Showing papers on "Dihedral angle published in 1976"
TL;DR: In this paper, the authors compared two different treatments of the degrees of freedom of bond stretching and bond angle bending in chain polymers by classical statistical mechanics, leading to different and nonequivalent expressions of the partition functions.
Abstract: Two different treatments of the degrees of freedom of bond stretching and bond angle bending in chain polymers by classical statistical mechanics lead to different and nonequivalent expressions of the partition functions. If we fix the bond lengths and bond angles at the outset and treat them as constraints (the classical rigid model), the partition function is given by an integral of (det G)-'12 exp(-@F(Q)) over the space of the dihedral angles Q in a poly- mer chain, where the elements of the matrix G are the coefficients in the quadratic expression (in terms of general- ized momenta conjugate to Q) for the kinetic energy of the polymer chain, and F(Q) is the conformational energy of the polymer chain. If we conceptually allow bond lengths and bond angles to vary under an infinitely strong potential (the classical flexible model) and perform the integration of the Boltzmann factor over the momenta conjugate to the Cartesian coordinates, we obtain the partition function in the form of an integral of exp(-@F(Q)) over the space of the dihedral angles Q. The origin of the difference in these two expressions lies in the different treatments of the vi- brational motions involving bond lengths and bond angles. In order to decide which of the two expressions is to be used as the basis of a statistical mechanical study of the polymer chain in equilibrium, an expression for the partition function that is quantum mechanically correct for these vibrational motions is derived, and the approximations in- volved to obtain each of the two non-equivalent classical expressions from the quantum mechanical expression are examined. The classical rigid model can be derived from the quantum mechanical one (a) by applying the ground state approximation for all vibrations associated with bond stretching and bond angle bending (i.e., by neglecting contributions to the partition function from excited vibrational states), and (b) by neglecting the conformational de- pendence of the zero-point energy of these vibrations. The classical flexible model can be derived by treating all these vibrations classically, which would appear to be unwarranted because many of these vibrations are of sufficiently high frequency to require a quantum mechanical treatment. However, a quantitative analysis of the approximations involved in each of the two models reveals that, of the two nonequivalent classical treatments, the classical flexible model is better than the classical rigid model.
315 citations
TL;DR: In this article, a theoretical analysis of the equilibrium geometry of an aggregate composed of second-phase β-particles located at α-cell corners is presented, and relationships between the volume fraction, β v, the fraction of cell-boundary area covered, β A, and the dihedral angle, θ, have been determined.
102 citations
TL;DR: Conformational energy calculations performed on the molecular fragment Calpha1C'ONHCalpha2, on N-methylacetamide, and on several peptide molecules shows that conformation-dependent properties of blocked dipeptides can be represented adequately without allowing omega to vary.
Abstract: Conformational energy calculations using ECEPP (Empirical Conformational Energy Program for Peptides) were performed on the molecular fragment Calpha1C'ONHCalpha2, on N-methylacetamide, and on several peptide molecules including N-acetyl-N'-methylglycineamide (Gly single residue), N-acetyl-N',N'-dimethylglycine-amide, and N-acetyl-N'-methylamide dipeptides of Gly-Gly and Gly-Pro. Energy minimization was carried out with peptide groups taken in both the cis and trans conformations, and the librational entropy and conformational free energy were determined at each minimum. It was found that the instability of cis in Gly-Gly comes primarily from interactions of the Calpha1 and HCalpha1 atoms with the Calpha2 and HCalpha2 atoms, and also from avorable interactions present in the trans form which are disallowed in the cis form, and from conformational entropy. The instability of cis in Gly-Pro is much less than in Gly-Gly because unfavorable interactions of the type CalphaH-CalphaH present in the cis conformation of Gly-Gly are present in both the cis and trans forms of Gly-Pro. The instability of cis in Gly-Pro arises mainly from the change in electrostatic energy caused by the restricted rotation about the N-Calpha bond of Pro. Entropy accounts for about 0.5 kcal/mol of the instability of cis in Gly-Pro compared with about 1.5 kcal/mol in Gly-Gly. The calculated fraction (4%) of cis in Gly-pro is in good agreement with the experimental value (5%) for related peptides in nonpolar solvents. When the dihedral angle omega of the central peptide bond in these dipeptides is allowed to vary during energy minimization, the deviations from planarity are only 1-3 degrees in low-energy minima of Gly-Gly but as much as 10 degrees in Gly-Pro. A comparison of these results with calculations in which the peptide bond was held fixed in the planar trans conformation shows that conformation-dependent properties of blocked dipeptides can be represented adequately without allowing omega to vary.
98 citations
TL;DR: In this article, the authors derived a 2n-dimensional parabola around the minimum point in the range of fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides.
Abstract: Fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino-acid residues can be approximated by a 2n-dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈ΔθiΔθj〉, the mean value of the product of deviations of dihedral angles ϕi and ψi (collectively designated by θi) from their energy minimum values, with a matrix inverse to the second derivative matrix F,n of the conformational energy function at the minimum point. A method of calculating the inverse matrix Fn−1 explicitly is given. The method is applied to calculating 〈ΔθiΔθj〉 for the α-helices of poly(L-alanine) and polyglycine. The autocorrelations 〈(Δϕi)2〉 and 〈(Δψi)2〉 at 300°K are found to be about 66 deg2 and 49 deg2, respectively, for poly(L-alanine), and 84 deg2 and 116 deg2, respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.
56 citations
TL;DR: In this article, it was shown that amorphous selenium is likely to consist of two-fold coordinated structural units in which the sign of the dihedral angle either alternates or is random in sign as one proceeds from atom to atom.
Abstract: It is shown that a reversal in the magnitude of two peaks in the density of electron states associated with the bonding p-band in trigonal, compared to amorphous, selenium can best be an interaction between lone-pair and bonding orbitals in the two structures. This interaction reverses its parity between a spiral and a ring structure. We conclude that amorphous selenium is likely to consist of two-fold coordinated structural units in which the sign of the dihedral angle either alternates or is random in sign as one proceeds from atom to atom. We are able, on energetic grounds, to rule out structures with a large change in magnitude of the dihedral angle. The hybridization present in each phase is also discussed.
45 citations
TL;DR: In this article, the microwave spectra of gauche-ethanethiol and its isotopic species were studied and the structure of the gauche isomer was determined from the observed moments of inertia.
Abstract: The microwave spectra of gauche-ethanethiol and its isotopic species were studied. Most of the observed spectra for the species having the plane of symmetry exhibited doublet structures with large spacings due to the internal rotation of the mercapto group. The rs structure of the gauche isomer was determined from the observed moments of inertia. The gauche isomer whose dihedral angle τ(CCSH) is 61°45′±58′ has structural parameters close to those for the trans isomer except the angles around the carbon atom in the methylene group. The difference in angle values around the carbon atom in the methylene group between the trans and gauche isomers can be explained by the 3°7′ tilt of the methylene group towards the lone pair electrons on the sulfur atom. The direction of the dipole moment in the molecule was discussed on the basis of data given by Schmidt and Quade. The potential barrier of the mercapto internal rotation was obtained from splittings of the observed spectra. The Fourier coefficients of this bar...
45 citations
TL;DR: In this paper, a single-crystal X-ray analysis of Pt(PPh3)2(PC6F5)2 has been performed and the structure has been solved by Patterson and Fourier methods and refined to R = 0.043 from three-dimensional diffractometer data.
41 citations
Patent•
26 Jul 1976
TL;DR: In this article, means for determining the aperture angle Ω c of a TV camera tube and the angles θ c and φ c of the camera's axis are given.
Abstract: A television object locator and image identifier, for use with a TV camera tube, having a lens whose axis is determined by the angles θ c and φ c . The angle θ c forms a dihedral angle between two vertical planes, one of which contains the axis of the lens. The angle φ c is formed by the vertical edge of the dihedral angle and the lens axis. The coordinates of the center of the lens are located at (x c , y c , z c ), at the intersection of the edge and the lens axis, these coordinates also being those of the origin of the locator for a fixed camera position. Means are provided for determining the aperture angle Ω c of the TV lens, as well as means for determining the angles θ c and φ c . Means are also provided for determining the coordinates (x o , y o , z o ) of the object which is to be identified with respect to the origin. First and second means for transforming coordinates, have as inputs signals representing the angle Ω c and the coordinates (x c , y c , z c ), and (x o , y o , z o ), and have as an output a signal representing the pair of coordinates (x T , y T ), which are scaled proportionally to the dimensions of the location of the image in the total field of view. Means are provided for computing the precise location on the TV raster of the object to be identified, in the horizontal and vertical directions.
37 citations
TL;DR: In this paper, it was shown that the γ-turn can exist in solution as an independent conformational feature in repeat penta- and hexapeptides of elastin.
35 citations
TL;DR: In this article, an SCF calculation followed by extensive configuration interaction between all singly-excited singlet states has been performed for 1,1′-binaphthyl as a function of the dihedral angle.
34 citations
TL;DR: In this article, 13C nmr chemical shifts and 13C-31P couplings through one to five bonds are reported for seven dimethylphosphono compounds of known geometry.
Abstract: 13C nmr chemical shifts and 13C–31P couplings through one to five bonds are reported for seven dimethylphosphono compounds of known geometry. Vicinal couplings are maximal for a dihedral angle of 180° and are severely attenuated by OH substitution, particularly when the OH is trans-coplanar to the carbon terminus of the coupling path. When a cyclopropyl system is part of the C–C–C–P path the J values are much less than those predicted on the basis of dinedral angle. A highly asymmetric dihedral dependence of vicinal J's is suggested. Some 'non-W' long range C–P couplings through saturated networks are found. The 'gauche-γ' shift of the —P(O)(OCH3)2 group is about 2 ppm.
TL;DR: In this article, the authors derived a relationship between the equilibrium degree of particle contact and the ratio of the interfacial energies, i.e., the energy of the contact boundary between particles and of the particle-matrix interface.
TL;DR: The electron diffraction study of azetidine yielded the following main geometrical parameters ( r a structure): dihedral angle (the angle between the C-C-C and C-N-C planes) φ = 33.1 ± 2.4°, r (C-N) = 1.482 ± 0.009A, r(C-H) =1.107 ± 0.003A, ∠C- N-C = 92.2 ± 0 4°,
TL;DR: In this paper, the effect of a heterosubstituent X on 13C chemical shifts, in conformations characterized by dihedral angles of 60°, was analyzed in terms of α-shifts, heteroatom-carbon (XC), hydrogen-heteroatom (HX) and carbon-heteroadom (CX) gauche interactions, and nonbonded γ(X), and δ(X) interactions.
Abstract: The effect of a heterosubstituent X on 13C chemical shifts, in conformations characterized by dihedral angles of 60°, is analyzed in terms of α-shifts, heteroatom–carbon (XC), hydrogen–heteroatom (HX) and carbon–heteroatom (CX) gauche interactions, and nonbonded γ(X) and δ(X) interactions. The more general parameters describe the β-heteroatom shifts in conformations in which the dihedral angles differ from 60°. The shielding effects of chlorine, exocyclic oxygen, and endocyclic nitrogen are analyzed.
TL;DR: In this article, a relationship between internuclear distance and the contribution to the coupling constant between an ortho-fluorine nucleus and the trifluoromethyl group was established.
TL;DR: In this article, the molecular structure of (1′-t-butyl-2′,2′-dimetnylpropyl)-π-(tricarbonylchromium)benzene, CrC 18 H 24 O 3, has been determined from three-dimensional X-ray data.
TL;DR: In this paper, the molecular structure of dimethylboric anhydride has been investigated by electron diffraction from the vapour and the data are consistent with a molecule of C 2 symmetry for the C 2 BOBC 2 skeleton.
TL;DR: The conformation of methyl ethyl disulfide was investigated by molecular mechanics calculations using a recently developed force field for sulfur-containing alkanes in this article, and the results indicated that in the gas phase the molecule exists predominantly in two conformations, both with the CSSC dihedral angle gauche (84°), and the SSCC dihedral angles either gauche or trans (179°) and the methyl protons staggered.
TL;DR: In this article, spectra from the L and DL optical isomers of thirteen amino acids have been observed after x-irradiation at 77 K, where ϑ is the dihedral angle between the C-N bond and the pz orbital occupied by the unpaired electron.
Abstract: ESR spectra from the L and DL optical isomers of thirteen amino acids have been observed after x‐irradiation at 77 K. For most of the acids, spectra from the L and DL isomers are different at corresponding temperatures in a range from 77 to 250 K. These differences are attributed to differences in crystal structure, and specifically to the conformation of the amino group with respect to the adjacent carboxyl group. The temperature at which deamination occurs is described by the equation T=13+137 sin2ϑ, where ϑ is the dihedral angle between the C–N bond and the pz orbital occupied by the unpaired electron.
TL;DR: X-ray structure analysis is carried out for three new complexes prepared by interaction of tetrakis(trifluoromethyl)allene with carbonylate anions as mentioned in this paper.
TL;DR: The chromophore molecule has crystallographic S4 symmetry with the oxygen atoms of the associated water molecules positioned on this symmetry axis above and below the porphinogen and linked in each case to two opposing pyrrole nitrogen atoms by hydrogen bridge bonds of length 3.13 as mentioned in this paper.
Abstract: Crystals of the title compound (I) are tetragonal, space group l41/a, with a= 13.801 (1), c= 18.575(6)A, Z= 4. The chromophore molecule has crystallographic S4 symmetry with the oxygen atoms of the associated water molecules positioned on this symmetry axis above and below the porphinogen and linked in each case to two opposing pyrrole nitrogen atoms by hydrogen bridge bonds of length 3.016 A(N–H 0.92, H ⋯ O 2.13 A). The atoms bonded to a bridging carbon atom form dihedral angles of –8.9 and 41.6° with the planes of the neighbouring pyrrole rings. Each of the four hydrogen atoms of tho two water molecules interacts with a ketone-oxygen atom of a neighbouring molecule such that each molecule of (1) is linked to four other similar molecules (O–H ⋯ O 2.832, O–H 0.89, H ⋯ O 2.01 A), resulting in the formation, of water-containing tubular cavities. The structure was solved by direct methods and refined to R 0.075 for 1 115 diffractometer measured unique reflections.
TL;DR: In this article, the X-ray crystal structure and the PMR spectrum in 2 H 2 O and DMSO-d 6 of cyclo-glycyl-4-thiaprolyl has been determined.
TL;DR: In this paper, the structure of glucyl-DL-phenylalanine was solved by symbolic addtion method and refined to an R index of 0.041 for 2271 reflections.
Abstract: Crystals of glucyl-DL-phenylalanine are orthorhombic, space Pbca, with a=9.241(2), b=28.41(1), and c=8.602(2) A. The structure has been solved by the symbolic addtion method and refined to an R index of 0.041 for 2271 reflections. The peptide group is non-planner, the torsion angle about the peptide bond being -170.2(2)° for tge L molecules. The strecture is stabilized by a network of intermolecualr hydregen bonds N-H…O; there is also evidence for the presence of C-H…O interactions.
TL;DR: In the crystal structure of D-glucaro-1,4-lactone monohydrate, C6H8O7·H2O, the molecules have the E3 lactone-ring conformation, with a small distortion of the ring to 3T2.
TL;DR: The vibrational spectra of a series of disordered two-fold coordinated chains of atoms, calculated using bond stretching and bending forces only, are presented in this paper, where the disorder is included by a distribution in the dihedral angle, the bond angles being set at the value for crystalline Se.
Abstract: The vibrational spectra of a series of disordered two-fold coordinated chains of atoms, calculated using bond stretching and bending forces only, are presented. The disorder is included by a distribution in the dihedral angle, the bond angles being set at the value for crystalline Se. Comparison of the results with experimental data for a-Se indicates the existence of a preferred magnitude for the dihedral angle along chain-molecular units. Further considerations suggest the sign of the dihedral angle is constant or random and may be distributed about the crystalline value with a standard deviation up to a maximum of about 10°. It is likely that this distribution is broader in a-Te than in a-Se.
TL;DR: In this article, a centrosymmetric quinol complex was solved by the heavy-atom method and refined by block-diagonal, least-squares calculations to a final R of 0.036 for 2204 reflexions.
Abstract: The complex is monoclinic, space group P21/c, with a=6-817 (1), b=7.897 (1), c= 19-351 (2) /~,, ,8= 102.7 (1) °, Z=2. The structure was solved by the heavy-atom method and refined by block-diagonal, least-squares calculations to a final R of 0.036 for 2204 reflexions. Each quinol molecule is hydrogen bonded to two Iions with O . . . Idistances 3.457 (3) A, and each Iis 0.68 A out of the quinol plane. Such centrosymmetric quinol. 2Iunits are stacked alternately with centrosymmetric bipyridylium ions in infinite columns along b. The tilt of these units is such that each pyridine ring has a quinol molecule lying over or under it on one side (with a dihedral angle between the two rings of 3.4 ° and an average perpendicular separation of 3"38 A) and an Iion on the other side (perpendicular distance from the ring 3.73 A) almost directly above or below the N atom at a distance of 3.736 (3) A. This arrangement is indicative of charge-transfer interaction between both quinol and Ias donors and the bipyridylium ion as acceptor.