SCF Molecular Calculations Research Articles

Dramatic relativistic and magnetic Breit effects for the superheavy reaction Og + 3Ts2 → OgTs6: prediction of atomization energy and the existence of the superheavy octahedral oganesson hexatennesside OgTs6

Our gargantuan ab initio all-electron fully relativistic Dirac–Fock (DF), nonrelativistic (NR) Hartree–Fock (HF) and Dirac–Fock-Breit-Gaunt (DFBG) molecular SCF calculations for the superheavy octahedral oganesson hexatenniside OgTs6 predict atomization energies (AEs) of 9.49, −5.54 and 9.37 eV, at the optimized Og-Ts bond distances of 3.35, 3.44 and 3.36 Å, respectively. There are dramatic effects of relativity for the atomization energy for OgTs6 (with seven superheavy atoms and 820 electrons) of ~15.0 eV at both the DF and DFBG levels of theory. Our calculated energies of reaction for the superheavy reaction Og + 3Ts2 → OgTs6 at the NR, DF and DFBG levels of the theory are exoergic by 8.81, 6.33 and 6.26 eV, respectively. The contribution to dispersion interactions increases the DFBG reaction energy for Og + 3Ts2 → OgTs6 by 0.94–7.20 eV. The AEs of OgTs6 to form Og + 6Ts are calculated to be −5.54 at the NR level of theory (that is, OgTs6 is unstable relative to the sum of the NR energies of its constituent atoms) and 9.49 and 9.37 eV at the DF and DFBG levels of theory, respectively. Dispersion interactions increase the AE(DFBG) by 1.30–10.67 eV. Ours are the first dispersion interaction corrected calculations for OgTs6 with seven superheavy atoms and 820 electrons. Mulliken population analysis (MPA) as implemented in the DIRAC code for our DF and NR calculations (using the dyall.cv4z basis) yields the charges Og+0.60 and Og+0.96, respectively, on the central Og atom indicating that our relativistic DF calculations predict octahedral OgTs6 to be less ionic compared to our NR HF calculations. However, due caution must be used to interpret the results of MPA, which are highly basis set dependent.

Modified B function basis sets with generalized hyperbolic cosine functions

Abstract Efficient exponential type basis sets constructed from new hyperbolic cosine type B functions have been used in self consistent field calculations for the ground states of the atoms from Helium to Argon and their ions. Different hyperbolic cosine type functions are incorporated into the B functions to increase the accuracy of atomic orbitals and correctly describe the electronic density of systems. The presented results for the minimal basis sets are shown that the quality of generalized hyperbolic cosine type B functions is one of the most appropriate basis sets of B functions, especially for increasing atomic number. A comparison with the standard B functions, hyperbolic cosine type B functions and the corresponding numerical Hartree-Fock values are given in tables. Our study shows that the modification of B functions can be an efficient way of increasing the accuracy of the atomic and molecular SCF calculations. These basis sets may also be used in the calculation of atomic properties such as cusp condition and density properties of atomic electrons. Some numerical results and comparisons are given to clarify the basis sets quality from the density point of view. An improved description of atomic orbitals based on the use of modified B functions will also play an important role in ion-atom collisions problems, semi-emprical and density functional methods.

Perturbative corrections to basis incompleteness in molecular SCF calculations

A unified summary is presented of the mathematical approach developed by McDowell for employing perturbation theory to correct for basis-set incompleteness in ab initio SCF calculations. Revised expressions for the corrections to the wavefunction both in terms of orbitals and spin-orbitals are presented with explicit incorporation of the spin variables. Employing H2O as an example, we show that this approach is considerably more powerful for computing molecular energies with standard basis sets than was indicated by previous work. In particular at the higher levels of approximation it accurately reproduces the effect of polarization functions in sets such as 6-31G* and 6-31G**. The equilibrium molecular structure of H2O was also computed by this approach and found to give good accuracy. In each case perturbing functions coupled to both occupied and virtual orbitals are required for acceptable results.

Extended floating spherical gaussian basis sets for molecules. Generation procedure and result for H 2O

A procedure is proposed to generate extended floating spherical gaussian orbital (FSGO) basis sets for molecular SCF calculations by projecting large basis set SCF results onto FSGOs. This replaces the need for repeated evaluation of energy integrals and SCF iterations for extensive non-linear optimizations of FSGOs.

Molecular SCF calculations on the F centre of LiF

A molecular ab initio SCF program has been used to calculate the energy levels of the F centre in LiF using a model crystal potential which includes explicitly the electrons of up to third neighbours to the defect and a truncated point-charge representation of the rest of the lattice. The most complete calculations underestimate the 2S→ 2P excitation energy by 35% and this suggests that the model potential needs to be further extended for this technique to be successful.

Molecular SCF calculations to model (III) surface relaxation of silicon

Ab-initio SCF-MO computations in a 4–31 Gaussian basis on a molecular system Si 4H 9, designed to model a silicon atom on the (III) surface of silicon, predict that the dangling bound silicon relaxes about 0.05 Å toward the bulk from its position on an extension of the silicon crystal lattice. This relaxation is much less than earlier empirical estimates.

Molecular SCF calculations to model (111) surface states and relaxation of diamond

Ab-initio SCF-MO computations in an STO-3G Gaussian basis on a molecular system, designed to model a carbon atom on the (111) surface of diamond, predict that the danglingbond carbon relaxes about 0.10 Å toward the bulk from its position on an extension of the diamond lattice. The dangling bond carbon cation relaxes Inward 0.30 Å, while the anion relaxes outward 0.10 A. Tentative ways to describe the dangling bond in terms of computed quantities are presented.

A simplified core pseudopotential model for use in valence-electron molecular SCF calculations

A molecular valence-electron-only model potential (VEOMP) method is proposed in which the core-valence interpenetration term is replaced by an exponential screening function and the core-valence orthogonality is represented by a pseudopotential term in which the required parametrization is minimized without compromising the effectiveness of the method. This model has been incorporated in the GAUSSIAN 70 programs, and sample calculations, using the STO-3G and STO-6G minimum basis sets, are reported for the orbital energies and equilibrium bond lengths of the ground states of N2, PN and P2.

Calculation of radial couplings between approximate wavefunctions in atomic collisions

A method is presented for the calculation of the radial coupling matrix elements which occur in the molecular approach to atomic collisions. The formalism is based on the earlier work of Bratos (1958) and provides a local method of evaluating analytically radial couplings between approximate wavefunctions when a Gaussian basis is used. The cases of CI and SCF molecular calculations are treated explicitly. Some examples of strong and weak radial couplings are chosen to show the efficiency of the procedure and an approximate formula is tested for the case of coupling between SCF orbitals.

Molecular SCF calculations for the ground state of some three-membered ring molecules: Cis and trans diaziridine, oxaziridine and the corresponding imminium ions

LCAO SCF MO calculations with minimal basis sets of Slater-type orbitals are performed for some three-membered heterocycles. A reinterpretation of the resulting wavefunctions in terms of localized (exclusive) orbitals is employed to show the bending of the ring bonds and to measure the degree of transferability of some groups among chemically different yet related molecules. The electrostatic potentials produced in the neighbouring space by the nuclear and electronic charge distributions are evaluated and employed to indicate the molecular sites most likely subject to electrophilic attack. Some features of the electrostatic potential may be easily related to the entities employed in the usual intuitive description of chemical binding (lone pairs, etc.).

A minimum gaussian lobe representation of 3d orbitals

A three speherical gaussian mimic for 3d orbitals has been fitted to yield an energy of -0.055 555 256 56 and < r 2 > = 124.007 734 79. Although there is contamination by other gerade orbitals, the computational economy outweights a pure l = 2 description, especially for second-row atoms in molecular SCF calculations.

Molecular SCF Calculations for GaF, GaH3, GeH4, AsH3, and H2Se

Exact minimum Slater basic sets have yielded LCAO–MO–SCF wavefunctions for the compounds GaF, GaH3, GeH4, AsH3, and H2Se. Chemical binding in these molecules is in accord with a very simple model of bond formation. Parameters for nonempirical molecular orbital (NEMO) calculations are computed from the Hamiltonian matrices of these molecules and from the previously published results on the model compounds ScH3NH3 and TiH3F. A planar geometry of the unobserved GaH3 is indicated by a NEMO calculation.

Molecular SCF Calculations for the Ground State of Some Three-Membered Ring Molecules: (CH2)3, (CH2)2NH, (CH2)2NH2+, (CH2)2O, (CH2)2S, (CH)2CH2, and N2CH2

LCAO SCF MO calculations with minimum basis sets of Slater-type orbitals are performed for some three-membered ring compounds. A reinterpretation of the resulting wavefunctions in terms of localized (exclusive) orbitals is presented and discussed: The bent bonds in the rings are closely evidenced. The electrostatic potentials produced in the neighboring space by the nuclear and electronic charge distributions are evaluated and employed to evidence the molecular sites more likely subject to electrophilic attacks.

Gaussian-Orbital Basis Sets for the First-Row Transition-Metal Atoms

Contracted Gaussian-type function basis sets have been produced for the first-row transition-metal atoms Sc through Cu for use in molecular SCF calculations. The basis functions consist of 15 s-type, eight p-type, and five d-type Gaussian primitives contracted to a four s-type, two p-type, and one d-type basis set and are exponent and coefficient optimized after contraction. It is shown that this basis set is of single-zeta quality for the core functions and of double-zeta quality for the valence-electron functions. Relaxation of the degree of contraction results in a significant lowering of the total energy.

Molecular SCF Calculations for ScH3NH3 and TiH3F

Exact minimum Slater basis sets have yielded LCAO–MO–SCF wavefunctions for the model compounds ScH3NH3 and TiH3F. The dative bond in ScH3NH3 has a small overlap population (0.11 electron) and a small charge transfer of only 0.12 electron from N into, primarily, 4pz and 3dz2 of Sc, but there are comparable redistributions among the orbitals of e symmetry as well. The charge on F in TiH3F is − 0.28e, and the Ti–F bond has overlap populations of 0.20e in bonding orbitals of a symmetry, and 0.18e in those of e symmetry. Changes on each H atom (attached to the metal) are − 0.28e in ScH3NH3 and − 0.30e in TiH3F.

Molecular SCF Calculations for SiH4 and H2S

Wavefunctions and Hamiltonian matrices are obtained for SiH4 and H2S by the LCAO MO SCF method. Integrals were calculated accurately over minimum basis sets of Slater-type atomic orbitals, augmented by the addition of the 3d orbitals. Best atom exponents were used, except for the H1s, Si3d, and S3d orbitals, which were optimized to values SiH4: H1s, 1.26; Si3d, 1.30, and H2S: H1s, 1.22; S3d, 1.71. The calculated molecular energies are − 290.5187 a.u. for SiH4, and − 397.8415 a.u. for H2S, and net atomic charges are +0.127 for each hydrogen in SiH4 and + 0.176 for each hydrogen in H2S.

Molecular SCF Calculations on PH3, PO, PO−, and P2

Wavefunctions, Hamiltonian matrices, and population analyses are obtained for PH3, PO, PO−, and P2 from accurate self-consistent-field calculations in which multicentered basis sets of Slater orbitals have been employed. The P3d exponent was optimized at 1.40 in PO and 1.10 in PO−, assuming Slater exponents for other orbitals. These 3d orbitals were found to be important in the bonding in each of these molecules. Studies were also made of dipole moments, ionization potentials, and binding energies.

Molecular SCF Calculations on CH4, C2H2, C2H4, C2H6, BH3, B2H6, NH3, and HCN

Molecular SCF Calculations on CH₄, C₂H₂, C₂H₄, C₂H₆, BH₃, B₂H₆, NH₃, and HCN