Hartree Fock instabilities in the S4N 4 2+ dication

The HF singlet stability of the S₄N ₄ ²⁺ dication is investigated. At the experimental bond length, R _SN=1.545 Å, the D _4h solution is stable but at 2.00 Å a C _2v broken symmetry solution is of lower energy. Population analysis shows that C _2v solution has a nitrogen -hole on one of the unique nitrogens. The sulphur -hole (found for the anion S₃N ₃ ^– at this distance) is not a local minimum.     

Eight- and 16-membered cyanuric-sulfanuric ring systems: C2N4S2-->C2N3S ring contraction

Eight- and 16-membered cyanuric-sulfanuric ring systems of the type Ar2C2N4S2(O)2Ar'2 (3a, Ar = 4-BrC6H4, Ar' = Ph; 3b, Ar = 4-CF3C6H4, Ar' = Ph; 3c, Ar = 4-CF3C6H4, Ar' = 4-CH3C6H4) and Ar4C4N8S4(O)4Ar'4 (4b, Ar = 4-CF3C6H4, Ar' = Ph; 4c, Ar = 4-CH3C6H4, Ar' = Ph; 4d, Ar = 4-CF3C6H4, Ar' = 4-CH3C6H4), respectively, were prepared in good yields by the reaction of the corresponding sulfur(IV) systems with m-chloroperbenzoic acid. The X-ray structures of 3b, 3c.C7H14, 4b.CH2Cl2, 4c, and the S(IV) system Ar4C4N8S4Ar'4 (2c, Ar = 4-CH3C6H4, Ar' = Ph) were determined. Upon oxidation the two oxygen atoms in 3b and 3c.C7H14 adopt endo positions leading to a twist boat conformation for the C2N4S2 ring. The 16-membered C4N8S4 rings in 4b and 4c retain a cradle conformation upon oxidation. The S-N bond distances are ca. 0.06 A shorter in all the S(VI) systems compared to those in the corresponding S(IV) rings. The thermolysis of 3b at ca. 220 degrees C occurs primarily via loss of a sulfanuric group, NS(O)Ph, to give the six-membered ring (4-CF3C6H4)2C2N3S(O)Ph (6). The structure of 6 was confirmed by X-ray crystallography. Crystal data: 2c, triclinic, space group P1 with a = 13.917(2) A, b = 15.610(4) A, c = 13.491(3) A, alpha = 95.77(2) degrees, beta = 114.82(1) degrees, gamma = 76.21(2) degrees, V = 2583(1) A3, and Z = 2; 3b, monoclinic, space group P2(1)/a with a = 7.316(2) A, b = 29.508(5) A, c = 12.910(2) A, beta = 101.30(2) degrees, V = 2733(1) A3, and Z = 4; 3c.C7H14, triclinic, space group P1 with a = 12.849(4) A, b = 12.863(4) A, c = 12.610(7) A, alpha = 110.61(3) degrees, beta = 105.77(3) degrees, gamma = 62.77(2) degrees, V = 1719(1) A3, and Z = 2; 4b.CH2Cl2, triclinic, space group P1 with a = 12.647(3) A, b = 19.137(3) A, c = 12.550(2) A, alpha = 105.765(11) degrees, beta = 93.610(15) degrees, gamma = 88.877(16) degrees, V = 2917.2(9) A3, and Z = 2; 4c, orthorhombic, space group Pba2 with a = 22.657(2) A, b = 10.570(2) A, c = 10.664(3) A, alpha = beta = gamma = 90 degrees, V = 2554(1) A3, and Z = 2; 6, triclinic, space group P1 with a = 7.4667(8) A, b = 11.3406(12) A, c = 13.5470(14) A, alpha = 108.000(2) degrees, beta = 105.796(2) degrees, gamma = 94.300(2) degrees, V = 1033.8(2) A3, and Z = 2.     

Coupled Hartree Fock calculation of static dipole polarizabilities and shielding factors of open shell systems

Static dipole polarizabilities and shielding factors for the 2p open shell atomic systems are presented using coupled Hartree Fock theory in the framework of the Roothaan formalism. Calculations have been performed for the ground as well as for some valence excited states. A variational approach has been adopted for the determination of the first-order perturbed functions. The results are compared with those obtained from the correlated calculations and other techniques. The shielding factor values are in excellent agreement with the theoretical N/Z ratio.     

Hartree–Fock High-Precision Analytical Functions of Open-Shell Atoms

The algorithm of high-precision optimization of basis functions suggested previously for calculating the analytical Hartree–Fock orbitals of closed-shell atoms is generalized to open-shell systems described by the Roothaan method (1960). Expressions for the first (free gradient) and second (Hesse matrix) derivatives of the system's energy with respect to the nonlinear parameters (orbital exponents) of the basis functions are derived in terms of density matrices for the filled and open shells. An algorithm is proposed for high-precision optimization of the nonlinear parameters using these equations based on Murtagh–Sargent and Newton minimization procedures. To illustrate the application of this algorithm, we give optimization of the basis sets of Slater type functions for atoms from the second row, as well as for Al, Si, P, K, Sc, and Fe atoms. The analytical Hartree–Fock orbitals giving nearly Hartree–Fock energies are calculated with a high degree of accuracy.     

The restriction of spin contamination in unrestricted Hartree Fock wave functions

A method is developed to study in detail the contaminating spin components in UHF calculations for free radicals. Applications are made to those cases previously reported in which normal parametrisation of PPP UHF calculations lead to values of S ² which increase on annihilation of the contaminating quartet component.

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Zusammenfassung Es wird eine Methode entwickelt, um detaillierte Untersuchungen der bindenden Spinkomponenten in UHF-Rechnungen für freie Radikale zu ermöglichen. Es werden Anwendungen für solche Fälle, über die schon früher einmal berichtet wurde, durchgeführt, bei denen die normale Parametrisierung von PPP-UHF-Rechnungen zu Werten von S ² führte, welche die Vernichtung der bindenden Quartettkomponente anwachsen lassen.

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Résumé Développement d'une méthode pour étudier en détail les composantes de spin étrangères dans les calculs UHF des radicaux libres. On l'applique aux cas précédemment considérés dans lesquels des calculs UHF avec paramétrisation PPP conduisent à des valeurs de S² qui croissent lorsque l'on annule la composante quartet.

     

Analytical Hartree–Fock gradients with respect to the cell parameter: systems periodic in one and two dimensions

Analytical Hartree–Fock gradients with respect to the cell parameter have been implemented in the electronic structure code CRYSTAL, for the case of one- and two-dimensional periodicity. As in most molecular codes, Gaussian type orbitals are used to express the wavefunction. Examples demonstrate that the gradients have a good.     

Analytical Hartree–Fock gradients with respect to the cell parameter for systems periodic in three dimensions

Analytical Hartree–Fock gradients with respect to the cell parameter have been implemented in the electronic structure code CRYSTAL, for the case of three-dimensional periodicity. The code is based on Gaussian-type orbitals, and the summation of the Coulomb energy is performed with the Ewald method. It is shown that a high accuracy of the cell gradient can be achieved.     

On the calculation of bonding energies by the Hartree Fock Slater method

A transition state method has been proposed for the calculation of bonding energies and bond distances within the Hartree Fock Slater Method. Calculations on a number of diatomic molecules and a few transition metal complexes show better agreement with experiment than corresponding Hartree Fock results. The proposed transition state method gives a direct connection between bond orders and bonding energies.     

Metal complexes of sulfur-nitrogen chelating agents. Part 12. The chemistry of nickel(II), palladium(II), cobalt(II) and copper(II) complexes of N2S2 and N3S2 donor systems

Summary Nickel(II), palladium(II), cobalt(II) and copper(II) complexes of the ligandN,N-1,2-propane-bis(methyl 2-amino-cyclopent-1-ene-dithiocarboxylate) (H₂L¹),N,N-1,3-propane-bis(methyl 2-aminocyclopent-1-ene-dithiocarboxylate) (H₂L²) andN,N-[bis(methyl 2-aminocyclopent-1-ene-dithiocarboxylate)] diethylenetriamine (H₂L³) have been synthesised. Both H₂L¹ and H₂L² form complexes of the type ML, and all but the copper(II) complexes, are square planar. In the copper(II) complexes tetrahedral distortion is significantly more with CuL². From H₂L³ square planar complexes of the type [M(HL³)X] (M=Ni, X=Cl, Br, I or SCN; M=Pd, X=Cl or Br) have been obtained in which the donor unit involved is N₂SX. The composition of the cobalt(II) and copper(II) complexes is [M(H₂L³)X₂] (X=Cl or Br) which contain the chromophore [MN₃X₂].     

Near Hartree Fock wave function and computed molecular properties of methinophosphide,HCP

A near Hartree Fock wave function for HCP has been calculated within the RHF approximation, using a large STO basis set and this is compared with geometry optimisation calculations using a polarised double zeta basis. The population analysis indicates a C≡P bond, and various one electron properties have been computed and compared with the limited experimental data.     

Towards a complete basis set limit of Hartree–Fock method: correlation-consistent versus polarized-consistent basis sets

In this paper the convergence pattern of correlation-consistent (cc-pVxZ) and polarized-consistent (PC-n) hierarchies relative to the complete basis set limit have been considered in a small set of diatomic molecules. Using the sequence of these basis sets it was demonstrated that potential energy surfaces derived from basis-set-dependent solution of the Hartree–Fock equations achieves the exact numerical derived potential energy surfaces (PESs) in an ordered manner. So it was possible to compute the spectroscopic parameters in the complete basis set limit with considerable accuracy using the most extended members of both hierarchies. On the other hand, for the first time the detailed convergence patterns of total energies in three separate inter-nuclear distances have been considered in these molecules and it was demonstrated that the total energies arrive at microhartree accuracy at a considerable rate. Possible performance of extrapolation schemes is discussed and it was demonstrated that reliable extrapolation procedures indeed exist. A successful test of the proposed extrapolation method, using the three most extended members of polarized-consistent basis sets, has been accomplished on selected polyatomic molecules.     

Combined Open Shell Hartree–Fock Theory of Atomic–Molecular and Nuclear Systems

In this study, the combined Hartree–Fock (HF) and Hartree–Fock–Roothaan equations are derived for multideterminantal single configuration states with any number of open shells of atoms, molecules and nuclei. It is shown that the postulated orbital-dependent energy and Fock operators are invariant to the unitary transformation of orbitals. This new methodology is based entirely on the spin-restricted HF theory. As an application of combined open shell theory of atomic–molecular and nuclear systems presented in this paper, we have solved Hartree–Fock–Roothaan equations for the ground state of electronic configuration C(1s ²2s ²2p ²) using Slater type orbitals as a basis.     

Ab initio Hartree—Fock calculations of model polyacetylene chains using a Christoffersen basis set

Ab initio crystal orbital calculations using a Christoffersen basis set have been performed on the relative stabilities of model polyacetylene chains. Results indicate the all-trans isomer as the most stable. Among the cis structures, the cis-transoid backbone is very slightly preferred to the trans-cisoid backbone.     

The performance of the Hartree–Fock–Wigner correlation model for light diatomic molecules

Results of the Hartree–Fock–Wigner correla- tion model for diatomic molecules with light atoms (H₂, LiH, Li₂, F₂, He₂, Ne₂) using two different atomic parametrizations and one molecular parametrization of the correlation kernel are presented and interpreted in terms of Wigner intracules as well as differences thereof. The molecular parametrization yields encouraging results for simple systems exhibiting covalent or ionic bonding. However, similar to the purely atomic parametrizations severe overestimations of the attractive interaction in van der Waals systems is observed. It is argued that the remaining shortcommings partly result from the restriction of the currently used correlation kernel to be symmetric in relative position and relative momentum.     

The calculation of electron localization and delocalization indices at the Hartree–Fock, density functional and post-Hartree–Fock levels of theory

 Localization, λ(A), and delocalization indices, δ(A,B), as defined in the atoms in molecules theory, are a convenient tool for the analysis of molecular electronic structure from an electron-pair perspective. These indices can be calculated at any level of theory, provided that first- and second-order electron densities are available. In particular, calculations at the Hartree–Fock (HF) and configuration interaction (CI) levels have been previously reported for many molecules. However, λ(A) and δ(A,B) cannot be calculated exactly in the framework of Kohn–Sham (KS) density functional theory (DFT), where the electron-pair density is not defined. As a practical workaround, one can derive a HF-like electron-pair density from the KS orbitals and calculate approximate localization and delocalization indices at the DFT level. Recently, several calculations using this approach have been reported. Here we present HF, CI and approximate DFT calculations of λ(A) and δ(A,B) values for a number of molecules. Furthermore, we also perform approximate CI calculations using the HF formalism to obtain the electron-pair density. In general, the approximate DFT and CI results are closer to the HF results than to the CI ones. Indeed, the approximate calculations take into account Coulomb electron correlation effects on the first-order electron density but not on the electron-pair density. In summary, approximate DFT and CI localization and delocalization indices are easy to calculate and can be useful in the analysis of molecular electronic structure; however, one should take into account that this approximation increases systematically the delocalization between covalently bonded atoms, with respect to the exact CI results. Received: 13 February 2002 / Accepted: 24 April 2002 / Published online: 18 June 2002     

S(N)2 ring opening of beta-lactones: an alternative to catalytic asymmetric conjugate additions

Merging catalytic asymmetric acyl halide-aldehyde cyclocondensation (AAC) reactions with ensuing Grignard-mediated ring opening of the derived enantiomerically enriched beta-lactones is presented as a generally useful asymmetric synthesis of beta-disubstituted carboxylic acids. Enantiomerically enriched beta-lactones are subject to efficient S(N)2 ring opening with a variety of copper-modified alkyl Grignard reagents, including highly branched nucleophiles. Considerable structural variation in the lactone electrophile is also tolerated. Phenyl- and vinyl-derived organometallics are not efficient nucleophiles for the ring-opening reactions.     

Application of second-order SCF perturbation theory to the solution of time-dependent Hartree—Fock equations

The self-consistent field based theory of frequency-independent hyperpolarizabilities is adapted to the treatment of the corresponding frequency-dependent quantities. Explicit expressions are given for the double and null frequency polarizations of a molecule in a long-established oscillating electric field.     

The instabilities of the Hartree–Fock solutions and the lattice instabilities for conjugated hydrocarbons: The bond-order and bond-length alternations

The instabilities, especially the singlet instabilities, of the conventional Hartree–Fock (HF ) solutions for a variety of alternant and nonalternant hydrocarbons, some of which have been known to show lattice instabilities (bond-length alterations), are examined. The HF solutions for nonalternant hydrocarbons in the pentalene series larger than heptalene and [4n + 2]-annulenes larger than C₂₂H₂₂ are found to be singlet unstable and there appear new solutions lower in energy than the conventional HF solutions and characterized by charge-density waves exhibiting bond-order alterations. It is found that such symmetry-breaking solutions are energetically further stabilized by distorting the nuclear framework so that it may match up with the distribution of bond-order matrix elements of the charge-density wave, which means that in conjugated systems the singlet instability of the HF solution is always accompanied with the lattice instability. Further, it is shown that in conjugated systems, even when the HF solution is singlet stable, if it is not sufficiently stable as, for example, in pentalene and heptalene, there is every possibility for the occurrence of lattice instability. It is also shown that the singlet instability as well as the lattice instability arises from the existence of a sufficiently low-lying singlet excited state.