An investigation of the reliability of the Galerkin-Petrov method with a special study of the helium atom ground state

A convergence characterization of the Galerkin-Petrov method by means of quantities characterizing pairs of subspaces is presented. The usefulness of our approach for setting up reliable computational schemes is demonstrated for the He atom ground state. Several methods of constructing pairs of subspaces for use in quantum chemistry are suggested.     

An investigation of the reliability of the Galerkin-Petrov method

The Galerkin-Petrov method is applied to the determination of the ground state energy of the beryllium atom. The basis set of the coordinate subspace consists of correlated wavefunctions of the combined configuration-interaction-Hylleraas type. The basis set of the projective subspace is of the configuration-interaction type. The usefulness of a previously proposed way of characterization of pairs of subspaces has been further confirmed. Experience in constructing close pairs of subspaces gathered in the case of two-electron systems is used for the larger system. Two methods for constructing pairs of subspaces are used in the calculations.     

A least-squares method applied to the hydrogen molecule

A least-squares approach is proposed to remedy some of the weaknesses of the method of moments. It is shown by an application to the hydrogen molecule that the least-squares procedure yields reliable results in cases where the method of moments fails. The prediction of equilibrium internuclear distances by the least-squares method is also found to be more reliable than the corresponding results obtained by the method of moments.     

Fourier representation method for electronic structures of linear polymers

The Fourier representation method described in the previous paper of this series is used to make electronic structure calculations for a linear chain of equally spaced hydrogen atoms. The electronic wavefunction is assumed to be a determinant of doubly-occupied crystal orbitals of modulated-plane-wave type, built from one 1s Slater-type orbital of screening parameter ζ centered on each atom. The energy is calculated from the electrostatic zero-order Hamiltonian with exact evaluation of all Coulomb and exchange contributions, and is optimized with respect to the lattice spacing and ζ value. Good agreement with work by others is noted, indicating a near-equivalence of modulated-plane-wave and tight-binding wavefunctions for this half-filled-valence-band system. The linear chain is calculated to be far more stable than cubic three-dimensional hydrogen crystals. This fact sheds light on the unusually large calculated nearest-neighbor distances in the cubic crystals, and is related to a suggestion that under certain conditions the most stable structure for solid atomic hydrogen may be of lower symmetry than cubic. The previous paper of this series: Harris, F. E.: J. Chem. Phys.56, 4422 (1972) [1]. Chargé de Recherches du F.N.R.S. (Fonds National Belge de la Recherche Scientifique).     

Molecular orbital calculations on the conformation of polypeptides and proteins

Quantum mechanical calculations using the PCILO method have been performed on the tripeptide model CH₃CO-X-Y-NHCH₃. Competition between C₅, C₇, C₁₀ rings and open structures has been investigated through mapping of the whole {φ, Ψ} conformational space and energy minimization. From these results, it appears that the C₁₀ ring simulating the folding named U-turn, involving a hydrogen bond between the i...i + 3 residues, is the most probable structure although not the most stable in energy. The results are used for predicting the frequency of U-turns in proteins, α-chymotrypsin is given as an example.     

Magnetic susceptibility of the BH molecule

The coupled Hartree-Fock (CHF) perturbation approach and its extension to multiconfiguration wavefunctions (MC CHF scheme) were used to calculate the magnetic susceptibility of the BH molecule. The results obtained for an SCF and two pair-excitation MC SCF functions confirm the paramagnetism of the BH molecule and indicate a rather weak dependence of the computed molecular susceptibility on the correlation effects. Sponsored by the Institute of Low Temperatures and Structure Research, Polish Academy of Sciences.     

Determination of molecular properties by the method of moments

Some precautions needed in the choice of weight functions when calculating wave functions by the method of moments are analysed. It appears that an important criterion for good weight functions is that the difference between the total and the truncated overlaps (both defined in the paper) be high.The method of moments is applied to wave functions involving Hylleraas-type correlation factors using weight functions made up of products of single-particle orbitals. The aim of the calculations is partly to test the criteria for good weight functions, partly a preparation of more extended calculations of a similar type.The new name of the institute is: Computer Application Research and Development Center of the Chemical Industries.     

A quantum-mechanical study of the interaction of glyoxal with guanine

A quantum molecular study by the SCFab initio method of the interaction of glyoxal with guanine provides for the formation of a stable covalent adduct in which the glyoxal fragment forms a complementary cyclic ring attached to the imino N₁ and amino N₂ atoms of guanine with the concomitant migration of the N-bonded H atoms to the oxygens of glyoxal. The reaction should proceed in two steps. The most plausible mechanism involves as the first step the interaction of a carbonyl group of glyoxal with the amino group of guanine followed by a similar interaction at the imino group of guanine, rather than the reverse order of interactions. The respective energy barriers are 49.7 and 63.9 kcal/mole. The intermediate product is also more stable when the adduct occurs first at N₂:30.7 kcal/mole versus 17.9 kcal/mole for the adduct at N₁.     

Spectra-structure relationships in the near ultraviolet optical activity of chiral barbituric acid derivatives

The chiroptical properties associated with then-π^* (singlet-singlet) transitions in dissymmetric barbituric acid derivatives are examined on the basis of two theoretical models. The lower singlet excited states of unsubstituted and alkyl substituted barbituric acids are calculated on the semi-empirical CNDO/S-CI molecular orbital model, and the spectroscopic properties associated with transitions to these states are computed. In the structures we examined, threen-π^* transitions are found at λ>220 nm, two of which are nearly degenerate. Each of these transitions is computed to be strongly magnetic dipole allowed and to be forbidden or very weak (depending upon the exact symmetry and geometry of the trioxopyrimidine moiety) in electric dipole radiation. Contributions from chiral distortions within the trioxopyrimidine chromophoric system to the rotatory strengths of the three lowest energyn-π^* transitions are calculated directly from wave functions obtained by the CNDO/S-CI method. Contributions to then-π^* rotatory strengths arising from “vicinal” interactions between the trioxopyrimidine chromophore and asymmetric substituent groups are calculated by a perturbation method based on an independent systems representation of the optically active compounds. Various spectra-structure relationships are considered and correlations between experimental data and theoretically calculated results are examined.     

Polarization functions for gaussian basis sets for the first row atoms

Exponent optimization was performed for a single set ofd-type Gaussians on the first row atoms C, N, and O in fifteen small molecules. The hydrogenp-exponents were kept at the fixed value of 1.0. For the underlying valence shell basis sets, Dunning's double zeta basis sets were used. Standard exponents of polarization functions are suggested for the most common valence states of the C, N, and O atoms.     

Electronic states of the NiCu molecule determined byab initio Hartree-Fock and configuration interaction methods

The interaction between a Ni atom and a Cu atom in the configurations (3d)⁹(4s)¹ and (3d)¹⁰(4s)¹, respectively, has been calculated usingab initio Hartree-Fock and configuration interaction methods. The chemical bond between the two atoms is due to a bonding 4sσ molecular orbital. Equilibrium distances, dissociation energies and vibrational frequencies are predicted for the low-lying states. Finally the influence of spin-orbit coupling on the low-lying states is considered.     

Determination of molecular properties by the method of moments

Basic principles of a possibility of simplifying the unrestricted spin-projected Hartree-Fock equations by means of the method of moments are outlined.     

On the contribution of higher-order excitations to correlation energies: The ground state of the water molecule

Using the results of a configuration interaction calculation reported by Rosenberg and Shavitt, we derive an approximation to the correlation energy which may be associated with the sum to infinite order of all linked diagrams involving singly- and doubly-excited states. This result is compared with that obtained by calculation of the energy through third-order. The fourth-order linked diagrams involving quadruply-excited states are computed. It is shown that there is a considerable degree of cancellation between the fourth-order linked diagram energy terms involving doubly-excited intermediate states only and those which contain quadruply-excited states.     

Molecular orbital theory of the electronic structures of one-dimensional molecular crystals

A non-empirical tight-binding LCAO SCF MO treatment of one-dimensional molecular crystals based on the SCF perturbation theory is presented. The simpler version of this method at the level of the CNDO/2 approximation is also given.     

The two-electron integral transformation and two-body density matrix transformation

Ann ⁵ algorithm for the transformation of quantum-mechanical four centre functions is presented in a form best suited for computers having a virtual memory capability. Part of the work to be submitted for the degree of Ph. D. in the University of Newcastle-upon-Tyne.     

A new interpretation of Hund's first rule

The diagonal elements of the first and second order spinless density matrices have been calculated for the lowest excited¹ P and³ P terms of Be, B⁺ and C⁺⁺ using wavefunctions at different levels of approximations published in the literature. The analysis of these functions has resulted in a new interpretation of Hund's first rule in terms of an anisotropic screening effect.     

The Jahn-Teller effect in icosahedral molecules and complexes

The adiabatic potential surface for icosahedral systems having three-, four- and five-fold degenerate orbital states interacting with five-fold degenerate vibrations (T-v,U-v andV-v problems) is investigated. It is shown that for theT-v andV-v Jahn-Teller cases the potential surface possesses respectively a two- or three-dimensional equipotential continuum of minima. For theU-v problem the potential surface contains 15 equivalent minima. The nature of the extremum points on the adiabatic potential surfaces is elucidated. In the linear approximation to theV-v problem in the minima points the lowest potential surface is double degenerate due to the accidental occurrence of axial symmetry.     

Behandlung der Strukturen 3 atomiger Dublett- und Triplett-Radikale auf der Grundlage von Slater-Exponenten

The sequence of the atoms M, Q, and R in neutral triatomic radicals of formula MQR is discussed in terms of the Slater-exponent (Z-s)/n ^* of the atoms involved. It is shown that the atom with the relatively smallest numerical value of (Z-s)/n ^* occupies the central position. This result is supplemented by Walsh's rule (linearity or nonlinearity of the radicals under consideration) and vice versa.

     

Comment on the recent controversy over the theory of chirality functions

Derflinger,et al., have criticized the concept of qualitative completeness on the grounds that a chirality function may be qualitatively complete and still vanish identically for certain nonracemic, non-isomeric mixtures. It is pointed out that the functions considered by them are ones in which the full chirality function splits into parts which can be thought of as contributions from “effective fragments” of the molecule, and that their mixtures are indeed racemic in these fragments. The function can be augmented in a very simple way so as not to vanish for such mixtures, and the idea of qualitative completeness is in no way disturbed by this process.     

Conformation of ethylene glycol: Isometric group,ab initio study of internal H bonding and ir-matrix spectra of the species CH2OHCH2OH,CD2OHCD2OH and CH2ODCH2OD

The isometric group of a semirigid model of the ethylene glycol molecule with 3 internal degrees of freedom is derived. Results of extensiveab initio computation of the electronic potential function with a Gaussian lobe basis set are presented from which two differentr _e conformations are predicted. Both feature one single internal H bond in which one of the lone electron pairs of the acceptor O atom is involved. Symmetry sets of isometricr _e-conformations and of transition points of the potential function are discussed. Infrared matrix spectra of glycol and 2 deuterated modifications are presented and discussed on the basis of two internally bonded conformations predicted byab initio calculations. Dedicated to Prof. H. Hartmann on the occasion of his 60th birthday.