Calculation of Negative Ions of B,C, N,O and F Using Noninteger n Slater Type Orbitals

Combined Hartree‐Fock‐Roothaan calculations have been performed using noninteger n Slater type orbitals for the ground states of the lowest electron configurations 1s²2s²2pⁿ (2 ≤ n ≤ 6) for negative ions of B, C, N, O and F. These results are compared with the corresponding results obtained from the use of integer n Slater type orbitals. All of the nonlinear parameters are fully optimized. The results of calculation of coupling‐projection coefficients, orbital and total energies and virial ratios are presented. It is shown that the noninteger n Slater type orbitals, in general, improve the orbital energies.     

Perturbation treatment of the Hartree–Fock equations of 1s2p3s 4Pθ state of the lithium isoelectronic sequence

The first order Hartree–Fock equations of the 1s2p3s ⁴P⁰ state of the three-electron atomic systems have been solved exactly. These solutions are used to evaluate Hartree–Fock energy up to third order with high accuracy. The third order Hartree–Fock energies for Li to Ne⁷⁺ are compared with those derived from experiment and other theoretical calculations.     

Near-Dirac–Hartree–Fock results for first-row atoms calculated with GTO basis sets

Relativistic basis sets for first-row atoms have been constructed by using the near-Hartree–Fock (nonrelativistic) eigenvectors calculated by Partridge. These bases generate results of near-Dirac–Hartree–Fock quality. Relativistic total and orbital energies, relativistic corrections to the total energy, and magnetic interaction energies for the first-row atoms have been presented. The smallest Gaussian expansions (13s8 p expansions) yield Dirac–Hartree–Fock total energies accurate through six significant digits, while the largest expansions (18s13p expansions) give these energies accurate through seven significant digits. These results are more accurate than some of the results reported earlier, particularly for the open-shell atoms, indicating that the basis employed is reasonably economical for relativistic calculations. © 1995 John Wiley & Sons, Inc.     

Perturbation calculation of atomic correlation energies for the first transition period

Results are presented for calculations of Hartree—Fock and correlation energies for the 3dⁿ 4s² and 3dⁿ⁺¹ 4s ground and excited states of the first transition series atoms using second-order Møller—Plesset perturbation theory starting with an unrestricted Hartree—Fock wavefunction.     

Electron pair correlation energies for ZN2+

Pair energies contributing to the correlation energies of the outer-shell electrons (n = 3) as well as for the 1s² and 2s² pairs are computed for the Zn²⁺ closed-shell ion by means of the variational-perturbation method starting with the sum of one-electron Hartree–Fock operators as the zeroth-order Hamiltonian. The results allow an understanding of the electron correlation for pairs of electrons of the p and d type. For 3p3d pairs it has been found that the correlation energy for the singlet pair of ¹D symmetry is lower than for the triplet pair ³D. The 3l-3l′ correlation energies are compared with the MBPT results of Kelly and Ron for Fe. The total correlation energy of the outer shell is ?1.032 a. u.     

Extended Hartree–Fock calculations for the helium ground state

The extended Hartree–Fock (EHF) wave function of an n-electron system is defined (Löwdin, Phys. Rev. 97 , 1509 (1955)) as the best Slater determinant built on one-electron spin orbitals having a complete flexibility and projected onto an appropriate symmetry subspace. The configuration interaction equivalent to such a wavefunction for the ¹S state of a two-electron atom is discussed. It is shown that there is in this case an infinite number of solutions to the variational problem with energies lower than that of the usual Hartree–Fock function, and with spin orbitals satisfying all the extremum conditions. Two procedures for obtaining EHF spin orbitals are presented. An application to the ground state of Helium within a basic set made up of 4(s), 3(p₀), 2(d₀) and 1 (f₀) Slater orbitals has produced 90% of the correlation energy.     

Geometry,basis set,and correlation energy dependence of computed protonation energies of imino bases

The nitrogen protonation energies of the imino bases HN?CHR, where R is H, CH₃, NH₂, OH, and F, have been evaluated to determine the dependence of absolute and relative protonation energies on geometry, basis set, and correlation effects. Reliable absolute protonation energies require a basis set larger than a split-valence plus polarization basis, the inclusion of correlation, and optimized geometries of at least Hartree–Fock 4-31G quality. Consistent relative protonation energies can be obtained at the Hartree–Fock level with smaller basis sets. Extending the split-valence basis set by the addition of polarization functions on all atoms decreases the computed absolute Hartree–Fock nitrogen protonation energies of the imino bases HN?CHR except when R is F, but increases the oxygen protonation energies of the carbonyl bases O?CHR.     

The elements of Flatland: Hartree-Fock atomic ground states in two dimensions for Z = 1–24

The Hartree–Fock problem in two dimensions (2D) has been solved for 1 ≤ Z ≤ 24 using a Gaussian basis and assuming r^?1 Coulomb interactions. The order of occupation of the one-electron states is like in the 3D case. The 1s shell is found to be particularly small and strongly bound, making the 2D hydrogen a “superhalogen” and the 2D He a “superinert gas.” In contrast to 3D, 4s¹3d² and 4s²3d³ configurations are preferred for the 2D “Sc” and “Cu,” respectively. The six first 2D atoms have stronger and the later ones weaker valence-bonding energies than do their 3D analogs. It is noted that the 2D Dirac energy expression for a hydrogenlike atom for m_j = l + 1/2 agrees with the 3D Klein–Gordon one.     

Calculations of Isoelectronic Series of He Using Noninteger n‐Slater Type Orbitals in Single and Double Zeta Approximations

Using integer and noninteger n-Slater type orbitals in single- and double-zeta approximations, the Hartree-Fock-Roothaan calculations were performed for the ground states of first ten cationic members of the isoelectronic series of He atom. All the noninteger parameters and orbital exponents were fully optimized. In the case of noninteger n-Slater type orbitals in double zeta basis sets, the results of calculations obtained are more close to the numerical Hatree-Fock values and the average deviations of our ground state energies do not exceed 2×10^－6 hartrees of their numerical results.     

A systematic preparation of new contracted Gaussian-type orbital sets. VIII. MINI-1 and MIDI-1 sets for Ga through Cd

Minimal contracted Gaussian basis sets are presented for Ga through Cd. Characteristically these Gaussian-based minimal sets give far better d orbital energies than those by minimal STO basis sets. These new basis sets were tested on Br₂ for which a new benchmark calculation was also performed. The test result is satisfactory in that these basis sets produce good general agreement with the near Hartree–Fock calculation with respect to the molecular spectroscopic constants.     

Theoretical studies of organometallic compounds. III. Structures and bond energies of FeCHn and FeCH (n = 1, 2, 3)

The geometries and dissociation energies for the Fe? C and C? H bonds of FeCH_n and FeCH (n = 1, 2, 3) have been calculated by ab initio quantum mechanical methods using different effective core potential models and Møller–Plesset perturbation theory. The HW3 ECP model, which has a configuration [core] (n?1)s², (n?1)p⁶, (n?1)d¹, (n)s^m for the transition metals, is clearly superior to the larger core LANL1DZ ECP model with the configuration [core] (n?1)d¹, (n)s^m. The Fe? C bond energies calculated at correlated levels using the HW3 ECP are in much better agreement with experiment than the LANL1DZ results. This effect is mainly due to the higher number of correlated electrons rather than the inclusion of the outermost core electrons in the Hartree–Fock calculation. At the PMP4/HW3TZ/6-31G(d)//MP2/HW3TZ/6-31G(d) level, the theoretically predicted Fe? C bond energies for FeCH are in the range of 80% of the experimental values and have nearly the same accuracy as all-electron calculations using large valence basis sets and the MCPF method for the correlation energy. © 1992 by John Wiley & Sons, Inc.     

Use of noninteger n‐generalized exponential type orbitals with hyperbolic cosine in atomic calculations

The efficiency of noninteger n‐generalized exponential type orbitals (NGETO) r^n*?1 e with hyperbolic cosine (HC) cosh (βr^μ) as radial basis functions in atomic ground state total energy calculations is studied. By the use of these functions, the combined Hartree‐Fock‐Roothaan calculations have been performed for some closed and open shell neutral atoms and their anions and cations with Z ≤ 21. The performance of new basis functions within the minimal basis framework has been compared with numerical Hartree‐Fock (NHF) results. Our total energy values are significantly close to NHF results. The presented minimal basis total energies obtained from the noninteger NGETO with HC are notably better than minimal basis functions total energies previously reported in the literature. It is found that the accuracy of new noninteger NGETO with HC almost correspond to the accuracy of the conventional double‐zeta functions. All the nonlinear parameters are fully optimized. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Excitation energies,oscillator strengths,and frequency dependent polarizabilities of Be: Comparison of TDHF,EOM (second order), and MCTDHF

Low-lying excitation energies from the ground state of Be were calculated using a basis set of 61 Cartesian Gaussian functions. Three approximations were employed: the time-dependent Hartree–Fock (TDHF ), second-order equations-of-motion (EOM ), and multiconfigurational time-dependent Hartree–Fock (MCTDHF ). The TDHF excitation energies are 0.5–1.1 eV lower than experiment, and the EOM values are 0.3–1.2 eV lower than experiment, whereas the MCTDHF excitation energies deviate on the absolute average from experiment by only 0.03 eV. We found that in an MCTDHF calculation, any proper MCSCF stationary point is a good reference (i.e., initial) state, not just the ground state. Experimental values for oscillator strength are accurately known only for the 2s²X¹S → 2s2p¹P⁰ transition. The TDHF value and the MCTDHF value agree with experiment, but the EOM value does not. The agreement of the TDHF value with experiment seems to be coincidental, because for higher lying transitions the TDHF values differ by approximately a factor of two or more from the more accurate MCTDHF . Frequency independent polarizabilities, α(0), were also calculated with the TDHF , HRPA , and MCTDHF and frequency dependent polarizabilities, β(ω), were calculated with the MCTDHF . No experimental data for Be polarizabilities exist, but we expect the MCTDHF values to be among the most accurate calculations available.     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

The 6-31G++ basis set: An economical basis set for correlated wavefunctions

The 6-31G ⁺⁺ basis set is described. This basis set is very similar to the existing 6-31G ^** set but is somewhat smaller through the use of five (rather than six) second-order Gaussians (d functions) and has polarization function exponents optimized for correlated rather than Hartree–Fock wavefunctions. The performance of 6-31G ⁺⁺ is compared with that of the 6-31G ^** and 6-31G ^** basis sets through calculation of the geometries and atomization energies for the set of molecules LiH, FH, H₂O, NH₃, CH₄, N₂, CO, HCN, and HCCH.     

A correlation study of Li ground state by the MCHF procedure

Results are reported for multiconfiguration Hartree–Fock studies of correlation in the lithium ground state, which maintain orthogonality of orbitals within a configuration. It is shown that when the 1s- and 2s-orbitals are fixed at their Hartree–Fock value, configurations for which Brillouin's theorem holds may be important, particularly for atomic properties other than energy. The Fermi contact term is considered as an example.     

Theoretical studies of organometallic compounds. II. All electron and pseudopotential calculations of M(CH3)nCl4 − n (M = C,Si, Ge,Sn, Pb; n = 0–4)

The performance of effective core potentials (ECP) for the main group elements of group IV has been studied by calculating the geometries and reaction energies of isodesmic reactions for the molecules M(CH₃)_nCl_{4 ? n} (M = C, Si, Ge, Sn, Pb; n = 0–4) at the Hartree–Fock level of theory. The results are compared with data from all electron calculations and experimental results as far as available. The all electron calculations were performed with a 3-21G(d) and a 6-31G(d) basis set for Si, a (43321/4321/41) basis set for Ge, and a (433321/43321/431) basis set for Sn. For the ECP calculations the potentials developed by Hay and Wadt with a configuration (n)s^a(n)p^b and the valence basis set (21/21), extended by a set of d functions, are employed. © 1992 by John Wiley & Sons, Inc.     

Ab initio studies of negative ion-molecule(s) clusters present in the atmosphere. III. OH−(CO2)n for n = 1, 2

Clusters formed by the OH^? ion and carbon dioxide are investigated using ab initio Hartree–Fock calculations, with 6–31 G and 6–31 G* basis sets. Geometries and binding energies are determined.     

Adapted Gaussian basis sets for atoms Cs to Lr based on the generator coordinate Hartree–Fock method

We have applied a discretized version of the generator coordinate Hartree–Fock method to generate adapted Gaussian basis sets for atoms Cs (Z=55) to Lr (Z=103). Our Hartree–Fock total energy results, for all atoms studied, are better than the corresponding Hartree–Fock energy results attained with previous Gaussian basis sets. For the atoms Cs to Lr we have obtained an energy value within the accuracy of 10⁻⁴ to 10⁻³ hartree when compared with the corresponding numerical Hartree–Fock total energy results. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 858–865, 1998