An efficient first-order CASSCF method based on the renormalized Fock-operator technique

Summary A new efficient first-order CASSCF method (multiconfiguration SCF (self consistent field) in a complete active space) is described. Its main characteristics are (i) use of the generalized Brillouin theorem (Fock-operator method), (ii) renormalization of single excitations, (iii) fast microiterations containing only two-index transformations, i.e. M ³N² steps. Convergence is generally reached in eight to twelve macroiterations. The method is applied to several examples (LiH, N₂, AlO) and compared to other MCSCF (multiconfiguration SCF) methods.     

Ab initio predictions of the molecular structures and harmonic vibrational frequencies of Ga2O2 isomers

The potential energy surface of Ga₂O₂ is examined at the SCF and MP2 levels employing basis set of triple- plus double polarization quality. Four stationary points located at the SCF level are characterized via their Hessian index. Electron correlation is important for the energy ordering and splitting of the isomers. For example, two minimum energy structures, a cyclicD _2h form and a linear Ga-O-Ga-O, separated by 25.69 kcal/mol at the SCF level have an energy difference of only 1.70 kcal/mol at the MP2 levels. Our computed harmonic vibrational frequency at 962 cm^–1 for the Ga-O-Ga-O minimum structure in in good agreement with the experimental predicted value of 967 cm^–1.     

Perturbation expansion theory corrected from basis set superposition error II. Charge transfer,pair correlationand dispersion terms

The second-order perturbation theory based on the locally projected molecular orbitals is developed. A few test calculations with cc-pVDZ and aug-cc-pVDZ basis sets are carried out for the dimers, (H₂O)₂ and (HF)₂. The charge transfer terms remove the deficiency of the locally projected self-consistent field method for molecular interaction (LP SCF MO MI), and the potential energy curves calculated with aug-cc-pVDZ are very close to the corresponding curves of the counterpoise-corrected SCF energy. Only after adding the spin-exchanged dispersion type to the dispersion and intra-molecular pair correlation terms, the calculated potential energy curves become close to those of the counterpoise-corrected second-order Møller–Plesset (MP2). Pragmatic approaches for reducing the influence of the basis set superposition error are proposed.     

Ab initio study of N2O+. Angular dependence of the 14A″(4Π) potential

The 1⁴A″(⁴Π) state of N₂O⁺ is found to be the most stable at bent conformations of the nuclei. Ab initio SCF, MC SCF, and MC SCF CI calculations with a double-zeta basis and typical bond-length values for R_NN and R_NO all yield minimum energy angles near 126°. The energy lowering is such that the total energy of N₂O⁺ (1⁴A″, 126°) is very near that of the lowest O, N₂ asymptote, ⁴S, X ¹Σ_g⁺. These results are shown to imply that the ionospheric reaction O⁺ + N₂ → NO⁺ + N, the rate-determining step in the electron removal reaction network, is adiabatic on the potential surface of the 1⁴A″ state.     

An ab initio study of the potential surface for the reaction H2COH → HCO + H2

The potential surface for the reaction H₂CO⁺H → HCO⁺ + H₂ has been studied by ab initio SCF calculations, using gaussian-type basis functions. A saddle point on the surface has been found, and a reaction path is proposed to explain the observed release of kinetic energy. The energy of activation and ΔE for the reaction have been estimated.     

Comparison of valence-only model potential and all-electron ab initio LCAO SCF MO studies of Li2 and LiH

A previously developed gaussian-based model potential theory for a single valence electron outside a core has been extended to the simple two-valence electron systems Li₂ and LiH within the LCAO SCF MO formulation, using an extended valence basis set. Comparisons of the results with corresponding ab initio calculations show excellent agreement of the total valence energy and the orbital energy in both systems, and for the dipole moment in LiH.     

Unsymmetrical 1B2 (ππ1) state of ozone

Using ab initio SCF CI calculations it is shown that the ππ1 singlet state of ozone has an unsymmetrical equilibrium geometry with one long and one short OO bond. A similar behavior has been experimentally demonstrated on the parent SO₂ molecule. The double-minimum potential energy surface of this state results from an avoided crossing involving (1) the singlet ππ1 state itself which is stabilized by an unsymmetrical stretching of the two bonds and (2) a lower lying (nπ1)² doubly excited state which is destabilized by the same distortion.     

Extrapolation of real-space quantum chemical calculations from finite-size supercells to the ideal infinite system. III. Application to two-dimensional systems

A previously presented extrapolation method of the density matrix of a standard finite supercell calculation to an infinite supercell is extended to two-dimensional systems. The density matrix of the finite supercell is transformed into q space where it is interpolated and extrapolated in such a way that all its fundamental properties are guaranteed by construction. The resulting modified density matrix contains information from a continuum of q points in the first Brillouin zone which allows for a more realistic calculation of properties like the total energy E_tot per atom and the band structure ϵ₁(q). It is shown that this more realistic calculation takes better care of the crystal symmetries and is essential in reproducing both important degeneracies in the band structure and rotationally symmetric results. In the special case of π electrons only, an exact analytical solution for the density matrix of the infinite supercell is presented. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 895–911, 1997     

Orbital relaxation in the Rydberg series of the lithium atom. An excited state SCF calculation

Self-consistent-field (SCF ) calculations for a series of Rydberg states (1s²ns)²S of the Li atom are performed using the generalized Brillouin theorem (GBT) method. The calculated energy is a proper upper bound to the excited state energy. The SCF term values of the Rydberg states are almost the same as those of the frozen-core approximation ones. The orbital behavior shows that the core is slightly expanded by the penetration of the Rydberg orbitals, and the higher Rydberg orbitals can be very well represented by the modified hydrogen-like orbitals.     

Interpretation of energy bands of polyethylene in terms of effective interactions between first- and second-neighboring CH2 groups

The alternative way of solving secular problems for the Hamiltonian matrices of regular quasi-one-dimensional systems developed previously [V. Gineityte, Int. J. Quant. Chem. 60 (3), 717 (1996)] has been applied to polyethylene. An implicit form of the dispersion relation has been obtained in terms of three local-structure-determined energy-dependent functions δ(ε), τ(ε), and η(ε), describing the effective interactions inside a separate CH₂ group and those between first- and second-neighboring CH₂ groups, respectively. The actual shapes of dispersion curves proved to be determined by relative mean values of the functions τ(ε) and η(ε) within the ε region under interest. The unusual minimum within the low-energy branch of dispersion curves situated at a low-symmetry point of the first Brillouin zone (k≈0.6π/a) has been established to appear owing to considerable values of effective interactions between the second-neighboring CH₂ groups within the respective energy interval. Just the latter type of interactions has been concluded to be responsible also for non-one-dimensionality of the polyethylene chain. The Hamiltonian matrix eigenfunctions of this chain have been expressed as the Bloch sums of eigenvalue-dependent local-structure-determined basis orbitals. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 481–494, 1997     

Topological analysis of the charge density response of a Ni4 cluster to a probe H2 molecule

Local density self-consistent field (SCF) discrete variationalX calculations are performed on a Ni₄ tetrahedron interacting with a probe H₂ molecule in special geometries. Optimized basis functions generated from the spherically averaged SCF potential are used. Topological charge-density analyses and binding energy calculations are used to study a portion of the energy surface for the approach of the H₂ molecule toward the Ni₄ tetrahedron. The effect of the H₂ molecule on Ni-Ni, Ni-H bonds and changes in the H-H covalent bond are investigated with the help of the field and various data at its critical points. The qualitative relationship between these data and the calculated binding energies is exploited.     

CAS SCF/CI calculations of potential energy surfaces of He3+ and He2+

Complete active space MC SCF (CAS SCF) calculations followed by second-order configuration interaction (SOCI) calculations are carried out on the potential energy surfaces (bending surface, linear surfaces) of the ²Σ_g⁺ ground state of He₃⁺. The potential minimum for the ²Σ_g⁺ state occurs at a linear geometry with HeHe bond length of 1.248 Å. The binding energy of He₃⁺ with respect to He + He⁺ + He was calculated to be 2.47 eV at the SOCI level. The energy required to dissociate He₃⁺ (²Σ_g⁺) into He₂⁺ (²Σ_u⁺) and He(¹S) is calculated to be 0.14 eV. The same level of SOCI calculations of He₂⁺ yield a D_e value of 2.36 eV.     

Potential energy surface of the (H2)2 dimer: an MP2 study

Fifteen structures of the (H₂)₂ dimer have been investigated at the MP2/[4s3p] level. The SCF and MP2 (2nd order Møller-Plesser treatment) interaction energies have been corrected for the basis set superposition error. Only the T-shaped structure has been established as a minimum on the potential energy surface. Two equivalent T-shaped structures are connected by a saddle point with a rhomboid structure.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

The optimization of MCSCF functions by application of the generalized brillouin theorem: The LiH2 potential energy surface

The generalized Brillouin theorem is used to construct an optimization procedure for MCSCF functions by iterative contracted CI calculations. Special attention is paid to the MO transformation step in each iteration. In this method the MCSCF calculation may easily be augmented by a restricted CI calculation involving a configuration set which is uniquely determined by the trial function. An application to the calculation of the potential energy surface for linear LiH₂ in the reaction LiH + HLi + H₂ leads to the conclusion that this restricted CI is necessary, in order to obtain satisfactory results for the potential energy barrier in this reaction.