Compact natural orbital expansions for the helium ground state

Using the natural orbital representation and optimizing the exponents in the Slater-type orbital basis, configuration interaction type wave functions for the helium atom are given which combine compactness and high accuracy.     

Molecular orbital momentum distributions and binding energies for nitric oxide

Binding energy spectra of the valence electrons of the open shell molecule NO have been obtained up to 55 eV at azimuthal angles of 0° and 7° using binary (e, 2e) spectroscopy at an impact energy of 1200 eV. The momentum distribution has been obtained for the least tightly bound (unpaired) electron, removal of which leads to formation of the X ¹Σ⁺ ground state of NO⁺. Momentum distributions have also been measured at 21.0 and 40.5 eV. The measured momentum distributions are compared with several literature wavefunctions of varying complexity. They are found to be in excellent agreement with those calculated using the natural spin orbital wavefunctions of Kouba and Ohrn.     

Orbital symmetry,orbital stability,and orbital pairing rules for organic reactions in the ground state

A generalization of the Hartree–Fock molecular orbital (MO) theory for treating diradical intermediates was explained pictorially by drawing molecular orbitals of diradical species such as ring-opened trimethylene. The generalized MO theory applied to elucidate electronic mechanisms of concerted, ionic, radical, and ion-radical reactions of organic reactants in the ground state. Generalized MO computations revealed the most essential characteristics of these reactions and mutal relationships between the worlds of Woodward–Hoffmann and Hughes–Ingold. Generalized MO studies supported our orbital symmetry, stability and pairing rules for concerted, ionic and radical reactions in the ground state, respectively. An extension of MO treatments to excited states reactions was briefly pointed out in relation to the density and spin correlation functions by the multireference CI wave functions.     

Compound I of nitric oxide synthase: the active site protonation state

A quantum mechanical/molecular mechanical (QM/MM) study of the formation of the elusive active species Compound I (Cpd I) of nitric oxide synthase (NOS) from the oxyferrous intermediate shows that two protons have to be provided to produce a reaction that is reasonably exothermic and that leads to the appearance of a radical on the tetrahydrobiopterin cofactor. Molecular dynamics and energy considerations show that a possible source of proton is the water H-bond chain formed from the surface to the active site, but that a water molecule by itself cannot be the source of the proton; an H3O+ species that is propagated along the chain is more likely. The QM/MM calculations demonstrate that Cpd I and H2O are formed from the ferric-hydrogen peroxide complex in a unique heterolytic O-O cleavage mechanism. The properties of the so-formed Cpd I are compared with those of the known species of chloroperoxidase, and the geometry and spin densities are found to be compatible. The M?ssbauer parameters are calculated and may serve as experimental probes in attempts to characterize NOS Cpd I.     

Natural spin orbital analysis of diatomic molecular wave functions in terms of generalized diatomic orbitals I. Outline of the method. Results for the ground state of H2

The method of linear combinations of generalized diatomic orbitals (LCGDO) is combined with the method of configuration interaction (CI). CI wave functions obtained in this way are finally submitted to a natural spin orbital analysis; the resulting natural spin orbitals are expansions in terms of generalized diatomic orbitals.For the ground state of H₂, a one-determinantal-approach with a single completely optimized one-electron basis function nearly reproduces the Hartree-Fock-result. The two-determinantal approach with two optimized basis functions of type _g and _u nearly gives the optimized double configuration SCF result.     

Quenching of the lowest benzene triplet state in the vapor phase by nitric oxide

the rate constant for quenching of the triplet state (³B_1u) of benzene vapor by nitric oxide has been determined from a study of the flash photosensitization of biacetyl phosphorescence. The rate constant has been found to be (1.08 ± 0.2) × 10^?11 cm³ molecule^?1 sec^?1. Although this value is much larger than expected, it is in agreement with rate constants reported for quenching of some liquid phase aromatics.     

Discrepancy between the spin distribution and the magnetic ground state for a triaminoxyl substituted triphenylphosphine oxide derivative

The magnetic interaction and spin transfer via phosphorus have been investigated for the tri-tert-butylaminoxyl para-substituted triphenylphosphine oxide. For this radical unit, the conjugation existing between the pi* orbital of the NO group and the phenyl pi orbitals leads to an efficient delocalization of the spin from the radical to the neighboring aromatic ring. This has been confirmed by using fluid solution high-resolution EPR and solid state MAS NMR spectroscopy. The spin densities located on the atoms of the molecule could be probed since (1)H, (13)C, (14)N, and (31)P are nuclei active in NMR and EPR, and lead to a precise spin distribution map for the triradical. The experimental investigations were completed by a DFT computational study. These techniques established in particular that spin density is located at the phosphorus (rho=-15x10(-3) au), that its sign is in line with the sign alternation principle and that its magnitude is in the order of that found on the aromatic C atoms of the molecule. Surprisingly, whereas the spin distribution scheme supports ferromagnetic interactions among the radical units, the magnetic behavior found for this molecule revealed a low-spin ground state characterized by an intramolecular exchange parameter of J=-7.55 cm(-1) as revealed by solid state susceptibility studies and low temperature EPR. The X-ray crystal structures solved at 293 and 30 K show the occurrence of a crystallographic transition resulting in an ordering of the molecular units at low temperature.     

Morphology and valence state evolution of Cu: Unraveling the impact on nitric oxide electroreduction

Ammonia(NH3) serves as a critical component in the fertilizer industry and fume gas denitrification.However,the conventional NH₃ production process,namely the Haber-Bosch process,leads to considerable energy consumption and waste gas emissions.To address this,electrocatalytic nitric oxide reduction reaction(NORR) has emerged as a promising strategy to bridge NH₃ consumption to NH₃ production,harnessing renewable electricity for a sustainable future.Copper(Cu) sta...     

Correlation factor for ground state of helium

If a variational trial function of form exp(–ar ₁ –ar ₂)f(r ₁₂) is postulated for the ground-state of helium-like ions, then for a given a it is shown that the variation principle leads to an ordinary second order differential equation for f, the solution of which represents the optimum function f for use with a trial function of this type, in the sense that this solution minimises the expectation value of the Hamiltonian for the system. A solution to the differential equation may be found by the usual series expansion method.

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Zusammenfassung Wenn ein Variationsansatz der Form exp(–ar ₁ –ar ₂ f(r ₁₂) für den Grundzustand von Heartigen Ionen vorausgesetzt wird, so wird gezeigt, daß (bei gegebenem a) das Variationsprinzip zu einer gewöhnlichen Differentialgleichung 2. Ordnung für f führt. Ihre Lösung stellt eine optimale, den Erwartungswert des Hamiltonoperators des Systems minimisierende Funktion des angegebenen Typs dar. Eine Lösung der Differentialgleichung kann mit der gewöhnlichen Methode eines Reihenentwicklungs-Ansatzes gefunden werden.

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Résumé Si l'on prend comme fonction variationnelle d'essai pour l'état fondamental des ions de type hélium: exp(–ar₁ –ar ₂)f(r ₁₂) le principe variationnel mène pour a constant à une équation différentielle du second ordre pour f. La solution de cette équation représente la «meilleure» fonction f à utiliser avec une fonction d'essai de ce type, car elle minimise la valeur moyenne de l'hamiltonien. Cette solution peut être obtenue par la méthode ordinaire de développement en série.

     

HD isotope effect of methyl internal rotation for acetaldehyde in ground state as calculated from a multicomponent molecular orbital method

We have analyzed the differences in the methyl internal rotation induced by the HD isotope effect for acetaldehyde (CH(3)CHO) and deuterated acetaldehyde (CD(3)CDO) in ground state by means of the multicomponent molecular orbital (MC_MO) method, which directly accounts for the quantum effects of protons and deuterons. The rotational constant of CH(3)CHO was in reasonable agreement with experimental one due to the adequate treatment of the protonic quantum effect by the MC_MO method. The C-D bond distances were about 0.007 A shorter than the C-H distances because of the effect of anharmonicity of the potential. The Mulliken population for CD(3) in CD(3)CDO is larger than that for CH(3) in CH(3)CHO because the distribution of wavefunctions for the deuterons was more localized than that for the protons. The barrier height obtained by the MC_MO method for CH(3)CHO was estimated as 401.4 cm(-1), which was in excellent agreement with the experimentally determined barrier height. We predicted the barrier height of CD(3)CDO as 392.5 cm(-1). We suggest that the internal rotation of the CD(3) group was more facile than that of the CH(3) group because the C-D bond distance was observed to be shorter than the C-H distance. Additionally the localized electrons surrounding the CD(3) group in CD(3)CDO caused the extent of hyperconjugation between the CD(3) and CDO groups to be smaller than that in the case of CH(3)CHO, which may have also contributed to the observed differences in methyl internal rotation. The differences in bond distances and electronic populations induced by the H/D isotope effect were controlled by the difference in the distribution of wavefunctions between the protons and deuterons.     

Accurate potential for the ground state of the hydrogen molecule

Starting from the spectroscopic constants, an electronic potential for the ground state hydrogen molecule is presented. Self-consistence is checked by numerical integration of the radial wave equation. The mean eigenvalue deviation is about 1 cm⁻¹. Comparison with the latest theoretical work is considered. New revised spectroscopic constants and vibrational quanta are calculated.     

A spectrophotometric method for the determination of nitric oxide

In dimethylsulfoxide, nitric oxide reduces copper(II) to copper(I) in the presence of p-chloroaniline. The resulting copper(I) is determined spectrophotometrically with 2,2′-biquinoline. The reactions are reproducible and the absorbance is proportional to the concentration of nitric oxide over the range 1.8–108 ppm (mg dm^?3. Most other atmospheric contaminants are without effect.     

Discovery of nitric oxide in marine ecological system and the chemical characteristics of nitric oxide

Nitric oxide was discovered in both the lab and the alga culture pond of Daya Bay (1―300 m3) before the growth of alga reached the maximum. The results included: (1) NO was detected before the growth of alga reached the maximum in the case of red tide alga and food alga, and the concentration of NO decreased rapidly after the growth maximum; (2) the curve between NO con-centration and time indicated that the concentration of NO in the daytime was more than that at night, and the maximal concentration of NO appeared in the midday (1―3 pm); (3) the growth of alga reached the maximum in the alga culture pond of Daya Bay in about 8―10 d, and NO was discovered in 5―7 d; (4) the measured NO concentration was 10-9 mol/L, 10-9―10-8 mol/L, and 10-8 mol/L for Haeterosigma akashiwo, mixed alga in Daya Bay and Chaetoceros Curvisetus individually; (5) the relation of illumination with NO production was discussed.     

Closed-form ground state expression for the chemical shift tensor

Steepest-descent perturbation theory is used to derive an equation for the chemical shift tensor elements that requires neither any knowledge of the excited states of the molecule nor an explicit calculation of the molecular wavefunction in the presence of the applied magnetic field. This result is compared to the ground state expression derived earlier from the average energy approximation.     

Configuration interaction benchmark for Be ground state

A set of 432 energy-optimized Slater-type radial orbitals together with spherical harmonics up to ? = 30 is used to approximate the corresponding full configuration interaction (CI) expansion for Be ground state. An analysis of radial and angular patterns of convergence for the energy yields a basis set incompleteness error of 8.7 μhartree of which 85% comes from radial basis truncations for ? ≤ 30. Select-divide-and-conquer CI (Bunge in J Chem Phys 125:014107, 2006; Bunge and Carbó-Dorca in J Chem Phys 125:014108, 2006) produces an energy upper bound 0.02(1) μhartree above the full CI limit. The energy upper bound E = ?14.6673473 corrected with these two truncation energy errors yields E = ?14.6673560 a.u. (Be) in fair agreement with the latest explicitly correlated Gaussian results of E = ?14.66735646 a.u. (Be). The new methods employed are discussed. It is acknowledged that at this level of accuracy traditional atomic CI has reached a point of diminishing returns. Modifications of conventional (orbital) CI to seek for significantly higher accuracy without altering a strict one-electron orbital formalism are proposed.     

The Hartree–Fock ground state of atomic two-electron systems and the Wilson–Silverstone 1s orbital

For the Hartree–Fock ground state of atomic two-electron systems, the variational function of Wilson and Silverstone, ?(r) = (a + kr)^?1 exp(-kr) / (4π)^1/2, can be optimized in two complementary ways. For small values of the atomic number Z, all intergrals have been calculated numerically and optimization can be performed accurately. However, as Z increases, loss of significant figures is increasingly detrimental to the optimization process. For sufficiently large values of Z, the integrals may be replaced by asymptotic expansions in terms of (2a)^?. As a result of optimization, the parameters and expectation values can be given as expansions in terms of (32Z)^?1/2. Both methods yield good results for Z ≈ 25, so that the whole range of Z can be treated accurately. The results have been compared with those derived from other analytical two-parameter functions. It is found that ?(r) is indeed the outstanding two-parameter function, at least for small and intermediate values of Z.     

Localized orbitals for the oxygen and nitric oxide molecules

Localized orbitals are derived for the ground states of the oxygen and nitric oxide molecules by applying localization methods separately to the orbitals containing electrons of alpha- and betaspin. Both the intrinsic energy localization and the uniform localization methods are used. The resulting localized orbitals are in good agreement with the formulae suggested by Linnett.

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Zusammenfassung Für die Grundzustände der Moleküle O₂ und NO werden lokalisierte Orbitale abgeleitet, indem die Lokalisierungsmethoden getrennt für die Orbitale mit- und-Spin angewendet werden. Dabei werden sowohl die eigentlichen Energielokalisierungsmethoden als auch die gleichförmigen Lokalisierungsmethoden benutzt. Die erhaltenen lokalisierten Orbitale stimmen gut mit den von Linnett vorgeschlagenen Formeln überein.

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Résumé Obtention d'orbitales localisées pour l'état fondamental des molécules d'oxygène et d'oxyde nitreux par localisation indépendante des orbitales de spin et des orbitales de spin. Emploi simultané de la localisation selon l'énergie intrinsèque et de la localisation uniforme. Les orbitales localisées résultantes sont en bon accord avec les formules suggérées par Linnett.