Ab initio study on NH+: Transition dipole moments,transition probabilities,and radiative lifetimes

The transition electric dipole moments between low-lying valence states of NH⁺ are calculated by an ab initio effective valence-shell Hamiltonian (H^v) method. The H^v calculated transition moments are found to be in good agreement with those by other accurate ab initio methods. The spontaneous emission probabilities for the A²− → X²Π, B²Δ → X²Π, and C²−⁺ → X²Π transitions of NH⁺ are computed. Also, radiative lifetimes for A²∑⁻, B²Δ, and C²∑⁺ states are all theoretically determined using the potential energy functions by H^v. Also, the H^v results are well compared with those computed using the Morse potentials and the rkr potentials which are obtained from experimental data. © 1996 John Wiley & Sons, Inc.     

Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane

Molar excess mixing enthalpies h ^E , Gibbs free energies g ^E and hence entropies s ^E have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C ₁₆ . The h ^E and g ^E are negative while Ts ^E are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to h ^E and Ts ^E , counterbalanced in the case of Ts ^E by the positive combinatiorial Ts ^E for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of h ^E and Ts ^E are now strongly positive, while those of g ^E are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C ₁₆ molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, h ^E and Ts ^E are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C ₁₆ segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature.     

Complex‐scaling calculations for resonance states of he with screened coulomb potentials

The doubly excited ¹S^e, ¹P^o, and ¹D^e resonance states of helium atom with screened Coulomb potentials are investigated. The complex scaling method with configuration interaction type basis functions are employed to extract the resonances associated with the He⁺(N = 2, 3, and 4) thresholds. 18 resonances (six below each of the He⁺ threshold) for each angular‐momentum state are calculated. The results lying below the He⁺(N = 2) threshold are in good agreement with previous calculations by the stabilization method with correlated basis wave functions. The ¹P^o and ¹D^e resonance states lying below the He⁺(N = 3 and 4) thresholds in the screening environment are reported for the first time. © 2013 Wiley Periodicals, Inc.     

Ab initio study of low-lying electronic states of the FNO2 molecule

Ab initio electronic structure calculations are reported for low-lying electronic states, ¹A₁, ¹A₂, ³A₂, ¹B₁, ³B₁, ¹B₂, and ³B₂ of the FNO₂ molecule. Geometric parameters for the ground state ¹A₁ are predicted by MRSDCI calculations with a double-zeta plus polarization basis set. The vertical excitation energies for these electronic states are determined using MRSDCI/DZ+P calculations at the ground-state equilibrium conformation. The oscillator strengths and radiative lifetimes for some electronic states are calculated based on the MRSDCI wave functions. © 1993 John Wiley & Sons, Inc.     

Electron-pair densities of singly charged atoms

For the singly charged 53 cations from Li⁺ to Cs⁺ and 43 anions from H⁻ to I⁻ in their ground states, spherically averaged electron-pair intracule (relative-motion) density h(u), extracule (center-of-mass-motion) density d(R), and their moments uⁿ and Rⁿ are examined, where u and R are the interelectronic distance and the center-of-mass radius of a pair of electrons, respectively. The intracule and extracule densities of all the 96 ions are found to be monotonically decreasing functions, as for neutral atoms. Approximate relations d(R)8h(2R) and uⁿ/Rⁿ2ⁿ are confirmed to be valid for the charged atoms as well.     

Some INDO calculations of the dependence of one-bond phosphorus-phosphorus coupling upon molecular geometry

Some INDO parameterized SCPT calculations of ¹J(P? P) and ¹J(P?P) are reported as a function of geometry. At structures corresponding to the gas-phase equilibrium configuration of diphosphine, all of the substituted diphosphines considered are predicted to have negative values of ¹J(P? P). Both contact and non-contact contributions to ¹J(P? P) are significant, whereas the angular variation of ¹J(P? P) is mainly due to the contact term. The non-contact interactions are dominant in determining the value of ¹J(P?P).     

13C NMR spectra of 2,3-dihydro-1H-benzo[b]azepines: Differentiation of diastereomers

The ¹³C NMR spectra of 23 2,3-dihydro-1H-benzo[b]azepines, including nine pairs of diastereomers separated by chromatography, [(2R*, 3R^*) and (2R^*), 3S^*)] are hereby assigned and discussed. The relative configurations of the diastereomers were assigned by two methods. The first, based on the chemical shifts of the asymmetric carbons C-2 and C-3 (with regression analysis), shows that the values for (R^*, R^*) are approximately 1 ppm lower than those for (R^*, S^*) diastereomers. The second method uses the chemical shifts, δ₃, of the R₃(CH₃) substituents. When these δ₃ values are compared by means of the δ₃-δ_m difference (δ_m is the mean value obtained from compounds where R₂=H), the difference is always negative for (R^*, R^*) and positive for (R^*, S^*). This is attributed to a γ-gauche effect between R₂ and R₃ in the case of (R^*, R^*) diastereomers (R₂ and R₃ are cis). The results corroborate those already obtained by ¹H NMR [J(23)(R^*, R^*)<J(23)(R^*, S^*)] and are a confirmation of the results of a radiocrystallographic examination carried out on two nitrogen acetylated diastereomers.     

Chromium(III) complexes ofd(−)tartaric andl(−) mandelic acids

The binary complexes of anhydrous chromium(III) chloride withd(−) tartaric acidl(−) mandelic acids have been characterized by elemental analyses, magnetic susceptibility, vibrational, electronic and circular dichroism spectra. The magnetic susceptibility data are close to the spin only value for a d³ chromium(III) ion. Three (Cr−Cl) vibrational modes in the region 420–290 cm⁻¹ are observed for the formed complexes indicatingC ₂ local symmetry of ligand atoms around the chromium(III) rather thanC ₃, which would allow two modes. In the visible spectra, two peaks in the 21052–22222 and 15384–16129 cm⁻¹ range are observed and are assigned to the⁴ A _2g → ⁴ T _1g (F) and⁴ A _2g → ⁴ T _2g transitions. The parameters (Dq, B,β ₃₅) place the ligands in the higher end of the spectrochemical series and provide reassurance that the hydroxy acid oxygen complexes to chromium(III) ion. The Cotton effects observed in the spin-forbidden band are assigned to the² E(² E _g ),² A ₂(² T _1g ) and² E(² T _1g ), while that in the spin-allowed band are a results of the splitting of the⁴ A _2g (⁴ T _2g ) to⁴ A ₁(⁴ T _2g) and⁴ E(⁴ T _2g ) transitions. The tartaric acid chelates are likely to befac in terms of ligand carboxylate and/or hydroxy groups since stronger and better defined Cotton effects are observed while mandelic acid chelates are weak suggesting formation of themer structure. TMC 2633     

Theoretical study of [F−; e+] and [CN−; e+]

Ab initio calculations are presented for the [F^?; e⁺] and [CN^?; e⁺] complexes. Positron affinities of 4.99 and 3.79 eV are obtained for F^? and CN^?, respectively. The excitation energies to the low-lying excited states of the positron complexes are also calculated.     

Calculating the molecular constants for the B1Πu, C1Πu, (1)1Πg, and (2) Σ g+ electronic states of the rubidium dimer

The vibrational, rotational, and centrifugal constants are calculated for the B ¹Π _u , C ¹Π _u , (1) ¹Π _g , and (2) electronic states of a ⁸⁵Rb₂ molecule. The calculations are based on the semi-empirical potential curves obtained in this work. The results from calculating the molecular constants are compared with experimental data. The Franck-Condon factors and R _v′v″ centroids are calculated for the electronic transitions B ¹Π _u -X ¹Σ _g ⁺, C ¹Π _u -X ¹Σ _g ⁺, C ¹Π _u -(1) ¹Π _g , and C ₁Π _u -(2) ¹Σ _g ⁺.     

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.     

13C?13C coupling constants in derivatives of trans-stilbene and tetraphenylethylene. Determination of relative signs II

Magnitudes and signs of ¹³C? ¹³C coupling constants in compounds of the type Ph¹³CR¹R²? ¹³CR¹R²Ph have been determined and the results are discussed in a broader context. Two types of coupling constants, J(C-i, C-α) and J(C-i, C-β), between aromatic carbon atoms and the benzylic carbons, probably with different coupling mechanisms, are considered. Whereas ²J(C-2, C-α) are always found positive, ²J(C-1, C-β) in the present compounds are found to be negative or about zero. ³J(C-3, C-α) has the same sign as ²J(C-2, C-α). A ⁴J and a ⁵J were observed in trans-stilbene.     

Crosslinked polymer chains with excluded volume: A new class of branched polymers?

In this note microgels with and without excluded volume interactions are considered. Based on earlier exact computations on Gaussian mircogels, which are formed by self-crosslinking (with M crosslinks) of polymer chains with chainlength N, Flory type approximations are used to get first insight to their behavior in solution. It is shown that two different types of microgels exist: A special type of branched polymer whose size scales as R ∝ N^2/5/M^−1/5, instead of R ∝ N^1/2. The second type are c^*-microgels whose average mesh sizes r are swollen and form self avoiding walks with a scaling law of the form r = a(N/M)^3/5.     

Some sum-over-states perturbation calculations of 19F?13C coupling constants for some carbocations and related fluorobenzenes

Sum-over-states perturbation calculations within the INDO framework are reported for 24 ¹J(FC) and 34 ³J(FC) couplings. In general, satisfactory agreement with the experimental data is obtained when the integral products S_F²(O) S_C²(O) and 〈r^?3〉_F 〈r^?3〉_C take the values of 136.543 au^?6 and 58.352 au^?6, respectively, for the ¹J(FC) couplings. The corresponding values for the ³J(FC) couplings are 29.520 au^?6 and 44.340 au^?6, respectively. All of the ¹J(FC) values are predicted to be negative, whereas all of the ³J(FC) values are calculated with positive signs. The results indicate the importance of including the contact, orbital and dipolar contributions in the calculations.     

Basis set quality versus size II. Approximate GTO wave functions for second row transition metal atoms

Basis sets ranging in size from (16, 10, 7) to (20, 14, 11) have been derived for the atoms Y–Cd. Separate sets represent the energy optimized wave functions for each of the s²dⁿ, s¹dⁿ⁺¹, and s⁰dⁿ⁺² configurations. The energies from the largest sets are within 3 mhartrees of the values obtained in numerical Hartree–Fock calculations. Reasonable Hartree–Fock s²dⁿ– s¹dⁿ⁺¹ and s²dⁿ– s⁰dⁿ⁺² excitation energies may be obtained either using the largest basis sets, or using d-orbitals optimized for the s⁰dⁿ⁺² configurations. The basis sets are slightly unbalanced in favor of the s-functions and in disfavor of the d-functions, but various alternative basis sets may be derived by combining parts of the five parent sets. The convergence of radial expectation values is discussed.     

Complex coordinates and the Stark effect

The theories of the dilatation, r → r e^iθ, and translation, x → x + iq, transformations as related to the Stark problem are reviewed, and new results obtained. Results for the hydrogen atom n = 1 and n = 2 levels and the ¹P⁰, 2s2p H^? shape resonance in dc fields are presented, and the extension to the ac Stark effect made. Spectral estimates are made using the technique of the numerical range and via discussion of several model problems, using both coordinate rotation and coordinate translation.     

Electronic and optical properties of pyrrole and thiophene oligomers: A density functional theory study

The conductive mechanism of pyrrole (Py) and thiophene (Th) oligomers is investigated in the framework of density functional theory. Geometric constructions and electronic structures of neutral n‐Py/n‐Th and oxidized n‐Py^m+/n‐Th^m+ oligomers (6 ≤ n ≤ 48, 2 ≤ m ≤ 18) are reported as a function of oligomer length. The charges in the oxidized oligomers have a localized distribution along the oxidized n‐Py^m+/n‐Th^m+ oligomers, and each set of two positive charges is localized in one area. Therefore, the charge carriers in oxidized n‐Py^m+/n‐Th^m+ oligomers are bipolarons. Furthermore, the nonlinear optical properties of the n‐Py/n‐Th oligomers are investigated, for which the static polarizability α, the first polarizability β, and the second polarizability γ are calculated. When the ratio of m/n is 1/3, the static polarizability <α> and the polarizability anisotropy Δα are maximized. In addition, neutral n‐Py/n‐Th oligomers have maximum <γ> values. The values of β were determined mainly by the dipole of the molecule, while the values of γ were closely related to the aromaticity of the oligomer. The stronger the aromaticity, the bigger the γ value. All calculations indicate that the polarizability and absorption spectrum can be tuned by controlling the oxidation level, making these oligomers applicable as good nonlinear optical materials.     

Electron‐Self‐Exchange Kinetics of the Cyclooctatetraene/Cyclooctatetraene Radical‐Anion Couple

Rate constants k_hom and k_het are reported for the homogeneous electron‐self‐exchange and the heterogeneous electrochemical electron‐transfer reactions, respectively, of the cyclooctatetraene/cyclooctatetraene^? (COT/COT^.?) redox couple. In acetonitrile, the values k_hom (298 K)=(5±3)×10⁵ M ^?1 s^?1 and k_het (295 K)=8×10^?3 cm s^?1 are found, whereas slightly faster rates are obtained in dimethylformamide, namely, k_hom (298 K)=(1.6±0.6)×10⁶ M ^?1 s^?1 and k_het (295 K)=2×10^?2 cm s^?1. The k_hom rates are obtained from electron spin resonance (ESR) line broadening whereas the k_het rates are measured at a mercurized Pt electrode by using Nicolson’s method. The slowness of both electron‐transfer reactions is caused by the high inner‐sphere reorganization energy that results from the inevitable conformational change that takes place upon going from the tub‐like COT molecule to the planar COT^.? anion. The rates are well‐understood in terms of Marcus theory, including an additional medium inner‐sphere mode which is responsible for the flattening of COT.     

Dérivés Alléniques du Phosphore. Influence de l'État de Coordination du Phosphore et de la Nature des Radicaux Liés au Phosphore sur les Signes de J(P?H)

The signs of the phosphorus-proton coupling constants in various allenic organophosphorus compounds have been determined by either analysis of the AB₂X spectra or double resonance. Probable absolute signs have been obtained by taking ³J(P? H) as positive. In allenic phosphine oxides, the following signs are obtained: ²J(P? H) +ve, ³J(P? H) +ve, ⁴J(P? H) ?ve, ⁵J(P? H) +ve and the ⁴J(P? H) coupling constant varies mostly with the inductive effect of the substituents bound to the phosphorus atom. In allenic phosphines, these sings are: ²J(P? H) +ve, ³J(P? H) +ve, ⁴J(P? H) ?ve and +ve and the ⁴J(P? H) coupling constant varies with both the inductive and resonance effects to the substituents. This coupling constant is negative except when the phosphorus atom is bound to groups which are electron-donating by resonance effects. These results are discussed in relation to the pπ? dπ bonding in phosphine.     

New expansion of the Boys function

We propose a new expansion for the Boys function ∫₀¹t^2jexp(−r²t²) dt appearing in the calculation of molecular two-electron matrix elements if Gaussian basis sets are employed. This expansion involves a power series involving the terms C_{i, j}(τ) (r²−R²)ⁱ multiplied by exp(−τr²), where τ is an optimized parameter τ∈[0, 1]. The performances of the introduced expansion are discussed and illustrated by some numerical experiments. It appears that the proposed expansion is considerably shorter than the customary Taylor series, which in turn is the special case for τ=0. This is of some importance, particularly for higher j values. Further, the proposed expansion enables a single expression for calculating erf(x) for the whole range of variable x. The recursive relations for the expansion coefficients are derived and the truncation errors are estimated. A new method for calculating the Boys function by means of asymptotic series is represented too. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 305–315, 1998