Generalized open shell SCF theory

A generalized form of the coupling operator technique in SCF theory has been developed. In the formalism presented here, the monoconfigurational problem may be treated as a particular case of the multiconfigurational framework. The matrix form of the operators has been analyzed; in the LCAO context a structure has been found which is very adequate for computational purposes. Some examples are also presented which show the usefulness of the theory, emphasising the CNDO and INDO approximations. Within the application of the method to ab initio calculations, some He and second row atoms states have been studied. The He first excited singlet is also studied, the result of the analysis of such a problem being that the nonorthogonality between the singlet functions of the fundamental and of the first excited states play a primordial role in the efficiency of the method. In no case have the calculation problems, appearing in the application of the theory, been of a more difficult nature than those normally found in the application of the formalism for closed shells.     

Restricted open shell Hartree-Fock theory

A new formula is introduced for the energy expectation value of multi-determinantal single configuration states with arbitrary open shells in terms of the 4-indexed electronic repulsion integrals. Applying the variational principle to this expression and introducing 2-indexed Coulomb and exchange operators, new forms of Hartree-Fock and Hartree-Fock-Roothaan equations for open shell systems are obtained. They are based entirely on the restricted Hartree-Fock formalism.     

Density matrix in the open shell theory

All the second-order density matrix spin components for the spin-projected Slater determinant are presented as expansions in direct products of powers of unprojected spin- and residual electron density matrices. Spin components of the second-order transition density matrices between spin-projected Slater determinants built of orthogonal orbitals are also obtained.     

Alternative implementation of the unitary group approach to the atomic shell theory

Subduction coefficients adapted to the group chain, which appeared in Racah's treatment of fⁿ configurations, are defined and calculated in the unitary group approach. The coefficients are then utilized to construct successively adapted term functions and evaluate other interesting coefficients. In addition the simplified expressions for the Coulomb and spin-orbit operators are obtained in terms of generators.     

The origin of energy functional in Roothaan open shell SCF theory

Different methods of averaging of energy over the states of electronic configurations γ^N (n_γ = 1, 2, 3 and N = 1, 2, …, 2n_γ ? 1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (VCC ) in energy functionals for various states as well as for average values of energy are presented. It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations t^N (N = 2–4) and e² there exist states for which VCC are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such “non-Roothaan” terms and peculiarities of its calculation by the restricted Hartree–Fock method are discussed.     

Trifluoroacetyl as an orthogonal protecting group for guanidines

The trifluoroacetyl moiety has been used as a new protecting group for guanidine functionality. The protecting group is easily cleaved under mild basic conditions and is complementary to the Boc, Cbz, and Ddpe protecting groups. The protecting group can be applied to peptide synthesis in solution as well as on a solid phase as it is orthogonal to a Boc and Cbz strategy and semiorthogonal to an Fmoc strategy.     

A self-consistent variation-perturbation theory for open shell atomic systems: Calculation of polarizabilities and shielding factors

In this paper a fully coupled variation-perturbation theory has been introduced for handling open-shell atomic systems in the presence of static perturbations. The static dipolar and quadrupolar polarizabilities and shielding factors for Li, Be⁺, B²⁺, B, C⁺, Na and Al have been calculated and compared with available results. Important sources of discrepancies in previous calculations of shielding factors have been noticed and critically examined. The dipolar shielding factors calculated in this paper show satisfactory agreement with the theoretical N/Z ratio. In the absence of any theoretical test for the quadrupolar shielding factor, the accuracy of the calculations of γ_∞, should be judged in the light of the accuracy of the corresponding β∞ values.     

Hydrogen adsorption on model adsorbents from the viewpoint of the theory of volumetric filling of micropores

Hydrogen adsorption on model microporous adsorbents with slit-shaped pores was calculated on the basis of Dubinin’s theory of volumetric filling of micropores using the property of linearity of adsorption isosters. Model adsorbents with micropore widths of 0.5, 0.9, and 1.2 nm obtained by the successive exclusion of one, two, and three layers of hexagonal carbon in the crystalline lattice of graphite were used. Hydrogen adsorption was calculated in the structures with single-layer and two-layer carbon walls at temperatures 20, 33, 77, 200, 300, and 400 K and pressures up to 20 MPa. The maximal hydrogen desorption for the AU structure (1:3) with the pressure drop from 20 to 0.1 MPa was 8 wt.% at 200K. The parameters of the porous adsorbent structure were calculated.     

Kohn's theory of the insulating state: a quantum-chemistry viewpoint

The qualitative difference between insulators and conductors not only manifests itself in the excitation spectra but also--according to Kohn's theory [Phys. Rev. 133, A171 (1964)]--in a different organization of the electrons in their ground state: the wave function is localized in insulators and delocalized in conductors. Such localization, however, is hidden in a rather subtle way in the many-body wave function. The theory has been substantially revisited and extended in modern times, invariably within a periodic-boundary-condition framework, i.e., ideally addressing an infinite condensed system. Here we show how the localization/delocalization of the many-body wave function shows up when considering either three-dimensional clusters of increasing size or quasi-one-dimensional systems (linear polymers, nanotubes, and nanowires) of increasing length, within the ordinary "open" boundary conditions adopted for finite systems. We also show that the theory, when specialized to uncorrelated wave functions, has a very close relationship with Boy's theory of localization [Rev. Mod. Phys. 32, 296 (1960)]: the Boys orbitals in the bulk of the sample behave in a qualitatively different way in insulating versus conducting cases.     

Sources of error in open shell Hartree-Fock calculations

It is demonstrated that single eigenvalue methods for solving open shell Hartree-Fock equations can give an energy that is not invariant to a unitary transformation of the orbitals. This is discussed with reference to potential curves for polyatomic molecules.     

On the theory for closed shell intermolecular forces

The electron gas model of Gordon and Kim is applied to the interaction of inert gases with a hydrogen molecule. Comparison of the isotropic potential wells with available experimental data shows clearly that modification of the exchange potential along the lines suggested by Rae produces greatly improved agreement when simple power series representations of the dispersion energy are included.     

Synthesis of the putative minimal FGF binding motif heparan sulfate trisaccharides by an orthogonal protecting group strategy

The synthesis of two trisaccharides, the putative minimal heparan sulfate sequences responsible for binding to acidic and basic fibroblast growth factors, respectively, is described from a common protected intermediate using an orthogonal protecting group strategy.     

An iterative process to calculate the SCF open shell orbitals

A method is described for calculating SCF open shell orbitals. In comparison with the coupling operator method, a greater velocity of convergency of the iterative process is obtained by taking into account not only the correct variational conditions, but also the best variations of orbitals step by step.     

Role of coupling operators on open shell RHF equations

We have derived the expressions for the extremum condition of E, corresponding to any wave function. These expressions are given as a function of the spin orbitals. We have carried out the derivation considering the spin orbitals as vectors belonging to an orthonormal basis. The corresponding variational equations have been derived introducing the condition that the norm of the wave function is constant, as the only additional constraint.From the expression obtained for the first variation of the matrix elements of H, as a function of the spin orbitals, we have derived the RHF equations for a simple case.In the present procedure, the couplings between orbitals of different shells appear directly, being defined explicitly, and they may be taken as corresponding with the elements of a Hermitian matrix.The calculations that we have carried out show that the coupling operators defined in the paper give results which are variationally correct.