Unrestricted Hartree-Fock Solutions Research Articles

Toward a magnetic description of metals in terms of interstitial molecular orbitals. II. One-dimensional infinite system: The lithium chain.

Using the unrestricted Hartree-Fock (UHF) version of the ab initio crystal computer program, the ferromagnetic HF solution is obtained for a one-dimensional chain of Li atoms. This solution is much lower in energy than the restricted Hartree-Fock solution for the singlet state and is built of bond-centered singly occupied monoelectronic functions. The lowest UHF solution is even much lower in energy and consists of an antiferromagnetic spin-density wave, i.e., a spin alternation on bond-centered singly occupied monoelectronic functions. These results support the validity of the interstitial picture of simple metals, as recently suggested by McAdon and Goddard. The delocalization between the interstices (here bonds) is weak and may be treated through a distance dependent Heisenberg Hamiltonian, whose parameters are extracted from the previous UHF solutions. The final estimate of the cohesive energy and bond distance are compared to the results of various density-functional methods.

Optimization of Initial State Vectorin the Ground State Algorithmof Lattice Fermion Simulations

Quantum simulation algorithm for the lattice fermions in the ground state is examined. Initial trial state is optimized using the unrestricted Hartree Fock solution. Convergence to the ground state average in the projection process is compared among several choices of the trial state. The optimized trial state provides a faster convergence for physical quantities as well as a better minus sign ratio in the sampling.

Potential nonrigidity of the NO3 radical

The equilibrium geometry and vertical excitation energies of the nitrate radical (NO3) have been determined at the coupled-cluster singles and doubles level. Unlike most previous theoretical methods used to study this problem, the present calculations circumvent the difficulties associated with symmetry-broken orbitals by using a reference function composed of orbitals obtained in a closed-shell self-consistent field (SCF) calculation for the NO3 anion. Although these orbitals do not satisfy the SCF equations for NO3 itself, they turn out to be more suitable for the correlation problem in the neutral molecule than the unrestricted Hartree–Fock solution for NO3. Nevertheless, our calculations agree with most previous studies in predicting that the high-symmetry D3h structure of NO3 is not a minimum on the potential energy surface. The potential near the D3h point is relatively flat and has seven stationary points: three (equivalent) C2v minima with one long and two short N–O bonds; three (equivalent) C2v transition states with two long and one short N–O bonds; and the D3h structure, which is unstable with respect to the in-plane degenerate mode (e′) and is consequently a saddle point of index two. Exchange of the oxygen positions via pseudorotation around the D3h stationary point is predicted to be an extremely facile process with a barrier height of ≊190 cm−1, suggesting that the molecule may be spectroscopically nonrigid, belonging to a molecule symmetry group which is isomorphic with D3h, as observed experimentally. Excitation energies are calculated for both the D3h structure and points on the pseudorotation pathway, in order to predict differences between values obtained from photodetachment spectroscopy of the NO3 anion and those determined by direct excitation of NO3.

Electron transfer due to through-bond interactions. Study of aliphatic chains

The electron transfer capability of systems of the type H 2H-(CH 2) n -NH 2 is studied using ab initio and semi-empirical methods. The coupling energy Δ between the nitrogen lone-pairs may, in the symmetric case, be defined as the energy difference between the symmetric and antisymmetric many-particle states of H 2N-(CH 2) n -NH 2 + where ionization has occurred in the lone-pair orbitals. Δ may be related to the energy splitting between the corresponding orbital energies in the neutral molecule according to Koopmans' theorem. A “broken-symmetry” correction (BSC) both in space and spin is introduced. The two localized unrestricted Hartree-Fock solutions are subject to configuration interaction using transformation to “corresponding orbitals”. In saturated chains H 2N-(CH 2) n -NH 2 +, the lowering of |Δ| amounts to about 25%. Ab initio and semi-empirical results show the same trends in the contributions to Δ. In cases when different contributions cancel, the relative difference may be large. The conformation dependence is studied. For the case of sp 3 lone-pairs, Δ is reduced for the cis case to a small fraction of the trans value and in some cases the sign is changed. The largest Δ is obtained for the all-trans conformation.

Methods for finding unrestricted Hartree-Fock solutions and multiple solutions

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTMethods for finding unrestricted Hartree-Fock solutions and multiple solutionsPeter. Pulay and Rui Feng. LiuCite this: J. Phys. Chem. 1990, 94, 14, 5548–5551Publication Date (Print):July 1, 1990Publication History Published online1 May 2002Published inissue 1 July 1990https://doi.org/10.1021/j100377a026RIGHTS & PERMISSIONSArticle Views192Altmetric-Citations25LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (527 KB) Get e-Alerts

Toward a magnetic description of metals in terms of interstitial molecular orbitals: Exploiting the multiplicity of symmetry-broken Hartree-Fock solutions on small alkali-metal clusters.

For one-dimensional (1D), 2D, and 3D finite clusters of Li atoms, numerous symmetry-broken unrestricted Hartree-Fock (UHF) solutions are of lower energy than the symmetry-adapted one. The lowest solution provides, after a localizing unitary transform, a set of interstitial singly occupied molecular orbitals (MO's), each of them being essentially between a few atoms. These MO's are very similar to those obtained by McAdon and Goddard from more elaborate wave functions and support their proposal of a new picture of the electronic assembly in metallic clusters. In the lowest UHF solution the spins are distributed among the interstices in order to achieve the best spin alternation between neighboring interstices. Starting from these interstitial MO's, one may change the spin distribution and obtain other UHF solutions of (slightly) higher energy, the spacing of which is ruled by a Heisenberg Hamiltonian. On two ${\mathrm{Li}}_{6}$ clusters the exact MO--configuration-interaction wave function in the basis was projected on the subspace of these various UHF solutions; the norm of the projection is close to 1, and the projected eigenvector is the lowest eigenvector of a Heisenberg Hamiltonian. From the energies of the various interstitial UHF solutions, a Heisenberg Hamiltonian may be obtained at very low cost and its diagonalization provides a good approximation of the exact energy (in the basis set). This procedure will be used for infinite lattices in order to calculate cohesive energies.

Intrinsic and extrinsic disorder effects

The interplay between the electron correlation and the disorder has been investigated with an unrestricted Hartree-Fock solution. Change from localization caused by electron correlation to Anderson localization is demonstrated.

Group Theoretical Classification of Instabilities and Interconnection Relation of the Unrestricted Hartree-Fock Solutions in a Molecular System with a Spatial Point Symmetry. II: -- Special Cases; RHF, ASDW, TSDW and TSW --

Group Theoretical Classification of Instabilities and Interconnection Relation of the Unrestricted Hartree-Fock Solutions in a Molecular System with a Spatial Point Symmetry. II: -- Special Cases; RHF, ASDW, TSDW and TSW --

Group Theoretical Classification of Instabilities and Interconnection Relation of the Unrestricted Hartree-Fock Solutions in a Molecular System with a Spatial Point Symmetry. I: General Theory

This paper describes a general theory on classification of instabilities and interconnection relation between UHF solutions in a molecular systems with a spatial point symmetry. It is shown that an instability of a UHF solution is characterized by an irreducible single valued representation over the real number field (R-rep) of the invariance group of the UHF solution. The general expression of the instability matrix characterized by an R-rep is given. It is shown that the possible symmetry of a UHF solution bifurcating from an instability is determined by the R·rep which characterizes the instability. Some criterions are given to determine what subgroup of the original invariance group can be the invariance group of the solution produced by an instability belonging to an R-rep. A general procedure is given to obtain all R-reps of the invariance group of a UHF solution.

Studies on the Electronic Structures of Hydrocarbon Diradicals by the Unrestricted Hartree-Fock Theory

Abstract Electronic structures of low-lying states of cyclobutadiene, trimethylenemethane (2), and tetramethyleneethane (3) are studied by the unrestricted Hartree-Fock (UHF) theory. Characteristics of electronic correlations, called dynamical spin polarization effect, in these molecules are well described by corresponding orbitals and spin density structures of low-lying UHF solutions. The spin polarization of σ electrons is found to be relatively small but not negligible for quantitative discussion. The two low-lying singlet states of 2 are described by two UHF solutions with different spin density structures. The fact that the singlet UHF state of 3 lies a little below the triplet UHF state is explained by the difference in the spin polarization of the bonding π electrons between the singlet and triplet states. Two rules are given which predict the spin structure of low-lying UHF states and the spin multiplicity of ground states of hydrocarbon diradicals. These rules are applied to 1,1,2,3,3-pentamethylenepropane and 1,3-dimethylenecyclobutadiene, which confirms their validity.

Multiple projections of unrestricted Hartree-Fock solutions in acetylene

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Unrestricted Hartree—Fock Solutions for Closed-Shell Molecules

Unrestricted Hartree—Fock Solutions for Closed-Shell Molecules