Multiconfiguration self-consistent wavefunctions for CH4, C2H4 and C2H6

The results of several MC SCF calculations on CH₄, C₂H₄ and C₂H₆ with minimun bases of Slater type AO's are reported. The computing method is a quadratically convergent process. Better final energies are obtained if localized MO's are used.     

An analysis of the through-bond interaction using the localized molecular orbitals—IV: Long-range proton hyperfine coupling in exo- and endo-hydrogens in bicyclo[2.1.1]hex-5-yl radical

The INDO calculations were performed on bicyclo[2.1.1]hex-5-yl radical. From these calculations, it was confirmed that the hyperfine coupling constants depend largely on the geometry of the α hydrogen. The localized MO's were obtained from the canonical MO's calculated by using the INDO method. With the use of the localized MO's thus obtained, the variation in the hyperfine coupling constants at the 6exo- and 6endo-protons in this radical was explained in terms of the through-bond and/or the through-space interactions according to the procedure which we proposed previously. That is by the procedure we can selectively pick up a particular interaction between the specified localized MO's. The hyperfine coupling constant in this radical can be expressed by the summation of several interaction terms. The difference in the hyperfine spin coupling constants of the H_6exo and H_6endo in the radical now concerned has been attempted to explain using MO coefficients of the occupied orbitals.     

A straightforward improvement of AB initio SCF wavefunctions

A way of estimating SCF MO's in terms of a large uncontracted basis set from known SCF MO's in terms of a small uncontracted basis set is suggested by using the principle of maximum overlap of both kinds of molecular orbitals. A significant improvement of contours and one-electron properties is observed from the test calculations for H₂O.     

Photoelectron He(I) Spectra of small silanes

The photoelectron He(I) spectra of methyl-, dimethyl-, trimethyl- and ethylsiliane are reported and assigned with the help of CNDO/2 calculations.For each silane the ordering of the valence MO's obtained from calculations is, very close to that of the corresponding alkane, and is in agreement with spectral evidence. Participation of silicon d orbitals in bonding is not substantial but is more important in the outermost SiC and SiH MO's than in the π MO's mainly localized on the alkyl groups.     

A Theoretical study of the structure and inversion barrier of PLi3

The structure and inversion barrier of PLi₃ has been studied using ab initio SCF CI calculations. The inversion potential is very flat, showing a minimum at a bond angle of ≈ 102° and a barrier of ≈2.2 kcal/mole. The effects of basis set on the calculated barrier are discussed.     

Length dependence of excitation energies in linear polyenes: Localized and delocalized descriptions

The length dependence of the lowest allowed transition energy of linear polyenes is studied using delocalized SCF and localized excitonic approaches. Within the PPP SCF approximations the calculated transition energies converge to a finite values as N^?1 as the number of double bonds (N) becomes large, when the excited state contains all singly excited configurations. On the other hand, the fully localized excitonic method at the level of single excitations, although it predicts a gap in the excitation spectrum of an infinite polyene, gives results which converge to this value as N^?2. The inclusion of double and triple excitations into the excitonic method by means of perturbation theory does not appear to change this behavior. The reasons for the discrepancy between the two approaches is analyzed. Experimentally, the transition energies in solution converge to a finite value as N^?1 to a good degree of approximation. If it is assumed that the solvent shift is constant for long polyenes, the available experimental results favour the delocalized approach as the starting point in describing the length dependence of the excitation energy of long polyenes.     

Fifth-order constant denominator perturbation theory within a localized bond model: Contributions from triple and quadruple excitations

The contributions of the triple and quadruple excitations to the fifth-order perturbation energy for the perturbation configuration interaction using localized orbitals (PCILO ) method are derived. This completes the development of a fifth-order constant denominator perturbation theory initiated in a previous paper [5] with the single and double excitations. This theory is tested on molecules containing strained ring geometries, stretched bonds, strongly polarized bonds, and delocalized pi systems: cases where the starting zero order reference wave function poorly describes the system. Although the perturbation expansions turn out to be slowly convergent, the Padé approximant taken from an energy series which itself is constructed from Padé approximants provides results accurate to within a few kilocalories/mole of benchmark calculations. Computational times as in the original PCILO procedure remain proportional to N³, where N is the number of bonds.     

Temperature dependence of vibrational energy transfer in the “low” pressure competitive two-channel 1,1-cyclopropane-d2 system

Intermolecular energy transfer has been studied in the two-channel competitive isomerization of 1,1-cyclopropane-d₂, both in the neat system and in the presence of helium bath gas at values of k/k^? centered around 0.02. The competing path ways differ in threshold energy by ≈ 0.6 kcal. The temperature range 773 K to 973 K was covered. Several methods of treating the data, whether by isotopic ratios of rate constants or by temperature dependence of fall off, are each independent of a knowledge of collision cross sections. Used in conjunction, they provide measurements of these quantities. Cyclopropane is an operationally strong collider (β_ω = 1) for itself at 773 K with an average down step size, <ΔE/s> >/ 10 kcal mole ^?1 (>/ 3500 cm^?1). At 973 K the substrate is no longer a strong collider; β_ω declines to ≈ 0.55 with <ΔE/s> ≈ 5.2 kcal mole^?1. For helium the corresponding quantities are β_ω ≈ 0.078 <ΔE/s> ≈ 1.1 kcal mole ^?1 declining to β_ω ≈ 0.010 and <ΔE/s> ≈ 0.53 kcal mole^?1. The several methods of measuring these quantities give excellent independent agreement. Comparison with the earlier theoretical formulation of Tardy and Rabinovitch gives good agreement, the temperature dependence of β_ω for the weak collider, helium, follows the relation β_ω ∝ T^?m, where m /s> 2.     

Calculations on the singlet-triplet energy separations of silaethylene

The total energy and the conformational hypersurface of the lowest singlet and triplet states of silaethylene, CH₂SiH₂ have been studied using ab initio SCF MO calculations with unrestricted and restricted Hartree-Fock methods. A minimal and an extended basis set was employed. The ground state is predicted to be a singlet and the lowest triplet state to lie 9.6 kcal/mole above. The estimated correlation energy correction would raise ΔE(T₁S₀) to ≈ 16 kcal/mole.     

Solution of large configuration mixing matrices arising in partitioning technique and applications to the generalized eigenvalue problem

A method is presented that can be used (a) to determine the several lowest eigenvalues and eigenvectors of large symmetric matrices, (b) to solve the generalized eigenvalue problem associated with energy-dependent operators, that arises in computations involving energy-dependent many-body Green's functions and in the evaluation of the true parameters of the effective valence shell hamiltonian, and (c) to directly evaluate the matrices associated with resolvent operators. The applicability to large configuration mixing calculations arises when the N-electron basis functions can be easily broken down to a few dominant configurations (the primary block) and their complement. Using the partitioning technique, the effective hamiltonian within the primary block is directly evaluated. The method is extended to evaluation of the dynamical polarizability tensor, which effectively contains the contributions from all of the eigenstates of a hamiltonian matrix, without the necessity of explicitly calculating its eigenvalues and eigenvectors.     

Estimation of activation energies from differential thermal analysis curves

An average activation energy ΔE3 of 31.7 ± 10.0 kcal/mole was calculated from exothermic peaks of urea nitrate differential thermal analysis (DTA) curves using the Murray and White equation and various other reaction rate equations developed by the authors. An average enthalpy of activation, ΔH3 of 30.8 ±9.7 kcal/mole was calculated from the same results. The values of ΔE3 and ΔH3 differed by a fraction of a kcal/mole indicating that ΔE3 <ΔH3 cannot be differentiated experimentally in our study. Application of the Kissinger method of calculating ΔE3 and ΔH3 produced respectively 21.6 ±7.9 and 20.7 ±8.0 kcal/mole, which are quite low. The values of ΔE3 and ΔH3 calculated thermogravimetrically were 28.1, ± 1.1 kcal/mole and 27.6 ± 1.2 kcal/mole which are close to those obtained from the Murray and White approach and the authors' approach to treatment of the DTA data. These results illustrate the pronounced effect of self heating on calculation of activation energies. The Kissinger method of calculating the reaction order developed for endothermic DTA peaks produced good results when applied to the present DTA study.     

Calculation of valence electron vertical ionization potentials using a limited Cl approach

A method is outlined for the calculation of valence electron vertical ionization potentials based on CNDO/2 and CNDO/S SCF molecular ground states improved by including a limited number of doubly excited configurations and ionic states obtained from a single Cl calculation considering a limited set of singly and doubly excited configurations based on the closed shell ground state MO's of the parent molecule. From numerical results on carbon dioxide, sulphur dioxide, ethylene, and trans-butadiene it is shown that the Cl procedure leads to the right sequence of ionic states and their reasonable relative location in contrast to respective Koopmans' ionic states predictions.     

One electron orbitals intrinsic to the reduced hamiltonian

One electron orbitals are determined from the reduced hamiltonian by a simple one-step diagonalization. These reduced hamiltonian orbitals (RHO's) are uniquely determined and virtual orbitals obtained in this procedure are on a par with filled orbitals. These RHO's appear well suited for CI calculations. Minimum basis set calculations are presented for H₂O and compared with similar SCF studies.     

Conformational analysis of intramolecular bonded amino alcohols : The conformational free energies of some intramolecular OH ⋯ N hydrogen bonds

Equilibrium positions between intramolecular OH ? N hydrogen bonded and free OH forms of some 3-piperidinols, decahydroisoquinolinols, a decahydroquinolinol, lupinine and N-methyl-3-piperidinemethanol have been determined from dilute solution IR spectral data at 33°. Conformational free energies of the H-bonds (ΔG°_OH?N, attractive) have been calculated. The results suggest a linear relationship between the apparent value of ΔG°_OH?N, as defined by the method of calculation, and the strength of the OH ? N bond expressed as Δν, within the limits of 0·5 ± 0·2kcal/mole per 100 cm^?1, from Δν 90 to 350 cm^?1. For cis-decahydroisoquinoline (N-Me or N-H) systems, a 0·4 kcal/mole difference has been calculated between the two possible ring-fused conformations, in favor of the so-called steroid form. For the corresponding cis-decahydroqumoline equilibrium, a 0·8 kcal/mole difference has been calculated, in favor of the nonsteroid form.     

Effect of water on the tautomeric equilibrium of uracil monoanions. A PCILO study

The PCILO method is used to calculate the stabilization energies of the anionic forms of uracil by water molecules forming the first hydration shell of the tautomers. The results show that the 1-HU^– tautomer is more stabilized by the solvent effect than the 3-HU^– tautomer by about 8 kcal/mole. The effect brings closer together the energies of the two tautomers which differ intrinsically by about 13 kcal/mole in favour of the 3-HU^– form. It operates in the direction inferred from experimental studies.This work was supported in part by R.C.P. 173 of the Centre National de la Recherche Scientifique of France and in part by the Polish Academy of Sciences within the project 09.3.1.     

The structure of the H3O+ (hydronium) ion

Near Hartree-Fock level ab initio molecular orbital calculations on H₃O⁺ and a minimum energy structure with θ(HOH) = 112.5° and r(OH) = 0.963 Å and an inversion barrier of 1.9 kcal/mole. By comparing these results to calculations on NH₃ and H₂O, where precise experimental geometries are known, we estimate the “true” geometry of isolated H₃O⁺ to have a structure with θ(HOH) = 110-112°, r(OH) = 0.97–0.98 Å and an inversion barrier of 2–3 kcal/mole. Our prediction for the proton affinity of water is ≈ 170 kcal/mole, which is somewhat smaller than the currently accepted value.     

Low resolution microwave spectroscopy and the conformational analysis of 4,4-difluoropiperidine

The low resolution and high resolution microwave spectra of 4,4-difluoropiperidine and the N deutero analog have been recorded. Based on a low resolution microwave adaptation of Kraitchman's equations, the species giving rise to the single observed low resolution band series is seen to be the N-H equatorial conformer. This result is verified by obtaining the principal axis coordinates of the amine hydrogen atom via an assignment of the high resolution microwave spectra of the normal and N-D compounds. Consideration of the least intensity of the N-H axial conformer's spectrum that would be necessary for it to be observed, leads to the result: ΔG ? O.89 kcal/mole for the equatorial ? axial equilibrium.     

Thermogravimetric investigation of the dehydration thermodynamics of amorphous silica after its hydrothermal and thermovaporous treatment

After hydrothermal and thermovaporous treatment of chemically pure amorphous aqueous silicic acid in solutions of NaOH and NH₄OH and in water vapour it is possible, using complex thermal analysis, to detect the weight loss and heat effects corresponding to evaporation of various forms of combined water, and to estimate the heats of evaporation of these forms. From the obtained data, the following water forms have been identified: (1) at 200–300° capillary-condensed water formations of the cluster type evaporate;ΔH _deh is about 8 kcal/mole H₂O; (2) at 250–400°, molecules of water linked by hydrogen bonds with hydroxyl groups on the surface and in the volume of the particles;ΔH _deh. is about 5 kcal/mole H₂O; (3) at 350 600°, molecules of water coordinated to silicon atoms in the volume of the particles;ΔH _deh is approximately 1 kcal/mole H₂O. The total evaporation heat changes from 10 kcal/mole H₂O when water of form 1 predominates, to 5 kcal/mole H₂O when forms 2 and 3 predominate.     

Relationship between the general laws of vapor-liquid equilibria and the analytical curve of emission spectrometry

The relationship between the vapor-liquid equilibrium and the analytical curve of emission spectrometry is discussed on the basis of Hirata's equation, i.e., $\text{y}{}_1\text{y}{}_2$ = α($\text{x}{}_1\text{x}{}_2$)^β, where y is the mole fraction in the vapor phase, x in the liquid phase, α and β are constants for binary systems in a certain concentration range, and the indices $\text{1}$ and $\text{2}$ refer to the two components. Evaporation produced by different atomization-excitation systems can be characterized by apparent evaporation constants, α' and β', the values of which fall between the true values, α and β, of the normal distillation, and unity. Two powder techniques were selected representing the limiting cases: injection spark excitation (α' ≈ α, β' ≈ β) and controlled arc excitation (α' ≈ 1, β' ≈ 1). Using these excitation methods, the analytical curves of the impurities in industrial alumina and electrocorundum were studied using cup-electrode techniques with arc excitation. As a result, one of Hirata's rules could be selected for a given pair of elements. An unambiguous correlation between the properties of the analytical curves and Hirata's rules could be established.