An interative scheme for electronic systems using one-electron green's functions

In this paper an iterative generalization of the minimum principle proposed for electronic systems by Hall, Hyslop, and Rees is investigated. It is shown that this generalization still retains the advantage of using members of a larger class of trial wave-functions, for example those with discontinuities, as initial approximations to the wave-functions. This scheme has the advantage that, at each stage of iteration, an upper bound is obtained which is at least as good as that obtained previously. The theory is first applied to the hydrogen atom. It is then adapted to estimate the Hartree–Fock energy of the helium atom, the Hartree–Fock limit being obtained after a relatively small number of iterations.     

Inclusion of 3d orbitals in calculations involving second row atoms

Valence-state ionisation potentials, I , and non-empirical one-centre electron repulsion integrals are evaluated for the separate 3s, 3p and 3d orbitals of Na, Mg, Al, Si, P, S, and Cl. These parameters are for use in the application of the CNDO SCMO method to molecules containing second row atoms.

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Zusammenfassung Die Ionisierungspotentiale des Valenzzustands, I und die nicht-empirischen Ein-Zentren-Elektronen-Absto\ungsintegrale werden für die 3s-, 3p- und 3d-Orbitale von Na, Mg, Al, Si, P, S und Cl angegeben. Diese Parameter werden bei der Anwendung der CNDO-SCMO-Methode auf Moleküle, die Atome der zweiten Reihe enthalten, benötigt.

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Résumé On détermine les potentiels d'ionisation de l'état de valence I et les intégrales de répulsion monocentriques pour les orbitales 3s, 3p, 3d de Na, Mg, Al, Si, P, S et Cl. Ces paramètres sont utilisés dans l'application de la méthode CNDO SCMO à des molécules contenant des atomes de la seconde colonne.

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We thank the S.R.C. for a maintenance grant (to K.A.L.).     

A mixed basis set of slater and gaussian functions for molecular calculations

A procedure for using simultaneously Slater and Gaussian basis functions in molecular calculations is presented here. The analytic expressions of the integral prototypes involving both Slater and Gaussian functions are explicitly derived.     

The use of single exponential orbitals in one-center molecular orbital calculations

Single-exponential Slater type orbitals of the form ψ₁ = (1 + L₁(r, θ) + L₂(r, θ) +…?+ L_n(r, θ)) exp (? αr) are examined for their potential use as one-center molecular orbitals. These are then to be used as molecular fragments in a LCMO study. The system examined is HeH^{+ +} with calculated energies and dipole moments being compared to the exact values. These functions behave best in the region of chemical interest (the bonding region) and thus demonstrate a possible usefulness in LCMO calculations and in the field of one-electron diatomics.     

Evaluation of two-center overlap integrals using slater type orbitals in terms of bessel type orbitals

Using the definition of STOs in terms of BTOs, we have presented analytical formula for two-center overlap integrals. The obtained formula contains generalized binomial coefficients and Mulliken integrals A_k and B_k. Taking into account the recent advances on the efficient calculation of Mulliken integrals (Harris, Int. J. Quantum Chem., 100 (2004) 142), we have obtained many more satisfactory results for two-center overlap integrals, for arbitrary quantum numbers, scaling parameters, and location of atomic orbitals.PACS No: 31.15.+qAMS Subject Classification: 81V55, 81–08     

The use of population localised orbitals to interpret molecular orbital calculations

An efficient and general method is derived to calculate population localised molecular orbitals (LMO's) from a given SCF eigenvector matrix, by reduction to an eigenvalue problem. Applications to both localised molecules (NH₃ and C₂H₂) and delocalised ones (B₂H₆, C₆H₆ and butadiene) are discussed in some detail. It is shown that unequal occupation of atomic energy levels leads to non-orthogonal LMO's. The consequences of non-orthogonal atomic hybrid orbitals are discussed, formulas for their overlap in terms of atomic occupation numbers are derived and it is shown that the occupation numbers are connected to LMO atomic orbital coefficients by various sum rules.     

On the nature of unrestricted orbitals in variational active space wave functions

Active space coupled cluster methods exhibit unusual, nonsmooth spin symmetry-breaking behavior where the unrestricted minimum lies higher in energy at short bond distances and crosses below the restricted solution at longer distances. The restricted solution is also observed to be a stable minimum slightly beyond the symmetry-breaking point. This behavior arises due to differences in the optimal active spaces defining the restricted and unrestricted wave functions and results in unrestricted wave functions that are not strictly size consistent. We suggest a new, size-consistent model that allows the orbitals to break spin symmetry only within the active space.     

On the use of UHF orbitals in ionization energy calculations

The UHF Hamiltonian and simple Löwdin-like annihilators are formulated in the second quantization formalism. The so formulated Hamiltonian was employed in many-body Rayleigh-Schrödinger perturbation theory to evaluate the corrections to the UHF orbital energies.     

Improved partition–expansion of two‐center distributions involving slater functions

The calculation of the electronic structure of large systems is facilitated by the substitution of the two‐center distributions by their projections on auxiliary basis sets of one‐center functions. An alternative is the partition–expansion method in which one first decides what part of the distribution is assigned to each center, and next expands each part in spherical harmonics times radial factors. The method is exact, requires neither auxiliary basis sets nor projections, and can be applied to Gaussian and Slater basis sets. Two improvements in the partition–expansion method for Slater functions are reported: general expressions valid for arbitrary quantum numbers are derived and the efficiency of the procedure is increased giving analytical solutions to integrals previously computed by numerical quadrature. The efficiency of the new version is assessed in several molecules and the advantages over the projection methods are pointed out. © 2013 Wiley Periodicals, Inc.     

Gaussian expansions of hydrogenic functions involving few variational parameters

Fully optimized lengthy Gaussian expansions of hydrogenic 1s and 2p_z functions have been practically reproduced by generating the variational parameters by means of suitably chosen functions involving only few parameters. Hydrogenic 3d_xy and 4f_xyz functions have been approximated in a similar way. The usefulness of such generating functions is briefly discussed.     

On the use of symmetry-adapted crystalline orbitals in SCF-LCAO periodic calculations. I. The construction of the symmetrized orbitals

A computational procedure for generating space-symmetry-adapted Bloch functions (BF) is presented. The case is discussed when BF are built from a basis of local functions (atomic orbitals [AOs]). The method, which is completely general in the sense that it applies to any space group and AOs of any quantum number, is based on the diagonalization of Dirac characters. For its implementation, it does not require as an input character tables or related data, since this information is automatically generated starting from the space group symbol and the AO basis set. Formal aspects of the method, not available in textbooks, are discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 299–309, 1998     

On expectation value calculations of one-electron properties using the coupled cluster wave functions

The ability of various approximate coupled cluster (CC) methods to provide accurate first-order one-electron properties calculated as expectation values is theoretically analysed and computationally examined for BH and CO. For actual calculations the infinite number of terms of the expectation value expansion (O=¦exp (T ⁺)O exp (T)¦_c) was truncated so that T ₁ T ₂, T ₃, and (1/2) T ₂T₂ clusters were retained on both sides of O. The role of individual clusters is carefully discussed. Inclusion of T ₁, is unavoidable, but if triples are essential in the energy evaluation, they may play an even more important role in the property expansion, as shown in the case of CO. It is shown that the CC wave function, which is exact to second order, effectively satisfies the Hellmann-Feynman theorem.