On the convergence of iterative computation in the LAOCOON 3 program

The reasons which sometimes cause failure of convergence in the iteration of NMR spectra by LAOCOON 3 are discussed. The problem can be avoided by retaining the sequence of the eigenfunctions throughout the iterative process. In addition, assignment of the lines to start the iterative analysis can be facilitated by considering the dependence of the transitions on the NMR parameters in the simulation stage. LAOCOON 3, modified and extended to handle eight spin systems, has been successfully tested in the iterative analysis of the ¹H NMR spectrum of naphthalene.     

Conformational study of 1,4-thiazinan-3-one

The proton NMR spectra of several 1,4-thiazinan-3-ones were analyzed using LAOCOON. The geminal and vicinal coupling constants indicate that the ring conformation of this heterocycle is a half-chair similar to δ-valerolactam. Molecular mechanics calculations show that the energy of the boat is only slightly higher than that of the half-chair. The conformational equilibria of methyl-substituted compounds were calculated by the coupling constant method. These energies are compared to those obtained by molecular mechanics.     

A tutorial comparison of the NMRIT and LAOCOON approaches for analyses of complex solution‐phase nuclear magnetic resonance spectra

For spin ½ nuclei the two most frequently used iterative approaches for determinations of NMR chemical shifts (h_i) and coupling constants (J_i), NMRIT and LAOCOON, are discussed. When multiple pulse techniques for extraction of these parameters fail or lead to complicated spectra in the cases of very strongly coupled spin systems and systems involving magnetically nonequivalent, chemical shift equivalent nuclei, recourse to these iterative methods is necessary. The former approach employs the energy levels derived from the observed transition frequencies, whereas the latter approach uses the observed transition frequencies. Derivations of the general iterative equations for both approaches are given, along with the specific equations for the ABC spin system. The matrix nature of the derivation of these equations is stressed. Also discussed is the modified NMRIT program, NMRENIT, which has major advantages over the former in cases with symmetry and in cases where not enough lines can be assigned to link all the energy levels. The advantages of the latter program over LAOCOON in certain cases are discussed. Some general advice on the use of both approaches is presented. The Hoffman energy level approach is also discussed and it is shown that it yields the same iterative equations as the LAOCOON approach. Copyright © 2002 John Wiley & Sons, Ltd.     

A caution regarding the use of LAOCOON III for AA′BB′ spin systems

It has been found that LAOCOON III can fail to converge for some strongly coupled AA′BB′ spin systems unless trial coupling constants and chemical shifts within a few tenths of a Hz of the real parameters are used to initiate the iteration. This problem seemed linked to those spin systems possessing two or more pairs of energy levels which are nearly degenerate. In the cases where LAOCOON III failed, the program NMRENIT always yielded the correct, converged, iterative solution even with completely arbitrary starting parameters. The latter program also appears to accomplish a given number of iterations with an AA′BB′ system roughly three times as fast as the former program.     

High resolution 1H NMR spectra of 2,2′-biquinoline

From analysis and refinement by the LAOCOON III program of the 220 MHz ¹H spectrum of 2,2′-biquinoline, recorded as a saturated solution in carbon disulphide, most derived chemical shifts and coupling constants are close to corresponding values in quinoline. However, H-3 is at 1.5 ppm lower field in 2,2′-biquinoline than in quinoline and the ortho-coupling ³J(34) in the heterocyclic ring is 0.5 Hz larger in 2,2′-biquinoline than in quinoline; fairly free rotation about the 2,2′ bond is inferred.     

NMR parameters of sulphur heterocycles: Solvent and concentration effects for thiophen and related systems

Infinite dilution data for six sulphur heterocycles have been obtained from second order analyses of their NMR spectra in CS₂, CDCl₃, CD₃COCD₃, or C₆D₆. Use of LAOCOON3 leads to accurate chemical shifts, but substantial errors remain in some of the coupling constants. Evidence is presented of specific association of chloroform with the sulphur heterocycles and of the interaction of acetone with the sulphur atom. An apparently anomalous geometry for the complex of benzene with thiophen and with other solutes is discussed. Dilution effects are considered in relation to the formation of solute dimers.     

1H NMR and IR spectra of methyl dichloropropanoates and butanoates

Methyl dichloropropanoates and butanoates were synthesized and their ¹H NMR and IR spectra were studied. Comparisons were made with the spectral characteristics of corresponding monochlorocompounds. Special attention was given to the elucidation of the characteristic spectral features associated with particular chlorine substitution patterns. The ¹H NMR of erythro and threo methyl 2,3-dichlorobutanoates were analyzed using a computer program MAOCON, a modified LAOCOON 3 program. In the spectrum of the threo form the order of the chemical shifts of protons on asymmetric carbons seems to be opposite to that reported in earlier literature. Also vicinal coupling constants J₂₃ were found to be greater than those reported earlier.     

NMR spectroscopy of cyclopentane derivatives: I. Cyclopentane and cyclopentanone

The deuterium-decoupled 100 MHz p.m.r. ¹³C-satellite spectra for cyclopentanone-2, 2,5,5-d₄ (2)) and cyclopentane-1,1,2,2,3,3-d₆ (5) have been determined at several temperatures and the LAOCOON 3 derived spectral parameters related to molecular conformation. For 2, the data were found to be consistent with the half-chair conformation; for 5, the data were fitted to an unrestricted pseudorotation model.     

The structure of the halogeno and nitro derivatives of N-vinylcarbazole. PMR spectral data and related MNDO calculations

The influence of Cl, Br, I and NO₂ substituents in the carbazole ring on the coupling constants and the chemical shifts of the high resolution spectrum of N-vinylcarbazole have been investigated. Verification of the experimental results was based on a simulation of the PMR spectra by the LAOCOON method for mono-, di-, tri- and tetrahalo derivatives of N-vinylcarbazole as well as for 3-nitro and 3, 6-dinitro N-vinylcarbazole. The influence of the substituent on the free rotation of the vinyl group on the electron densities of α and β carbons of this group and the influence of the substituents on the geometry of N-vinylcarbazole were estimated using the quantum-mechanical semiempirical SCF MNDO method.     

1H NMR spectra of E and Z pyridine-2-carbaldehyde 2′-pyridylhydrazone and related compounds

Proton magnetic resonance spectra at 100 MHz are reported for the E- and Z-isomers of pyridine-2-carbaldehyd 2′- pyridylhydrazone in carbon tetrachloride, d₆-dimethylsulphoxide and d₆-benzene solutions, and for various monomethylated derivatives in d₆-dimethylsulphoxide. The spectral parameters obtained by analysis with the help of LAOCOON 3 are discussed in terms of solvent effects and the chemical shift changes consequent upon isomerisation are evaluated. Some conclusions are reached concerning the preferred conformations of the E- and Z-isomers of pyridine-2-carbaldehyde 2′-pyridylhydrazone.     

Agreement between experiment and hybrid DFT calculations for O--H bond dissociation enthalpies in manganese complexes

Information on the accuracy of DFT functionals for redox reactions in transition metal systems is rather limited. To analyze the performance of some popular functionals for redox reactions in manganese systems, calculated O--H bond dissociation enthalpies for Mn-ligands in six different complexes are compared to experimental results. In this benchmark, B3LYP performs well with a mean absolute error of 3.0 kcal/mol. B98 gives similar results to B3LYP (error of 3.8 kcal/mol). B3LYP* gives lower O--H bond strengths than B3LYP and has a mean error of 5.0 kcal/mol. Compared to B98 and B3LYP, B3LYP* has an error trend for the manganese ligands that is more similar to the error for a free water molecule. The nonhybrid functional BLYP consistently and significantly underestimates the O--H bond strengths by approximately 20 kcal/mol. HCTH407 has a rather large mean error of 9.4 kcal/mol and shows no consistent trend. The results support the use of hybrid functionals and the present computational method for large model systems containing manganese. An example is the oxygen evolving complex in photosystem II where hybrid functionals predict the appearance of a Mn(IV)-oxyl radical before the O--O bond formation step.     

Etude RMN 13C d'un Dérivé Uniformément Enrichi en 13C. Signe des Valeurs des Constantes de Couplage Observées

The ¹³C NMR parameters of 3-O-acetyl-1,2:5,6-di-O-isopropylidène-α-D-[U-¹³C] glucofuranose, used as a sample for analysis in double labelling biosynthetic experiments, have been measured. Homonuclear double resonance experiments ¹³C? {¹³C} at 62.8 MHz have permitted the determination of all the ¹³C? ¹³C coupling constants. By theoretical computation of spectra, in connection with the second order effects existing at 25.2 MHz and 15.08 MHz, the sign of the coupling constants has been determined. The theoretical computation of spectra took into account all the isotopomers and was calculated with the help of a program (adapted from the LAOCOON program) allowing for the weighted addition of the spectra.     

High-resolution NMR spectra of fluorene and its derivatives: VI—1-methylfluorene,truxene and decacyclene

The overlapping spin systems in the 220 MHz ¹H spectra of 1-methylfluorene (1) in carbon disulphide and deuteriated chloroform solutions have been analysed separately and refined by LAOCOON with the aid of methyl- and methylene-decoupled spectra. Ortho-coupling constants in the 6-membered rings are similar to each other and to those in fluorene (4). Solvent and concentration shifts suggest loose pairing of solute molecules. 220 MHz ¹H spectra of α-truxene (2) in carbon tetrachloride and deuteriated nitrobenzene, 220 MHz ¹H spectra of decacyclene (3) in carbon tetrachloride, and 90 MHz FT ¹H spectra of 3 in deuteriated chloroform show steric deshielding; the solvent dependence of shifts also suggests solute pairing in 2. Shifts in ¹H decoupled 22.6 MHz ¹³C spectra of 2 in deuteriated chloroform were assigned with the aid of Cr(acac)₃ relaxation agent.     

Benzofurobenzthiazole: VI—1H- und 13C-NMR-Spektren von 2-Aminobenzofuro[2,3-f] benzthiazol und 2-Aminobenzofuro[2,3-e]benzthiazol im Vergleich mit Dibenzofuran und 2-Aminobenzthiazol

Cyclization of 3-dibenzofurylthiourea under the conditions of the Hugershoff reaction gives the linear structure 1. ¹H n.m.r. and ¹³C n.m.r. spectra of the two isomeric aminobenzofurobenzothiazoles (1 and 3), recorded at 220 MHz, 60 MHz and 22,62 MHz respectively, were used as aids for the structure determination. The magnetic parameters were obtained partly by first-order analysis and partly by simulation of spectra using LAOCOON 3. The assignments were made by comparing the chemical shifts and coupling constants with those of the parent compounds dibenzofuran (4a) and 2-aminobenzothiazole (5c). In so far as the assignments of ¹H n.m.r. and ¹³C n.m.r. frequencies of the parent compounds themselves were unknown or supported by analogy only, they have been determined using experimental criteria such as deuterium substitution and investigation of changes in chemical shifts caused by derivation.     

Spatial evaluation of radionuclide concentrations and the associated radiation hazards using the Kriging method

Spatial variations of natural and artificial radiation hazards are evaluated by combining high-resolution gamma spectrometry with the Kriging method. The coupling of both methods was applied on radionuclides’ concentration measurements of northern Jordan soil, and the generated smooth surfaces had mean standardized error and root mean square standardized error values ranging from 6?×?10^?3 to 26?×?10^?3 and from 0.89 to 1.19, respectively. The spatial assessment shows that some radiation hazard indices are higher than the global average values. The produced maps show that the observed increase in uranium and thorium concentrations could be related to the spread of phosphate-rich rock compositions.     

Accuracy of geometries: influence of basis set,exchange–correlation potential,inclusion of core electrons,and relativistic corrections

The geometries of a set of small molecules were optimized using eight different exchange–correlation (xc) potentials in a few different basis sets of Slater-type orbitals, ranging from a minimal basis (I) to a triple-zeta valence basis plus double polarization functions (VII). This enables a comparison of the accuracy of the xc potentials in a certain basis set, which can be related to the accuracies of wavefunction-based methods such as Hartree–Fock and coupled cluster. Four different checks are done on the accuracy by looking at the mean error, standard deviation, mean absolute error and maximum error. It is shown that the mean absolute error decreases with increasing basis set size, and reaches a basis set limit at basis VI. With this basis set, the mean absolute errors of the xc potentials are of the order of 0.7–1.3 pm. This is comparable to the accuracy obtained with CCSD and MP2/MP3 methods, but is still larger than the accuracy of the CCSD(T) method (0.2 pm). The best performing xc potentials are found to be Becke–Perdew, PBE and PW91, which perform as well as the hybrid B3LYP potential. In the second part of this paper, we report the optimization of the geometries of five metallocenes with the same potentials and basis sets, either in a nonrelativistic or a scalar relativistic calculation using the zeroth-order regular approximation approach. For the first-row transition-metal complexes, the relativistic corrections have a negligible effect on the optimized structures, but for ruthenocene they improve the optimized Ru–ring distance by some 1.4–2.2 pm. In the largest basis set used, the absolute mean error is again of the order of 1.0 pm. As the wavefunction-based methods either give a poor performance for metallocenes (Hartree–Fock, MP2), or the size of the system makes a treatment with accurate methods such as CCSD(T) in a reasonable basis set cumbersome, the good performance of density functional theory calculations for these molecules is very promising; even more so as density functional theory is an efficient method that can be used without problems on systems of this size, or larger.     

Daily doses of biologically active UV radiation retrieved from commonly available parameters

A multiple linear correlation is done between atmospheric transmissivity for four biologically active radiation daily doses (UVB, erythemal, DNA and plant damage) T, and three parameters (daily sunshine fraction σ, cosine of the daily minimum solar zenith angle μ_min and daily total ozone column Ω). T is defined as the ratio of a daily dose to its extra‐atmospheric value. The data used are spectral UV measurements (390–400 nm at 0.5 nm step) recorded along year 2000 and over 8 months of year 2001 at Briançon Station (Alps, 1300 m above sea level) that forms part of the French UV network. The coefficients obtained from year 2000 correlation permit to retrieve daily doses for year 2001 with an average error running from 3 to 9% for monthly mean values and from 2 to 4.5% for 3‐monthly mean values, depending on daily dose type. The retrieval of yearly mean value gives an error between 4 and 7.5%. Retrieving the daily dose of a given day, where σ≥ 0.2, introduces error running from 16 to 32% depending on daily dose. An attempt to retrieve the yearly mean UVB daily dose for a northern France site, from the previous coefficients, gives encouraging results.     

Predicting binding affinities of host-guest systems in the SAMPL3 blind challenge: the performance of relative free energy calculations

Relative free energy calculations based on molecular dynamics simulations are combined with available experimental binding free energies to predict unknown binding affinities of acyclic Cucurbituril complexes in the blind SAMPL3 competition. The predictions yield root mean square errors between 2.6 and 3.2 kcal/mol for seven host-guest systems. Those deviations are comparable to results for solvation free energies of small organic molecules. However, the standard deviations found in our simulations range from 0.4 to 2.4 kcal/mol, which indicates the need for better sampling. Three different approaches are compared. Bennett's Acceptance Ratio Method and thermodynamic integration based on the trapezoidal rule with 12 λ-points exhibit a root mean square error of 2.6 kcal/mol, while thermodynamic integration with Simpson's rule and 11 λ-points leads to a root mean square error of 3.2 kcal/mol. In terms of absolute median errors, Bennett's Acceptance Ratio Method performs better than thermodynamic integration with the trapezoidal rule (1.7 vs. 2.9 kcal/mol). Simulations of the deprotonated forms of the guest molecules exhibit a poorer correspondence to experimental results with a root mean square error of 5.2 kcal/mol. In addition, a decrease of the buffer concentration by approximately 20 mM in the simulations raises the root mean square error to 3.8 kcal/mol.     

On the use of the mean squared error as a proficiency index

The mean squared error is presented as a convenient parameter to be used in assessing laboratories participating in proficiency tests. Its main advantages and disadvantages are presented and compared with the z score and the normalized error. A proficiency index is proposed as the ratio of an estimate of the mean squared error over a reference uncertainty.