Theoretical approach to fluorine substitution in X2NO and X2CN free radicals. Comparison between ab initio UHF and RHF + perturbation treatments

Non-empirical calculations have been performed to analyze the effects of fluorine substitution on the geometry and electronic properties of two series of π and σ radicals. Both UHF and RHF + perturbation methods have been used and the results are compared as a function of the basis set quality. As concerns geometry and spin-free electronic properties the results are independent of the UHF or RHF formalism, but highly sensitive to the basis set. The STO-3G basis is unable to reproduce even general trends. Polarization functions always play a relevant role and correlation effects seem not negligible at least for fluorine-containing radicals. The molecular shape of π radicals changes from a planar to a pyramidal geometry when increasing the electronegativity of the substituents. On the contrary, σ radicals always remain planar. Unprojected UHF spin densities are closer to the RHF + perturbation results for small spin contamination (X₂NO). On the contrary, it is the projected UHF spin density which is in better agreement with the RHF + perturbation value for large spin contamination (X₂CN). No simple correlation can be found between spin densities and gross atomic spin populations. For H₂NO the spin density at nitrogen is smaller than at the oxygen nucleus, but substitution may enhance or reverse this trend.     

Spin density distributions in radical anions of heterocyclic amine N-oxides

The unrestricted Hartree-Fock (UHF) method of Snyder and Amos is used to calculate, in the -electron approximation, the spin density distributions in radical anions of heterocyclic amine N-oxides. The computed spin densities are observed to be in good agreement with the experimental values. The computed spin density distribution of the radical anion of pyridine N-oxide is consistent with the greater susceptibility of pyridine N-oxide relative to pyridine to electrophilic nitration. Also, the calculations are consistent with the lower basicity of the N-oxides relative to the parent bases.     

Chirality and spin density: Ab initio and density functional approaches

The spin distribution in a stable nitroxide biradical that shows ferromagnetic interactions in the solid phase has been studied at three levels of theory: First, at the UHF level; then, including correlation effects in UMP 2 calculations; and finally, the results are compared with the spin density obtained using the local density functional (LDF ) approximation. It is shown that LDF spin densities are closer to UMP 2 than to UHF predictions; the difference between the UHF and the (UMP 2, LDF ) results points to a redistribution of the spin repartition between N and O due to electronic correlation. For planar conformations of the NO group, there is symmetric distribution (D_2d) of the spin density on the adamantane skeleton. For nonplanar nitroxides, the molecule is chiral (C₂), which results in a breakdown of the spin transmission on part of the adamantane cage. © 1993 John Wiley & Sons, Inc.     

Application of the independent electron pair approach to the calculation of excitation energies,ionization potentials,and electron affinities of first row atoms

Excitation energies, first ionization potentials and electron affinities of first row atoms are calculated with a spin-adapted independent electron pair approximation (IEPA) combined with the direct determination of pair natural orbitals (PNOs). To enable comparison with molecular calculations Gaussian basis sets are used which are small enough to be also applicable to molecules. IEPA results for the above mentioned properties are accurate to 0.1–0.3 eV which is almost one order of magnitude better than the corresponding SCF-results. The same accuracy can be expected for molecules in which a localization of the doubly and singly occupied orbitals is possible, for instance for small hydrides. This is supported by the results of calculations on carbon hydrides.     

Accuracy and limitations of the pseudopotential method

Molecular model potential calculations have been performed within the SCF approximation on nine di- and triatomic molecules from the first row of the periodic table. We compare the molecular constants with ab initio SCF values and with model potential results obtained by other authors. Our results are accurate to a few per cent. The three most significant approximations in molecular model potential theory are: 1) The molecular model potential is the sum of atomic model potentials; 2) The atomic model potential is energy-independent; 3) The electron interaction model operator is l/r ₁₂. We arrive at the following general conclusions concerning these approximations: 1) The first approximation does not hold for strongly ionic molecules and for some highly excited molecular states. 2) Approximations 2 and 3 cancel to a large extent in molecules as they do in atoms, except in the case where approximation 1 breaks down. 3) Although various model- and pseudo-potentials yield reasonable results for atoms, not all of them are suitable for molecular calculations.     

Band structure of nonclassical polymers

It is shown that fully conjugated alternant nonclassical polymers are comparatively stable systems as a result of the considerable delocalisation energy.The energy characteristics of the polymers are strongly determined by the electron spin distribution of the degenerate nonbonding molecular orbitals; the full spin configuration,S>0, is favoured. The spin densities depend on the electron correlation and alternate; this corresponds to a ferrimagnetic state of the polymer at 0°K.     

Applicability to atoms of a large set of correlation energy functinals

An extensive study of the application of a large set of correlation energy functionals to atomic systems is presented. Hartree–Fock densities and, sometimes, generalized-valence-bond wave functions are used. The functionals have been grouped into four sets: (I) local density and local spin density, (II) local spin density with self-interactioon correction, (III) local spin density with gradient correction, and (IV) methods found on the correlation factor approach. In this bench mark, we report the results of calculations made for the ground states of the first and second rows, their anions and cations, and the two- and four-isoelectronic series. © 1994 John Wiley & Sons, Inc.     

Model calculation of the spin density for trapped muonium in ionic solids

A previously developed perturbation formula for calculating the spin density of trapped normal muonium in diamond is applied to the trapped muonium in the ionic solids of MgO, KCl and KBr. To obtain an improved molecular electrostatic potential (MEP) inside the cubic lattice, we performed MO calculations using clusters of MgO, KCl and KBr with additional surrounding point charges. Calculated spin densities (ƒ-values) in these potentials are compared with experimental results. We also report ab initio UHF MO calculations for these clusters with a trapped hydrogen atom at the centre of the clusters.     

Ground state and excitational properties of atoms

We have carried out self-consistent electronic structure calculations on atoms, positive and negative ions and on X-ray transition energies by employing a generalized version of the Kohn-Sham theory which applies to anyN-electron eigenstate. This theory has recently been developed by Fritsche (Phys. Rev. B33, 3976 (1986)). As in the original Kohn-Sham version of density functional theory, it turns out that exchange and correlation can rigorously be described by a local energy-independent potential. The latter is in the present paper approximated by using correlation factors that have the form of a Gaussian or of a Lorentzian to the power 5/2. The width of these functions is determined via the familiar sum rule. We present results on atoms of the first three rows of the periodic table and on some heavier atoms. It is furthermore shown that the generalized Kohn-Sham theory can successfully be applied to multiplet states of free atoms. We discuss results on helium, carbon, oxygen and silicon. It may generally be stated that our approach yields a better overall agreement with the experimental data than any other approximation that has been used so far within density functional theory.     

Electronic properties of the low‐lying spin states of dimethylnitrosamine coordinated to Fe(III) heme models: An ab initio study

The unusual O‐coordination mode of nitrosamines to Fe(III) heme models has been observed in the bis(dimethylnitrosamine)(meso‐tetraphenylporphyrinate)iron(III) cation. For the first time, this latter as well as the simpler bis(dimethylnitrosamine)(porphinate)iron(III) heme model cations have been studied through ab initio methods. The sextet, quartet, and doublet spin states of both cations have been studied through single‐point calculations based on the experimental (X‐ray) geometry. Their energies, charges, and spin densities have been analyzed. The obtained results (at the UHF/cc‐pVDZ and ROHF/cc‐pVDZ levels) indicate that the peripheral benzene rings are of secondary importance for the coordination of dimethylnitrosamine to the Fe(III) porphyrin core. The obtained energy ordering is sextet < quartet < doublet, at all computational levels. The UHF, ROHF, and UMP2 results indicate an excess of alpha spin density around the Fe atom, a low covalency for the Fe? O bond and a substantial charge transfer to the Fe atom. Our best estimates [obtained at ROMP2 level with the mixed cc‐pVDZ/cc‐pVTZ‐DK(Fe) basis set] for the energy differences (in eV) between the three spin states considered are 0.929 for the sextet‐quartet gap and 0.812 for the quartet‐doublet gap, which indicate that the spin crossover (at room temperature) is very unlikely. These results represent the substantial decrease in the uncorrelated values. The implications of spin contaminations at the UHF and UMP2 levels for subsequent geometry optimizations to be performed in the smaller cation have also been discussed. © 2013 Wiley Periodicals, Inc.     

Roothaan INDO CI spin density calculation

Spin densities have been calculated by the Roothaan INDO CI method in the parametrization of Pople and Kaufman. The dependence of the spin densities on both the type and the number of configurations in CI has been followed. Results have been compared with the UHF and spin-projected UHF methods.     

Determination of one-centre core integrals from the average energies of atomic configurations

One-center core integrals for valence orbitals are determined from the experimental average energies of neutral atomic configurations from Li through Zn. These values are compared with those estimated from CNDO /1, “INDO /1”, CNDO /2, “INDO /2” and with theoretical values calculated from a pseudo-potential method. The agreement is good between values obtained from neutral atoms and from the psuedo-potential calculation except for the 3d orbitals of the transition elements where the theoretically calculated integrals over single ξ functions are not realistic. These two methods reproduce both term and average configuration energies for the first two rows of atoms; the semiempirical method reliably reproduces them for the third row. The CNDO /1 and INDO /1 methods underestimate atomic energies, while the CNDO /2 and INDO /2 procedures fail rather poorly. The propriety of using core integrals estimated semiempirically in molecular orbital calculations is discussed.     

Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar

Correlation consistent basis sets have been optimized for use with explicitly correlated F12 methods. The new sets, denoted cc-pVnZ-F12 (n=D,T,Q), are similar in size and construction to the standard aug-cc-pVnZ and aug-cc-pV(n+d)Z basis sets, but the new sets are shown in the present work to yield much improved convergence toward the complete basis set limit in MP2-F12/3C calculations on several small molecules involving elements of both the first and second row. For molecules containing only first row atoms, the smallest cc-pVDZ-F12 basis set consistently recovers nearly 99% of the MP2 valence correlation energy when combined with the MP2-F12/3C method. The convergence with basis set for molecules containing second row atoms is slower, but the new DZ basis set still recovers 97%-99% of the frozen core MP2 correlation energy. The accuracy of the new basis sets for relative energetics is demonstrated in benchmark calculations on a set of 15 chemical reactions.     

Combination of pseudopotentials and density functionals

Semilocal pseudopotentials have been determined for first–row (Li to Ne), second row (Na to Ar), and third-row atoms (K, Ca). Core–valence correlation is included by adjusting the pseudopotentials to experimental energies of ions with a single valence electron. Correlation within the valence shell is taken into account by using the spin–density functional formalism. The approximations involved in this approach are tested for atomic ionization energies as well as binding energies of monohydrides and alkali diatomics, agreement with experiment is usually satisfactory, but in certain applications density functionals should be already included in the fitting of the local part of the pseudopotential. In addition, 3s/3p and 3s/2p basis sets (for first and second row, respectively), designed for use in connection with our pseudopotentials, are given; it is shown that they yield reasonable results for both SCF and correlation energies.     

Enumeration of internal rotation reactions and their reaction graphs

Threefold and twofold internal rotation reactions and their reaction graphs are enumerated using the generalized wreath product method developed by the author in an earlier paper. The correspondence between reaction directed graphs (digraphs) and finite topologies on isomers is established. It is shown that the reaction digraphs can be represented by Borel fields. Atropisomerism in polyphenyl compounds is discussed. Applications to spontaneous generation of optical activity and NMR spectroscopy are considered. Borel fields are enumerated by bumping squares of the upper rows of Young diagrams starting from the Young diagram containing just one row.     

Some electronic properties of TMPD,CA and TCNQ molecules and their mono- and diions

Semiempirical RHF and UHF PPP calculations have been performed on three molecules involved in charge transfer systems. The same set of parameters has been used for the three ionic states of each molecule. Particular attention has been given to the choice of both number and type of configurations taken into account in the Cl treatment following the RHF SCF calculation; it is shown that they have a great influence on the results. Calculations carried out for several experimental molecular geometries showed that their influence is not always negligible. Experimental data have been collected in a critical way. The unique set of parameters gives satisfactory results for the optical spectra of the neutral molecules and monoions but gives a poor agreement for diions. Spin densities appeared to be very sensitive to both the methods of calculations and the variation of parameters.     

Electronic structure and magnetic properties of the PO32− radical: A molecular-orbital study

Spin-polarized and non-spin-polarized molecular-orbital MS Xα calculations have been performed for the radical PO₃^2?31P and ¹⁷O magentics hyperfine tensors are determined together with the spin densities in the different orbitals of these tow atoms. The results are in good agreement with the experimental values. It is shown that ≈ 20% of the Fermi contact coupling is due to inner-shell polarization.     

A comparison of different DODS methods when the number of electrons increases

We have performed RHF , UHF , UHF with subsequent spin projection, and EHF calculations for the π-electrons of some polyene chains of different lengths in order to investigate the relations among these methods when the number of electrons increases. Special attention is paid to the importance of spin projection for different energetic quantities.