A quantum mechanical Hamiltonian for unhindered macromolecular chains: consistency with Gaussian models

A model for an open unhindered three-dimensional macromolecular chain, based upon quantum mechanics and proposed in previous works, is studied in order to investigate its physical properties and consistency. The chain is formed by N particles interacting through harmonic-like vibrational potentials in the high-frequency limit (in which all successive bond lengths become fixed). This formulation leads to a specific Hamiltonian for the chain: it constitutes an improvement in comparison with standard Gaussian models, which do not. The classical partition function Z_c resulting from the quantum formulation is represented through an integral, which exhibits explicitly rotational invariance in the integrand and provides the basis for further approximations for large N. Approximate formulae are obtained for correlations between pairs of bond vectors, the distribution function for the end-to-end vector, distribution functions for individual bond vectors, “rubber eleasticity” (when stretching forces act) and the structure factor for small wave vector. In all cases, the results which have arisen from the quantum mechanical formulation coincide with those obtained for the standard Gaussian chain. This agreement appears to confirm the physical consistency of the quantum Hamiltonian characterizing the model.     

Quantum statistical mechanics of closed‐ring molecular chains

A model for a closed‐ring unhindered three‐dimensional macromolecular chain, based on Quantum Mechanics, is presented. Upon starting from an exact non‐relativistic Hamiltonian operator, we integrate out all electronic degrees of freedom, in the Born‐Oppenheimer framework, giving rise to an effective vibro‐rotational Hamiltonian for the chain. Then, assuming a harmonic oscillator‐like vibrational potential between nearest‐neighbour atoms, the integration of the atomic radial degrees of freedom is carried in the limit of high frequencies. Thus, all bond lengths become fixed, including the one which makes the chain to become a closed ring. This formulation leads to a specific Hamiltonian for the remaining angular variables of the closed‐ring chain, and constitutes an alternative in comparison with standard Gaussian models, which do not. Use is made of a variational inequality by Peierls to find an approximate quantum partition function for the angular variables of the system. We then proceed to obtain approximately another representation for the angular partition function in the classical limit. Several features of the classical partition function are discussed.     

Open three-dimensional unhindered molecular chains: Partition function

An open molecular chain, formed by N classical particles moving in three dimensions and having N − 1 bonds of constant lengths between successive neighbours, is considered. Hamiltonian methods with manifest rotational invariance allow to characterize all constraints. The classical partition function, Z₀, for a large open chain in thermal equilibrium is analyzed in general. Simpler integral representations for Z₀ are obtained, with the following advantages: (i) explicit rotational invariance in the integrands, (ii) only tridiagonal matrices appear and, moreover, approximations for their determinants can be obtained. For a two-dimensional open chain, an approximate factorized formula for Z₀ is presented, and its essentials are generalized to the three-dimensional case. In both cases, the features of the partition functions bear certain similarities to that for a classical ideal gas. The approximate partition functions lead to approximate analytical computations of the correlations between pairs of different bond vectors, of the squared end-to-end distance, of the probability distribution for the end-to-end vector and of the structure factor, which display some novel features. Some comparisons with the corresponding results for the Gaussian chain are made.     

Molecular mechanics (MM3) parameterization of hydroxylamine and methyl derivatives

Based on results of electron diffraction, gas phase infrared spectroscopy (IR), and MP2/6-31 + G* ab initio calculations, a set of molecular mechanics (MM3) parameters was developed for molecules containing the N(sp³)—O(sp³) moiety. Using this set of parameters, MM3 is able to reproduce structures (bond lengths and bond angles) and vibrational spectra satisfactorily. © 1994 by John Wiley & Sons, Inc.     

Crystal Structure and Conformation of a 10-Thiabilirubin

 A crystal structure determination of a bilirubin analog with a sulfur instead of a C(10)–CH₂ linking the two dipyrrinones is reported. Conformation-determining torsion angles and key hydrogen bond distances and angles are compared to those obtained from molecular dynamics calculations as well as to the corresponding data from X-ray determinations and molecular dynamics calculations of bilirubin. Like other bilirubins, the component dipyrrinones of the analog are present in the bis-lactam form with (Z)-configurated double bonds at C(4) and C(15). Despite the large differences in bond lengths and angles at –S–vs.–CH₂–, the crystal structure shows considerable similarity to bilirubin: both pigments adopt a folded, intramolecularly hydrogen-bonded ridge-tile conformation stabilized by six hydrogen bonds – although the interplanar angle of the ridge-tile conformation of the title compound is smaller (∼ 86°) than that of bilirubin (∼ 98°). The collective data indicate that even with long C–S bond lengths and a smaller C–S–C bond angle at the pivot point on the ridge-tile seam, intramolecular hydrogen bonding persists.     

Quasi-Hamiltonian equations of motion for internal coordinate molecular dynamics of polymers

Conventional molecular dynamics simulations of macromolecules require long computational times because the most interesting motions are very slow compared to the fast oscillations of bond lengths and bond angles that limit the integration time step. Simulation of dynamics in the space of internal coordinates, that is, with bond lengths, bond angles, and torsions as independent variables, gives a theoretical possibility of eliminating all uninteresting fast degrees of freedom from the system. This article presents a new method for internal coordinate molecular dynamics simulations of macromolecules. Equations of motion are derived that are applicable to branched chain molecules with any number of internal degrees of freedom. Equations use the canonical variables and they are much simpler than existing analogs. In the numerical tests the internal coordinate dynamics are compared with the traditional Cartesian coordinate molecular dynamics in simulations of a 56 residue globular protein. For the first time it was possible to compare the two alternative methods on identical molecular models in conventional quality tests. It is shown that the traditional and internal coordinate dynamics require the same time step size for the same accuracy and that in the standard geometry approximation of amino acids, that is, with fixed bond lengths, bond angles, and rigid aromatic groups, the characteristic step size is 4 fs, which is 2 times higher than with fixed bond lengths only. The step size can be increased up to 11 fs when rotation of hydrogen atoms is suppressed. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1354–1364, 1997     

Crystal Structure and Conformation of a 10-Thiabilirubin

Summary.  A crystal structure determination of a bilirubin analog with a sulfur instead of a C(10)–CH₂ linking the two dipyrrinones is reported. Conformation-determining torsion angles and key hydrogen bond distances and angles are compared to those obtained from molecular dynamics calculations as well as to the corresponding data from X-ray determinations and molecular dynamics calculations of bilirubin. Like other bilirubins, the component dipyrrinones of the analog are present in the bis-lactam form with (Z)-configurated double bonds at C(4) and C(15). Despite the large differences in bond lengths and angles at –S–vs.–CH₂–, the crystal structure shows considerable similarity to bilirubin: both pigments adopt a folded, intramolecularly hydrogen-bonded ridge-tile conformation stabilized by six hydrogen bonds – although the interplanar angle of the ridge-tile conformation of the title compound is smaller (∼ 86°) than that of bilirubin (∼ 98°). The collective data indicate that even with long C–S bond lengths and a smaller C–S–C bond angle at the pivot point on the ridge-tile seam, intramolecular hydrogen bonding persists. Received August 16, 2001. Accepted September 12, 2001     

Crystal Structure and Conformation of a Bilirubin Ester

Summary. Crystal structures determined for three bilirubin analogs with gem-dimethyl groups at C(10) are reported, including the first X-ray structure of a bilirubin dimethyl ester. Conformation-determining torsion angles and key hydrogen bond distances and angles were compared to those from molecular dynamics calculations. Like other rubins, the component dipyrrinones of the three compounds were found to adopt the syn conformation, with Z-configuration double bonds at C(4) and C(15) and bis-lactam tautomeric structures of the end rings. No large differences in bond lengths and bond angles at C(10) were found, and the crystal structures of the two 10,10-dimethyl rubin acids showed considerable similarity to that of bilirubin: both pigments adopt a folded, intramolecularly hydrogen bonded ridge-tile conformation stabilized by six hydrogen bonds, with an interplanar angle in ridge-tile of 98° and 86°. In contrast, the dimethyl ester is intermolecularly hydrogen bonded in the crystal. Each molecule of the ester has its two syn-Z-dipyrrinones rotated into a conformation syn to the gem-dimethyl group, whereas in the acids they are anti.     

Vibrational spectra and structure of methyl-derivatives of imidazo[4,5-c]pyridine based on DFT quantum chemical calculations and XRD studies

The molecular structures, vibrational energy levels and potential energy distribution of 4-methyl-imidazo[4,5-c]pyridine (4MIPc) and 7-methyl-imidazo[4,5-c]pyridine (7MIPc) are derived from the quantum chemical calculations and compared to the experimental results obtained from the X-ray diffraction (XRD), IR and Raman studies. The B3LYP/6-311G(2d,2p) quantum model and PED contributions have been applied for the assignment of the vibrational modes. 4MIPc crystallizes in an orthorhombic structure, space group Pna2₁ and Z = 4 and 7MIPc crystallizes in a triclinic structure, space group P−1 and Z = 4. The almost planar conformation of the molecules and presence of the N–H?N hydrogen bonds formed with the pyridine and imidazole nitrogen atoms was found to be characteristic for the studied systems. The presence of hydrogen bonds is also confirmed by the results of IR studies.     

IR Spectra of Paracetamol and Phenacetin. 1. Theoretical and Experimental Studies

IR spectra of paracetamol and phenacetin have been measured for powder crystals of these compounds and for their solutions in chloroform and dimethylsulfoxide. Ab initio calculations of their equilibrium geometry and vibrational spectra were carried out for spectrum interpretation. Differences between the experimental IR spectra of solutions and crystalline samples have been analyzed. Variations of molecular structure from the isolated state to molecular crystal were estimated based on the difference between the optimized molecular parameters of free molecules and the experimental bond lengths and angles evaluated for the crystal forms of the title compounds. The role of hydrogen bonds in the structure of molecular crystals of paracetamol and phenacetin is investigated, and spectral ranges with maximal intermolecular interactions are determined.     

3-单酰胺喹唑啉酮衍生物的表征及密度泛函理论研究

Several 3-aminoquinazolin-4-(3H)-one derivatives were synthesized and characterized.Using proton nuclear magnetic resonance (NMR) spectra,we have investigated the barriers to rotation around the N ― N bond as a function of temperature.Changes in the NMR spectra at high temperatures are explained in terms of hindered rotations of the N ― N bond.Free energies of activation for the rate determining stereochemical process were calculated to be as high as 67-75 kJ · mol-1.Ground state molecular geometries and vibrational frequencies were calculated using the HF/6-31G and B3LYP/6-31G level of theories.The optimized bond lengths and bond angles are in good agreement with experimental values at both theoretical levels.     

Synthese und Röntgenkristallstruktur eines (15E)-Dihydrobilatrien-abc-Derivats

The crystal structure of the (15E)-configurated 2,3-dihydrobilatriene-abc2, representing a model compound for the active form of the phytochrome chromophore, was determined at room temperature and at 97 K. Compared to the crystal structure of the corresponding (15Z)-derivative1, the molecule of2 shows a similar helix conformation, but with considerably larger helix pitch. The azide hydrogen atoms are localized at the nitrogen atoms of rings A, C and D. The distribution of bond lengths and bond angles is compatible with previous crystal structures and with the canonical formula. Tautomeric form, conformation and crystal packing are understandable on the basis of the observed intra- and intermolecular hydrogen bonds.

     

Molecular Structure of BiBr3: An Electron Diffraction Study

The molecular structure of BiBr₃ was determined by gas-phase electron diffraction. The principal geometrical parameters are r (Bi—Br) = 2.567 ± 0.005 Å and _221D;Br—Bi—Br = 98.6 ± 0.2°. The force field of the molecule was obtained by a normal coordinate analysis utilizing both experimental vibrational frequencies and electron diffraction mean amplitudes of vibration. The variation of bond lengths and bond angles within the Group 15 trihalides is consistent with the expected trend, except that all bismuth trihalide bond angles appear to be somewhat large.     

Molecular mechanics (MM3) parameterization for oxocarbenium ions

The physical properties of a diverse group of 12 oxocarbenium ions have been studied with ab initio calculations at the MP2/6‐31+G* level of theory. Based on theoretically derived properties such as molecular equilibrium geometry, dipole moment, and vibrational frequencies, a molecular mechanics (MM3) force field has been developed with the assistance of the programs TORSMART and MPMSR, components of our artificial parameter development and refinement method. The MM3 force field is now able to reproduce bond lengths, bond angles, moments of inertia, dipole moments, torsional energy profiles, and vibrational frequencies of oxocarbenium ions, which will allow further studies of glycoside hydrolysis and their rates of reaction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 329–339, 2000     

Silicon nanotubes with distinct bond lengths

In this paper, we extend both the rolled-up and the polyhedral models for single-walled silicon nanotubes with equal bond lengths to models having distinct bond lengths. The silicon nanotubes considered here are assumed to be formed by sp³ hybridization with different bond lengths so that the nanotube lattice is assumed to comprise only skew rhombi. Beginning with the three postulates that all bonds lying on the same helix are equal, all adjacent bond angles are equal, and all atoms are equidistant from a common axis of symmetry, we derive exact formulae for the polyhedral geometric parameters such as chiral angles, bond angles, radius and unit cell length. The polyhedral model presented here with distinct bond lengths includes both the rolled-up model with distinct bond lengths which arises from the first term of an asymptotic expansion, and an existing polyhedral model of the authors which assumes equal bond lengths. Finally, some molecular dynamics simulations are undertaken for comparison with the geometric model. These simulations start with equal bond lengths and then stabilize in such a way that two distinct bond lengths emerge.     

The Structure of 3-Phenyl-4-(N-Carbamyl-1,4,2-Oxathiazolimin-3-yl)Sydnone,C11H7N5O4S·0.8 CH2Cl2

The title compound (M_r = 373) crystalizes in the othorhombic space group P bna with a = 10.410(2), b = 11.658(4), c = 23.108(3) Å, V = 2804.4 Å Z = 8. The single crystal intensity data were collected using MoK∞ radiation (λ = 0.7093Å) at room temperature. The crystal and molecular structure was solved with the final agreement index R = 0.039 for 1046 observed reflections. The bond lengths N(1)- C(7) and C(7)-C(8) of the title compound are slightly longer than those of 3-substituted sydnone derivatives. This may be attributed to the steric effect arising from the interaction of the phenyl ring and the 4-substituent with the neighboring atoms of sydnone ring. Both the title compound and 4-acetyl-3-(p-tolyl)sydnone have smaller dihedral angles between the sydnone ring and the plane of the sp² orbital of the double bond of the 4-substituent and both have shorter C(7)-C(9) bond lengths than those of other similar sydnone derivatives.     

FT-IR spectra, vibrational assignments, and density functional calculations of imidazo[1,2-a]pyridine molecule and its Zn(II) halide complexes

The geometry, frequency, and intensity of the vibrational bands of imidazo[1,2-a]pyridine (which is abbreviated as impy) were obtained by the density functional theory (DFT) calculations with BLYP, B3LYP, and B3PW91 functionals and 6-31G(d) basis set. The optimized geometric bond lengths and bond angles are in good agreement with the available X-ray data. The infrared spectrum of imidazo[1,2-a]pyridine was computed by the DFT method in order to reproduce the vibrational wavenumbers and intensities with an accuracy, which allows reliable vibrational assignments. Total energy distribution and isotopic shifts have been calculated in order to help for the perfect assignment of the vibrational modes. The zinc halide complexes Zn(impy)₂X₂ [X = Cl, Br, and I] have also been synthesized. The compounds were characterized using the elemental analysis, FT-IR spectra, and quantum chemical calculations. The geometry optimization of Zn(impy)₂X₂ yields distorted tetrahedral environment around Zn ion.     

Beiträge zur Chemie der Pyrrolpigmente, 24. Mitt. Über die Beziehung zwischen Lichtabsorption und Struktur von Bilatrienen-abc

Using the recently established solution structure of a bilatriene-abc derivative the parameter set of thePPP-SCF-LCAO-MO-Cl model was refined. The general trend, that molecular configuration itself does not so much determine the absorption spectra as was deduced by investigation of partial bile pigment structures, was confirmed for the bilatrienes-abc. Instead, the configuration at a particular double bond induces a certain torsional angle at the adjacent single bond which leads to dramatic spectral changes on isomerization of this double bond. Isomerization without this torsional effect brings about different relative intensities of the two main spectral bands. Comparing measured spectra of several bilatrienes-abc and calculated spectra a helicalsyn, syn, syn-conformation with three torsional angles at the methine fragments of appr. 20° was deduced for systems with (Z, Z, Z)-configuration. For a recently prepared (E, Z, Z)-derivative a nearly helicalsyn, syn, syn-conformation with torsional angles of 40°, 20° and 20° at the methine single bonds is the most probable.

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23. Mitt.:H. Falk, K. Grubmayr undK. Thirring, Z. Naturforsch.33b, 924 (1978).     

Ab initio scf and Ci study of the electronic structure of the trichlorine radical

Ab initio SCF and CI calculations using a double-zeta plus polarization basis set have been carried out on the trichlorine radical Cl₃ to determine its electronic structure. The minimum in energy is determined for a bent structure at a bond angle of 146° and bond lengths of 2.18 Å (SCF ) or 2.22 Å (CI ). At linear geometry a ²Π_u state is found to be lowest, approximately 7 kcal above the bent minimum, followed by a ²∑_g⁺ state, which is around 4 kcal higher. This situation suggests that already for low quantum numbers a complex vibrational pattern in the Cl₃ infrared spectrum is to be expected due to spin-orbit coupling as well as coupling of electronic, vibrational, and rotational motion.     

The Scent of Maibowle – π Electron Localization in Coumarin from Its Microwave-Determined Structure

The microwave spectra of the natural substance coumarin, a planar aromatic molecule with the specific scent of maibowle, a popular fruit punch served in spring and early summer, were recorded using a molecular jet Fourier transform microwave spectrometer working in the frequency range from 4.0 to 26.5 GHz. The rotational constants and centrifugal distortion constants were determined with high precision, reproducing the spectra to experimental accuracy. The spectra of all singly-substituted ¹³C and ¹⁸O isotopologues were observed in their natural abundances to determine the experimental heavy atom substitution r_s and semi-experimental equilibrium r_e^SE structures. The experimental bond lengths and bond angles were compared to those obtained from quantum chemical calculations and those of related molecules reported in the literature with benzene as the prototype. The alternation of the C−C bond lengths to the value of 1.39 Å found for benzene reflects the localization of π electrons in coumarin, where the benzene ring and the lactone-like chain −CH=CH−(C=O)−O− are fused. The large, negative inertial defect of coumarin is consistent with out-of-plane vibrations of the fused rings.