Ab initio studies of structural features not easily amenable to experiment: Part 20. Structural aspects of ethyl groups

The molecular structures of a number of stable conformations of ethanol, ethylamine, methylethyl ether, methylethylamine and of the ethyl anion have been determined by ab initio geometry optimizations using Pulay's Force method on the 4–21G level. The calculated geometries characterize the extent to which structural groups in a molecule are sensitive to asymmetries in their environment. Characteristic structural trends are consistently found for the CH bond distances and CCH angles in the C₂H₅ groups of trans-ethanol, trans-methylethyl ether and in the ethyl anion. They differ from those previously found for C₂H₅ groups in hydrocarbons. There is qualitative disagreement between the trends calculated for CH bond distances in trans-ethanol and trans-methylethyl ether and those found in the microwave substitution structures of these compounds. Since the substitution parameters are unresolved because of relatively large experimental or model uncertainties, it is presently impossible to decide whether this discrepancy is the result of computational or experimental deficiency. The methyl groups in methylethyl ether and methylethylamine exhibit the characteristic structural distortions which are usually found for CH₃ groups adjacent to electron lone pairs. The CC bond distances in C₂H₅ in the systems studied here are sensitive to the conformational arrangement of ethyl relative to the rest of a system in a way which can be rationalized by orbital interactions involving antibonding orbitals on sp³-hybridized carbon atoms. The calculated conformational stabilities agree qualitatively with experimental trends, except in the case of ethanol where the trans — gauche energy difference is small (about 0.1 kcal mol^?1) and within the uncertainties of the calculations. Our conformational energies for CH₃CH₂NH₂ are in disagreement with a previous ab initio investigation based on a comparison of unoptimized standard geometries. In general, the agreement between calculated structural parameters and corresponding reliable experimental values is very good in all comparable cases.     

Equilibrium structure and spectroscopic constants of maleic anhydride

The quadratic, cubic, and semi-diagonal quartic force fields of maleic anhydride have been calculated at the MP2 level of theory employing the cc-pVTZ basis set. The spectroscopic constants derived from the force field are in excellent agreement with the corresponding experimental values. The semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational corrections calculated from the cubic force field. This semi-experimental equilibrium structure is in excellent agreement with the ab initio structures computed at the CCSD(T) level of theory and it is closer to the ab initio structure than the purely experimental (or empirical) structures r ₀, r _m⁽¹⁾, and r _m⁽²⁾ obtained by microwave spectroscopy as well as the equilibrium structure derived from gas-phase electron diffraction data.     

Semiexperimental equilibrium structures for the equatorial conformers of N-methylpiperidone and tropinone by the mixed estimation method

N-Methylpiperidone (MPIP) and tropinone, which contain a structural motif found in numerous alkaloids, are too large to determine an accurate equilibrium structure either by ab initio methods or by experiment. However, the ground state rotational constants of the parent species and of all isotopologues with a substituted heavy atom ((13)C, (15)N, (18)O) are known from microwave spectroscopy. These constants have been corrected for the rovibrational contribution calculated from an ab initio cubic force field. These semiexperimental equilibrium rotational constants have been supplemented by carefully chosen structural parameters from medium level ab initio calculations. The two sets of data have been used in a weighted least-squares fit to determine reliable equilibrium structures for both molecules. This work shows that it is possible to determine reliable equilibrium structures for large molecules (34 degrees of freedom in the case of tropinone) at a detailed level of accuracy, and the method could be applied without too much difficulty to still larger molecules.     

Toward ab initio refinement of protein X-ray crystal structures: interpreting and correlating structural fluctuations

The refinement of protein crystal structures currently involves the use of empirical restraints and force fields that are known to work well in many situations but nevertheless yield structural models with some features that are inconsistent with detailed chemical analysis and therefore warrant further improvement. Ab initio electronic structure computational methods have now advanced to the point at which they can deliver reliable results for macromolecules in realistic times using linear-scaling algorithms. The replacement of empirical force fields with ab initio methods in a final refinement stage could allow new structural features to be identified in complex structures, reduce errors and remove computational bias from structural models. In contrast to empirical approaches, ab initio refinements can only be performed on models that obey basic qualitative chemical rules, imposing constraints on the parameter space of existing refinements, and this in turn inhibits the inclusion of unlikely structural features. Here, we focus on methods for determining an appropriate ensemble of initial structural models for an ab initio X-ray refinement, modeling as an example the high-resolution single-crystal X-ray diffraction data reported for the structure of lysozyme (PDB entry “2VB1”). The AMBER force field is used in a Monte Carlo calculation to determine an ensemble of 8 structures that together embody all of the partial atomic occupancies noted in the original refinement, correlating these variations into a set of feasible chemical structures while simultaneously retaining consistency with the X-ray diffraction data. Subsequent analysis of these results strongly suggests that the occupancies in the empirically refined model are inconsistent with protein energetic considerations, thus depicting the 2VB1 structure as a deep-lying minimum in its optimized parameter space that actually embodies chemically unreasonable features. Indeed, density-functional theory calculations for one specific nitrate ion with an occupancy of 62% indicate that water replaces this ion 38% of the time, a result confirmed by subsequent crystallographic analysis. It is foreseeable that any subsequent ab initio refinement of the whole structure would need to locate a globally improved structure involving significant changes to 2VB1 which correct these identified local structural inconsistencies.     

X–NO2 rotational energy barriers: Local density functional calculations

The X–NO₂ rotational energy barriers of nitromethane, nitroethylene, nitrobenzene, and a group of nitramines have been computed using a local density functional (LDF ) procedure, using ab initio Hartree–Fock (HF )-optimized structures of the ground and rotational transition states. The results have been discussed in relation to HF and some correlated ab initio values and the available experimental data. Our LDF barriers are overall quite reasonable, in generally satisfactory agreement with the experimental and correlated ab initio results. © 1993 John Wiley & Sons, Inc.     

Conformational stability,barriers to internal rotation,structural parameters,ab initio calculations,and vibrational assignment of cyclopropanecarboxaldehyde

The asymmetric torsional potential function, conformational energy difference, vibrational frequencies, and structural parameters of Cyclopropane-carboxaldehyde have been obtained from ab initio calculations at the 3–21G and/or 6-31G^* baiss set levels. These results have allowed for a reinterpretation or clarification of some of the corresponding results obtained from experiment. The conformations that have the oxygen atom oriented cis and trans to the three-membered ring are observed and calculated to be the most stable and high energy forms in the gaseous phase, respectively. From the ab initio calculations using the 6–31 G^* basis set, the energy difference between the two conformers is 114 cm^–1. For the liquid, the trans conformer is more stable and is the only rotamer present in the annealed solid. Based on a combination of results obtained from ab initio calculations, microwave spectroscopy, and the electron diffraction technique,r _o structural parameters have been obtained for both conformations.     

Accurate equilibrium structures obtained from gas-phase electron diffraction data: sodium chloride

A novel method has been developed to allow the accurate determination of equilibrium gas-phase structures from experimental data, thus allowing direct comparison with theory. This new method is illustrated through the example of sodium chloride vapor at 943 K. Using this approach the equilibrium structures of the monomer (NaCl) and the dimer (Na(2)Cl(2)), together with the fraction of vapor existing as dimer, have been determined by gas-phase electron diffraction supplemented with data from microwave spectroscopy and ab initio calculations. Root-mean-square amplitudes of vibration (u) and distance corrections (r(a) - r(e)) have been calculated explicitly from the ab initio potential-energy surfaces corresponding to the vibrational modes of the monomer and dimer. These u and (r(a) - r(e)) values essentially include all of the effects associated with large-amplitude modes of vibration and anharmonicity; using them we have been able to relate the ra distances from a gas-phase electron diffraction experiment directly to the re distances from ab initio calculations. Vibrational amplitudes and distance corrections are compared with those obtained by previous methods using both purely harmonic force fields and those including cubic anharmonic contributions, and the differences are discussed. The gas-phase equilibrium structural parameters are r(e)(Na-Cl)(monomer) = 236.0794(4) pm; r(e)(Na-Cl)(dimer) = 253.4(9) pm; and <(e)ClNaCl = 102.7(11) degrees. These results are found to be in good agreement with high-level ab initio calculations and are substantially more precise than those obtained in previous structural studies.     

The ab initio gradient revolution in structural chemistry: The importance of local molecular geometries and the efficacy of joint quantum mechanical and experimental procedures

The use of ab initio gradient calculations to determine structural information is reviewed. The significance of local geometries is discussed. Many calculated structural trends in local geometries are often unobservable by direct quantitative experimental techniques, presenting a challenge to develop more powerful experimental methods. The applications of calculated structural data in interpreting experimental results in microwave spectroscopy and electron diffraction are discussed.     

Semiempirical and ab-initio calculations of semiconductor clusters: variation of structure and symmetry with size for different compounds

Semiempirical (by extended Hückel method) and ab initio RHF SCF calculations are used for the wide range of cluster structures M_xX_y, where M = Cd,Ag; X = S,I: semiempirical - up to M₂₀X₃₅, and ab initio - for small clusters less than ten atoms. Variation of electronic structure with size for the fragments with tetrahedral coordination (bulklike sphalerite structures) and for some clusters of the lower symmetry allows to predict their possible geometries which are compared with experimental data. The chemical bonding factor (the chemical nature of bounded atoms, coordination number for metal and non-metal atoms, hybridization, etc) is of more importance in properties of the clusters than the familiar quantum confinement effect of semiconductor clusters (like CdS, CdSe, PbS, etc. ). The essential difference in regularities of small cluster formation is analysed for CdS- and AgI- based structures.     

More user-friendly phosphines? Molecular structure of methylphosphine and its adduct with borane, studied by gas-phase electron diffraction and quantum chemical calculations

The molecular structures of methylphosphine (CH(3)PH(2)) and methylphosphine-borane (CH(3)PH(2).BH(3)) have been determined from gas-phase electron diffraction data and rotational constants, employing the SARACEN method. The experimental geometric parameters generally showed a good agreement with those obtained using ab initio calculations and previous microwave spectroscopy studies. In order to assess the accuracy of the calculated structures a range of ab initio methods were used, including the CCSD(T) method, with correlation-consistent basis sets. The structural environment around the phosphorus atom was found to change significantly upon complexation with borane, with the P-C bond length shortening and the bond angles widening.     

Microwave spectra and molecular structures of (Z)-pent-2-en-4-ynenitrile and maleonitrile.

Accurate equilibrium structures have been determined for (Z)-pent-2-en-4-ynenitrile (8) and maleonitrile (9) by combining microwave spectroscopy data and ab initio quantum chemistry calculations. The microwave spectra of 10 isotopomers of 8 and 5 isotopomers of 9 were obtained using a pulsed nozzle Fourier transform microwave spectrometer. The ground-state rotational constants were adjusted for vibration-rotation interaction effects calculated from force fields obtained from ab initio calculations. The resultant equilibrium rotational constants were used to determine structures that are in very good agreement with those obtained from high-level ab initio calculations (CCSD(T)/cc-pVTZ). The geometric parameters in 8 and 9 are very similar; they also do not differ significantly from the all-carbon analogue, (Z)-hex-3-ene-1,5-diyne (7), the parent molecule for the Bergman cyclization. A small deviation from linearity about the alkyne and cyano linkages is observed for 7-9 and several related species where accurate equilibrium parameters are available. The data on 7-9 should be of interest to radioastronomy and may provide insights on the formation and interstellar chemistry of unsaturated species such as the cyanopolyynes.     

Structural determination of a recalcitrant molecule (S2F4)

The structure determination of S₂F₄ (or SF₃SF), the dimer of SF₂, is made difficult by the large variety of possible conformers and the instability of the compound. An electron diffraction and microwave study succeeded only with the help of a molecular model derived from ab initio calculations, after initial experimental attempts had failed. The force field required for a joint electron diffraction and microwave spectroscopy analysis was calculated by ab initio methods and adjusted to the experimental vibrational frequencies. The structure of S₂F₄ is a trigonal bipyramid with the electron lone pair, the SF group and one fluorine atom in equatorial positions. The SF₃ group is strongly distorted with the two axial SF bonds differing by 0.10 Å and bond angles between axial bonds and equatorial plane of about 77° and 92°, respectively. The geometric structure of S₂F₄ in combination with the ab initio calculations allows one to visualize the dissociation process SF₃SF → 2 SF₂ more clearly.     

Ab initio studies of structural features not easily amenable to experiment: the molecular structures of some hydrogenfluoride clusters

The completely relaxed ab initio structures of some forms of H₂F₂ and H₃F₃ reflect the cooperative nature of hydrogen bonding and can be used to estimate the order of magnitude of the variations in local geometry which are neglected when interactive potentials for HF in clusters or in the liquid state are evaluated with constrained geometries.     

Prediction of Vapor–Liquid Equilibria for Pb–Pd and Pb–Pt Alloys Using Ab Initio Methods in Vacuum Distillation

The vapor–liquid equilibrium (VLE) phase diagrams of Pb–Pd and Pb–Pt alloy systems in vacuum distillation were obtained based only on pure-component properties and the structures of the atoms. The interaction energies between pairs of atoms were calculated from ab initio methods and were used as the input energy parameters for the Wilson equation. The calculated activity data of the components, using energy parameters which were obtained by ab initio methods, are in good agreement with the experimental data. It is revealed that a cluster size of eight atoms, optimized using the NVT ensemble at 300 K, a time step of 1 femtosecond, and the simulation time 10 ps gives a good representation of the liquid phase systems. This approach can be used to obtain accurate VLE predictions for alloy systems in vacuum distillation. The VLE phase diagram has a significant advantage in guiding experiment and industrial production in vacuum metallurgy.     

Sensitivity of the H + CH3 → CH4 recombination rate constant to the shape of the CH stretching potential

Using a potential-energy surface obtained in part from ab initio calculations, the H + CH₃ → CH₄ bimolecular rate constant at T = 300 K is determined from a Monte Carlo classical trajectory study. Representing the CH stretching potential with a standard Morse function instead ofthe ab initio curve increases the calculated rate constant by an order of magnitude. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio stretching potentials.Two properties of the H + CH₃ α CH₄ potential-energy surface which significantly affect the recombination rate constant are the shape of the CH stretching potential and the attenuation of the H₃CH bending frequencies. Ab initio calculations with a hierarchy of basis sets and treatment of electron correlation indicate the latter is properly described [13]. The exact shape of the CH stretching potential is not delineated by the ab initio calculations, since the ab initio calculations are not converged for bond lengths of 2.0–3.0 Å [12]. However, the form of this stretching potential deduced from the highest-level ab initio calculations, and fit analytically by eq. (2), is significantly different from a Morse function. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio CH stretching potentials. This indicates that the actual CH potential energy curve lies between the Morse and ab initio curves. This is consistent with the finding that potential energy curves for diatomics are not well described by a Morse function [12].     

Comparative study of DFT methods applied to small titanium/oxygen compounds

The performance of a number of different local and nonlocal density functional theory (DFT) methods has been investigated for some small titanium—oxygen systems. Equilibrium geometries, ionization potentials, dipole moments, atomization energies, and harmonic vibrational frequencies have been calculated for the TiO, TiO₂, and Ti₂ molecules, and the results are compared with experimental data and ab initio calculations. It is shown that most DFT methods perform much better than the ab initio Hartree—Fock (HF), second-order perturbation theory (MP2), and configuration interaction including single and double excitations (CISD) treatments. For good agreement with experimental data, gradient corrections to the exchange part of the DFT functional are needed, as well as some type of correction for the errors in the calculated energy splittings between different atomic states of titanium. Hybrid methods including a mixture of HF exchange with DFT exchange correlation do not perform as well as “pure” DFT methods for the studied systems. © 1996 John Wiley & Sons, Inc.     

The S−S Bridge: A Mixed Experimental-Computational Estimation of the Equilibrium Structure of Diphenyl Disulfide

The disulfide bridge (−S−S−) is an important structural motif in organic and protein chemistry, but only a few accurate equilibrium structures are documented. We report the results of supersonic-jet microwave spectroscopy experiments on the rotational spectra of diphenyl disulfide, C₆H₅−S−S−C₆H₅ (including all ¹³C and ³⁴S monosubstituted isotopologues), and the determination of the equilibrium structure by the mixed estimation (ME) method. A single conformation of C₂ symmetry was observed in the gas phase. This disulfide is a challenging target since its structure is determined by 34 independent parameters. Additionally, ab initio calculations revealed the presence of three low-frequency vibrations (<50 cm⁻¹) associated to phenyl torsions which would prevent the calculation of an accurate force field. For this reason, instead of the semiexperimental method, we used the mass-dependent (r_m) method to fit the structural parameters concurrently to moments of inertia and predicate parameters, affected with appropriate uncertainties. The predicates were obtained by high-level quantum-chemical computations. A careful analysis of the results of different fits and a comparison with the ab initio optimizations confirms the validity of the used methods, providing detailed structural information on the title compound and the disulfide bridge.     

Ab initio and density functional calculations of core excitation spectra of CO, H2CO and F2CO

Calculations of the discrete core excitation spectra, including Rydberg transitions, are reported for CO, H₂CO and F₂CO employing ab initio and density functional approaches. The highly correlated QDPTCI approach compares well with experimental data and other accurate ab initio results. It appears that reliable values can be currently obtained for small molecules, although considerable uncertainty still affects intensity values, notably those experimentally derived. Comparison with the simpler 1h–1p CI approach indicates some deficiencies of the latter, attributed to the use of inadequate orbitals. The density functional approach proves generally reliable and can be profitably employed for the interpretation of experimental data in large systems, although presently limited to the case of nondegenerate core holes.     

Vibrational structures of dimethyl sulfide and ethylene sulfide cations studied by vacuum-ultraviolet mass-analyzed threshold ionization (MATI) spectroscopy

Adiabatic ionization energies of dimethyl sulfide (DMS) and ethylene sulfide (thiirane) are both accurately and precisely determined to be 8.6903 +/- 0.0009 and 9.0600 +/- 0.0009 eV, respectively, by vacuum-UV mass-analyzed threshold ionization (MATI) spectroscopy. Also reported are vibrational frequencies of DMS and thiirane monocations. Simulations using a Franck-Condon analysis based on ab initio molecular structures reproduce the experimental findings quite well. Detailed vibrational structures are discussed with the aid of ab initio calculations. Ionization-induced structural changes provide the information about the role of the sulfur nonbonding orbital in the geometrical layout of the title compounds.