Conformational properties of polar polymers. II. Poly(vinylidene chloride)

A recently developed polarization model for representing polar bond effects in conformational energy calculations is applied to poly(vinylidene chloride) (PVDC). The geometries and conformational energies of a number of conformers of 2,2,4,4,6,6-hexachloroheptane were calculated. The geometries were found to be similar to the hydrocarbon analog polyisobutylene (PIB) in that steric crowding results in the usual T, G, G′ states being split into + or ? distortions of the torsional angles away from the traditional values. Only distortions of the same sign occur in the same pair of bonds interior to CCl₂ groups. Distortions of G states towards eclipsed were found to be much more stable than those away. The interior skeletal valence angle is also distorted to an unusually large value, ca. 121°. The calculated dipole moments were used to infer a group moment for CCl₂ of 1.56 D. The calculated conformational energies were fitted by linear combinations of interaction parameters representing the stabilities of G₊, G_? bonds (relative to T₊, T_?) and the interactions between bonds across intervening CCl₂ groups. These parameters were used in statistical mechanical calculations of the characteristic and dipole-moment ratios. In order to make comparison with experiment, the dipole-moment/repeat unit of a 90% (by weight) PVDC copolymer with PVC was measured and found to be 1.42 ± 0.05 D. From this, the dipole-moment ratio for PVDC homopolymer is inferred to be ca. 0.8. The characteristic and dipole-moment ratios calculated from the interaction parameter set were somewhat too high but adjustment of the gauche energies downward brings the calculated ratios into agreement with experiment. The same statistical model along with energy parameters previously calculated also gives agreement with experiment for the characteristic ratio of PIB. The calculated geometries are in agreement with the conformation in the crystal being ? (T₊G′₊T_?G_?)? .     

An ab initio calculation of K-spectra in molecules HCl and HF

An ab initio calculation of energies and intensities of K-emission and K-absorption spectra in molecules HCl and HF are carried out. An electronic readjustment due to a hole in a molecular core is taken into account. A vibrational structure of K-emission and K-absorption spectra is also calculated. The calculation shows that it is possible to detect a vibrational structure of valence bonding levels in X-ray emission spectra. A good agreement with experiment is obtained.     

Computation of the influence of chemical substitution on the pK a of pyridine using semiempirical and ab initio methods

The physical properties of chemicals are strongly influenced by their protonation state, affecting, for example, solubility or hydrogen-bonding characteristics. The ability to accurately calculate protonation states in the form of pK _as is, therefore, desirable. Calculations of pK _a changes in a series of substituted pyridines are presented. Computations were performed using both ab initio and semiempirical approaches, including free energies of solvation via reaction-field models. The selected methods are readily accessible with respect to both software and computational feasibility. Comparison of calculated and experimental pK _as shows the experimental trends to be reasonably reproduced by the computations with root-mean-square differences ranging from 1.22 to 4.14 pK _a units. Of the theoretical methods applied the best agreement occurred using the second-order M?ller–Plesset/6-31G(d)/isodensity surface polarized continuum solvation model, while the more computationally accessible Austin model 1/Solvent model 2 (SM2) approach yielded results similar to the ab initio methods. Analysis of component contributions to the calculated pK _as indicates the largest source of error to be associated with the free energies of solvation of the protonated species followed by the gas-phase protonation energies; while the latter may be improved via the use of higher levels of theory, enhancements in the former require improvements in the solvation models. The inclusion of alternate minimum in the computation of pK _as is also indicated to contribute to differences between experimental and calculated pK _a values. Received: 27 April 1999 / Accepted: 27 July 1999 / Published online: 2 November 1999     

Influence of madelung (interatomic Coulomb) energy on Wolfsberg–Helmholz calculations

A model is presented for the estimation of ionicities in molecules and complex ions. The model uses the minimization of total energy by the method of differential ionization energies. The effect of Madelung corrections to the energies is considered, and the model is refined by evaluating the covalent-bond energies. Wolfsberg–Helmholz calculations have been applied to the same type of model, also incorporating Madelung corrections. The Madelung corrections make the metal ionization energy curves less steep, and the ligand ionization energies are nearly invariant with charge. This creates a situation which has previously been artificially imposed by selecting the ligand ionization energies to give desirable terms in the Wolfsberg–Helmholz secular determinant. The effect of Madelung energy is shown to be the primary influence in describing the ionicity and total energy of a chromophore; covalent bonding effects are shown to be secondary when the ligands and the central atom have fairly different electronegativities.     

Structure and properties of metal-exchanged zeolites studied using gradient-corrected and hybrid functionals. III. Energetics and vibrational spectroscopy of adsorbates

The influence of the exchange-correlation functional (semilocal gradient corrected or hybrid functional) on density-functional studies of the adsorption of CO and NO in Cu- and Co-exchanged chabazite has been investigated, extending the studies of the structural and electronic properties of these materials [F. Go?ltl and J. Hafner, J. Chem. Phys. 136, 064501 (2012); 136, 064502 (2012)] and including for comparison carbonyls and nitrosyls of Cu and Co. Hybrid functionals predict much lower adsorption energies than conventional semilocal functionals, in better agreement with experiment as far as data are available for comparison. The calculated adsorption energies show a strong linear correlation with the stability of the cation sites. For Cu(I)-chabazite the calculated adsorption energies span almost the interval between the adsorption energies calculated for pure neutral and positively charged Cu-carbonyls and nitrosyls. For divalent Cu(II) and Co(II) the adsorption energies at cations in chabazite are much lower than the metal-molecule binding energies in the free carbonyls or nitrosyls, especially for the most stable cation location in a six-membered ring of the chabazite structure. For the stretching modes of adsorbed CO only hybrid functionals reproduce the blueshift of the frequency reported for all Cu(I)- and Co(II)-zeolites. For Cu(II)-chabazite both types of functionals predict a blueshift, the larger value calculated with hybrid functionals being in better agreement with observation. For NO adsorbed on Cu(I)-chabazite all functionals produce a redshift, the smaller value derived with hybrid functionals being in better agreement with experiment. For NO adsorbed in Cu(II)- and Co(II)-chabazite gradient-corrected functionals produce the best agreement with experiment for cations located in a six-membered ring. Semilocal functionals tend to underestimate the frequencies, while hybrid functionals tend to overestimate. The decisive factors determining the influence of the functionals are the larger HOMO-LUMO gap and the larger bandgap of the zeolite host, as well as the larger exchange-splitting of the cation eigenstates predicted with hybrid functionals. For Co(II)-chabazite the tendency to overestimate the exchange-splitting and to stabilize a high-spin state lead to better results with semilocal functionals. Finally, a comprehensive discussion of the influence of the exchange-correlation functional on the physico-chemical properties of these complex systems, based all three papers of this series is presented.     

An analytic potential energy function for the amide–amide and amide–water intermolecular hydrogen bonds in peptides

An analytic potential energy function is proposed and applied to evaluate the amide–amide and amide–water hydrogen‐bonding interaction energies in peptides. The parameters in the analytic function are derived from fitting to the potential energy curves of 10 hydrogen‐bonded training dimers. The analytic potential energy function is then employed to calculate the N? H…O?C, C? H…O?C, N? H…OH₂, and C?O…HOH hydrogen‐bonding interaction energies in amide–amide and amide–water dimers containing N‐methylacetamide, acetamide, glycine dipeptide, alanine dipeptide, N‐methylformamide, N‐methylpropanamide, N‐ethylacetamide and/or water molecules. The potential energy curves of these systems are therefore obtained, including the equilibrium hydrogen bond distances R(O…H) and the hydrogen‐bonding energies. The function is also applied to calculate the binding energies in models of β‐sheets. The calculation results show that the potential energy curves obtained from the analytic function are in good agreement with those obtained from MP2/6‐31+G** calculations by including the BSSE correction, which demonstrate that the analytic function proposed in this work can be used to predict the hydrogen‐bonding interaction energies in peptides quickly and accurately. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Adsorbate binding energies for ammonia on cobalt and nickel clusters

Equilibrium reactions of ammonia with cobalt and nickel clusters are analyzed to determine cluster-adsorbate binding energies. The temperature dependence of reaction equilibrium constantsK _eq are measured and ?ΔH ⁰ values obtained from plots of lnK _eq vs 1/T. We find that binding energies generally decrease with increasing ammonia coverage, and that for a given number of NH₃ molecules binding energies increase with increasing cluster size. The pattern of binding energies is found to be consistent with proposed geometrical structures for Co₁₉ and for clusters in the 55-atom size range. Cluster-ammonia binding energies are generally somewhat higher than for bulk metal surfaces, an expected result considering the character of the cluster surface and the nature of the NH₃-metal interaction.     

Conformational properties of polar polymers. I. Poly(vinyl chloride)

A recently developed method for including polar bonds in conformational energy calculations is applied to poly(vinyl chloride). Inductive effects on dipole moments and the effects of intervening atoms on electrostatic interaction energies are represented by polarizability centers in conjunction with bond centered dipoles. Solvation energies are estimated by means of a continuum dipole–quadrupole electrostatic model. Calculated energies of a number of conformations of meso and racemic 2,4-dichloropentane and the iso, syndio, and hetero forms of 2,4,6-trichloroheptane give satisfactory representations of isomer and conformer populations. Electrostatic effects are found to be quite important. However they appear to be effectively of sufficiently short range that the calculated conformer energies are found to be fit well by a linear combination of interaction parameters (consisting of gauche, skew chlorine, four-bond CH₂…CH₂, CH₂…Cl, and Cl…Cl interactions) conventional to vinyl polymers and a special four-bond interaction that arises when the bond sequence Cl? CH? CH²? CH? Cl is (nearly) coplanar. These interaction parameters when assembled into statistical weight matrices lead to calculated values of both the characteristic ratio and the dipole moment ratio in satisfactory agreement with experiment. Least energy paths for transitions between the most stable conformations are also calculated.     

Projected electron density method of π-eletron systems II. Excited states

A perturbation theory based on the time-dependent Schrödinger equation is presented; Coulombic interactions are taken into account and spin properties are neglected. Using wave functions given by the projected electron density method described in Part I as a basis set the energies of excited π-electron states are calculated. For a series of porphyrin compounds the electronic spectra are calculated and are found to be in good agreement with experiment.     

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.     

The nature of the bonding of Li+ to H2O and NH3; A3 initio studies

Ab initio wavefunctions have been calculated for the complex of Li⁺ with NH₃ and H₂O in order to better characterize the nature of the bonding. Hartree—Fock and generalized valence bond calculations were performed using a double zeta basis plus polarization functions. The binding energies obtained at the GVB level are D_e (Li⁺ — NH₃) = 40.4 kcal/mol and D_e (Li⁺ ? H₂O) = 37.6 kcal/mol, in reasonable agreement with experimental values. Model calculations indicate that the Li⁺ ? base bond is basically electrostatic. Small basis sets were found to lead to D_e as large as 75 kcal/mol for Li⁺ — NH₃, a significant overestimation. Repulsions due to the Li⁺ core are responsible for keeping the Li⁺ too far away for significant relaxation effects.     

Dilute solution properties of styrene–acrylonitrile and styrene–methyl methacrylate copolymers. II. Short-range and long-range interactions from intrinsic viscosity data

Experimental data on styrene–acrylonitrile (St–AN), and styrene–methyl methacrylate (St–MMA) copolymers reported in Part I of this series are tested by “two-parameter” theoretical relations. The Fox–Flory (F–F) parameter K is estimated using the F–F, Stockmayer–Fixman (S–F), and Inagaki–Ptitsyn (I–P) equations. In general, the K values obtained by the F–F equation are low for the three St–AN copolymer samples in the systems studied while the values obtained from S–F and I–P equations agree within the limits of experimental error. Values of K obtained from Kurata–Stockmayer (K–S) equation for sample SA₁ agree with values obtained by the S–F and I–P equations. The specific solvent effect on the K values is discussed. Values of the unperturbed dimension r?0²/M?_w, calculated from the K values estimated from the S–F equation and from the homopolymer data are compared. Except in one case, the calculated r?0²/M?_w values from homopolymer data are low in comparison with the values obtained from experimental data, which shows that the presence of the repulsive interactions between unlike monomer units brings about an expansion of copolymer molecule. The effect of composition on the steric factor σ values is discussed. The long-range interaction parameter B, the excess interaction parameters ΔB_AB, and χAB are calculated. The effects of composition and solvent on these parameters are discussed.     

Electronic structure of transition-metal complexes. I. Parametrization for CNDO/2 method

A new parameterization for the first transition metal has been proposed in the framework of CNDO /2 method. We carried out CNDO /2 calculation of hexamine complexes [M(NH₃)₆]²⁺ and hexa-aquo complexes [M(OH₂)₆]²⁺ in the high spin state where M = Mn, Fe, Co, Ni, and Cu, using new parameters. It is shown that the calculated order of binding energy is Mn? L < Fe? L < Co? L < Ni? L ≈ Cu? L (where L means the ligand), and is in good agreement with experiment. We discussed how the orbital nodes affect the nature of bonding between metal and ligand.     

Theoretical Study of the Interplay between Lithium Bond and Hydrogen Bond in Complexes Involved with HLi and HCN

The lithium‐ and hydrogen‐bonded complex of HLi? NCH? NCH is studied with ab initio calculations. The optimized structure, vibrational frequencies, and binding energy are calculated at the MP2 level with 6‐311++G(2d,2p) basis set. The interplay between lithium bonding and hydrogen bonding in the complex is investigated with these properties. The effect of lithium bonding on the properties of hydrogen bonding is larger than that of hydrogen bonding on the properties of lithium bonding. In the trimer, the binding energies are increased by about 19 % and 61 % for the lithium and hydrogen bonds, respectively. A big cooperative energy (?5.50 kcal mol^?1) is observed in the complex. Both the charge transfer and induction effect due to the electrostatic interaction are responsible for the cooperativity in the trimer. The effect of HCN chain length on the lithium bonding has been considered. The natural bond orbital and atoms in molecules analyses indicate that the electrostatic force plays a main role in the lithium bonding. A many‐body interaction analysis has also been performed for HLi? (NCH)_N (N=2–5) systems.     

Ground states of molecules. 56. MNDO calculations for molecules containing sulfur

MNDO has been extended to sulfur, but without inclusion of 3d AO s. Calculations are reported for heats of formation, geometries, dipole moments, and ionization energies of a variety of sulfur-containing molecules. The average discrepancy between calculated and observed heats of formation is larger than for compounds of other elements, a difference probably due, at least partly, to the lower accuracy of the thermochemical data for sulfur compounds. The calculated dipole moments agree well with experiment as do the calculated ionization energies, except for those corresponding to ionization from sulfur “lone-pair” orbitals which are too high by ca. 1 eV, probably as a result of the neglect in NDDO of interactions between inner and valence shell orbitals. As in the case of other third-period elements, the calculated heats of formation of compounds of sulfur in its higher valence states (S^IV, S^VI) were too positive by large amounts, due presumably to the neglect of 3d AO s.     

Electric field gradient calculation in V2O5

The electric field gradient at the ⁵¹V nucleus in V₂O₅ has been calculated by the Mulliken–Wolfsberg–Helmholtz method. In contrast to the results obtained from crystal field theory, covalency effects in the MO method are shown to give rise to a valence contribution comparable with the lattice contribution. The total electric field gradient correlates with NMR experiments and confirms the adequacy of the method of calculation used.     

A DV-Xα study on the electronic structures of cubane-like iron-sulfur cluster compounds

The electronic structures of six cubane-like cluster compounds of the type [Fe₄S₄L₄]ⁿ (L = SH, OH, and Cl, n=-2 and ?3; L=NO, n = 0 and ?1) have been calculated by using DV-X_α method, and the bonding properties are discussed with emphasis on the ligand effect on cluster bonding. The comparisons of MO energies and cluster charge distributions with the experimental data are made, and the differences between the early studies and the present one are also briefly commented.     

Surface Tension Calculations for Liquid Metals

Abstract

We present a class of models for the surface of a liquid metal, which may be part of an electrochemical interface. The particles of the system, for the purpose of derivation of thermodynamic properties, are the charged ion cores, while the energy of the electrons is evaluated using the electron density functional formalism, previously principally applied to solids. An expression for the surface energy U^s , defined as the energy required to create unit area of surface by separation of a volume of homogeneous metal into two parts, is derived (Eqs. 18–20). The surface tension γ is obtained by differentiating the Helmholtz free energy with respect to the area of the system, keeping volume and particle number constant (Eqs. 27–37). The surface tension is also equal to the difference between the free energy of the system containing a surface and the free energy of a reference system. It thus defines a surface energy through the Gibbs-Helmholtz equation, and this surface energy is shown to be identical to U^s .

The expressions for U^s and γ are made explicit (Eqs. 45–57) by insertion of particular assumptions for the ion-density profile, the electron-density profile, the interionic interaction and pair distribution function, and the electronic energy. Only information about bulk liquid metal is used. The parameter in the electron-density profile is obtained by minimizing the surface energy. The simplest assumption for the interionic interaction, hard-sphere and Coulombic repulsions, requires a choice for the hard-sphere diameter, which is made such that the pressure of bulk metals is given correctly (52–55). For the alkali metals, the surface tension calculated from this model is about half the experimental value in each case, while calculated surface energies are too high (1/5 too high for Cs, but three times too high for Li). For the electrical potential difference between the inside and the outside of a metal, and for the electrochemical potential, agreement with experiment is good. The main reason for the disagreements in the other properties is traced to the simple form used for the ion pair distribution function.     

A molecular mechanics study of the Si?O bond and alkyl-silanes

The standard MM2 force field and program have been modified to include Si? O groups, the force constants being derived from ab initio wavefunctions, and using partial atomic charges calculated from the empirical algorithm CHARGE2. Molecular mechanics calculations have been carried out on disiloxane, dimethoxy-dimethylsilane, methyl silyl ether, and cyclotrisiloxane, and reasonable agreement has been obtained between the observed and calculated geometries. In addition, the energies obtained using the modified force field have been tested against experimental data on alkyl silanes where energetic and structural information is available. Again good agreement is obtained. The application of the force field to extended Si? O systems will also be discussed.