Bond Length Dependence Research Articles

Dynamic and Static Disorder of Alkali Halide Solid Solutions studied by Temperature-dependent Extended X-Ray-Absorption Fine Structure

Interatomic potential of ionic bonds in alkali halide solid solutions has been studied by temperature dependent EXAFS (extended X-ray absorption fine structure). As a typical ionic bond in alkali halide solid solutions, K–Br bond of KCl 0.8 Br 0.2 and KBr 0.2 I 0.8 solid solutions have been focused. The K–Br bond was contracted for KCl 0.8 Br 0.2 , while it was elongated for KBr 0.2 I 0.8 , as compared to that in KBr. The longer K–Br bond was softer and less anharmonic than the shorter K–Br bond. We could explain this bond length dependence of the force constants in terms of the interatomic potential of the K–Br bond. The static disorder also increased with the K–Br bond length.

Time development during growth and relaxation of amorphous carbon films. Tight-binding molecular dynamics study

The growth of amorphous carbon (a-C) thin film on a [1 1 1] diamond surface has been studied by a tight-binding (TB) molecular dynamics (MD) technique. Six different three-dimensional networks were constructed with periodic boundary conditions in two dimensions. Time-dependent non-equilibrium growth was simulated with atom-by-atom deposition and it was described as in real experiments without an artificial model of energy dissipation. An additional seventh structure was constructed by a melt quenching procedure which is widely used in computer generations of amorphous networks. The final structures consist of over 100 atoms. Densities, radial distribution functions (RDFs), coordination numbers, bond angle distributions and ring statistics were analyzed. During relaxation the temperature in the amorphous film decreases with stretched-exponential function. The time dependence of bond length and bond angle deviations were also investigated.

High-resolution excitation-energy-dependent study of the Auger decay of the O1s−1πgcore-excited state in oxygen

We report new measurements of the decay of the core-excited O $1s--1{\ensuremath{\pi}}_{g}{}^{3}{\ensuremath{\Pi}}_{u}$ state in molecular oxygen under Auger resonant Raman conditions. The spectral features are interpreted with the aid of ab initio calculations using standard lifetime-vibrational interference, and in some cases, employing a model in which the bond-length dependence of the Auger transition rates is taken into account. By analyzing a series of Auger-decay spectra using different excitation energies, several instances of fixed kinetic energy are pointed out in the spectra; the nondispersive behavior arises from the decay between two potentials that are essentially parallel.

Badger's rule revisited

Numerical experiments demonstrate that the accuracy of stretching force constants k e provided by Badger's rule is unlikely to be substantially improved either by modification of the functional dependence on the equilibrium bond length R e or the inclusion of bond parameters related to electron density. These results, based upon both the experimental and QCISD/6-311++G(3d2f, 3p2d) values of R e and k e, imply that most of the universal characteristics of the bond strength vs. bond length dependence are accounted for by Badger's rule, the more detailed features being unexplainable by first-order response properties such as electron density.

Spin and orbital ordering in double-layered manganites

We study theoretically the phase diagram of the double-layered perovskite manganites taking into account the orbital degeneracy, the strong Coulombic repulsion, and the coupling with the lattice deformation. Observed spin structural changes as the increased doping are explained in terms of the orbital ordering and the bond-length dependence of the hopping integral along $c$-axis. Temperature dependence of the neutron diffraction peak corresponding to the canting structure is also explained. Comparison with the 3D cubic system is made.

Density, temperature, and bond-length dependence of dynamic friction on a molecular bond

We apply the theoretical formalism developed by us earlier [M. Vergeles and G. Szamel, J. Chem. Phys. 110, 6827 (1999)] to study density, temperature, and bond-length dependence of the dynamic friction on a molecular bond. We show that the theory reproduces all the trends seen in molecular dynamics (MD) simulations. The theoretical predictions agree reasonably well with the results of MD simulations except for very low densities or very short bond lengths.

The interaction between He and H+ 2: anisotropy, bond length dependence and hydrogen bonding

An extensive high level ab initio study of the ground electronic state of HeH+ 2 has been used to generate an improved intermolecular potential for He + H+ 2 that includes a more complete account of the long range forces, the short range anisotropy, and the dependence of the potential on H+ 2 bond length r. In good agreement with earlier work, the potential is found to have a minimum for collinear geometry, with a well 7.799 kcal mol−1 (2728 cm−1) deep with respect to separated He + H+ 2(r = r e = 1.9982 a 0) at an intermolecular distance R = 2.963 a 0(1.5684 Å) and a bond length r = 2.0742 a 0 (1.098 Å).

The interaction between He and H+2: anisotropy, bond length dependence and hydrogen bonding

The interaction between He and H+2: anisotropy, bond length dependence and hydrogen bonding

Temperature and pressure dependence of hydrogen bond strength: A perturbation molecular orbital approach

Lengths and strengths of hydrogen bonds are exquisitely sensitive to temperature and pressure. Temperature and pressure sensitivity is the result of the fact that hydrogen bonds are so weak that the internal energy of the bond is important to bond strength, and the equilibrium bond distance is controlled by a combination of thermodynamics and quantum mechanics, rather than quantum mechanics alone. The importance of thermodynamics in the bond length, and strength, of hydrogen bonds is the result of a breakdown in the Born-Oppenheimer approximation that occurs when the energy of the first vibrational excitation of a bond is of the order of kT. Variation of water–water hydrogen bond length and strength with temperature and pressure is discussed in light of the data for the specific volume of ice Ih, the enthalpy of vaporization of liquid water, and the internal energy of the liquid. In most chemical contexts, correction of covalent bond strength for internal energy is not necessary. For hydrogen bonds this is not the case. In hydrogen bonded systems, like liquid water, the internal energy associated with hydrogen bonding is a significant fraction of the internal energy of the system. The variation of hydrogen bond length with temperature is approximately quadratic. Bond strength should also be quadratic with temperature because bond strength depends linearly on bond distance in second order. The internal energy correction is empirically quadratic in temperature. The net result is a linear dependence of apparent hydrogen bond strength on temperature. This can be seen directly in the variation of ΔHvaporization0/T for water with the reciprocal of temperature. The known variations in hydrogen bond equilibria with temperature in liquid formamide are discussed. Variation of the density of ice Ih with pressure, at constant temperature, demonstrates the nonlinear pressure dependence of hydrogen bond length. Because hydrogen bond strengths depend upon temperature and pressure, equilibria that involve hydrogen bonds explicitly depend upon temperature and pressure in addition to the universally appreciated dependence of the equilibrium constant on temperature. The temperature and pressure dependence of hydrogen bond length needs to be explicitly considered when one is modeling the properties of hydrogen bonded networks such as liquid water. Temperature dependence can be easily introduced by utilization of the hydrogen bond length, temperature relationship that is known for ice Ih and using a perturbation molecular orbital (PMO) treatment for bond formation. Our PMO treatment of hydrogen bonding involves second order perturbations between the donor and acceptor molecules. A random structural network model for liquid water based on this approach should be relatively easy to construct. The PMO model gives the relationship between hydrogen bond strength and hydrogen bond length as linear. This quantum mechanical result is quite distinct from the bond strength–bond length relationships obtained in classical models.

Calculated spin-spin coupling surfaces in the water molecule; prediction and analysis of J (O,H), J (O,D) and J (H,D) in water isotopomers

Ab initio symmetry and internal valence coordinate oxygen–proton and proton–proton spin–spin coupling surfaces for the water molecule have been computed for the first time. Calculations have been performed at the SOPPA (CCSD) level using a large basis set and a grid of forty-nine geometries on the two surfaces. Equilibrium values differ significantly from some other calculated values especially for the Fermi contact terms. The bond length dependence of J(O, H) is ‘normal’ i.e. J(O, H1) is much more sensitive to stretching the O–H1 bond than the O–H2 bond. This contrasts greatly with the corresponding situation in methane. The surfaces have been averaged over the nuclear motion using a recent highly accurate force field to give values of J (O, H) and J (O, D) for H2 17O, HD17O and D2 17O and J(H, D) for HD16O, HD17O and HD18O over a range of temperatures. For J (O, H) and J (O, D) bond stretching at first order is the dominant part of the nuclear motion correction with second order bending making an important contribution. For J (H, D) the second order bending is by far the largest contribution to the nuclear motion corrections although the other terms partially cancel this contribution. Non-additivity can be largely attributed to the bending term for J (O, H). As expected, the bending terms also contribute relatively more to the temperature dependence of the couplings for J (O, H), J (O, D) and J (H, D). Our calculated J (O, H) in H2 17O of -77.22Hz at 293K is in very good agreement with Wasylishen and Friedrich's observed value of -78.70 (±0.02) Hz in cyclohexane at this temperature. Our calculated J(H, D) in HD 16O at 323K of -1.233Hz is close to a recent experimental value of -1.114 (±0.003) Hz in nitromethane-d 3 observed by Sergeyev et al. at that temperature.

Multiphoton ionization ofH2+by intense light: A comparison of Floquet and wave-packet results

Multiphoton ionization rates from the dressed $1s{\ensuremath{\sigma}}_{g}^{+}$ and$2p{\ensuremath{\sigma}}_{u}^{+}$ states of${\mathrm{H}}_{2}^{+}$ are calculated within the Floquet approach. For linearly polarized light, and parallel transitions, we determine ionization rates for a range of internuclear separations. A rich structure of multiphoton resonances has been found. These features are not reproduced by quasistatic field models. The values of ionization rates as well as their bond-length dependence are studied and compared with wave-packet calculations. Differences between results and reasons for discrepancies are discussed. Finally, we present plots of dressed-state wave-function densities in order to illustrate laser-induced orbital hybridization.

Thermal expansion and compressibility ofSr2RuO4

The thermal expansion and compressibility of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ have been investigated using neutron-powder diffraction. Our results confirm that the temperature dependence of the Ru-O2 apical bond length is linear with no structural anomaly (reported previously) corresponding to the metal-to-insulator transition. The response of the crystal lattice of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ to pressure is similar to that of the superconducting cuprate ${(\mathrm{L}\mathrm{a},\mathrm{S}\mathrm{r})}_{2}{\mathrm{CuO}}_{4}.$ However, the Ru-O2 apical bond is much harder to compress than the corresponding Cu-O2 bond.

A new He–CO interaction energy surface with vibrational coordinate dependence. I. Ab initio potential and infrared spectrum

The intermolecular potential energy surface of the He–CO complex including the CO bond length dependence has been calculated using symmetry-adapted perturbation theory (SAPT). The potential has a minimum of εm=−23.734 cm−1 with Rm=6.53 bohr at a skew geometry (ϑm=48.4°) if the molecular bond length is fixed at the equilibrium value of 2.132 bohr. We have applied the potential in the calculation of bound state levels and the infrared spectrum for the He–CO3 and He–CO4 complexes. The computed ab initio transition frequencies are found to agree within 0.1 cm−1 with experiment. In paper II [J. P. Reid, H. M. Quiney, and C. J. S. M. Simpson, J. Chem. Phys. 107, 9929 (1997)], the potential surface is used to calculate vibrational relaxation cross sections and rate constants.

Size dependence of bond length and binding energy in palladium and gold clusters

AbstractAll‐electron density functional calculations on a series of highly symmetric palladium clusters up to nuclearity 147 yield an essentially linear correlation between the average bond length and the average coordination. The average binding energy per atom is found to be proportional to the inverse cluster radius and thus mainly determined by the decreasing surface to volume ratio. Comparison to recently obtained results for the corresponding series of gold clusters confirms the wider validity of these size dependence relationships.

Ab-Initio Total Energy Studies of the Static and Dynamical Properties of Ice Ih

We present a detailed study of the structural and dynamical properties of ice Ih. Methods used include the ab-initio pseudopotential and molecular orbital techniques. In order to simulate the proton disorder present in ice Ih supercells are constructed with the orientation of water molecules determined in such a way that all possible nearest neighbor orientations are included while still obeying the Bernal−Fowler ice rules. For structures considered all structural parameters are relaxed. The dependence of bond length on the orientation of surrounding molecules in both the dimer and fully coordinated system is discussed. All local dimer orientations are accounted for in the supercell of ice Ih considered. The dynamical properties of a 16-molecule supercell model of ice Ih are then investigated via direct determination of the zone center dynamical matrix. Here the dynamical matrix is calculated directly from atomic forces obtained when each atom is shifted away from its equilibrium position. The vibrational...

Low-Temperature Neutron Diffraction Study of the Silver Perchlorate–Benzene π Complex

The crystal structure of the AgClO4.C6H6 \pi complex, earlier determined by X-ray diffraction at room temperature, has been redetermined at 18, 78 and 158 K by neutron diffraction. Crystal data: orthorhombic, space group Cmcm, Z = 4, F(000) = 225.318 fm, T: 18, 17, 158 K; D x = 2.591 (2), 2.570 (1), 2.523 (1) g cm−1; \mu n = 0.166, 0.165, 0.162 cm−1; a = 7.913 (1), 7.973 (1), 8.100 (1), 8.336 (1) Å (at 295 K); b = 7.837 (2), 7.857 (1), 7.902 (1), 7.996 (1) Å (at 295 K); c = 11.798 (3), 11.777 (2), 11.739 (2), 11.638 (2) Å (at 295 K); wR(F 2) = 0.037, 0.035, 0.045, S = 1.18, 1.08, 1.10 for 782, 628, 800 reflections and 51 variable parameters. This study confirms the principal features reported in the X-ray investigation and reveals details of structure not observable at room temperature. Distortions of the benzene molecule from D 6h symmetry ascribed to Ag+...C6H6 interactions are small, but significant. At 18 K the two C—C bonds complexed by Ag+ are 1.405 (1) Å in length; the other four are 1.398 (1) Å. The C—H bonds are equal in length at 1.087 (2) (two) and 1.089 (1) Å (four). The H atoms nearest to Ag+ are displaced 0.064 (1) Å from the C6 plane, away from the silver. The shortest Ag+...C distance of the complex is 2.565 (1) Å. This value and bond lengths of the benzene molecule are invariant between 18 and 158 K within 2 e.s.d.'s or less. The nonequivalent bond lengths of ClO^{-}_4, 1.451 (1) (two) and 1.441 (1) Å (two) at 18 K, are foreshortened by −0.007 and −0.005 Å at 158 K by effects of thermal motion. The O—Cl—O angles, 109.08 (7), 109.98 (2) and 107.83 (8)° at 18 K, are virtually unchanged by temperature. The Ag+...ClO^{-}_4 interactions occur at Ag+...O distances of 2.785 (1) and 2.612 (1) Å (18 K), where the shorter values involve ClO^{-}_4 acting as a bidentate group. Rigid-body and riding-motion models do not adequately account for the observed temperature dependence of bond lengths in ClO^{-}_4 nor provide significant corrections to the C6H6 bond lengths at 18, 78 and 158 K beyond their uncertainty limits. A harmonic potential rationalizes the motion of Ag+ at these three temperatures.

On the electric properties of Br2

Electric multipole moments and polarizabilities for Br2 are obtained from finite field self consistent field (SCF), many-body perturbation theory and coupled cluster calculations with large gaussian-type basis sets. At the MP2 level of theory the bond length dependence of the mean and the anisotropy of the dipole polarizability (ααβ/e 2 a 0 2 E h -1) around the equilibrium bond length of Re = 2·28105 A is adequately described by , . A very large \\[18s15p12d6f] basis set consisting of 330 basis functions yields SCF values α = 44·10 and Δ α = 28·31 e 2 a 0 2 E h -1. Adding electron correlation corrections obtained at the CCSD(T) level of theory and vibrational corrections obtained at the MP2 level, the mean dipole polarizability at the ground vibrational state is estimated at α = 44·74 (to be compared with the experimental value of 45·0) and the anisotropy at Δ α = 25·39 e 2 a 0 2 E h -1. At the MP2 level the mean second dipole hyperpolarizability γ/ e 4 a 0 4 E h -1 varies around R e as . SCF, MP2 and CCSD(T) results are combined to give as final theroeticalprediction the estimate of γ = (10·2 ± 1·0) x 103 e 4 a 0 4 E h -3.

XAS Studies on "Costa Type" Model Compounds of Coenzyme B12

We report XAS studies on several Costa type compounds with different alkyl groups in the axial position. Especially the XANES part of the spectra shows differences in the electronic and structural features due to the different electronic donor power of the substituent and to a variation of the degree of the octahedral symmetry around the metal site. The EXAFS analysis, performed by using the package GNXAS, has permitted the study of the Co-C bond length dependence on the chemical nature of the alkyl group. The bond length appears to depend on the Taft σ* constant of the alkyl group. The relationship between the information obtained by EXAFS and XANES analysis is also discussed.

ø/ψ-Torsional dependence of peptide backbone bond-lengths and bond-angles: comparison of crystallographic and calculated parameters

The crystallographic NC(α), C(α)C′ and NC(α)C′ backbone parameters of 43 oligopeptides and the NC(α)C′ angles of 37 proteins were compared with peptide conformational geometry surfaces derived from ab initio calculations of N-acetyl N′-methyl alanine amide. The calculated values were obtained by spline-function representations of ab initio dipeptide conformational geometry maps which allow one to predict backbone bond lengths and angles in peptides and proteins as functions of the ø[NC(α)]/ψ[C(α)C′]-torsions. When the parameters are ordered by regions in ø/ψ-space defined by a 30° grid and region-average values calculated, the rms deviations between the crystallographic and calculated parameters in the most populated regions of the oligopeptides are 0.009Å, 0.013Å and 1.2°, for NC(α), C(α)C′ and NC(α)C′ respectively; and 1.2° for the NC(α)C′ angles in proteins. The flexibility in ø/ψ-space is significant for the NC(α)C′ angles (observed variations of > 8°), but of lesser importance for the bond lengths (conformational variations of ∼0.02 A ̊ ). Thus, torsion dependent ideal geometry functions are recommended for the former, but not necessarily the latter, for use in various areas of protein study, such as protein crystallography and empirical molecular modeling procedures.

Recursive density-matrix-spectral-moment algorithm for molecular nonlinear polarizabilities

An iterative algorithm is developed for calculating nonlinear optical polarizabilities using a series of generalized sum rules that resemble the Lanczos algorithm and connect spectral moments of the driven single-electron density matrix to ground state charge distributions and bonding network. The size scaling and saturation of off-resonant polarizabilities (up to seventh order) of polyacetylene oligomers with up to 300 carbon atoms is analyzed in terms of collective electronic oscillators. Simple analytical expressions for size and bond-length alternation dependence of off-resonant polarizabilities are derived using a single-oscillator approximation.