Correlated Orbitals for the Ground State of Heliumlike Systems

Roothaan, C. C. J.; Weiss, A. W.

doi:10.1103/revmodphys.32.194

Cited by 263 publications

(119 citation statements)

References 17 publications

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“…Table 4 and Fig. 8 compare the LYP, G 2 (s) and G 3 (s) estimates (using HF-limit wavefunctions) with the exact values 54 for nuclear charges 1 r Z r 10. It is clear that, whereas LYP is over-sensitive to Z, the G n (s) models are almost independent of it, perhaps reflecting an intrinsic deficiency of the action-only ansatz (3.50).…”

Section: Atomic Resultsmentioning

confidence: 99%

A family of intracules, a conjecture and the electron correlation problem

Gill

Crittenden

O’Neill

et al. 2006

Phys. Chem. Chem. Phys.

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We present a radical approach to the calculation of electron correlation energies. Unlike conventional methods based on Hartree-Fock or density functional theory, it is based on the twoelectron phase-space information in the Omega intracule, a three-dimensional function derived from the Wigner distribution. Our formula for the correlation energy is isomorphic to the Hartree-Fock energy expression but requires a new type of four-index integral. Preliminary results, obtained using a model that is based on the known correlation energies of small atoms, are encouraging.

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Section: Atomic Resultsmentioning

confidence: 99%

A family of intracules, a conjecture and the electron correlation problem

Gill

Crittenden

O’Neill

et al. 2006

Phys. Chem. Chem. Phys.

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“…If we introduce electron correlation into the wavefunction explicitly (2), our calculation becomes much more difficult.…”

Section: Generalized Valence Bond Pair Energiesmentioning

confidence: 99%

“…(VGVB XACT= V11 + V22 + J12 -(V)EXAcT [2] where V, J, K, and S refer to nuclear attraction, coulomb, exchange, and overlap integrals respectively. The plus and minus signs refer to singlet and triplet states and we have assumed normalization of the orbitals.…”

Section: Generalized Valence Bond Pair Energiesmentioning

confidence: 99%

The Pairwise Correlated Generalized Valence Bond Model of Electronic Structure I; The Estimation of Pair Energies from Orbital Overlaps

Petersson

1974

Proc. Natl. Acad. Sci. U.S.A.

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A new method for the accurate a priori calculation of atomic and molecular energies is proposed. The The description of the electronic structure of atoms and molecules in terms of one electron orbitals provides a simple and therefore useful starting point for any more detailed theory. The energy obtained from calculations based upon orbitals is generally in error by about 0.015 au (10 kcal/ mole) * for each electron. Although these errors comprise a small fraction of the total energy, they are quite large by chemical standards. It is, therefore, necessary to go beyond an orbital picture to obtain a chemically adequate description of electronic structure.The errors inherent in an orbital model can be accounted for in terms of the correlated motion of the electron pairs (1). The novel feature of the new method is that the correlation correction is determined in an a priori fashion directly from the orbitals. This allows us to treat much larger systems than we could by calculating correlation energies using an ab initio variational approach, but maintains our ability to predict these correlation energies as functions of molecular geometry. The latter is absolutely necessary if we are to examine potential energy surfaces for chemical reactions. It is with an eye towards the study of transition states and reaction pathways that the new method has been developed. GENERALIZED VALENCE BOND PAIR ENERGIESIf we introduce electron correlation into the wavefunction explicitly (2), our calculation becomes much more difficult.If we use configuration interaction (3), the wavefunction is no longer easy to interpret. We shall, therefore, follow Sinanoglu (1), and express the total energy as the sum of the energy resulting from an orbital calculation, plus a sum of pair energies. Since we want the orbital pair energies to include only the effects of real dynamic electron correlation, (4) In order to picture the general behavior of GVB electron pair correlation energies, let us consider two hydrogen atoms, A and B, at large separation (Fig. la). The electron repulsion is RB and is not altered -by electron correlation (if we ignore the small Van Der Waals attraction). As we bring the two atoms closer together, the charge distributions begin to overlap (Fig. lb). The electron repulsion is now RAB plus an additional term arising from the overlapping of the two charge distributions where r12 is very small. It is this additional term that is removed by electron correlation. In the correlated wavefunction, only one electron will occupy this region at a time. Hence, the correlation energy is determined by the overlapping of the two charge distributions, rather than by the total electron repulsion. This is-true not only for the large bond lengths we have considered above, but also for the

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“…Since a bAl(Tu) orbital is occupied, the asymptotic fragments would be H + H -with Li+ for electrical neutrality. The correlation energy [15] for H-is only a little less than that for H2 and the usual large asymptotic correlation error is avoided. For H2 separations less than about 1.5 a. u. the correlation energy in the Hz pair should be comparable for the A" BI, and B2 state s. At R(H -H) = 2.5 a.u.…”

mentioning

confidence: 99%

Interaction energy surfaces for Li(22S) and Li (22P) with H2

Krauß¹

1968

J. RES. NATL. BUR. STAN. SECT. A.

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Interac tion e ne rgy surfaces for the inte rac tion of Li(2'S) a nd Li(2' P) with H, a re ca lcul ated us in g ap proxlll~a t e Hart~ee-Fo c k tn al fun ctIOns. Th e c ross lll g of e nergy c urves is obse rv ed for C' v conformatIon s If th e H, Inte rnucl ea r dIsta nce IS s uffi cle ntl:, la rge. No c ross in g is obse rved for co lin ea r co l-" ss lO ns for a ny H, d ista nce.Th e w av~ functio n of the stron gly a ttrac tiv e sta te involved in th e c rossin g is re la ted to th e me tastabl e negatIv e-Ion sta tes that a re postulated to account for reso na nt elec tron-molec ule scalle rin g. S uc h a c harge-tra nsfe r state ca n on ly be bound for C'v co nformatio ns for th e H, mol ec ul e. The lik e lih ood a nd geome try of th e c ro ss ing co mpl exes for othe r molecul es inte ractin g with alk ali s is di sc ussed in te rm s of the form a tIOn of th ese reso nan ce c harge· tran sfer sta tes.Key Word s: Ene rgy surface; Li(2'S); Li (2' P); H,(X ll;); Hartree-Foc k; e nergy tran sfer; reso na nce state : c harge-tran sfe r.

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Correlated Orbitals for the Ground State of Heliumlike Systems

Cited by 263 publications

References 17 publications

A family of intracules, a conjecture and the electron correlation problem

A family of intracules, a conjecture and the electron correlation problem

The Pairwise Correlated Generalized Valence Bond Model of Electronic Structure I; The Estimation of Pair Energies from Orbital Overlaps

Interaction energy surfaces for Li(22S) and Li (22P) with H2

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