Self-consistent Perturbation Theory Research Articles

New self-consistent many-body perturbation theory: Application to the Hubbard model

A new many-body theory perturbationally consistent to all orders of the perturbation is presented and applied to the Hubbard problem as an example. Use is made of the recent Kim and Wilson commutator projection operator to derive the Dyson equation for the one-particle Green's function and an exact set of coupled differential equations for the damping or self-energy term which are solved self-consistently. The Hubbard $I$ result follows in our first approximation and the Esterling-Lange (EL)-type result in the second. Since we keep the hopping finite throughout the calculation, no degeneracy problem is encountered as in EL.

Self-consistent perturbation theory of diamagnetism

An ab initio gauge-invariant molecular orbital theory is developed for nuclear magnetic shielding. The molecular orbitals are written as linear combinations of gauge-invariant atomic orbitals, the wavefunctions in the presence of a uniform external magnetic field being determined by self-consistent field perturbation theory. The final magnetic shielding result is broken up into contributions which can be related to various features of electronic structure. Calculated magnetic shielding constants are presented using three sets of atomic orbitals, all of which are taken as contracted gaussian-type functions. The first two sets are minimal and the third is slightly extended. All three levels of theory give good descriptions of shielding at first row and hydrogen atoms. Carbon and hydrogen chemical shifts calculated at the extended level are in excellent agreement with experimental values.

Self-consistent perturbation theory calculations of nuclear spin coupling constants in thiophenes

The ring proton-proton coupling constants of thiophene and 14 monosubstituted derivatives have been calculated using the perturbated SCF INDO method. The results reproduce satisfactorily signs, magnitudes and some trends of the experimental values, but the internal order of long-range constants in the 3-substituted thiophenes is not reflected.

Erratum: Self-consistent perturbation theory of nuclear spin-coupling constants: Application to couplings involving fluorine

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Calculations of hydrogen—fluorine and fluorine—fluorine nuclear magnetic spinspin coupling anisotropies for fluorinated ethenes and benzenes oriented in liqiud crystal solvents

Spinspin coupling tensors are calculated using self-consistent perturbation theory and INDO wavefunctions, in order to estimate whether neglect of their anisotropy influences molecular dimensions deduced from the NMR spectra of partially oriented solutes. It is found that anisotropy of cis and trans and many aromatic HF couplings can be neglected but that trans FF couplings are markedly anisotropic. Comparisons are made with the limited experimental results.

Application of SCF-perturbation theory to hydrogen bonding in water dimers

The usefulness of Self-consistent perturbation theory and of a variation perturbation treatment both in semiempirical form (CNDO/2) is tested by application to hydrogen bonding in water dimers. The results are comparable to variational calculations. A splitting of the total energy in various components provides insight into the nature of hydrogen bonding.

Analysis of ketene cycloadditions by self-consistent perturbation theory

Analysis of ketene cycloadditions by self-consistent perturbation theory

Vicinal fluorine nuclear coupling constants in fluoroethanes: self-consistent perturbation theory calculations

Values of vicinal fluorine nuclear coupling constants for the stable rotamers of (CH 2F) 2, CHF 2, CH 2F, (CHF 2) 2 and CF 3. CH 2F are obtained from the first-order self-consistent perturbation theory equation with the INDO molecular orbital approximations. A clear distinction is found between gauche and trans values. A comparison with experimental values for similar compounds is made.

Molecular-Orbital Theory for Infinite Systems: Self-Consistent Field Perturbation Treatment of Hydrogen-Bonded Molecules

A self-consistent field perturbation theory of intermolecular interactions is introduced with a view to its application to the study of hydrogen-bonded molecular crystals. A numerical perturbation scheme is also introduced that permits a very detailed numerical check to be made on both the perturbation equations and the corresponding computer program. From a numerical study of the (HF)2 and (HCN)2 systems it is shown that, if taken to the third order, the perturbation method yields dimerization energies and changes in charge densities to within 7% of the values obtained by direct calculations. Structural data calculated from perturbation theory are still more accurate.

Theoretical Studies of Solvent Effects on Nuclear Spin—Spin Coupling Constants. II A Cubic Closest Packed Cluster Model

A theoretical study of the solvent dependence of nuclear spin—spin coupling constants is presented in terms of a model which assumes a cubic closest packed cluster in which six solvent molecules are arranged around the solute molecule. This model is described theoretically by means of a group function modification of self-consistent perturbation theory. Calculations for individual molecular groups were performed by the semiempirical INDO (intermediate neglect of differential overlap) approximation of self-consistent-field molecular orbital theory. Intermolecular integrals associated with solute and solvent molecules were evaluated theoretically. This model provides some improvement over the previous theoretical study in this series, which was based on the reaction field model. The improvement can be attributed to the inclusion of electrostatic effects arising from the real charge distributions of the solvent molecules, especially those which are perpendicular to the solute dipole moment axis. A most important result is the good agreement found for the solvent dependence of the geminal H–H coupling constant in formaldehyde, as the reaction field results for this case were of the wrong sign. The calculated solvent dependence of the coupling constants of 1, 1-difluoroethylene in solvents of almost identical dielectric constant exhibits a greater range of values than either the experimental values or the reaction field results. On this basis, it is concluded that the cluster model is too specific and that improvement in the theoretical description of this phenomenon will incorporate rotational effects associated with the solvent molecules.

Self-Consistent Perturbation Theory of Nuclear Spin-Coupling Constants: Application to Couplings Involving Carbon and Fluorine

A self-consistent perturbation theory is presented which permits efficient calculation of the contact, orbital, and dipolar contributions to nuclear spin coupling. The theory is applied with the INDO molecular orbital method to a number of couplings involving carbon and fluorine. The usually neglected orbital and dipolar terms are found to be very important in FF and CF coupling, and the orbital interaction plays a significant role in certain CC couplings. Generally good agreement is obtained between theory and experiment with the exception that the incorrect sign is obtained for cis JFF. The value of JCF in difluoroacetic acid is predicted to be − 235 Hz.

Theoretical Studies of Solvent Effects on Nuclear Spin–Spin Coupling Constants. I. The Reaction Field Model

A theoretical study of the solvent dependence of nuclear spin–spin coupling constants is presented in terms of Onsager's reaction field model and self-consistent perturbation theory in the semiempirical INDO (intermediate neglect of differential overlap) approximation of self-consistent-field molecular orbital theory. A possible mechanism for reaction field induced changes in coupling constants is discussed in terms of the sum over virtual orbital method, corresponding to the uncoupled Hartree–Fock approximation. Although the latter method does not give satisfactory values for coupling constants, the reaction field induced shifts are reasonable. Finite perturbation theory, which corresponds to the coupled Hartree–Fock approximation, gives much better coupling constant results. Calculated reaction field induced shifts for a variety of H–H and H–F coupling constants are compared with the experimental results in a variety of solvents. Although the calculated results are linear functions for very large values of the reaction field, best agreement with experiment is obtained in solvents of low dielectric constant. The importance of solute dipole orientation in a series of fluoroethylenes is investigated.

Theoretical studies of solvent effects on nuclear spin-spin coupling constants

A theoretical study is presented of the effects of solvent molecular motion on nuclear spin-spin coupling constants. Solvent molecules are treated as point dipoles arranged around the solute molecule in a cubic closest packed arrangement. Average dipole moment vectors are given by a rotational Boltzmann average and the resulting perturbation is included in the Fock matrices. Calculations of nuclear spin-spin coupling constants were performed by self-consistent perturbation theory in the INDO (intermediate neglect of differential overlap) approximation of self-consistent-field molecular orbital theory. Calculated results are compared with the experimental data as well as the results of previous models.

Self-consistent perturbation theory for interacting electron systems

The self-consistent perturbation theory of the preceding paper is simplified for the use in semi-empirical valence-shell SCF calculations. The validity and limitations of the procedure are tested for the combination of two methylene moieties to ethylene by comparing the numerical results of the perturbation treatment with valence-shell calculations of elongated ethylene. The application to the cycloaddition of the unconjugated dienophile cyclopropene to cyclopentadiene yields qualitative and quantitative information about the factors determining the stereochemical course of such additions, a hitherto poorly understood aspect of the Diels-Alder reaction.

Bond length dependence of the nuclear magnetic shielding of the hydrogen molecule

Self-consistent perturbation theory has been used to obtain the components of the nuclear magnetic shielding tensor of the hydrogen molecule at several values of the internuclear distance. A basis set consisting of 1s and 2p atomic orbitals on each atom was chosen for the ground state. The perturbing magnetic field was allowed to mix in two perpendicular 2p orbitals on each atom. The origin of the vector potential of the field was taken at the bond mid-point. The results show that the nuclear shielding for the field parallel or perpendicular to the bond diminishes as the bond length increases. Furthermore, the shielding with the field along the bond is greater than when the field is perpendicular to the bond, for all the bond lengths dealt with. The shielding anisotropy reaches its maximum at 0·9 A.U.

Time-dependent self-consistent perturbation theory and applications to molecules

Time-dependent self-consistent perturbation theory and applications to molecules

Self-consistent perturbation theory for interacting electron systems

A general self-consistent perturbation formalism is developed for two interacting closed-shell molecules. The zero-order many-electron wavefunction of the coupled system is represented by an antisymmetrized product of the mutually orthogonal single-determinant wavefunctions of the constituent parts. The method involves the application of perturbation theory directly to the Fock-Dirac density matrix and thus avoids the calculation of perturbed orbitals. Self-consistency to first order is maintained by an iterative determination of the matrix elements of the Hartree-Fock perturbation operator. Explicit expressions are given for the matrix elements of the one-electron and two-electron perturbations and for the energy changes to first and second order.

Removing the Divergence at the Kondo Temperature by Means of Self-Consistent Perturbation Theory

Removing the Divergence at the Kondo Temperature by Means of Self-Consistent Perturbation Theory

Optimum parametrization in SCF π-electron theory

An attempt has been made to obtain ground-state charge distributions (as reflected by proton and carbon-13 magnetic shielding constants), ionization potentials, and pi-electron excitation energies for a number of substituted benzenes. A standard SCF-LCAO-MO method was employed, with the total-spin-differential overlap approximation. Excitation energies were obtained by the method of configuration interaction using all singly-excited configurations. Approximations were introduced so that only two parameters had to be specified for each atom. Since the two-centre repulsion integrals introduced by Mataga gave the best results for benzene, they were used throughout. Heteroatom parameters were chosen empirically, with the help of McWeeny's self-consistent perturbation theory, to give the best overall results for monosubstituted compounds. In general the calculated results were very reasonable.

Effects of Off-Diagonal Randomness in the Tight-Binding Model of Random Binary Alloys: Weak-Coupling Limit

The single-band tight-binding model of random binary alloys is studied in the limit of second-order self-consistent perturbation theory, allowing the off-diagonal, as well as the diagonal, matrix elements of the model Hamiltonian to be dependent upon alloy composition. Fluctuations of both types of matrix elements about their configurational averages are assumed to be small but comparable, so that the randomness introduced into both parts of the Hamiltonian must be treated on an equal footing. Only nearest-neighbor hopping between constituent atoms (type $A$ or $B$) is considered, with the hopping integrals parametrized by the three numbers $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\gamma}$ for $A\ensuremath{-}A$, $B\ensuremath{-}B$, and $A\ensuremath{-}B$ hopping, respectively. The single-particle alloy spectrum and the alloy density of states are obtained from an equation for the effective single-particle self-energy using standard techniques and with the dependence on model parameters explicitly displayed. With the assumption that $\ensuremath{\gamma}=\frac{1}{2}(\ensuremath{\alpha}+\ensuremath{\beta})$, the theory is found to be rather simply characterized by the wave-vector-dependent displace ment ${E}_{A}(\mathrm{k})\ensuremath{-}{E}_{B}(\mathrm{k})$ of the pure constituent spectra ${E}_{A}(\mathrm{k})$ and ${E}_{B}(\mathrm{k})$.