Bond lengths and location of the inner-ring protons in the corrole molecule

Ps IR laser pulse induced dissociation of vibrationally excited ABA* molecular resonances is simulated by simple model calculations. The stretching vibrations of ABA are represented by the Rosen-Thiele-Wilson coupled Morse oscillator hamiltonian with time dependent potential V(t) describing the interaction with a gaussian laser pulse in the semiclassical dipole approximation. The Schrödinger-equation is solved by Fast-Fourier-Transform propagation. The resulting wavefunctions ψ_t yield mode selective effects, e.g. the decays of hyperspherical and local modes with natural life times 5·92 ps and 0·07 ps are accelerated by the laser by factors 40 and 2, respectively. The mechanisms of photodissociation are analysed in detail, including laser-induced oscillations of the potential V(t) which transform dissociative frontier lobes of the wavefunction ψ_t of a slowly decaying hyperspherical mode into those of a rapidly dissociating local resonance.     

Evidence for slow exchange in E.S.R. spectra of nitroxide biradicals

Force constants have been calculated for H₂NF and HNF₂ from ab initio Hartree-Fock wavefunctions by the force method, using 7s3p/1 gaussian basis sets. The force field of HNF₂, obtained from a combination of the theoretical results with the experimental frequencies, can be considered as the most reliable one at present. Previous force fields are discussed critically. From a full optimization the predicted geometry of H₂NF is: NF = 1·399 Å, NH = 1·018 Å, HNF = 102·9° and HNH = 105·9°.     

Exact solution of coupled equations and the hyperspherical formalism: Calculation of expectation values and wavefunctions of three Coulomb-bound particles

Exact solutions of one-dimensional coupled differential equations are developed by substituting in power series. The properties of these solutions and the possibility of their application to the few-body problem in the framework of the hyperspherical method are studied. The necessity of logarithmic terms in the nonrelativistic many-body wavefunctions, as well as their absence in the relativistic case, is stressed. Explicit form of the solution of the one-dimensional hyperspherical matrix equation corresponding to the three-body Coulomb problem is found and used to obtain Schroedinger and Faddeev bound state wavefunctions, correlation integrals and probabilities of different hyperspherical states. The results of calculations with inclusion of up to 25 hyperspherical harmonics (K_m = 16) for the ground and excited state of the helium atom, the ground state of the positronium ion and the negative hydrogen ion are given and compared with those obtained by the multiconfigurational Hartree-Fock and variational methods as well as with other hyperspherical calculations. We find that generally the correlation integrals converge as the energies, that is, as $\text{1}\text{K}{}_{\mathrm{<mtext>m</mtext>}}{}^4$. While the method is essentially exact, computer round-off error limits the precision for K_m > 12 in the positronium calculations.     

Isotope effect of hydrated clusters of hydrogen chloride,HCl(H2O) n and DCl(H2O) n (n = 0–4): application of dynamic extended molecular orbital method

The recently proposed dynamic extended molecular orbital (DEMO) method is applied to the HCl(H₂O) _n and DCl(H₂O) _n (n = 0–4) clusters in order to explore the isotope effect on their structures, wavefunctions, and energies, theoretically. Since the DEMO method determines both electronic and nuclear wavefunctions simultaneously by optimizing all parameters including basis sets and their centres variationally, we can get the different nuclear orbitals for proton and deuteron as well as their electronic wavefunctions. The positions of the centres of nuclear orbitals show that the deuteron has weaker hydrogen bonding than the proton. There are three isomers in the case of n = 3 clusters, and less stable isomers have hydrogen transferred and non-transferred structures. In the conventional MO calculation, both hydrogen transferred and non-transferred isomers are calculated to be energy minima. When we have applied the DEMO method, only the hydrogen transferred structure is obtained for HCl(H₂O)₃, while both structures are optimized for DCl(H₂O)₃. Such strong H/D dependence on the structures of the HCl(H₂O) _n and DCl(H₂O) _n clusters can be expressed directly by using the DEMO method. The present application demonstrates that the DEMO method is a useful tool for analysing the anharmonicity and vibronic effects of a hydrogen bonding system.     

Analytical ab initio computation of force constants and dipole moment derivatives: LiH,Li2 and BH

Ab initio calculations of harmonic force constants and dipole moment derivatives have been performed for the diatomic molecules LiH, Li₂ and BH, using Hartree-Fock perturbation theory for a series of spherical gaussian SCF-MO wavefunctions. The results of these computations support the conclusion made in a previous paper that the so-called general method of calculation is the most reliable. The results obtained with the energetically best wavefunctions are (experimental values in parentheses, atomic units throughout): Force constants: LiH 0·071 (0·066); Li₂ 0·019 (0·016); BH 0·210 (0·196). Dipole moment derivatives: LiH - 0·48 (-0·42±0·06); BH - 0·67 (-0·4).     

A general pseudopotential model for molecules with many valence electrons

Criteria are discussed for the practical application of ‘valence-electron only’ calculations aimed at simulating ab initio all-electron calculations on molecules containing heavy atoms with many core electrons. A theoretical model is outlined based on the use of pseudopotentials derived from atomic SCF calculations. The model has been used in calculations for NaH, Na₂, H₂S, S₂, H₂S₂, HCl, Cl₂ and NaCl, and has been tested by comparison with reference all-electron calculations. Most of these tests employ double-zeta basis sets and SCF wavefunctions, although polarization functions and complete valence-electron CI wavefunctions have been used in some cases. The model is generally successful for ground-state equilibrium structures, charge distributions and orbital energies.     

Effect of (H2O)n (n = 1–3) clusters on H2O2 + HO → HO2 + H2O reaction in tropospheric conditions: competition between one-step and stepwise routes

ABSTRACT

Effects of (H₂O)_n (n?=?1–3) on the H₂O₂?+?HO?→?HO₂?+?H₂O reaction have been investigated by the reactions of H₂O₂L(H₂O)_n (n?=?1–3)?+?HO and H₂O₂?+?HOL(H₂O)_n (n?=?1–3) at the CCSD(T)/CBS//M06-2X/aug-cc-pVTZ level of theory, coupled with rate constant calculations by using canonical variational transition state theory. Interestingly, for the former reactions, one-step process and stepwise mechanism are involved, where one-step processes occurring though cage-like hydrogen bonding network complexes and the transition states are favourable. Due to larger effective rate constants, these favourable processes are also favourable than the corresponding latter reactions. Meanwhile, the catalytic effect of (H₂O)_n (n?=?1–3) is mainly taken from water monomer, because the effective rate constant (k'(R_WM2)) of H₂O₂···H₂O?+?HO reaction is, respectively, larger by 3, 6–10 orders of magnitude than that of H₂O₂···(H₂O)₂?+?HO (k'(R_WD1)) and H₂O₂···(H₂O)₃?+?HO (k'(R_WT1)) reactions. Furthermore, the enhancement factor of water molecular (k'(R_WM2)/k_tot) is only 0.28% at 240?K, while at high temperature (such as at 425?K), the positive water vapour effect enhances up to 27.13%. This shows that at high temperatures the positive water effect is obvious under atmospheric conditions.     

Uncoupled Hartree-Fock calculations of the 13C shielding by means of ab initio and NEMO-wavefunctions

¹³C shielding constants of some molecules are approximatively evaluated by decoupling the equations of the single excitation scheme of Caves and Karplus. The ab initio minimal basis wavefunctions of Palke and Lipscomb of CH₄, C₂H₂, C₂H₄, C₂H₆, HCN and NEMO-wavefunctions are used. It is shown that for the molecules under study these UPHF calculations reveal the same trends as the finite perturbation method by Ditchfield et al.     

The rotational levels of the ground vibrational state of formaldehyde

A variational procedure for rovibrational energy levels and wavefunctions of centrally connected tetra-atomic molecules is extended to include high rotational states, and in particular, J ? 10 levels for the vibrational ground state of formaldehyde. It is very important to do this because it has made possible the calculation of the usual rotational spectroscopic constants which correspond to the forcefield and geometry. A direct comparison with the ‘observed’ spectroscopic constants is therefore possible. The geometry and forcefield are refined against 65 J = 0 levels of H₂CO, 6 J = 0 levels of D₂CO, 42 J = 1, 70 J = 2 and 98 J = 3 levels of the ground and fundamentals of H₂CO and D₂CO, using an iterative scheme. The mean absolute error of the J = 0 levels is 1·10 cm^?1 and that for J ≠ 0 is 0·005 cm^?1, and the predicted geometry is CH = 1·10064 Å, CO = 1·20296 Å and HCO = 121·648°. Finally, the rotational constants A, B, and C for the ground state are 281956, 38846 and 34003 MHz, compared with the observed values 281971, 38836, and 34002 MHz. The centrifugal distortion constants Δ_J , Δ_JK , Δ_K and δ_J , are 77, 1275, 18113 and 11 kHz compared with 75, 1291, 19422 and 10 kHz. These results underline the accuracy of the new quartic forcefield.     

Raman spectroscopic study of the uranyl titanate mineral holfertite Ca x U2−x Ti(O8−x OH4x )·3H2O and the lack of metamictization

Raman spectra of the uranyl titanate mineral holfertite Ca _x U_2?x Ti(O_8?x OH_4x )·3H₂O were analyzed and related to the mineral structure. Observed bands are attributed to the TiO and (UO₂)²⁺ stretching and bending vibrations, U–OH bending vibrations, and H₂O stretching and bending. The mineral holfertite is metamict, as is evidenced by the order/disorder of the mineral. Unexpectedly, the Raman spectrum of holfertite does not show any metamictization. The intensities of the UO stretching and bending modes show normal intensity and the bands are sharp.     

XRD studies,vibrational spectra,and molecular structure of 1H‐imidazo [4,5‐b]pyridine based on DFT quantum chemical calculations

The molecular structures and vibrational properties of 1H‐imidazo[4,5‐b]pyridine in its monomeric and dimeric forms are analyzed and compared to the experimental results derived from the X‐ray diffraction (XRD), infrared (IR), and Raman studies. The theoretical data are discussed on the basis of density functional theory (DFT) quantum chemical calculations using Lee–Yang–Parr correlation functional (B3LYP) and 6‐31G(d,p) basis. This compound crystallizes in orthorhombic structure, space group Pna2₁(C_2v⁹) and Z = 4. The planar conformation of the skeleton and presence of the N H···N hydrogen bond was found to be characteristic for the studied system. The temperature dependence of IR and Raman modes was studied in the range 4–294 K and 8–295 K, respectively. The normal modes, which are unique for the imidazopyridine derivatives are identified. Copyright © 2009 John Wiley & Sons, Ltd.     

Raman spectroscopy of gallium‐ and zinc‐based hydrotalcites

Insight into the unique structure of hydrotalcites (HTs) has been obtained using Raman spectroscopy. Gallium‐containing HTs of formula Zn₄ Ga₂(CO₃)(OH)₁₂ · xH₂O (2:1 ZnGa‐HT), Zn₆ Ga₂(CO₃)(OH)₁₆ · xH₂O (3:1 ZnGa‐HT) and Zn₈ Ga₂(CO₃)(OH)₁₈ · xH₂O (4:1 ZnGa‐HT) have been successfully synthesised and characterised by X‐ray diffraction (XRD) and Raman spectroscopy. The d(003) spacing varies from 7.62 Å for the 2:1 ZnGa‐HT to 7.64 Å for the 3:1 ZnGa‐HT. The 4:1 ZnGa‐HT showed a decrease in the d(003) spacing, compared to the 2:1 and 3:1 compounds. Raman spectroscopy complemented with selected infrared data has been used to characterise the synthesised gallium‐containing HTs. Raman bands observed at around 1050, 1060 and 1067 cm⁻¹ are attributed to the symmetric stretching modes of the (CO₃²⁻) units. Multiple ν₃ (CO₃²⁻) antisymmetric stretching modes are found between 1350 and 1520 cm⁻¹, confirming multiple carbonate species in the HT structure. The splitting of this mode indicates that the carbonate anion is in a perturbed state. Raman bands observed at 710 and 717 cm⁻¹ and assigned to the ν₄ (CO₃²⁻) modes support the concept of multiple carbonate species in the interlayer. Copyright © 2010 John Wiley & Sons, Ltd.     

Weakly interacting molecular clusters of CO with H2O,SO2, and NO+

Intermolecular interactions in three dimers, CO···H₂O, CO···SO₂, and CO···NO⁺, were studied at the CCSD(T) level of theory, using a series of the augmented correlation consistent polarised basis sets. Interaction energy and its components as well as vibrational spectra for local minima were computed using both harmonic and anharmonic approximations. While CO···H₂O and CO···SO₂ are weakly bound with the binding energies ?7.4 and ?6.4 kJ/mol, CO···NO⁺ is much more stable with the binding energy of ?32.8 kJ/mol corresponding to ΔG = ?4.7 kJ/mol at 254 K.     

The HO4H → O3 + H2O reaction catalysed by acidic,neutral and basic catalysts in the troposphere

A detailed effects of catalyst X (X?=?H₂O, (H₂O)₂, NH₃, NH₃···H₂O, H₂O···NH₃, HCOOH and H₂SO₄) on the HO₄H → O₃?+?H₂O reaction have been investigated by using quantum chemical calculations and canonical vibrational transition state theory with small curvature tunnelling. The calculated results show that (H₂O)₂-catalysed reactions much faster than H₂O-catalysed one because of the former bimolecular rate constant larger by 2.6–25.9 times than that of the latter one. In addition, the basic H₂O···NH₃ catalyst was found to be a better than the neutral catalyst of (H₂O)₂. However it is marginally less efficient than the acidic catalysts of HCOOH, and H₂SO₄. The effective rate constant (k'_t) in the presence of catalyst X have been assessed. It was found from k'_t that H₂O (at 100% RH) completely dominates over all other catalysts within the temperature range of 280–320?K at 0?km altitude. However, compared with the rate constant of HO₄H → H₂O?+?O₃ reaction, the k _eff values for H₂O catalysed reaction are smaller by 1–2 orders of magnitude, indicating that the catalytic effect of H₂O makes a negligible contribution to the gas phase reaction of HO₄H → O₃?+?H₂O.

Highlights

• A detailed effects of catalyst of H₂O, (H₂O)₂, NH₃, NH₃···H₂O, H₂O···NH₃, HCOOH and H₂SO₄ on the HO₄H → O₃?+?H₂O reaction has been performed.

• From energetic viewpoint, H₂SO₄ exerts the strongest catalytic role in HO₄H → O₃?+?H₂O reaction as compared with the other catalysts.

• At 0 km altitude H₂O (at 100% RH) completely dominates over all other catalysts within the temperature range of 280–320 K.

• HO₄H → H₂O?+?O₃ reaction with H₂O cannot be compete with the reaction without catalyst, due to the fact that the effective rate constants in the presence of H₂O are smaller.

     

Die Eigenschwingungen des Metall-Hydratkomplexes in BeSO4·4H2O und BeSO4·4D2O

Infrared reflection spectra of single crystals of BeSO₄·4H₂O and BeSO₄·4D₂O have been obtained in polarized light at 300°K and at 14°K in the region between 4000 cm^?1 and 300 cm^?1. By a Kronig-Kramers analysis, the frequencies of the infrared active transitions have been calculated. These transitions are attributed to internal vibrations of the water molecules and sulfate ions and, in the region between 1000 cm^?1 and 300 cm^?1, especially to internal and external vibrations of the tetrahedral Be⁺⁺·4aqu-complexes. The vibrational modes of these complexes consist of a superposition of translational and librational modes of the water molecules and translational modes of the central Be⁺⁺-ion. The vibrational frequencies and normal modes of this complex have been calculated in a central-force model, and force-constants have been determined by fitting the calculated frequencies to the observed spectra. The calculations have shown that the modes, which comprise mainly translational motions of the water molecules, are strongly coupled with librational motions of the water molecules. On the other hand, there exist pure librational modes with practically no admixture of translational motions. The optimum sets of force constants for the BeSO₄·4H₂O crystal and the BeSO₄·4D₂O crystal differ in a manner which can be understood under the assumption that the dimensions of the Be(D₂O)₄ complex are about 0.1 Å larger than those of the Be(H₂O)₄ complex. Some arguments supporting this conclusion will be discussed.     

Pressure-induced phase transitions in gypsum

Abstract

We report high-pressure Raman scattering spectroscopy and energy dispersive X-ray diffraction investigations on gypsum, CaSO₄ · 2H₂O, at room temperature in a diamond cell. With increasing pressure, measurements indicate that CaSO₄ · 2H₂O undergoes two stages of crystalline-state phase transitions at 5 and 9 GPa, and then converts to a disordered phase above 11 GPa. The structures of the three high-pressure phases of gypsum have not been determined yet. These phases are tentatively named as “post-gypsum-I” (PG-I), “post-gypsum-II” (PG-II) and “disordered” according to the sequence of their appearance with pressure.

Gypsum shows anisotropic compressibility along three crystallographic axes with b > c > a below 5 GPa. The difference in the behavior of the two OH stretching modes in gypsum is attributed to the different reduction rate in the hydrogen bonding distances by the anisotropic axial compressibility.     

Theoretical study of chemi- and physisorption processes of H2 molecules on a (1 0 0) surface of silver

A model system consisting of a cluster of 13 Ag atoms and n (n = 1, 2, 3) H₂ molecules has been used to study, by ab initio methods, the structural and energetic characteristics of the chemi- and physisorption processes of H₂ on a (1 0 0) surface of silver. The dissociative chemisorption of a first H₂ molecule is analyzed in terms of hydrides formation and it is shown that several electronic states are interacting in the vicinity of the activation barrier leading to complex electronic processes. The energy of the physisorption interaction of the first H₂ molecule for different orientations and that of further H₂ molecules coming directly on top of the first chemisorbed one are determined with highly correlated wavefunctions. As for the (H₂)_nCu₁₃ system, already studied with similar approaches, it is found for the (H₂)_nAg₁₃ system that the physisorption energy of the second layer is enhanced by a factor close to two compared to that of the first layer due to dipolar interactions with the polarized surface. The physisorption energy of the third and further layers tends to the van der Waals H₂/H₂ interaction energy.     

Dielectric relaxation of α-cyclodextrin-polyiodide complexes (α-cyclodextrin)2 · BaI2 · I2 · 8H2O and (α-cyclodextrin)2 · KI3 · I2 · 8H2O

The frequency and temperature dependence of the real (ε′) and imaginary (ε″) parts of the dielectric constant of the polycrystalline complexes (α-CD)₂ · Bal₂ · I₂ · 8H₂O and (α-CD)₂ · KI₃ · I₂ · 8H₂O (α-CD = α-cyclodetrin) have been investigated over the frequency and temperature ranges 0–100 kHz and 120–300 K, respectively. The temperature dependences of ε′, ε″ and the phase shift φ show two steps, two peaks and two minima, respectively, revealing the existence of two kinds of water molecule, the tightly bound and the easily movable water molecules, in both complexes. The first peak of (T) or the first minimum of φ(T) presents the transformation of flip-flop hydrogen bonds to the normal state. The second ε″ (T) peak or φ(T) minimum corresponds to the easily movable water molecules or to a partial transformation of tightly bound to easily movable water molecules. For T > 270K both samples show semiconductive behaviour with energy gaps of 1.84eV for the (α-CD)₂ · BaI₂ · I₂ · 8H₂O complex and 1.36eV for the (α-CD)₂ · KI₃ · I₂ · 8H₂O complex. The conductivity at room temperature decreases in the order: (α-CD)₂ · BaI₂ · I₂ · 8H₂O > (α-CD)₂ · LiI₃ · I₂ · 8H₂O > (α-CD)₂ · KI₃ · I₂ · 8H₂O > (α-CD)₂ · Cd_0.5 · I₅ · 26H₂O. The relaxation time varies in a Λ-like curve (from 120 to 250 K) and rises rapidly for temperatures greater than 250 K, indicating the process of ionic movements. The activation energies around the transition temperature 0.98–1.09 k _B T _trans for (α-CD)₂ · BaI₂ · I₂ · 8H₂O and 1.06-1.55 k _B T _trans for (α-CD)₂ · KI₃ · I₂ · 8H₂O reveal the greater stability of the α-K complex against that of the α-Ba complex.     

The first order of the hyperspherical harmonic expansion method

The hyperspherical harmonic expansion method is studied in this work. Our attention is focused on the properties of the L_m-approximation in which only the hyperspherical harmonics of minimal order are taken into account. Exact solutions of the Schrödinger equation for a few simple hyperspherical potentials are given. Recipes for constructing antisymmetric hyperspherical harmonics for fermions are investigated, and various procedures to derive the effective potential in the L_m-approximation are discussed. The method is applied to the calculation of ground state and hyperradial excited states (which are identified as the breathing modes) of doubly-magic nuclei. Finally, the energy per particle is derived in the L_m-approximation with Skyrme like forces for an infinitely heavy self-conjugate nucleus.     

Raman spectroscopy of gallium‐based hydrotalcites of formula Mg6Ga2(CO3)(OH)16· 4H2O

Insight into the unique structure of hydrotalcites has been obtained using Raman spectroscopy. Gallium‐containing hydrotalcites of formula Mg₄Ga₂(CO₃)(OH)₁₂· 4H₂O (2:1 Ga‐HT) to Mg₈Ga₂(CO₃)(OH)₂₀· 4H₂O (4:1 Ga‐HT) have been successfully synthesized and characterized by X‐ray diffraction and Raman spectroscopy. The d(003) spacing varied from 7.83 Å for the 2:1 hydrotalcite to 8.15 Å for the 3:1 gallium‐containing hydrotalcite. Raman spectroscopy complemented with selected infrared data has been used to characterize the synthesized gallium‐containing hydrotalcites of formula Mg₆Ga₂(CO₃)(OH)₁₆· 4H₂O. Raman bands observed at around 1046, 1048 and 1058 cm⁻¹ are attributed to the symmetric stretching modes of the CO₃²⁻ units. Multiple ν₃ CO₃²⁻ antisymmetric stretching modes are found at around 1346, 1378, 1446, 1464 and 1494 cm⁻¹. The splitting of this mode indicates that the carbonate anion is in a perturbed state. Raman bands observed at 710 and 717 cm⁻¹ assigned to the ν₄ (CO₃²⁻) modes support the concept of multiple carbonate species in the interlayer. Copyright © 2009 John Wiley & Sons, Ltd.