Internal orbitally resolved charge sensitivity analysis

The intramolecular (internal) charge sensitivity analysis (ICSA ) is presented in the molecular orbital (MO ) resolution, with diagonal idempotency constraints being imposed on the MO occupations, n, which can then be considered as independent electron population variables of the system for the assumed fixed shapes of MOS . The standard closed-shell (C.S.) SCF MO framework is adopted with the energy function E(n) approximated by the average energy of a configuration expression to cover fractional MO occupations. The components of the gradient of the auxiliary energy function, including the constraint terms, with respect to n, identified as negative MO internal electron potentials, vanish identically for the ground-state c.s. configuration, whereas their responses to hypothetical intramolecular charge displacements assure the system stability. An application of the ICSA to the iterative SCF procedure is suggested. Illustrative results for the water molecule are reported and general properties of molecular normal orbitals (eigenvectors of the hardness matrix) are discussed. © 1992 John Wiley & Sons, Inc.     

Normal (decoupled) representation of electronegativity equalization equations in a molecule

The decoupled (normal) representation of the electronegativity (chemical potential) equalization equations, in which the hardness tensor {η_ij}={?μ_i/?N_j} becomes diagonal, is examined in the atoms-in-a-molecule (AIM ) approximation; μ_i=?E/?N_i is the chemical potential of the i-th AIM , N_i is its electron population, and E is the system energy. All relevant chemical potential, hardness, softness, and Fukui function quantities corresponding to the normal electron redistribution channels, Q_y, are discussed and expressed in terms of the canonical AIM parameters. The normal chemical potentials, μ _γ=?E/?Q_γ, provide a natural classification of the normal modes into three groups: (a) acceptor normal modes (μ _a < 0, positive mode Fukui function, hardness, and softness), (b) donor normal modes (μ _d > 0, negative mode Fukui function, hardness, and softness), and (c) polarization normal modes (μ _p=0, zero mode Fukui function, hardness, and softness). The implications of the normal mode analysis for the theory of chemical reactivity are briefly summarized.     

Hooke numbers of polymers

Hooke numbers He ≡ σ_b/(E) are calculated from published ultimate tensile strengths σ_b, tensile moduli E, and ultimate elongations ?_b. Data for common thermoplastics and natural fibers each follow a function He = [1 + (?_b/?_crit)^ab]^?1/b with a Hookean region I (He = 1) at ?_b ? ?_crit, a non-Hookean region III at ?_b ? _crit, and a transition region II for ?_b ≈ ?_crit. Only non-Hookean regions III were found for semisimultaneous interpenetrating networks from polyisobutylene-polymethyl methacrylate, thermoplastic elastomers from segmented polyamide-polyethers, molecular composites from poly(p-phenylene benzobisthiazole) and poly[2,5(6)-benzimidazole], and three groups of various synthetic fibers. The Hooke numbers of lyotropic and thermotropic liquid-crystalline polymers vary with the heat treatment and depend on orientation angles for orientation angles greater than ca. 10°. Hooke numbers much greater than 1 are observed for highly stressed polymers. ©1995 John Wiley & Sons, Inc.     

Comparison between theoretical and experimental values of the volume changes accompanying rubber extension

The molecular theory of rubber elasticity assumes the free energy to consist of two parts: a liquidlike free energy that is governed by intermolecular interactions and is independent of strain at constant volume and an intramolecular interaction free energy equal to the sum of the free energies of the chains making up the network. The volume increases of rubber samples as a function of their length were found to be considerably larger than predicted by the molecular theory. Therefore, contrary to common belief, the values of (?E/?L)_V,T might not be related solely to changes in intramolecular interactions with extension. Also, the usual procedure to obtain values of (?E/?L)_V,T from measurements of (?f/?T)_p,L with the aid of the molecular theory is not correct.     

Ab initio molecular orbital calculations of the cobalt porphine complex. I. LCAO SCF MO calculation of low-spin,high-spin,and π-ionized states of Co-porphine

Ab initio LCAO SCF MO calculations are carried out on planar Co-porphine with a basis set of roughly double zeta quality for Co and N and of single zeta quality for C and H. The net charge on Co and N and the overlap population between them are 1.78, ?0.57, and 0.06, respectively, in the ²A_1g, state, which is known to be the ground state by experiment. The bonding in this complex is thus largely ionic. The first and second calculated ionization potentials are 6.51 and 6.77 eV, respectively, and are in reasonable agreement with the observed ionization potentials of 6.44 and 6.62 eV for Ni-tetraphenylporphine. CI calculations within the framework of the ligand field theory are also performed. The calculated order of the five lowest states is ⁴B_2g ≈ ⁴E_g, ⁴A_2g, ²A_1g, ⁴E_g from below and is not in agreement with the semiempirical order of ²A_1g ≈ ⁴B_2G, ⁴A_2g, ²E_g, ⁴E_g determined by Lin.     

Energetics of Zn2+ binding to a series of biologically relevant ligands: A molecular mechanics investigation grounded on ab initio self-consistent field supermolecular computations

Detailed investigations are performed of the binding energetics of Zn²⁺ to a series of neutral and anionic ligands making up the sidechains of amino acid residues of proteins, as well as ligands which can be involved in Zn²⁺ binding during enzymatic activation: imidazole, formamide, methanethiol, methanethiolate, methoxy, and hydroxy. The computations are performed using the SIBFA molecular mechanics procedure (SMM), which expresses the interaction energy under the form of four separate contributions related to the corresponding ab initio supermolecular ones: electrostatic, short-range repulsion, polarization, and charge transfer. Recent refinements to this procedure are first exposed. To test the reliability of this procedure in large-scale simulations of inhibitor binding to metalloenzyme cavities, we undertake systematic comparisons of the SMM results with those of recent large basis set ab initio self-consistent field (SCF) supermolecule computations, in which a decomposition of the total ΔE into its four corresponding components is done (N. Gresh, W. Stevens, and M. Krauss, J. Comp. Chem., 16 , 843, 1995). For each complex, the evolution of each individual SMM energy component as a function of radial and in- and out-of-plane angular variations of the Zn²⁺ position reproduces with good accuracy the behavior of the corresponding SCF term. Computations performed subsequently on di- and oligoligated complexes of Zn²⁺ show that the SIBFA molecular mechanics (SMM) functionals, E_pol and E_ct, closely account for the nonadditive behaviors of the corresponding second-order energy contributions determined from the ab initio SCF calculations on these complexes and their nonlinear dependence on the number of ligands. Thus, the total intermolecular interaction energies computed with this procedure reproduce, with good accuracy, the corresponding SCF ones without the need for additional, extraneous terms in the intermolecular potential of polyligated complexes of divalent cations. © 1995 by John Wiley & Sons, Inc.     

DR. Maurits Dekker: A Pioneer in Scientific Publishing

Abstract

Organic salts as initiators [A? ⁺B^?: Ph?₃C⁺ClO^? ₄, Ph?₃C⁺SbCl^? ₆, (?)Sp? ⁺ClO^? ₄, and (?)(Sp)?₂ ³⁺(ClO₄)^? ₃] and catalysts [A ⁺B?^?: (+)CSA?; A? ⁺B?^?: ph?₃C⁺(+)CSA?^? and (?)Sp?⁺(+)CSA?^?] are prepared and characterized by the dissociation constant (K _d), fraction of free ions (α), and specific rotation. The asymmetrically stereoselective induction of the initiators and catalysts in the polymerization of N-vinylcarbazole is in the order A? ⁺B?^? > A ⁺B?^? > A? ⁺B^?. The specific rotations of the poly(N-vinylcarbazole) (PVCZ)s obtained are generally in this order.     

Two‐Orbital Three‐Electron Stabilizing Interaction for Direct Co2+As3+ Bonds involving Square‐Planar CoO4 in BaCoAs2O5

The quest for new oxides with cations containing active lone‐pair electrons (E) covers a broad field of targeted specificities owing to asymmetric electronic distribution and their particular band structure. Herein, we show that the novel compound BaCoAs₂O₅, with lone‐pair As³⁺ ions, is built from rare square‐planar Co²⁺O₄ involved in direct bonding between As³⁺E and Co²⁺ d_z2 orbitals (Co? As=2.51 Å). By means of DFT and Hückel calculations, we show that this σ‐type overlapping is stabilized by a two‐orbital three‐electron interaction allowed by the high‐spin character of the Co²⁺ ions. The negligible experimental spin‐orbit coupling is expected from the resulting molecular orbital scheme in O₃AsE–CoO₄ clusters.     

A Theoretical Study of Complex Formation between Formaldehyde and Lithium

Ab initio SCF and CI calculations on the cationic and neutral complexes of formaldehyde and lithium are reported. For the cationic complex CH₂O/Li⁺, the stabilization energy of 41.7 kcal/mol obtained from the SCF calculation increases to 51.6 kcal/mol if a configuration interaction is introduced. For the neutral complex CH₂O^?/Li⁺, the C_2v-conformer of the ²A₁-state with the equilibrium bond distances of d(C? O) = 1.23 Å and d (O? Li) = 1.90 Å is calculated to be more stable than the ₂B₁-state with d (C? O) = 1.34 Å, and d (O? Li) = 1.65 Å. Charge transfer and polarization effects upon complex formation are discussed.     

Broken orbital symmetry and the description of valence hole states in the tetrahedral [CrO4]2− anion

The localization of ligand-based valence holes in the tetrahedral complex ion [CrO₄]^2? in a crystalline environment is studied by SCF calculations on the hole states, with progressively less restrictions on the spatial symmetry of the molecular orbitals. The final wavefunctions are obtained by constructing, from the symmetry broken SCF solutions, wavefunctions that exhibit again the proper transformation properties under the operations of T _d . The crystal environment of the [CrO₄]^2? anion is represented by a point charge model. In contrast with the situation for core hole states, the projection afterwards into T _d symmetry is important. The final ionization energies, which are obtained from projected C _3v adapted SCF solutions, are reduced considerably (?3 eV) with respect to the T _d ΔSCF results, but the ordering of the states has not changed essentially. The calculated ionization energies compare favourably with results of XPS experiments on Na₂CrO₄. The evaluation of the energies of projected symmetry broken SCF solutions requires the calculation of hamiltonian matrix elements between determinantal wavefunctions built from mutually non-orthogonal orbital sets. An efficient method for the calculation of such matrix elements is presented.     

Molekulares SSi(H)CI Matrix-IR-Untersuchungen und ab- initio SCF-Rechnungen

The Molecule S?Si(H)CI. Matrix IR Investigation and Initio SCF Calculation Molecular S?Si(H)CI is formed in an argon matrix after the Photochemically induced reaction of SiS with HCI. From the isotopic splittings (H/D and ³⁵,CI/³⁷CI) of the IR absorptions the C_s-structure of the species with silicon as the central atom can be deduced. By an normal coordinate analysis a value of 4.83 mdyn/Å is obtained for the SiS force constant. These experimental results are confirmed by ab initio SCF calculations of the IR spectrum.     

Quantum chemical ab initio calculations for excited states of F IV

Quantum chemical ab initio calculations have been performed for the ground state and for several excited states of the F³⁺ ion (F IV). Three levels of accuracy have been used: Frozen-core SCF calculations (FRC-SCF) to determine orbital energies ε _nl and quantum defects δ _l for excited Rydberg orbitalsnl; frozen-core SCF followed by CI calculations (FRC-CI) which account for multiplet splittings and configuration mixings, and multi-configuration coupled-electron-pair approximation (MC-CEPA) calculations which include dynamic correlation effects. The accuracy of the calculated excitation energies is in the order of 5000 cm^?1 at the FRC-CI level and in the order of 500 cm^?1 at the MC-CEPA level. This latter error amounts to about 0.1% for excitation energies in the range of 400000 to 600000 cm^?1. The MC-CEPA calculations have been performed for 17 experimentally known states and for 14 experimentally unknown states, in particular for the configurations 2s2p ² (² D)3s, 2s 2p ²(² S)3s, 2s ² 2p 4p, and 2s ² 2p 5p.     

1H and 13C NMR study of α-acetylenic PIII and PIV derivatives. Signs and magnitudes of J(P?C) and J(P?H)

All J(P? H) and J(P? C) values, including signs, have been obtained in acetylenic and propynylic phosphorus derivatives, R₂P(X)? C?C? H and R₂P(X)? C?C? CH₃ (X ? oxygen, lone pair and R ? C₆H₅, N(CH₃)₂, OC₂H₅, N(C₆H₅)₂, Cl) from ¹H and ¹³C NMR spectra. In P^IV derivatives the following signs are obtained: ¹J(P? C)+, ²J(P? C)+, ³J(P? C)+, ³J(P? H)+, ⁴J(P? H)? . Linear relations are observed between ¹J(P? C), ²J(P? C) and ³J(P? C) versus ³J(P? H), indicating that these coupling constants are mainly dependent on the Fermi contact term, though the other terms of the Ramsey theory do not seem to be negligible for ¹J(P? C) and ²J(P? C). In P^III derivatives these signs are: ¹J(P? C)- and +, ²J(P? C)+, ³J(P? C)-, ³J(P? H)-, ⁴J(P? H)+. Only ³J(P? C) and ³J(P? H) reflect a small contribution of the Fermi contact term while in ¹J(P? C) and ²J(P? C) this contribution seems to be negligible relative to the orbital and/or spin dipolar coupling mechanisms.     

Ab initio MO studies of nuclear spin-spin coupling constants in CH4, SiH4, AlH 4 − and GeH4 systems

Summary Ab initio molecular orbital calculations of electron coupled nuclear spin-spin coupling constants are performed for CH₄, SiH₄, AlH ₄ ^– and GeH₄ systems using the SCF perturbation theory. Basis set dependence of the major contributing terms such as orbital diamagnetic, orbital paramagnetic, spin dipolar and Fermi contact terms are studied. The study also illustrates the relative importance of bond centred functions and nuclear centred polarization functions in predicting the directly bonded and geminal couplings in the systems selected. Basis sets having uncontracted cores functions and augmented with bond functions seem to predict most of these couplings fairly satisfactorily when compared to the experimental values.     

UV photoelectron and ab initio quantum mechanical characterization of nucleotides: The valence electronic structure of anionic 2′-deoxyadenosine-5′-phosphate

He(I) ultraviolet (UV) photoelectron spectroscopy and ab initio, self-consistent field (SCF) calculations with the 6-31G basis set have been employed to characterize the valence electronic structures of anionic 2′-deoxyadenosine-5′-phosphate (5′-dAMP⁻). Theoretical ionization potentials (IPs) of 5'-dAMP^-, of the neutral model compounds 9-methyladenine (9-MeA) and 3-hydroxytetrahydrofuran (3-OH-THF), and of the model anion CH₃HPO₄⁻ have been obtained by applying Koopmans' theorem to ab initio SCF results. The ionization potentials predicted from the SCF calculations have been compared to He(I) photoelectron spectra of 9-MeA and 3-OH-THF. The SCF calculations predict a value (8.45 eV), for the highest occupied π orbital in 9-MeA which agrees well with the experimental vertical IP (8.39 eV). However, IPs for the highest occupied lone-pair orbitals in 3-OH-THF are predicted to be more than 1.52 eV higher than the experimental IPs. Results from recently reported [H. S. Kim and P. R. LeBreton, Proc. Natl. Sci. USA 91, 3725–3729 (1994), and N. S. Kim and P. R. LeBreton, J. Am. Chem. Soc., 118, 3694 (1996)] second-order Møller-Plesset perturbation (MP2) calculations and configuration interaction calculations using the configuration interaction singles (CIS) method indicate that configuration interaction effects strongly influence the energies of the first five ionization events arising from removal of electrons from the closed-shell model anion CH₃HPO₄⁻. Results from the 6-31G SCF calculations of 5′-dAMP⁻, 9-MeA, 3-OH-THF, and CH₃HPO₄⁻ indicates that valence orbital electron distributions in the nucleotide and in the model compounds and anion are similar. The correspondence between the orbital structure of the nucleotide, and the model compounds and anion makes it possible, employing experimental photoelectron data and MP2/CIS computational results for the model compounds and anion, to individually correct IPs calculated for the nucleotide at the 6-31G SCF level. Here, this approach has provided values for the 13 lowest IPs of 5′-dAMP⁻ and indicates that the first IPs of the base, sugar, and phosphate groups are 6.1, 7.8, and 5.5 eV, respectively. © 1996 John Wiley & Sons, Inc.     

SCF Wave functions for (CuO2)n lamella in crystal field of T′–Nd2CuO4

An SCF analysis has been carried for ensembles that simulate the CuO₂ conduction layer in the tetragonal layer crystal T′—Nd₂CuO₄ (Fig. 1). In this work, the CuO₂ layer is described by a planar macromolecule, (CuO₂)_n, subject to the crystal field produced by the point charges in the ionic layers of D_4h symmetry The computations were carried out using the KGNMOL, HONDO, and KGNGRAF codes in MOTECC -91. The computations were carried out with different oxygen and copper basis sets and energy convergence to less than 10^?8 Hartrees. The purpose of the SCF computation was to estimate the cohesive energy of the ensembles, the electron density for the individual molecular orbitals, and the excess correlation energy, to ascertain the nature of the Cu? O bond in the conduction layer. The results indicate the following: (1) The cohesive energy of the ensembles (measured by the SCF energy plus the correlation energy, above the atomic values): ΔU_c ≡ ΔE_SCF + ΔE_C = ?4.35 to ?4.17 Hartrees per CuO bond as n increases from 4 to 9. Further insight was obtained by considering the electrostatic energy contributions to ΔU_c; E_{electrostatic} (ensemble) → E_Modeling (infinite lattice) were evaluated by replacing the oxygen and copper atoms by point charges determined by a Mullion population analysis. The larger oxygen basis set (13, 8/5,3) gave consistent results for the different ensembles of ΔE_covalent ≡ ΔU_c ? E_{electrostatic} = ?1.1 Hartrees per CuO bond. (ii) The electron density indicates that covalent bonds are formed and that the oxygen atoms play an important role in the structure stability. The covalent bonds formed indicate that nominal ionic valences do not apply. Mulliken population analyses gave valences of the order of one at the copper and oxygen atoms. The CuO bond orders are 0.47 between neighboring atoms and 0.048 for those separated by two atoms. (iv) The covalent nature of the CuO bonds in (CuO₂)_n was compared to that for the H₂ molecule using as a measure the electron density and the excess correlation energy. The excess correlation energy per CuO bond above the atomic values is one order of magnitude lower that that for the H₂ molecule and that for the C?C bond in alternant hydrocarbons. © 1993 John Wiley & Sons, Inc.     

NMR of enaminones. Part 7 1H-, 13C-, and 17O-NMR and X-ray structure determinations of 1,2-disubstituted conjugated 3-[(tert-Butyl)amino]enones

¹H-, ¹³C-, and ¹⁷O-NMR spectra for the 2-substituted enaminones MeC(O)C(Me)?CHNH(t-Bu) ( 1 ), EtC(O)C(Me)?CHNH(t-Bu) ( 2 ), PhC(O)C(Me)?CHNH(t-Bu) ( 3 ), and MeC(O)C(Me)?CHNH(t-Bu) ( 4 ) are reported. These data show that 3 exists mainly in the (E)-form, 4 in (Z)-form, and 1 and 2 as mixtures of both forms. Polar solvents favour the (E)-form. The (Z)- and (E)-forms exist in the 1,2-syn,3,N-anti and 1,2-anti,1,N-anti conformations A and B , respectively. The structures of the (E)- and (Z)-form are confirmed by X-ray crystal-structure determinations of 3 and 4. The shielding of the carbonyl O-atom in the ¹⁷O-NMR spectrum by intramolecular H-bonding (Δλ_HB) ranging from ?28 to ?41 ppm, depends on the substituents at C(l) and C(2). Crystals of 3 at 90 K are monoclinic. with a = 9.618(2) Å, b = 15.792(3) Å, c = 16.705(3) Å, and β = 94.44(3)°, and the space group is P2₁/c with Z = 8 (refinement to R = 0.0701 on 3387 independent reflections). Crystals of 4 at 101 K are monoclinic, with a = 16.625(8) Å, b = 8.637(6) Å, c = 11.024(7) Å, and β = 101.60(5)°, and the space group is Cc with Z = 4 (refinement to R = 0.0595 on 2106 independent reflections).     

The 1H, 13C and 31P NMR spectra of EZ pairs of some phosphorus substituted alkenes

The olefins Ph₂P(X)CH?CHR [X=lone pair, O, S, Ch₃I; R?Ch₃, ph, P(X)ph₂] have been prepared and their ¹H, ¹³C and ³¹P NMR spectra measured. trans ³J[P(IV)C] (range 18.3–25.7 Hz) is greater than cis ³J[P(IV)C] (range 6.9–11 Hz) but this relationship does not hold for P(III) compounds. In the ³¹P spectra the E isomer absorbs to higher field than the Z isomer for P(III) and P(IV) compounds. The ¹H data are in accord with previous results; average substituent shielding coefficients for ph₂P(X) substituted alkenes are reported.     

Cation–ligand interactions: Reproduction of extended basis set Ab initio SCF computations by the SIBFA 2 additive procedure

In the framework of the additive SIBFA 2 procedure, the intermolecular interaction energy is computed as a sum of five terms: ΔE = E_MTP + E_rep + E_pol + E_CT + E_disp. In order to assess the accuracy of the procedure to compute cation–ligand interactions, the interaction of alkali (Na⁺, K⁺) and alkaline-earth (Mg²⁺, Ca²⁺) cations with two representative ligands H₂O and HCOO^? has been studied and the results compared with those of ab initio SCF extended basis set computations. The additive procedure reproduces very satisfactorily the results of ab initio computations as concerns the numerical values of the interaction energies and the equilibrium cation–ligand distances, as well as the evolution of the energy components. A detailed study of these components at different distances helps, in particular, to delineate the relative weights of the charge-transfer and polarization contributions within the second-order energy.