Roothaan Theory Research Articles

Use of combined Hartree–Fock–Roothaan theory in evaluation of lowest states of K[Ar]4s 03d 1 and Cr + [Ar]4s 03d 5 isoelectronic series over noninteger n-Slater type orbitals

By the use of integer and noninteger n-Slater Type Orbitals in combined Hartree-Fock-Roothaan method, self consistent field calculations of orbital and lowest states energies have been performed for the isoelectronic series of open shell systems K [Ar]4s^0 3d^1 2(D) (Z=19-30) and Cr+ [Ar] 4s^0 3d^5 6(S) (Z=24-30). The results of calculations for the orbital and total energies obtained from the use of minimal basis sets of integer- and noninteger n-Slater Type Orbitals are given in tables. The results are compared with the extended-basis Hartree-Fock computations. The orbital and total energies are in good agreement with those presented in the literature. The results are accurately and considerably can be useful in the application of non-relativistic and relativistic combined Hartree-Fock-Roothaan approach for heavy atomic systems.

Application of combined open shell Hartree–Fook–Roothaan theory to molecules using symmetrical one-range addition theorems of Slater type orbitals

We study the efficiency of symmetrical one-range addition theorems for Slater type orbitals which are used in the calculation of multicenter integrals arising in the combined open shell Hartree–Fook–Roothaan equations for molecules. As an example of application, the calculations are performed for the ground state of electronic configuration of molecules NH3 and CH2 that have the closed and open shells, respectively. The results of computer calculations for the orbital and total energies (in a.u.), and linear combination coefficients for symmetrical molecular orbitals are presented.

Use of noninteger n‐Slater type orbitals in combined Hartree–Fock–Roothaan theory for calculation of isoelectronic series of atoms Be to Ne

AbstractThe ground state calculations in the combined Hartree–Fock–Roothaan approach are performed for the neutral and the first 20 cationic members of the isoelectronic series of atoms from Be to Ne using noninteger n‐Slater type orbitals. For the total energies obtained, only a small deviation has been found. At the same time, the size of the present noninteger n‐Slater type orbitals is smaller than that of the usual extended integer n‐Slater functions in literature. All of the nonlinear parameters are fully optimized. The relationship between optimized parameters and atomic number Z is also investigated. For each atom, the total energies are given in tables. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Application of combined Hartree–Fock–Roothaan theory to molecules with arbitrary number of closed and open shells

In this study, the applicability of the combined Hartree–Fock–Roothaan (CHFR) theory of atomic-molecular and nuclear systems (Guseinov, J Math Chem 42:177, 2007) to the molecules is demonstrated using minimal basis set of Slater type orbitals (STO). As an example of application of CHFR theory, the calculations have been performed for the ground state of electronic configuration of methylene molecule CH2 which has two open shells. The results of computer calculations for the orbital, kinetic and total energies, linear combination coefficients of symmetrized molecular orbitals and virial ratios are presented.

Molecular Orbital Theory: Spinor Representation

The algebra representing electron is spinor. The many electron problem is investigated with the Nambu 2 ×2 spinor. Operators then are expressed 2 ×2 matrices. The electron–electron interaction is decomposed into couplings between various electron densities by using the Pauli spin matrices. The diagonal ones of them refer to the direct and exchange interactions and the off-diagonal terms to those for superconducting. The Roothaan theory is rewritten. The approximation beyond the Hartree–Fock is discussed.

Unified analytical treatment of multicenter multielectron integrals of central and noncentral interaction potentials over Slater orbitals using Ψα-ETOs

Using expansion formulas for the translation of Slater-type orbitals (STOs) obtained with the help of complete orthonormal sets of Ψα-exponential type orbitals the addition theorems for STOs and interaction potentials are established. These addition theorems enable us to evaluate the multicenter t-electron integrals which arise in the solution of N-electron atomic and molecular problem (2⩽t⩽N) when a Hylleraas approximation is employed in Hartree–Fock–Roothaan theory. The relationships obtained are valid for the arbitrary location, quantum numbers, and screening constants of STOs.

Partially restricted Hartree-Fock method for singlet excited states

A version of the partially spin-restricted Hartree-Fock method is proposed to construct a reference Slater determinant in calculations of singlet excited states having the same symmetry as the ground one. On the one hand, this approach can be used for a rather simple, in comparison with the fully unrestricted determinant, construction of a pure spin state. On the other hand, it is suitable, in contrast to the Roothaan theory for open shells, for the development of the perturbation scheme for taking into account correlation effects in an excited state, which retains the calculation advantages of the Moller-Plesset perturbation theory with single annihilation for the ground state. The efficiency of the method is demonstrated by calculations of electronic excitation energies for BH and CH+ molecules.

The relation between the open shell energy functional in the Roothaan method and the symmetry of the system

The origin of terms not described in the Roothaan theory in molecular systems with one open shell is discussed. The appearance of these terms can be formally considered as a result of the splitting of the levels of the pN configuration of the atom (or the NπN of the linear molecule) in a low symmetry field. For the atomic shell of the pN state we obtained the concept of two-particle spinless density through the one-particle density, which allows the expression of the a and b coefficients in the corresponding Roothaan energy functional through the orbital and spin moments and the number of electrons.

The electronic/positronic structure of positron/pseudohalide systems: [OH−; e+], [SH−; e+], [CN−; e+], and [N−3; e+

A theoretical examination of the [OH−;e+], [SH−;e+], [CN−;e+], and [N−3;e+] at the approximate Hartree–Fock level is presented. Large Gaussian basis sets are used to represent both the electronic and positronic orbitals in conventional Hartree–Fock–Roothaan theory. Quality studies are given for [F−;e+] and [OH−;e+] and some consideration of dependence with molecular geometry is considered. The basic energy results are presented and a cycle argument is followed to suggest that [CN−;e+] and [N−3;e+] are stable to Ps detachment while [OH−;e+] and [SH−;e+] are not stable. The corresponding angular correlation curves N(θ) are given and compared. Finally, interpretative aspects are presented and discussed in terms of positron localization and contrast to proton behavior.

Rotational invariance of INDO theories including d‐orbitals into the basis set

AbstractIt is proved that in general the INDO approximation to the full Roothaan theory does not lead to expressions which are invariant under a rotation of local atomic axes. However, when only s‐ and p‐functions are used in the atomic basis set, the equations obtained are invariant due to the special properties of the p‐functions. When d‐orbitals are included into the basis set, rotational invariance is lost but can be restored if a supplementary approximation is introduced.

A Theory of Molecules in Molecules. I

A theory of molecules in molecules is presented in which the wavefunction of a molecule is constructed from the wavefunctions of possible molecular fragments. In the formalism of the Hartree–Fock–Roothaan theory further approximations are introduced. In the formation of the new molecule from the molecular fragments the effects of the interaction on the charge distribution are regarded as important only in the molecular parts neighboring each other, but neglected in the other parts, which are regarded as unperturbed. The localized molecular orbitals constituting the wavefunctions of the fragments can therefore be transferred unaltered, if they lie outside the region of interaction, or are redetermined with the help of the variational principle. Our aim is to construct the wavefunction of a large molecule from the wavefunctions of two (or few) large fragments and in this way save in the computational time. No approximations in the Hamilton operator or in the integrals are made in the first formulation, but some approximations are required in the treatment of the orthogonality problem inherent in a theory of molecules in molecules. In a restricted form (calculation of only two modified orbitals) the theory is applied to determine the potential energy curve of two hydrogen fluoride molecules along the reaction coordinate FH–HF. A comparison with exact SCF–MO calculations demonstrates that good results are obtained for intermolecular distances larger than one atomic unit. On the basis of this justification the theory is generalized and reformulated. An arbitrary number of orbitals can be modified, where the orbitals are an expansion only over a subset of the total set of basis functions. This approach gives a high flexibility in the calculation of approximate wavefunctions.

Quadratically convergent iteration procedure for geminal determinations

AbstractA general formalism is presented for the determination of the optimum natural orbitals within the various strongly orthogonal geminals of a wavefunction describing a 2N‐electron closed‐shell molecule or atom. The relationship to Hartree–Fock–Roothaan theory is established; the algorithm that is developed is quadratically convergent to the desired result, and does not ignore off diagonal Lagrangian multipliers, or require an infinite series of 2 × 2 orthogonal transformations of the original basis.