Attempts to introduce overlap and exchange into a purely general study of interatomic or intermolecular long‐range forces lead to complicated, physically opaque expressions for the interaction energy. A study is made...
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Attempts to introduce overlap and exchange into a purely general study of interatomic or intermolecular long‐range forces lead to complicated, physically opaque expressions for the interaction energy. A study is made of a most simple system, two hydrogen atoms at large distances, taking overlap and exchange rigorously into account. This system is especially interesting due to the failure of the Heitler—London wavefunction to describe adequately the lowest‐triplet (3Σ u +)—lowest‐singlet (1Σ g +) separation at very large distances. A formal study separates the interaction energy into a ``generalized dispersion'' and ``generalized exchange—correlation'' energy. A many‐configuration calculation performed at an internuclear distance of 8 a.u. shows that, whereas certain configurations yield the well‐known dispersion energy, other configurations, particularly those of the excited charge‐transfer type, correct for the erroneous triplet—singlet separation. This distinction reflects the introduction of two distinct types of correlation effects which are investigated in terms of the two‐electron distribution function.
The adiabatic correction C to the Born-Oppenheimer approximation is calculated for H2, HD, LiH, LiD, HCl, DC with self-consistent-field and configuration interaction wavefunctions of varying qualities. The effect of c...
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Atomic and molecular energies depend strongly on the correlation in the motions of electrons. Their complexity necessitates the treatment of a chemical system in terms of small groups of electrons and their interactio...
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Atomic and molecular energies depend strongly on the correlation in the motions of electrons. Their complexity necessitates the treatment of a chemical system in terms of small groups of electrons and their interactions, but this must be done in a way consistent with the exclusion principle. To this end, a nondegenerate many-electron system is treated here by a generalized second-order perturbation method based on the classification of all the Slater determinants formed from a complete one-electron basis set. The correlation energy of the system is broken down into the energies of pairs of electrons including exchange. Also some nonpairwise additive terms arise which represent the effect of the other electrons on the energy of a correlating pair because of the Pauli exclusion principle. All energy components are written in approximate but closed forms involving only the initially occupied H.F. Orbitals. Then each term acquires a simple physical interpretation and becomes adoptable for semiempirical usage. The treat-ment is applied in detail to two particular problems: (a) The correlation energy between an outer electron in any excited state and the core electrons, e.g., in the Li atom, is represented by a potential acting on the outer one. This potential can be regarded as the mean square fluctuation of the Hartree-Fock potential of the core, and applies even when the outer electron penetrates into the core. The magnitudes of some of the correlation effects are calculated for Li. (b) Starting from a complete one-electron basis set of SCF MO's, the energy of a molecule is separated into those of groups of electrons and of infra-molecular dispersion forces acting between the groups. The assumptions that are usually made in discussing dispersion forces at such short distances are then removed and generally applicable formulas are given. Some three or more electron-correlation effects and limitations in the use of "many electron group functions" for overlapping systems
We revise formal and numerical aspects of collinear and noncollinear density functional theory (DFT) in the context of a two-component self-consistent treatment of spin-orbit coupling (SOC). While the extension of the...
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We revise formal and numerical aspects of collinear and noncollinear density functional theory (DFT) in the context of a two-component self-consistent treatment of spin-orbit coupling (SOC). While the extension of the standard one-component theory to a noncollinear magnetization is formally well-defined within the local density approximation, and therefore results in a numerically stable theory, this is not the case within the generalized gradient approximation (GGA). Previously reported formulations of noncollinear DFT based on GGA exchange-correlation potentials have several limitations: (i) they fail at reducing (either formally or numerically) to the proper collinear limit (i.e., when the magnetization is parallel or antiparallel to the z axis everywhere in space); (ii) they fail at ensuring a quantitative rotational invariance of the total energy and even a qualitative rotational invariance of the spatial distribution of the magnetization when a SOC operator is included in the Hamiltonian; (iii) they are numerically very unstable in regions of small magnetization. All of the above-mentioned problems are here shown (both formally and through test examples) to be solved by using instead a new formulation of noncollinear DFT for GGA functionals, which we call the "signed canonical" theory, as combined with an effective screening algorithm for unstable terms of the exchange-correlation potential in regions of small magnetization. All methods are implemented in the CRYSTAL program and tests are performed on simple molecules to compare the different formulations of noncollinear DFT.
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