Serafin Fraga

Self‐Consistent‐Field Theory. I. General Treatment

A general method is described for obtaining SCF orbitals for electronic systems without restriction on the number or the symmetry of open‐shell orbitals. A separation on the basis of symmetry designation is made at the beginning. The pseudo‐eigenvalue equations are obtained from the SCF equations by the introduction of a new form of coupling operator. The new equations must be solved individually for orbitals of a separate symmetry designation. Some examples are given.

Self‐Consistent‐Field Theory. II. The LCAO Approximation

In Part I of this series, eigenvalue equations which apply to any electronic system were developed by means of a general coupling operator. These equations are here adapted to the method of linear combinations of atomic orbitals. The resultant matrix equations are applied to the helium atom for the configurations: 1S, (1s)2; 3S, (1s) (2s); 1S, (1s) (2s), using Slater 1s and 2s orbitals as basis functions.

Hartree--Fock values of coupling constants, polarizabilities, susceptibilities, and radii for the neutral atoms, helium to nobelium

Abstract Presented here are the values, obtained with Hartree-Fock functions, for the spin-orbit, magnetic-dipole, and electric-quadrupole coupling constants, electric-dipole polarizabilities, magnetic susceptibilities, and atomic radii for the ground and some excited states of the neutral atoms from He to No.

Self‐Consistent‐Field Theory. IV. LCAO Approximation for Excited States

The pseudo‐eigenvalue equations previously obtained for any state of an electronic system are brought into the form required by the LCAO approximation. The matrix formulation involved is discussed and some practical methods for reducing the value of the maximum error of the evaluated energy are given.

Recognition of amino acids in solution

Abstract The basic solvation shells of all the amino acids, of use in the study of their recognition in aqueous solutions, are determined by means of a method based on the use of 1/R expansions parameterized on the basis of the results from accurate SCF calculations. The accuracy of the calculations is tested in a more extensive study of the solvation of glycine, for which the results of Monte Carlo calculations are reproduced.

Self‐Consistent‐Field Theory. III. General Treatment for Excited States

The general coupling operator defined in the first paper of this series is used, in conjunction with the modified variation method due to Weinstein and MacDonald, to formulate a general self‐consistent‐field scheme. In principle this permits the determination of the eigenfunctions and eigenvalues of any state of an electronic system with no restrictions on orbital occupancy, symmetry, or multiplicity. A tentative generalization of the concept of a Hartree—Fock function is given and the meaning of correlation energy, in the context of the modified variation method, is discussed.

Theoretical studies of protein structures: prediction of antigenic determinants

Abstract The determination of stable conformations of proteins by means of a 1/R formulation, developed previously at this laboratory for the study of molecular interactions, is discussed. The details of the method (and of the corresponding program) are presented and its practical applicability is examined on the basis of the results obtained for some chosen systems. This method may be used as an auxiliary tool, in conjunction with the results obtained from hydrophilicity-recognition profiles, for the theoretical prediction of the antigenic determinants of proteins.

ORBIT--ORBIT INTERACTION IN MANY-ELECTRON ATOMS.

The formulation of Wybourne and Jucys and co‐workers has been used for the evaluation of the orbit—orbit interaction (for pn configurations) and the corresponding parameters α, β, and δ (for dn configurations). Values are presented for positive ions, neutral atoms, and negative ions, and for a number of isoelectronic series.

Theoretical prediction of secondary structures of proteins using recognition factors

Abstract A knowledge of the secondary structure of a protein will aid in improving the theoretical prediction of its tertiary structure, at a considerably reduced cost in terms of computing time. It is shown in this work that the fragments of a protein may be predicted from the information contained in the recognition and flexibility profiles, constructed from the corresponding factors. The accuracy of the predictions for 88 proteins highlights the significance of the recognition factors of theoretical origin developed at this laboratory.

Complete orbit-orbit interaction in many-electron atoms

The complete spin-orbit coupling constants have been evaluated, including both the spin-own orbit and the spin-other orbit terms, for all the positive ions, neutral systems, and negative ions from He to Kr, as well as for various isoelectronic series.