hydrogen-like atoms.     

Temperature effect on the single and double hydrogen atom transfer reactions in o-, m-and p-toluic acid butyl esters

The temperature effect on the single and double hydrogen atom transfer reactions in o-, m- and p-toluic acid n-butyl esters and isobutyl esters has been investigated. For the meta and para isomers, the abundance of the m/z 137 ion [C₈H₉O₂]⁺ generated by a double hydrogen atom transfer reaction increases relative to the m/z 136 ion [C₈H₈O₂]⁺˙ generated by a single hydrogen atom transfer reaction upon lowering the temperature of the ionization chamber. On the other hand, the ratio of the peak abundances [137]⁺/[136]⁺ for the ortho isomers is nearly constant when the temperature is changed. It is shown that this is due to the difference between the appearance energies of the m/z 136 and m/z 137 ions.     

Simulations of the large kinetic isotope effect and the temperature dependence of the hydrogen atom transfer in lipoxygenase

Elucidating the role of nuclear quantum mechanical (NQM) effects in enzyme catalysis is a topic of significant current interest. Despite the great experimental progress in this field it is important to have theoretical approaches capable of evaluating and analyzing nuclear quantum mechanical contributions to catalysis. In this study, we use the catalytic reaction of lipoxygenase, which is characterized by an extremely large kinetic isotope effect, as a challenging test case for our simulation approach. This is done by applying the quantum classical path (QCP) method with an empirical valence bond potential energy surface. Our computational strategy evaluates the relevant NQM corrections and reproduces the large observed kinetic isotope effect and the temperature dependence of the H atom transfer reaction while being less successful with the D atom transfer reaction. However, the main point of our study is not so much to explore the temperature dependence of the isotope effect but rather to develop and validate an approach for calculations of nuclear quantum mechanical contributions to activation free energies. Here, we find that the deviation between the calculated and observed activation free energies is small for both H and D at all investigated temperatures. The present study also explores the nature of the reorganization energy in the enzyme and solution reactions. It is found that the outer-sphere reorganization energy is extremely small. This reflects the fact that the considered reaction involves a very small charge transfer. The implication of this finding is discussed in the framework of the qualitative vibronic model. The main point of the present study is, however, that the rigorous QCP approach provides a reliable computational tool for evaluating NQM contributions to catalysis even when the given reaction includes large tunneling contributions. Interestingly, our results indicate that the NQM effects in the lipoxygenase reaction are similar in the enzyme and in the reference solution reactions, and thus do not contribute to catalysis. We also reached similar conclusions in studies of other enzymes.     

Molecular Zeeman effect of 3-oxetanone and 3-methylene oxetane,and the comparison of the magnetic-susceptibility anisotropies,molecular quadrupole moments,and other magnetic parameters with other four-membered rings

The molecular Zeeman effect is reported for 3-oxetanone and 3-methylene oxetane at fields near 20000 G. The results for 3-oxetanone are molecular g-values: g_aa = ?0.1059 ± 0.0008, g_bb = ?0.0581 ± 0.0004,g_cc = ?0.0437 ± 0.0004, magnetic susceptibility anisotropies:2x_aa -x_bb - x_cc = (9.6±0.5) x 10^?6 erg/G²mole, 2x_bb - x_aa - x_cc = ?(7.8±0.6) x 10^?6 erg/G²mole, and molecular quadrupole moments: Q_aa = ?(12.8±0.8) x 10^?26 esu cm,Q_bb = (7.9±0.8) x 10^?26 esu cm, and Q_cc = (4.9±0.8) x 10^?26 esu cm. For 3-methylene oxetane, the results are g_aa = ?0.0510 ± 0.0018, g_bb = ?0.0435 ± 0.0010, g_cc = ?0.0313 ± 0.0010, 2x_aa - x_bb - x_cc = ?(10.9±0.5) x 10^?6 erg/G² mole, 2x_bb - x_aa - x_cc = (2.3±0.9) x 10^?6 erg/G² mole, Q_aa = -?5.4±1.0) x 10^?26 esu cm, Q_bb = (5.1 ± 1.2) x 10^?26 esu cm, and Q_cc = (0.2±1.5) x 10^?26 esu cm. The bulk magnetic susceptibility for 3-oxetanone was measured to be x = 1/2 (x_aa+x_bb+x_cc) = ?(30.6±1.5) x 10^?6 erg/G² mole. The out-of-plane minus average in-plane magnetic-susceptibility anisotropies in four-membered rings show larger paramagnetism than predicted on the basis of localized group susceptibility anisotropies. This effect is discussed and a possible explanation presented.     

Correlation potentials for the He atom and the hydrogen molecule: A comparison between the correlation factor approach and DFT correlation energy functionals

Two points about correlation potentials have been dealt with in this article. The first one is related to the shape of some of the most representative correlation potentials applied to the ground state of the He atom. It is shown here that both LDA and two-body density correlation potentials compare well with that obtained through the quantum chemistry definition of correlation energy. This is an interesting result because, in previous works, it had been shown that none of the correlation potentials compared well with the Kohn–Sham one. The gradient-corrected correlation potentials exhibit a very different behavior to that of both exact potentials (quantum chemistry and Kohn–Sham ones). The other question posed here refers to how a reference to the two-body density must modify DFT functionals for the correlation energy, when a multideterminant wave function is needed. This question has been addressed by analyzing the variation of correlation potentials as the bond length of the H₂ molecule increases. The results show that an external reference to the two-body density qualitatively improves DFT correlation potentials and also that only those functionals explicitly depending on two-body density can give the quantitative correct trends. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 143–156, 1998     

Zeeman effect electrothermal atomic absorption spectrophotometry with matrix modification for the determination of arsenic in urine

Arsenic was determined in urine by electrothermal atomic absorption spectrophotometry using Zeeman Effect background correction and after matrix modification with 5% nickel nitrate. Mean recovery of urine samples spiked with 100 micrograms . L-1 dimethylarsinic acid was 97.9 micrograms . L-1. Within-run CV was 2.4%, between-run CV was 7.3% and the detection limit was determined to be 10.0 micrograms . L-1. The method can be used for the rapid screening of urine samples for elevated arsenic levels.     

Calibration curve equation in the local voltammetry of eutectic alloys with anomalous and divorced eutectics

An equation i = f(c) is proposed for a calibration curve under the conditions of local voltammetry based on the previous study of the anode dissolution of heterogeneous eutectic alloys with anomalous and divorced eutectics.     

Detailed comparison of the pnicogen bond with chalcogen,halogen, and hydrogen bonds

The characteristics of the pnicogen bond are explored using a variety of quantum chemical techniques. In particular, this interaction is compared with its halogen and chalcogen bond cousins, as well as with the more common H‐bond. In general, these bonds are all of comparable strength. More specifically, they are strengthened by the presence of an electronegative substituent on the electron‐acceptor atom, and each gains strength as one moves down the appropriate column of the periodic table, for example, from N to P to As. These noncovalent bonds owe their stability to a mixture in nearly equal parts of electrostatic attraction and charge transfer, along with a smaller dispersion component. The charge transfer arises from the overlap between the lone pair of the electron donor and a σ* antibond of the acceptor. The angular characteristics of the equilibrium geometry result primarily from a compromise between electrostatic and induction forces. Angular distortions of the H‐bond are typically less energetically demanding than comparable bends of the other noncovalent bonds. © 2012 Wiley Periodicals, Inc.     

Dual-level direct dynamics studies for the reactions of dimethyl ether with hydrogen atom and methyl radical

The dual-level direct dynamics approach is employed to study the dynamics of the CH(3)OCH(3) + H (R1) and CH(3)OCH(3) + CH(3) (R2) reactions. Low-level calculations of the potential energy surface are carried out at the MP2/6-311+G(d,p) level of theory. High-level energetic information is obtained at the QCISD(T) level of theory with the 6-311+G(3df,3pd) basis set. The dynamics calculations are performed using variational transition state theory (VTST) with the interpolated single-point energies (ISPE) method, and small-curvature tunneling (SCT) is included. It is shown that the reaction of CH(3)OCH(3) with H (R1) may proceed much easier and with a lower barrier height than the reaction with CH(3) radical (R2). The calculated rate constants and activation energies are in good agreement with the experimental values. The calculated rate constants are fitted to k(R1) = 1.16 x 10(-19) T(3) exp(-1922/T) and k(R2) = 1.66 x 10(-28) T(5) exp(-3086/T) cm(3) mol(-1) s(-1) over a temperature range 207-2100 K. Furthermore, a small variational effect and large tunneling effect in the lower temperature range are found for the two reactions.     

The substituent effect on the single and double hydrogen atom transfer reactions in para-substituted benzoic acid isobutyl esters

The substituent effect on the single and double hydrogen atom transfer reactions in para-substituted benzoic acid isobutyl esters has been investigated by electron impact mass spectrometry. Electron-donating substituents favour formation of the [M? C₄H₈]⁺˙ ion generated by single hydrogen atom transfer reaction (McLafferty rearrangement), whereas electron-withdrawing substituents favour formation of the [M? C₄H₇]⁺ ion generated by double hydrogen atom transfer reaction. In the case of the latter compounds, the m/z56 ([C₄H₈]⁺˙) ion, which is generated by single hydrogen atom transfer reaction with charge migration, is very intense, while in the former compounds, the m/z56 ion is very weak. These observations can be reasonably explained on thermochemical grounds based on the sum of the standard heats of formation of the fragments.     

Rate constants for 1,5- and 1,6-hydrogen atom transfer reactions of mono-, di-, and tri-aryl-substituted donors, models for hydrogen atom transfers in polyunsaturated fatty acid radicals

Rate constants for 1,5- and 1,6-hydrogen atom transfer reactions in models of polyunsaturated fatty acid radicals were measured via laser flash photolysis methods. Photolyses of PTOC (pyridine-2-thioneoxycarbonyl) ester derivatives of carboxylic acids gave primary alkyl radicals that reacted by 1,5-hydrogen transfer from mono-, di-, and tri-aryl-substituted positions or 1,6-hydrogen transfer from di- and tri-aryl-substituted positions to give UV-detectable products. Rate constants for reactions in acetonitrile at room temperature ranged from 1 x 10(4) to 4 x 10(6) s(-1). The activation energies for a matched pair of 1,5- and 1,6-hydrogen atom transfers giving tri-aryl-substituted radicals were approximately equal, as were the primary kinetic isotope effects, but the 1,5-hydrogen atom transfer reaction was 1 order of magnitude faster at room temperature than the 1,6-hydrogen atom transfer reaction due to a less favorable entropy of activation for the 1,6-transfer reaction. Solvent effects on the rate constants for the 1,5-hydrogen atom transfer reaction of the 2-[2-(diphenylmethyl)phenyl]ethyl radical at ambient temperature were as large as a factor of 2 with the reaction increasing in rate in lower polarity solvents. Hybrid density functional theory computations for the 1,5- and 1,6-hydrogen atom transfers of the tri-aryl-substituted donors were in qualitative agreement with the experimental results.     

Kinetics of the hydrogen atom reactions with benzene,cyclohexadiene and cyclohexene: hydrogenation mechanism and ring cleavage

The hydrogen atom reaction with benzene and the subsequent elementary reactions with H-atoms were studied in detail, using a fast gas flow in a linear reactor at pressures in the mbar region, with a mass spectrometer for the product analysis. The rate-constant determinations were based on a kinetic model, which includes the strong catalytic H-atom recombination on the wall, caused by adsorbed reactant molecules, and also corrects for the pressure drop within the reactor. The H-atom concentration was determined by scavenging with NO₂. The method was checked by determining the rate constant k(H + trans-butene-2) = (4.6 ± 1.2) × 10⁸ M^?1 s^?1, which agrees with the literature value of Daby et al. within experimental error limits. The rate constants determined are:

H + benzene is the rate determining step for benzene hydrogenation. From the rate constant for H + C₆D₆ it is concluded, that benzene is reformed from some intermediate reaction products (C₆H^*₇ and/or C₆H^*₈). These back reactions should be suppressed at high pressures, in agreement with results by Sauer and Ward (1–54 bar). The mass spectra show that H + benzene at mbar pressures predominantly initiates ring cleavage to form methyl radicals, methane, and C₂-hydrocarbons as the main products. However for H + cyclohexene 85% of the products is cyclohexane. The results for H + cyclohexadiene are intermediate to these extremes. It is argued that accumulation of vibrational energy over two consecutive reactions must be responsible for the ring cleavage, which most likely occurs from C₆H^**₈ and C₆H^**₁₀.     

An investigation of the mechanism of single and double hydrogen atom transfer reactions in alkyl benzoates by the ortho effect

Single and double hydrogen atom transfers in reactions (1) and (2) in the mass spectra of ethyl benzoate, isopropyl benzoate, and isobutyl benzoate have been investigated with reference to the ortho effect: (1) [C₆H₅CO₂R]⁺? → [C₆H₅CO₂H]⁺? (m/z 122) + (R-H); (2) [C₆H₅CO₂R]⁺? → [C₆H₅CO₂H₂]⁺ (m/z 123) + · (R-2H). It is demonstrated that the intermediate ion [C₆H₅CO₂H₂]⁺ has the protonated benzoic acid structure with the hydrogen atom on the carbonyl group.