IRPD spectroscopy and ensemble measurements: Effects of different data acquisition and analysis methods

Three different commonly used infrared photodissociation (IRPD) spectroscopy acquisition and analysis methods are described, and results from these methods are compared using the same dataset for an extensively hydrated metal cation, La³⁺(H₂O)₃₆. Using the first-order laser-induced photodissociation rate constant as an IRPD intensity has several advantages over photodissociation yield and depletion/appearance methods in that intensities can be more directly compared with calculated infrared absorption spectra, and the intensities can be readily corrected for changes in laser power or irradiation times used for optimum data acquisition at each frequency. Extending IRPD spectroscopy to large clusters can be complicated when blackbody infrared radiative dissociation competes strongly with laser-induced photodissociation. A new method to obtain IRPD spectra of single precursor ions or ensembles of precursor ions that is nearly equivalent to the photodissociation rate constant method for single precursor ions is demonstrated. The ensemble IRPD spectra represent the “average” structure of clusters of a given size range, and this method has the advantage that spectra with improved signal-to-noise ratios can be obtained with no increase in data acquisition time. Results using this new method for a precursor ensemble consisting of La³⁺(H₂O)_35–37 are compared with results for La³⁺(H₂O)₃₆.     

Calculation of the Gibbs Energy of the Reaction OH-·(H2O)n-1 + H2O = OH-·(H2O)n by the Monte-Carlo Method

The energy, the Gibbs energy of the reaction OH^-·(H₂O) _{n- 1} + H₂O = OH^-·(H₂O) _n are calculated by the Monte-Carlo method with a large canonical ensemble for n = 1, ..., 20. The ion-waternonpair interaction potential was obtained by numerical fitting of calculated Gibbs energy and entropy of (H₂O)_n clusters (n = 1, ..., 5) to experimental ones. A good fit to experiment both of the internal energy and the Gibbs energy can be obtained in terms of a model allowing for nonpair interaction. It is shown that constructing an ion-water interaction potential without allowance for the entropy factor can lead to considerable errors in the Gibbs energy of cluster formation and in the nucleation rate.     

A theoretical study of the acetylide anion, HCC−

The results of various ab initio calculations are reported for the electronic ground state of the acetylide anion. An “Eyring's lake” in the T-shaped configuration is identified with six different methods (SCF, MP2, CCSD, CCSD-T, CCSD(T), and CEPA–1). The equilibrium bond lengths of HCC⁻ are estimated to be r _e (CH)=1.0689(3) ? and R _e (CC)=1.2464(2) ?, and the ground-state rotational constant is predicted to be B ₀=41636(20)MHz. The large permanent dipole moment of μ₀=−3.093D should facilitate detection of the anion by microwave spectroscopy. The band centers are predicted to be 3211.3cm⁻¹(ν₁), 511.1cm⁻¹(ν₂), and 1805.0cm⁻¹(ν₃). A large transition dipole moment of 0.477 D is calculated for the ν₂ band. Rovibrational levels of HCC⁻ up to approximately 20 000 cm⁻¹ above equilibrium are calculated with DVR-DGB and FBR methods on the basis of a previous CEPA–1 potential energy surface. Different energy patterns are found and discussed, for which anharmonic and Coriolis resonances are shown to play an important role. Received: 27 July 1998 Accepted: 12 August 1998 / Published online: 19 October 1998     

Axial force fluctuations in long-chain molecules

The fluctuations Δf in the axial force f acting on a long-chain molecule whose end-to-end displacement r is fixed are computed for a freely jointed model in which the covalent bonds are represented by stiff linear springs. It is found that the relative fluctuation Δf/f remains large regardless of the length of the chain. A time-dependent computer simulation of the model serves both to verify the theoretical calculation of Delta;f and to provide physical insight. The result helps to clarify the difference in behavior of the strain ensemble (r is fixed and f fluctuates) and the stress ensemble (f is fixed and r fluctuates) for which, in the absence of excluded volume, the strain ensemble predicts that f = 0 for r = 0, while for the stress ensemble with f = 0 it is found that 〈r²〉₀ > 0.     

17‐Oxo‐5α‐androstane‐3α,4β‐diyl diacetate and 17‐oxo‐5β‐androstane‐3α,4β‐diyl diacetate

The title compounds, both C₂₃H₃₄O₅, are the 5α and 5β configurations of two diacetate epimers. The 5β‐diacetate crystallizes in an hexagonal structure, unusual for steroid molecules. The unit cell has an accessible solvent volume of 358 ų, responsible for clathrate behaviour. The 5β‐epimer also features some shorter than average bond lengths in the 3α,4β‐acetoxy groups. The conformations of the molecules of both epimers are compared with those obtained through abinitio quantum chemistry calculations. Cohesion of the crystals can be attributed to van der Waals and weak molecular C—H⋯O interactions.     

Water vapor nucleation on ion pairs under the conditions of a planar nanopore

Computer simulation has been employed to study the effect of a confined space of a planar model pore with structureless hydrophobic walls on the hydration of Na⁺Cl^– ion pairs in water vapor at room temperature. A detailed many-body model of intermolecular interactions has been used. The model has been calibrated relative to experimental data on the free energy and enthalpy of the initial reactions of water molecule attachment to ions and the results of quantum-chemical calculations of the geometry and energy of Na⁺Cl^– (H₂O)_N clusters in stable configurations, as well as spectroscopic data on Na⁺Cl^– dimer vibration frequencies. The free energy and work of hydration, as well as the adsorption curve, have been calculated from the first principles by the bicanonical statistical ensemble method. The dependence of hydration shell size on interionic distance has been calculated by the method of compensation potential. The transition between the states of a contact (CIP) and a solvent-separated ion pair (SSIP) has been reproduced under the conditions of a nanopore. The influence of the pore increases with the hydration shell size and leads to the stabilization of the SSIP states, which are only conditionally stable in bulk water vapor.     

Modeling of mass and charge transfer in an inverted rotating disk electrode (IRDE) reactor

In this work, the validation of a newly constructed inverted rotating disk electrode (IRDE) reactor is reported. Compared to the rotating disk electrode (RDE) reactor, the working electrode is changed in position from the top to the bottom of the electrochemical cell. The IRDE reactor is designed to facilitate the actual study of gas evolution reactions. It is studied whether the first-order analytical expression for the velocity field in an RDE reactor is also acceptable for an IRDE configuration. To that purpose, the kinetic parameters of the well-known ferri/ferro cyanide redox system are determined in both configurations and compared. This is done qualitatively by comparing the polarization curves obtained in the inverted and the conventional RDE configuration. Additionally, a statistically founded fitting algorithm is used to quantitatively determine the model parameters of the oxidation and reduction reaction. Not only the diffusion coefficients of Fe²⁺ and Fe³⁺ are calculated, but also the rate constants (k_ox and k_red) and the transfer coefficients (α_ox and α_red) are quantified and compared together with their respective standard deviation. It is found that the parameters of mass and charge transfer in both configurations agree well. So it is concluded that the same analytical equations of mass and charge transfer can be used in both the RDE and the IRDE reactor.     

One - determinantal pure state versus ensemble Kohn-Sham solutions in the case of strong electron correlation: CH2 and C2

The possibility that the Kohn-Sham (KS) solution for a noninteracting auxiliary electron system is not the conventional one-determinantal pure state but a few-determinantal ensemble has been investigated. The KS solutions (the exchange-correlation potential v _xc and the orbitals) have not been approximated by local-density or density-gradient approximations but have been constructed from an accurate ab initio electron density. The lowest singlet states of the CH₂ and C₂ molecules have been selected for this investigation since for these cases the ground-state wave function Ψ is nondegenerate but has an essentially multideterminantal character (electron correlation is strong). For C₂ the dependence of the type of KS solution on the bond distance R(C–C) has been studied at the QZ level. For the shortest distance considered, R(C–C)=1.8 a.u., a pure-state KS solution has been obtained. For the equilibrium distance R _e(C–C)=2.348 a.u. and at larger distances ensemble solutions have been obtained with widely varying weights of the individual determinants, depending on the bond distance. For CH₂ the dependence of the type of KS solution on the basis has been studied: calculation in the triple zeta (TZ) basis for the KS orbitals yields an ensemble solution, while the pure-state KS solution has been obtained in the quadruple zeta (QZ) basis. The form of the KS orbitals has been compared with that of the natural orbitals (NOs). It has been shown for the model example of the stretched H₂ molecule as well as for CH₂ and C₂, that the KS orbitals of the pure state may be rather different from the corresponding NOs, while the occupied KS orbitals of the ensemble solution can be considered as plausible approximations to the corresponding NOs. Received: 10 February 1998 / Accepted: 10 June 1998 / Published online: 3 September 1998     

The origin of energy functional in Roothaan open shell SCF theory

Different methods of averaging of energy over the states of electronic configurations γ^N (n_γ = 1, 2, 3 and N = 1, 2, …, 2n_γ ? 1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (VCC ) in energy functionals for various states as well as for average values of energy are presented. It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations t^N (N = 2–4) and e² there exist states for which VCC are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such “non-Roothaan” terms and peculiarities of its calculation by the restricted Hartree–Fock method are discussed.     

Electrostatic,sequential bond energies and structures of Li+·(N2)n complexes: computational study

The MP2 and CCSD calculations of the geometries and binding energies of the Li⁺·(N₂)_n (n?=?1–4) complexes are obtained. The potential energy surface showed that these complexes exhibit one minimum state and one transition state. The mono- and di-ligated complexes exhibit linear configurations with a binding energy of 11.1 and 21.2 kcal mol^?1, respectively. Trigonal planar and tetrahedral configurations are obtained for tri- and tetra-ligated complexes, respectively. The computed sequential bond dissociation energies (BDEs) of Li⁺·(N₂)_n (n?=?1–4) complexes are also calculated in which the mono-ligated complex has the largest BDE value. The obtained trend is mainly dependent on the variation in the ion-quadrupole interaction of these ion complexes. These calculations predict that these complexes are of purely electrostatic nature.

     

A density functional study of the electronic spectrum of permanganate

Multiplet splittings for six excited electronic configurations of the permanganate ion, MnO₄⁻, are calculated. Earlier density functional calculations on the same subject are improved upon by the numerical evaluation of some two-electron integrals to resolve certain multideterminantal states. Excellent agreement with the experimental spectrum is obtained, and a reassignment of bands in the 25,000–35,000 cm⁻¹ range is proposed. Fully symmetric (a₁) vibrational frequencies are calculated, and the origin and magnitude of the most significant Jahn-Teller distortions of the excited states are discussed. © 1996 John Wiley & Sons, Inc.     

Thermo‐Viscoelastic Response of Polycarbonate Reinforced with Short Glass Fibers

Observations are reported for oscillatory torsion tests at several temperatures ranging from room temperature to 100 °C on a polymer composite consisting of a polycarbonate matrix reinforced with short glass fibers. Constitutive equations are derived for the linear viscoelastic behavior of the polymer composite, which is treated as an equivalent heterogeneous network of chains bridged by junctions (entanglements and glass fibers). The network is thought of as an ensemble of meso‐regions with arbitrary shapes and sizes. With reference to the concept of cooperative relaxation, the time‐dependent response of an ensemble is associated with the rearrangement of meso‐domains. The rearrangement events occur at random times as meso‐regions are agitated by thermal fluctuations. Stress–strain relations for isothermal deformation of an ensemble of meso‐domains are derived by using the laws of thermodynamics. The governing equations are determined by five adjustable parameters that are found by fitting the experimental data. The effects of temperature and filler content on the material parameters are studied in detail.

The shear modulus G GPa versus the content of short glass fibers ν wt.‐%. Symbols: treatment of observations in oscillatory torsion tests at T = 25 (unfilled circles) and T = 100 °C (filled circles). Solid lines: approximation of the experimental data by Equation (27). Curve 1: G₀ = 1.05, G₁ = 3.83 × 10⁻². Curve 2: G₀ = 0.91, G₁ = 3.65 × 10⁻².     

Ab initio calculations find 2,2-disilylcyclopentane-1,3-diyl is a singlet diradical with a high barrier to ring closure

Ab initio calculations on the lowest singlet and triplet states of 2,2-disilylcyclopentane-1,3-diyl find that the singlet lies well below the triplet. The C ₂ singlet diradical is calculated to be a minimum on the potential energy surface with an enthalpic barrier to ring closure of ΔH ^‡ ₂₉₈ = 13.5 kcal/mol at the CASPT2/6-31G* level of theory. The energy of the 1,3-divinyl-substituted singlet diradical is calculated to be only 0.8 kcal/mol higher than that of 5,5-disilyl-1,3-divinylbicyclo[2.1.0]pentane at this level of theory, but the transition state for their equilibration is computed to be 12.8 kcal/mol above the diradical in energy. Received: 2 July 1998 / Accepted: 4 August 1998 / Published online: 16 November 1998     

Ab initio Hartree–Fock and configuration-interaction treatment of the interaction between two nickel atoms

The interaction between two nickel atoms in the configurations (3d)⁸(4s)² and (3d)⁹ (4s)¹ has been calculated using ab initio methods (Hartree–Fock and configuration interaction). The results of the calculations compare favorably with the optical spectrum. The discrepancy between the calculated and the experimental dissociation energy is discussed, and a new estimate of the dissociation energy is given. The configuration-interaction calculations show that the interaction between the two nickel atoms is of a very complex nature. In spite of this the binding can be interpreted in a simple way. The bond is minly due to the 4sσ_g molecular orbital while the 3d orbitals of the two nuclei are exchange coupled.     

Ab initio Study of the Geometrical and Electronic Structures of Sc(MDA)2 and Sc(MDA)3 Molecules

The geometrical parameters, force fields, and vibrational spectra of various geometrical configurations of Sc(MDA)₂ and Sc(MDA)₃ molecules were calculated using the restricted Hartree—Fock method taking into account electron correlation by second–order Möller–Plesset perturbation theory. The calculations were performed using effective pseudopotentials for describing atomic cores and valence double zeta basis sets supplemented by polarization functions. It was shown that the configurations of D ₃ [Sc(MDA)₃] and D _2h [Sc(MDA)₂] symmetry correspond to the minimum on the potential energy surface of the ground electronic state. The configurations of D _3h symmetry for Sc(MDA)₃ and D _2d for Sc(MDA)₂ correspond to first–order saddle points. The ground electronic states of Sc(MDA)₂ and Sc(MDA)₃ molecules are the states of ² A _g and ¹ A ₁ symmetries, respectively. For both configurations (D _2h and D _2d of the Sc(MDA)₂ molecule, the energies of vertical electron transitions were calculated using the CASSCF method. The formation of chemical bonding in the compounds considered was analyzed. It was shown that the Sc–O bond is predominantly ionic and the conjugation is characteristic only of the oxygen–carbon skeleton of the chelate fragment. The results obtained are compared with literature experimental and theoretical data for related compounds.     

A Computational Study of 3‐D Helium Clusters

Physical and thermodynamic properties have been calculated and analyzed for the best and optimized geometries of the 3‐D clusters with N = 3 to N = 10 atoms and unit cells of three types of crystalline systems using ab initio RHF/6–31G^** method. Dependence of the lattice binding energy on the cluster parameter, R, has been studied. Similar behavior observed for the binding energies for all clusters shows that probabilities of their existence in the condensed phase are more or less the same. In the next step, thermodynamic properties have been calculated and analyzed for He₂₇ 3‐D helium clusters with simple cubic, body centered cubic (bcc), trigonal and hexagonal (hcp) configurations. The results show that the hexagonal cluster is more favored over other clusters. It is found that these clusters are electronically stable over a limited range of the values for the lattice parameter. Δ_fH is constant in this stability region and thus the Δ_fG exactly follows the variations of TΔ_fS. Surface effects have been investigated by comparing the square and hexagonal He₉ 2‐D lattices with the cubic and hexagonal He₂₇ 3‐D lattices, respectively. The lattice parameters, densities and molar volumes calculated for the clusters with hcp and bcc configurations have satisfactory agreement with the available experimental values. Properties of the He₁₃, He₃₄ and He₁₀₄ hcp clusters have also been calculated and analyzed.     

Static hyperpolarizability of the van der Waals complex CH4?N2

The static first hyperpolarizability of the van der Waals CH₄ N₂ complex was calculated. The calculations were carried out in the approximation of the rigid interacting molecules for a broad range of intermolecular separations (R = 6–40 a₀) and for six configurations at CCSD(T) level of theory using the correlation consistent aug-cc-pVTZ basis set with the basis set superposition error correction. It was shown that the long-range classical approximation, including the terms up to R⁻⁶, is in a good agreement with ab initio calculations for R > 11 a₀. It was found out that for the family of most stable configurations of the complex, the first hyperpolarizability invariants practically do not change (the changes are less than 0.1%). Under forming the stable van der Waals CH₄ N₂ complex, the intensity and degree of depolarization of the hyper-Rayleigh scattering are noticeable decreased (by ∼10%) to be compared with the free CH₄ and N₂ molecules. © 2012 Wiley Periodicals, Inc.     

Ab initio MO and TST calculations for the rate constant of the HNO+NO2→HONO+NO reaction

Potential-energy surfaces for various channels of the HNO+NO₂ reaction have been studied at the G2M(RCC,MP2) level. The calculations show that direct hydrogen abstraction leading to the NO+cis-HONO products should be the most significant reaction mechanism. Based on TST calculations of the rate constant, this channel is predicted to have an activation energy of 6–7 kcal/mol and an A factor of ca. 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ at ambient temperature. Direct H-abstraction giving NO+trans-HONO has a high barrier on PES and the formation of trans-HONO would rather occur by the addition/1,3-H shift mechanism via the HN(O)NO₂ intermediate or by the secondary isomerization of cis-HONO. The formation of NO+HNO₂ can take place by direct hydrogen transfer with the barrier of ca. 3 kcal/mol higher than that for the NO+cis-HONO channel. The formation of HNO₂ by oxygen abstraction is predicted to be the least significant reaction channel. The rate constant calculated in the temperature range 300–5000 K for the lowest energy path producing NO+cis-HONO gave rise to © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 729–736, 1998     

United atom force field for phospholipid membranes: Constant pressure molecular dynamics simulation of dipalmitoylphosphatidicholine/water system

We refined the united atom field for the simulations of phospholipid membranes. To validate this potential we performed 1000-ps constant pressure simulation of a dipalmitoylphosphatidicholine (DPPC) bilayer at T=50° C. The average area per head group (61.6±0.6) Ų obtained in our simulation agrees well with the measured one of (62.9±1.3) Ų. The calculated S_CD order parameters for the Sn-2 hydrocarbon tail also display a good agreement with the experiment. The conformations of head groups in our simulations of the liquid crystal phase are different than the ones observed in the crystal structure. ©1999 John Wiley & Sons, Inc. J Comput Chem 20, 531–545, 1999