Evaluation of integrals over STOs on different centers and the complementary convergence characteristics of ellipsoidal‐coordinate and zeta‐function expansions

One‐electron integrals over three centers and two‐electron integrals over two centers, involving Slater‐type orbitals (STOs), can be evaluated using either an infinite expansion for 1/r₁₂ within an ellipsoidal‐coordinate system or by employing a one‐center expansion in spherical‐harmonic and zeta‐function products. It is shown that the convergence characteristics of both methods are complimentary and that they must both be used if STOs are to be used as basis functions in ab initio calculations. To date, reports dealing with STO integration strategies have dealt exclusively with one method or the other. While the ellipsoidal method is faster, it does not always converge to a satisfactory degree of precision. The zeta‐function method, however, offers reliability at the expense of speed. Both procedures are described and the results of some sample calculation presented. Possible applications for the procedures are also discussed. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 1–13, 1999     

Molecular integrals over the gauge-including atomic orbitals. II. The Breit-Pauli interaction

Each accompanying coordinate expansion (ACE) formula is derived for each of the orbit-orbit interaction, the spin-orbit coupling, the spin-spin coupling, and the contact interaction integrals over the gauge-including atomic orbitals (GIAOs) by the use of the solid harmonic gradient (SHG) operator. Each ACE formula is the general formula derived at the first time for each of the above molecular integrals over GIAOs. These molecular integrals are arising in the Breit-Pauli two-electron interaction for a relativistic calculation. We may conclude that we can derive a certain ACE formula for any kind of molecular integral over solid harmonic Gaussian-type orbitals by using the SHG operator. The present ACE formulas will be useful, for example, for a calculation of a molecule in a uniform magnetic field, for a relativistic calculation, and so on, with the GIAO as a basis function.     

Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψα ‐ETO using auxiliary functions

By the use of expansion and one‐range addition theorems, the one‐electron molecular integrals over complete orthonormal sets of Ψ^α ‐exponential type orbitals arising in Hartree–Fock–Roothaan equations for molecules are evaluated. These integrals are expressed through the auxiliary functions in ellipsoidal coordinates. The comparison is made using Slater‐, Coulomb‐Sturmian‐, and Lambda‐type basis functions. Computation results are in good agreement with those obtained in the literature. The relationships obtained are valid for the arbitrary quantum numbers, screening constants, and location of orbitals. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Resonances and pseudoresonances in a potential with attractive coulomb tail: A study using analytic‐continuation techniques

The performance of the complex absorbing potential (CAP) and the complex scaling (CS) methods in the detection and calculation of complex Siegert energies is studied using a 1‐D long‐range attractive model potential. This potential is constructed to mimic molecular properties, in particular an attractive Coulombic term, to allow one to draw conclusions on molecular ab initio studies. Analyzing the spectrum of the model potential, one compact bound state embedded in the manifold of Rydberg states is found that shows artificial resonance characteristics when applying the CAP and the CS methods. This pseudoresonance problem is less pronounced in the calculation using the CS method than in that using the CAP method. Despite this deficiency, the CAP method is shown to possess advantages over CS when dealing with physical resonances under conditions that simulate the application of standard basis sets in ab initio calculations. The accuracy of the Siegert energy is shown to be maintained when applying a subspace projection technique to the CAP method. This technique reduces the computational demand significantly and leads to an important improvement of the CAP method, which should be of particular significance in molecular applications. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Direct detection of non‐proton‐bearing 15N nuclei by long‐range couplings using polarization transfer

The application of the QDEPT and QHSQC principles to long‐range interactions for the direct detection of non‐proton‐bearing ¹⁵N is proffered as a general solution together with multiselective polarization transfer and triple INEPT for overcoming convoluted responses. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation of the use of density functionals in second‐ and third‐row transition metal dimer calculations

We explore the use of density functionals in calculating the equilibrium distances, dissociation energies, and harmonic vibrational frequencies of the homonuclear diatomics of the second‐row transition metals, platinum, and gold. The outermost s–d interconfigurational energies (ICEs) and the outermost s and d ionization potentials (IPs) were also calculated for the second‐ and third‐row transition metal atoms. Compared with the first‐row transition metal dimer calculations (J Chem Phys 2000, 112, 545–553), the binding energies calculated using the combination of the Becke 1988 exchange and the one‐parameter progressive correlation (BOP) functional and Becke's three‐parameter hybrid (B3LYP) functional are in better agreement with the experiment. However, the pure BOP functional still gives the deep and narrow dissociation potential wells for the electron configurations containing high‐angular‐momentum open‐shell orbitals. Analysis of the s–d ICEs and the s and d IPs suggests that the overestimation may be due to the insufficient long‐range interaction between the outermost s and d orbitals in the exchange functional. The hybrid B3LYP functional seems to partly solve this problem for many systems by the incorporation of the Hartree–Fock exchange integral. However, this still leads to an erroneous energy gap between the configurations of fairly different spin multiplicity, probably because of the unbalance of exchange and correlation contributions. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1995–2009, 2001