L. Schäfer

Normal coordinate ab initio force relaxation

Abstract A procedure for optimization of molecular geometries is presented, combining ab initio calculations with vibrational molecular data from spectroscopy or empirical force fields. Theoretical cartesian forces are transformed to vibrational normal coordinate forces from which geometry increments are calculated. Test results indicate that the method saves considerable effort compared to other optimization schemes.

The molecular orbital constrained electron diffraction (moced) structural model of quadricyclane determined by electron diffraction combined with ab initio calculations of potential and geometrical parameters

Abstract The gas electron diffraction (GED) data of quadicyclane (previously recorded by the University of Tokyo group) were reinvestigated using constraints taken from ab inito (4–21G) gradient geometry and force field calculations. It was the purpose of this study to determine the MOCED structural model for this compound that is obtained when the differences between some unrasolved bond distances and angles in the GED data analysis are constrained to the calculated values. In addition, a novel procedure was tested, in which a scale factor for the ab initio calculated vibrational amplitudes was refined from the diffraction data together with the variable structural parameters. This novel procedure greatly reduces parameter correlation in the least-squares analysis and is expected to be useful whenever extraneous constraints of unresolved parameters are needed for fitting molecular models to the diffraction data. Subject to the ab initio constraints, the analysis yields the following model ( r g -distances, r α -angles; numbers in parentheses are six times the standard deviations of the least-squares intensitv refinements): (CH) = 1.109(1) A, (CC) = 1.526(2) A 1 C 1 C 2 = 1.525(24) A, C 2 C 6 = 1.525(12) A 1 C 2 C 3 = 1.543(24) A 1 C 1 C 7 = 1.514(42) A 1 and C 1 C 7 C 4 = 98.7(6)°. With these parameters, the dependent angles are C 1 C 2 C 3 = 104.3°, C 1 C 2 - C 4 = 60°, C 2 C 1 C 6 = 60 °, and C 2 C 1 C 7 = 110.6°.

Structural and vibrational kinetics of photoexcitation processes using time resolved electron diffraction

Abstract This paper describes the historical background and current status of structural and vibrational kinetic studies of photoexcitation processes using pulsed beam gas electron diffraction. The development of time resolved electron diffraction (TRED) required essential changes in the traditional experimental and theoretical procedures of gas electron diffraction. On the experimental side, over the last decade or so, research at the University of Arkansas has led to construction of a prototype on-line data recording system that, combined with a laser-driven pulsed photocathode, enables time-resolved investigations spanning the time domain from microseconds to picoseconds. On the theoretical side, new techniques allow one to model TRED data in terms of a molecules potential energy surface or, alternatively, to apply stochastic procedures to solve the inverse problem, i.e. to determine the PES from the diffraction data. The importance of considering appropriate vibrational properties is demonstrated. Diverse aspects of TRED modeling of dissociation and pre-dissociation processes are described, including formalisms based on wave packet dynamics, spatial anisotropy, chaotic nuclear dynamics, Wigner distribution functions, tomographic reconstruction, and coherently excited molecular ensembles.

A combined ab initio and gas electron diffraction study of the molecular structure of 1,1-dicyanocyclobutane

Abstract The molecular structure of 1,1-dicyanocyclobutane was investigated by gas electron diffraction and the results are compared with 4–21G ab initio gradient geometry refinements. In the cyclobutane ring C1–C2 > C2–C3 in contrast to structural trends generally observed for cyclobutyl systems with a single electronegative substituent. The CCN groups are slightly non-linear, with the CN groups bent away from one another. The structural features observed can be rationalized in terms of a special electronic interaction between the geminal cyano groups, which is also suggested by the 13 C NMR spectrum.

Crystal structures of 4,4′-dimethoxydithiophene and comparison with quantum mechanical calculations

Abstract Crystallographic data: 4,4′-dimethoxydithiophene (4,4′-dimethoxy-2,2′-dithienyl), C10H10O2S2, Mr = 226.32, triclinic, P 1 , a = 6.450(1), b = 8.089(1), c = 10.948(1) A, α = 81.01 (1)°, β = 86.91 (1)°, γ = 66.93 (1)°, V = 519.06 A3, Dx = 1.448, Dm = 1.45 Mgm−3 (flotation in aqueous K2HgI4 solution), λ (MoKα) = 0.710 A, μ = 0.445 mm−1, T = 293 K, R = 0.052, Rw = 0.046, 2417 observed [F2 > σ(F2)] of 2522 unique reflections. The two planar five-membered rings are exactly co-planar. The sulfur atoms are trans relative to one another. The compound crystallizes with two molecules in the unit cell, located on crystallographic centres of symmetry. The system is an interesting case for study of crystal-packing effects on molecular structure, because molecules in different halves of the unit cell have different geometries (differences of up to 0.014 A and 0.8° in equivalent bond distances and angles involving non-H atoms, and about 0.1 A and 4–5° in H atom parameters). In addition to the crystallographic study of the title compound, ab initio 4-21G geometry refinements were performed for the homologous 4,4′-dihydroxydithiophene. Characteristic trends in the calculated equilibrium structure and the observed crystal structures are in good agreement. Deviations in comparable bond-distance differences in the three sets, involving non-H atoms, are found at the 0.01 A level.

Ab initio structural investigation of methyl and ethyl carbamate, and carbamyl choline

The molecular structures of four conformations of methylcarbamate, three forms of ethylcarbamate, four forms of ethylacetate, and of the trans-form of carbamylcholine, were determined by ab initio gradient geometry refinement on the 4-21G level, and the results are compared with the geometries of homologous systems. Significant changes in bond distances and angles are observed with torsional changes, but, barring long-range non-bonded interactions, they are to a large extent localized in that part of the system which is directly involved with the torsional transition; i.e., through-bond effects in a bond distance chain begin to be insignificant after a sequence of three bonds.

Standard geometry functions for ethanol, ethylamine, propanol and propylamine☆

Abstract The dependence of bond distances and angles on the central CC bond torsions was determined for ethanol, ethylamine, propanol and propylamine. In all cases the conformationally dependent variations in the central CC bond distances are larger than in terminal CX bonds, and changes of up to 2—3° are found for some XCC angles. Thus, the results allow identification of those structural parameters which should be treated as non-rigid in conformational analyses of systems with structural components of the same type. The effects of constraints on non-equilibrium, minimum-energy coordinates are discussed. For parameters whose non-equilibrium values are not significantly affected by differences in constraints, it seems useful to define standard geometry functions which describe parameter dependence on internal rotation.

SOME GENERAL ASPECTS OF TORSIONAL SENSITIVITY AND THE GG-EFFECT

Abstract The geometries of 28 compounds of type X–C1–C2–C3–Y, with X,Y=CH 3 , F, Cl, OH, NH 2 , COH, and COOH, were fully optimized by ab initio HF/4-21G calculations at 30° grid points in their respective φ (X–C1–C2–C3), ψ (C1–C2–C3–Y)-torsional spaces. The results make it possible to construct parameter surfaces and their gradients in φ , ψ -space. The magnitude of the gradient, |∇ P |=[( ∂P / ∂φ ) 2 +( ∂P / ∂ψ ) 2 ] 1/2 , of a structural parameter P (a bond length, bond angle, or non-bonded distance) in φ , ψ -torsional space is a measure of torsional sensitivity (TS); i.e. a measure of the extent to which bond lengths, bond angles, and non-bonded distances change at a point in φ , ψ -space with backbone torsional angles. It is found that TS is not constant throughout the conformational space of a molecule, but varies in a characteristic way. It seems that, regardless of the nature of X or Y, extended forms are typically in regions of low TS; puckered conformations, of high TS. Conformations with two sequential gauche torsional angles (GG sequences) are characterized by high TS of 1,5-non-bonded distances concomitant with relatively low TS of other internal coordinates. This property of GG sequences is the source of a stabilizing and cooperative energy increment that is not afforded by other torsional sequences, such as trans – trans or trans – gauche . A structural data base, consisting of thousands of HF/4-21G structures of X–C–C–Y and X–C–C–C–Y systems has been assembled and is available on a CD.

Ab initio structural trends and torsional sensitivity in n-hexane and comparisons with crystallographic structural results

Abstract The molecular structures of n -hexane were determined by RHF/4-21G ab initio geometry optimization at 30° grid points in its three-dimensional τ 1 (C11–C8–C5–C1), τ 2 (C14–C11–C8–C5), τ 3 (C17–C14–C11–C8) conformational space. Of the resulting 12×12×12=1728 grid structures, 468 are symmetrically non-equivalent and were optimized constraining the torsions τ 1 , τ 2 , and τ 3 to the respective grid points, while all other structural parameters were relaxed without any constraints. From the results, complete parameter surfaces were constructed using natural cubic spline functions, which make it possible to calculate parameter gradients, |∇ P |=[(∂ P /∂ τ i ) 2 +(∂ P /∂ τ j ) 2 ] 1/2 , where P is a C–C bond length or C–C–C angle. The parameter gradients provide an effective measure of the torsional sensitivity of the system and indicate that dynamic activities in one part of the molecule can significantly affect the density of states, and thus the contributions to vibrational entropy, in another part. This opens the possibility of dynamic entropic conformational steering in complex molecules; i.e. the generation of free energy contributions from dynamic effects of one part of a molecule on another. When the conformational trends in the calculated C–C bond lengths and C–C–C angles are compared with average parameters taken from some 900 crystallographic structures containing n -hexyl fragments or longer C–C bond sequences, some correlation between calculated and experimental trends in angles is found, in contrast to the bond lengths for which the two sets of data are in complete disagreement. The results confirm experiences often made in crystallography. That is, effects of temperature, crystal structure and packing, and molecular volume effects are manifested more clearly in bond lengths than bond angles which depend mainly on intramolecular properties. Frequency analyses of the τ 1 , τ 2 and τ 3 torsional angles in the crystal structures show conformational steering in the sense that, if τ 1 is trans peri-planar (170°≤ τ 1 ≤180°; −180°≤ τ 1 ≤−170°), the values of τ 2 and τ 3 are clustered closely around the ideal gauche (±60°) and trans (±180°) positions. In contrast, when τ 1 is in the region (50°≤ τ 1 ≤70°), there is a definite increase in the populations of τ 2 and τ 3 at −90 and −150°.

Mean amplitudes of vibration of ruthenocene

Abstract The mean amplitudes of vibration and the perpendicular amplitude correction coefficients are reported for ruthenocene. The result is compared to the corresponding electron diffraction values as far as available.